Digital Control Techniques Based on Voltage Source Inverters in Renewable Energy Applications: a Review

electronics

Review Digital Control Techniques Based on Voltage Source Inverters in Renewable Energy Applications: A Review

Sohaib Tahir 1,2, Jie Wang 1,*, Mazhar Hussain Baloch 1,3 and Ghulam Sarwar Kaloi 1,4

1 School of Electronic, Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200000, China; [email protected] (S.T.); [email protected] (M.H.B.); [email protected] (G.S.K.) 2 Department of Electrical Engineering, COMSATS Institute of Information Technology, Sahiwal 58801, Pakistan 3 Department of Electrical Engineering, Mehran University of Engineering & Technology, Khairpur Mirs 67480, Pakistan 4 Department of Electrical Engineering, Quaid e Awam University of Engineering & Technology, Larkana 77150, Pakistan * Correspondence: [email protected]

Received: 4 December 2017; Accepted: 2 February 2018; Published: 7 February 2018

Abstract: In the modern era, distributed generation is considered as an alternative source for power generation. Especially, need of the time is to provide the three-phase loads with smooth sinusoidal voltages having ﬁxed frequency and amplitude. A common solution is the integration of power electronics converters in the systems for connecting distributed generation systems to the stand-alone loads. Thus, the presence of suitable control techniques, in the power electronic converters, for robust stability, abrupt response, optimal tracking ability and error eradication are inevitable. A comprehensive review based on design, analysis, validation of the most suitable digital control techniques and the options available for the researchers for improving the power quality is presented in this paper with their pros and cons. Comparisons based on the cost, schemes, performance, modulation techniques and coordinates system are also presented. Finally, the paper describes the performance evaluation of the control schemes on a voltage source inverter (VSI) and proposes the different aspects to be considered for selecting a power electronics inverter topology, reference frames, ﬁlters, as well as control strategy.

Keywords: voltage source inverters (VSI); voltage control; current control; digital control; predictive controllers; advanced controllers; stability; response time

1. Introduction Nowadays, energy demand is getting increased with the passage of time and distributed generation (DG) power systems especially through wind, solar and fuel cells as well as their related power conversion systems are conferred immensely. Many problems like grid instability, low power factor and power outage etc. for power distribution have also been increased with increase in energy demand [1]. However, DG power systems are found to be a sensible solution for such problems as they have relatively robust stability and causes additional ﬂexibility balance. Moreover, their utilization can also improve the distribution networks management and carbon release is also reduced. VSIs are extensively necessitated for the commercial purpose as well as for the industrial applications as they play a key role in converting the DC voltage and current, usually produced by various DG applications, into AC before being discharged into the grid or consumed by the load. Several control systems are introduced, various schemes are proposed and numerous techniques are updated in order to facilitate the control of three-phase VSI. The objectives of these control schemes are to constrain the high and low-frequency electromagnetic pollution and to inject the active power with zero power factor into the

Electronics 2018, 7, 18; doi:10.3390/electronics7020018 www.mdpi.com/journal/electronics Electronics 2018, 7, 18 2 of 37 grid [2]. The smooth and steady sinusoidal waveform can be a good input to a load for getting the most suitable response, therefore, the output of the inverter, which normally enjoys special standards and characteristics, should be controlled for providing an aforementioned waveform to load and grid. Generally, it is observed that several problems are caused in linking the DG power system to a grid or grid to load in bidirectional inverters, i.e., grid instability, distortion in the waveform, attenuation as well as major and minor disturbances. Hence, in order to overcome these problems and to provide high-quality power, appropriate controllers with rapid response, compatible algorithm, ability to remove stable errors, less transit time, high tracking ability, less total harmonic distortion, THD value and smooth sinusoidal output should be designed. Various controllers are designed for achieving these qualities. The cascade technologies are introduced in the literature comprises of an inner current loop and outer voltage loop [3–12]. As the inner-loop current controller plays a fundamental role in closed-loop performance, various control approaches like PI [3–6], H∞ [7,8], deadbeat [9–11,13] and µ-synthesis [11] are extensively applied. Outer voltage loop in the aforementioned cases refines the tracking ability and decreases the tracking error. In case of no input limitations, aforesaid PI controllers are the best choice for stabilizing the inner loop performance. However, input constraints restrict their performance and no optimization is usually observed by using PI controllers. The deadbeat control method is proposed in [9] to enhance the closed-loop performance but unfortunately, it was found highly sensitive to the disturbances, parameters mismatches and measurement noise. Later on, some observed based deadbeat controllers are introduced in order to provide compensation for these discrepancies, however, a trade-off was observed between phase margin and closed-loop performance [9,10]. Afterwards, H∞ controllers in [7,8] are offering robust output response instead of input constraints, however, guaranteeing only the local stability like the µ-synthesis controller in [12]. Several other manuscripts are also amalgamated with literature for fulfilling the demand of electric power regarding fulfilling the environmental principles concerning green-house effects [14–18]. Various structures and topologies for interconnecting DGs are presented in [19–21] for parallel operation and in [22–24] for independent operation. For this reason, various control strategies are anticipated for stabilizing the system to control the voltage and frequency in case of unbalanced load and nonlinear loads. Many researchers have proposed several schemes for designing the controller in order to refine the quality of output voltage of DC to AC inverter. In [25], a control scheme is presented for a DG unit in islanded mode, this control technique is suitable for balanced load conditions for a DG unit when it is electronically coupled. However, this technique is constrained to small load variations and remain unable to stabilize the system in large load variations. A robust controller is proposed in [26] for balanced as well as unbalanced systems. However, it fails to address non-linear load properly. In [27], a repetitive control is implemented for controlling the inverters but the relatively slow response and absence of a systematical technique for stabilizing the error dynamics are the core problems. In [28], the uncomplicatedly designed controller is used to mitigate the load disturbances up to a significant extent through a feedforward compensation element, however, it is only restricted to balanced load conditions. In [29], a spatial repetitive control technique is implemented for controlling the current in a single-phase inverter. The results are satisfactory under non-linear load conditions; however, it is not guaranteeing the optimal tracking ability for a three-phase inverter. In [30], a discrete-time sliding mode current controller is proposed, it is optimally operating to control the system at a sudden load change, an unbalanced load and a nonlinear load, however, the system is quite intricate. In [31], the voltage and frequency controller is presented through a discrete-time mathematical model in order to operate the distributed resource units. This technique is achieving good voltage regulations under different load conditions but the results are not verified through the experimental setup. In [32], a controller is proposed having an adaptive feedforward compensation method applied through a Kalman filter for estimating the variation in parameters, the response was robust; however, tuning of covariance matrices are not appropriately described in the paper. In [33], a corresponding controller is recommended for distributed generation systems in grid applications, the anticipated controller is good in handling the grid disturbances and handling the nonlinearities, however, it is not suitable Electronics 2018, 7, x FOR PEER REVIEW 3 of 37

variation in parameters, the response was robust; however, tuning of covariance matrices are not appropriately described in the paper. In [33], a corresponding controller is recommended for Electronics 2018, 7, 18 3 of 37 distributed generation systems in grid applications, the anticipated controller is good in handling the grid disturbances and handling the nonlinearities, however, it is not suitable in stand-alone mode indue stand-alone to the nonexistence mode due of tovoltage the nonexistence loop. In [34,35], of voltage the adaptive loop. controller In [34,35], isthe used adaptive and voltage controller tracking is usedis achieved and voltage precisely. tracking The is system achieved is precisely.guaranteed The under system systems is guaranteed parameter under variations, systems parameter however, variations,complexity however, in computation complexity exists in and computation a certain pre-defined exists and a value certain is pre-definedneeded for valueparameters. is needed In [36], for parameters.an output voltage In [36], controller an output based voltage on controller the resonant based harmonic on the resonant filters is harmonic presented. filters It measures is presented. the Itcapacitor measures current the capacitor and load current current and in loadthe same current sensor. in the Unbalanced same sensor. voltage Unbalanced condition voltage and conditionharmonic anddistortion harmonic are distortioncompensated are in compensated this controller. in this However, controller. THD However, value is not THD defined value isappropriately, not defined appropriately,therefore, it is complicated therefore, it istocomplicated assess the quality to assess of the the controller. quality of An the adaptive controller. control An adaptive technique control based techniqueproportional based derivative proportional controller derivative is presented controller in [37], is presentedfor a pulse in width [37], modulated for a pulse widthinverter modulated operation inverterin islanded operation distributed in islanded generation distributed system, generation voltage system,regulation voltage under regulation numerous under load numerous conditions load is conditionsevaluated, isthough evaluated, it is not though easy it to is achieve not easy the to achievesuitable thecontrol suitable gains control as par gains the designing as par the procedure designing procedurespecified in specified the paper. in the Moreover, paper. Moreover, voltage and voltage frequency and frequency are optimally are optimally controlled, controlled, active and active reactive and reactivepower unbalancing power unbalancing is aptly iscompensated aptly compensated through through small signal small modeling signal modeling of inverters of inverters in [38]. in [38]. TheThe keykey purposepurpose ofof thisthis studystudy isis toto provideprovide aa comprehensivecomprehensive reviewreview ofof thethe digitaldigital controlcontrol strategiesstrategies for different different types types of ofthree-phase three-phase inverter inverterss in stand-alone in stand-alone as well as as well grid-connected as grid-connected modes. modes.Correspondingly, Correspondingly, explanation, explanation, discussion discussion and andcomp comparisonarison of ofthe the various various control control strategies strategies areare describeddescribed inin thisthis manuscriptmanuscript inin detail.detail. TheThe manuscriptmanuscript is is organized organized as: as: classification classification of of voltage voltage source source inverters inverters is is described described in in Section Section2. Section2. Section3 discusses 3 discusses the characteristicsthe characteristics of control of control systems, systems, followed followed by a depiction by a depiction of reference of reference frames inframes Section in 4Section. The control 4. The control strategy strategy in decoupled in deco dqupled frame dq andframe time-delay and time-delay sampling sampling scheme scheme for VSI for areVSI depicted are depicted in Sections in Sections5 and 5 6and respectively. 6 respectively. An overviewAn overview of the of the most most commonly commonly used used filters filters and and dampingdamping techniques techniques is illustratedis illustrated in Sections in Sections7 and 8 7respectively. and 8 respectively. The grid synchronization The grid synchronization techniques followedtechniques by followed modulation by modulation techniques are techniques described are in described Sections9 andin Sect 10 ionsof the 9 and manuscript, 10 of the respectively. manuscript, Moreover,respectively. control Moreover, Techniques control along Techniques with their along pros. with & cons. theirare pros. described & cons. inare Section described 11. Inin SectionSection 1211., comparativeIn Section 12, analysis comparative and future analysis goals and for future the researchers goals for arethe elaborated.researchers Whereas,are elaborated. conclusions Whereas, are drawnconclusions in Section are drawn 13. in Section 13.

2.2. ClassiﬁcationClassification ofof VSIsVSIs ThereThere areare variousvarious types,types, inin whichwhich thethe invertersinverters areare categorized.categorized. FigureFigure1 1shows shows the the complete complete detaildetail ofof categoriescategories inin whichwhich voltagevoltage sourcesource invertersinvertersare are classiﬁed. classified.

High Power Drives

Indirect Direct Conversion Conversion

Voltage Source Current Source Cycloconverters Inverters Inverters

Load Commutated Multilevel 2-level High- PWM-CSI Inverter VSI Power VSI

Cascaded Neutral Point Flying Capacitor H-Bridge VSI Diode Clamped VSI VSI

FigureFigure 1.1. ClassiﬁcationClassification ofof voltagevoltage sourcesource invertersinverters (VSIs)(VSIs) inin highhigh powerpowerdrives. drives.

2.1. Multilevel Diode Neutral-Point Clamped Inverter

Multilevel inverter (MLI) was proposed in 1975, its design was like a cascade inverter with diodes facing the source. This inverter was later transformed into a Diode Clamped Multilevel Inverter, Electronics 2018, 7, x FOR PEER REVIEW 4 of 37

2.1. Multilevel Diode Neutral-Point Clamped Inverter ElectronicsMultilevel2018, 7, 18inverter (MLI) was proposed in 1975, its design was like a cascade inverter 4with of 37 diodes facing the source. This inverter was later transformed into a Diode Clamped Multilevel Inverter,which is alsowhich named is also as a Neutral-Pointnamed as a Neutral-Point Clamped Inverter Clamped (NPC) [Inverter39]. In this (NPC) type of[3 multilevel9]. In this inverters,type of multilevelthe integration inverters, of voltage the integration clamping of diodes voltage is indispensable.clamping diodes An is ordinaryindispensable. DC-bus An is ordinary separated DC- by busan evenis separated number by of an bulk even capacitors number connectedof bulk capacitors in series connected with a neutral in series point with in thea neutral middle point of the in linethe middlethat is dependentof the line that on theis dependent voltage levels on the of voltage the inverter. levels Inof the Figure inverter.2, a ﬁve-level In Figure NPC-MLI 2, a five-level is shown, NPC- MLIhere is the shown, clamping here diodes the clamping are interlinked diodes are to M-1 interlinked regulatory to M-1 pairs regulatory if M is considered pairs if M as is voltage considered levels as of voltagethe inverter. levels of the inverter.

+ S Vdc a 2

Ca Da Sb

Vdc

4 Sc

Cb Sd Vdc Load Dc n ′ ′ Sa Da

′ Db ′ Sb

Cc V - dc 4 ′ ′ Dc Sc

Cd Vdc - ′ 2 Sd -

FigureFigure 2. 2. Five-levelFive-level diode diode neutral-point neutral-point clamped clamped inverter. inverter.

The neutral point converter was designed by Nabae, Takahashi and Akagi in 1981, this was The neutral point converter was designed by Nabae, Takahashi and Akagi in 1981, this was basically a three-level diode-clamped inverter [40]. A three-phase Three-level diode-clamped inverter basically a three-level diode-clamped inverter [40]. A three-phase Three-level diode-clamped inverter is shown in Figure 3. is shown in Figure3. The NPC-MLI is considered as an important device in conventional high-power ac motor drive The NPC-MLI is considered as an important device in conventional high-power ac motor drive applications like mills, fans, pumps and conveyors, moreover, it also offers solutions for industries applications like mills, fans, pumps and conveyors, moreover, it also offers solutions for industries including chemicals, gas, power, metals, oil, marine, water and mining. The back-to-back including chemicals, gas, power, metals, oil, marine, water and mining. The back-to-back configuration configuration of inverters for reformative applications is also considered as a major plus point of this of inverters for reformative applications is also considered as a major plus point of this topology, used, topology, used, for example, in regenerative conveyors, mining industry and grid interfacing of for example, in regenerative conveyors, mining industry and grid interfacing of renewable energy renewable energy sources like wind power [41]. sources like wind power [41]. There are several benefits as well as drawbacks of multilevel diode-clamped [39,42]. A common There are several benefits as well as drawbacks of multilevel diode-clamped [39,42]. A common dc dc bus is shared by all the phases, this results in the reduction of capacitance requirements of the bus is shared by all the phases, this results in the reduction of capacitance requirements of the inverter. inverter. Due to this reason, implementation of a back-to-back topology is not only credible but can Due to this reason, implementation of a back-to-back topology is not only credible but can also be also be applied practically for performing different operations in an adjustable speed drive and a applied practically for performing different operations in an adjustable speed drive and a high-voltage high-voltage back-to-back inter-connection. The capacitors can be recharged as a group. On back-to-back inter-connection. The capacitors can be recharged as a group. On fundamental frequency, switching efficacy is relatively higher. However, real power flow is problematic in case of a single Electronics 2018, 7, x FOR PEER REVIEW 5 of 37 Electronics 2018, 7, 18 5 of 37 fundamental frequency, switching efficacy is relatively higher. However, real power flow is problematic in case of a single inverter as the intermediate dc levels will tend to overcharge or dischargeinverter as due the to intermediate inappropriate dc levelsmonitoring will tend and to control. overcharge The ornumber discharge of clamping due to inappropriate diodes are quadraticallymonitoring and associated control. Thewith number the number of clamping of leve diodesls, which are quadraticallycan be unwieldy associated for units with with the numbera high numberof levels, of which levels. can be unwieldy for units with a high number of levels.

Vdc S S C Sa a a 2 1

S S Sb b b n

Vdc

S S Sc c c

Vdc - C S Sd Sd 2 2 d -

a b c FigureFigure 3. 3. Three-levelThree-level diode diode neutral-point neutral-point clamped clamped inverter. inverter.

2.2.2.2. Multilevel Multilevel Capacitor Capacitor Clamped/Flying Clamped/Flying Capacitor Capacitor Inverter Inverter AA corresponding corresponding topology topology for for the the NPC-MLI NPC-MLI topology topology is is the the Flying Flying Capacitor Capacitor (FC), (FC), or or Capacitor Capacitor Clamped,Clamped, MLI topology, itit isis depicteddepicted in in Figure Figure4. 4. As As an an alternative alternative to clampingto clamping diodes, diodes, capacitors capacitors are areused used for for holding holding the the voltages voltages to the to the referred referred values. values. In the In the NPC-MLI, NPC-MLI, M − M1 − number 1 number of capacitorsof capacitors are areintegrated integrated on aon shared a shared DC-bus, DC-bus, where where M is M the is level the level number number of the of inverter the inverter and 2(M and− 2(M1)switch-diode − 1) switch- dioderegulatory regulatory pairs are pairs used. are Though, used. Though, for the FC-MLI,for the FC instead-MLI, ofinstead clamping of clamping diodes, one diodes, or more one capacitors or more capacitorsare used toare produce used to theproduce output the voltages output dependsvoltages depends upon the upon position the position and the leveland the of thelevel inverter. of the inverter.They are They coupled are coupled to themidpoints to the midpoints of two of regulatory two regulatory pairs pairs on the on samethe same position position on on each each side side of of a midpoint [42], see capacitors Ca, Cb and Cc in Figure 5. a midpoint [42], see capacitors Ca,Cb and Cc in Figure5. TheThe basic basic difference difference is is the the usage usage of of clamping clamping capacitors capacitors in in plac placee of of clamping clamping diodes, diodes, as as using using themthem increases increases thethe numbernumber ofof switching switching combinations combinations as as capacitors capacitors do do not not block block reverse reverse voltages voltages [42]. [42].Numerous Numerous switching switching states states would would be be able able to to produce produce the the same same voltage voltage levellevel andand the redundant redundant switchingswitching states states would would also also be be available. available. DCDC side side capacitors capacitors in in this this topology topology have have a a ladder- ladder-likelike structure structure and and the the voltage voltage on on each each capacitor capacitor deviatesdeviates from from that that of of the the other other capacitor. capacitor. The The vo voltageltage increment increment between between two two adjacent adjacent legs legs of of the the capacitorscapacitors provides provides the the size size of ofthe the voltage voltage steps steps in the in output the output waveform. waveform. One advantage One advantage of the flying- of the capacitor-basedflying-capacitor-based inverter inverter is the isredundancies the redundancies for inner for inner voltage voltage levels; levels; i.e., i.e., two two or or more more effective effective switchingswitching amalgamations amalgamations can can produce produce an an output output voltage. voltage. UnlikeUnlike thethe diode-clampeddiode-clamped inverter, inverter, the the flying-capacitor flying-capacitor inverter inverter never never requires requires all of the all switches of the switchesto be on to (conducting be on (conducting state) in state) a consecutive in a consecut series.ive series. Moreover, Moreover, the flying-capacitorthe flying-capacitor inverter inverter has hasphase phase redundancies, redundancies, while while the the diode-clamped diode-clamped inverters inverters have haveonly only thethe line-line redundancies redundancies [40]. [40]. TheseThese redundancies redundancies provide provide selective selective charging charging and and discharging discharging of of specific specific capacitors capacitors and and it it can can be be incorporatedincorporated in in the the control control system system for for the the vo voltageltage balancing balancing across across the the various various levels. levels.

Electronics 2018, 7, 18 6 of 37 Electronics 2018, 7, x FOR PEER REVIEW 6 of 37

+ S Vdc a 2

C d Sc

Vdc Cc 4 Cd C b Sd Vdc

n Ca Load Cc

C ′ b Sa Cd V - dc 4 Cc

′ Cd Sb

′ Sc

V - dc 2 S′ - d

Figure 4. Multilevel (Five-level) capacitor clamped/ﬂyingclamped/flying capacitor capacitor inverter. inverter.

There are several advantages and disadvantages of multilevel flying capacitor inverters [41,43]. There are several advantages and disadvantages of multilevel flying capacitor inverters [41,43]. Phase redundancies are offered for balancing the voltage levels between the capacitors. Active and Phase redundancies are offered for balancing the voltage levels between the capacitors. Active and reactive power flow can be regulated. The presence of various capacitors allows the inverter to ride reactive power flow can be regulated. The presence of various capacitors allows the inverter to ride through outages for short duration and deep voltage sags. However, the control system is complex through outages for short duration and deep voltage sags. However, the control system is complex for for tracking the voltage levels for all of the capacitors. Correspondingly, recharging all the capacitors tracking the voltage levels for all of the capacitors. Correspondingly, recharging all the capacitors to to the same voltage level and startup are complex. Switching operation and efficacy are poor for real the same voltage level and startup are complex. Switching operation and efficacy are poor for real power transmission. The installation of large numbers of capacitors is not much economical and it power transmission. The installation of large numbers of capacitors is not much economical and it also also makes the system bulky as compared to the clamping diodes in multilevel diode-clamped makes the system bulky as compared to the clamping diodes in multilevel diode-clamped converters. converters. Likewise, packing is also tougher in the inverters with a higher number of levels. The Likewise, packing is also tougher in the inverters with a higher number of levels. The five-level and five-level and three-level FC-MLIs are represented in Figures 4 and 5 respectively. three-level FC-MLIs are represented in Figures4 and5 respectively.

Electronics 2018, 7, 18 7 of 37 Electronics 2018, 7, x FOR PEER REVIEW 7 of 37

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Sa Sa Sa + Vdc Sa Sa Sa 2 C1 Vdc

2 C1 Sb Sb Sb Vdc

Sb Sb Sb Vdc Ca C C n b c Ca C C n b c Sc Sc Sc

Sc Sc Sc

V C2 - dc 2V C2 - dc Sd Sd Sd 2- Sd Sd Sd - a b c a b c FigureFigure 5.5.Three-level Three-levelcapacitor capacitorclamped/ﬂying clamped/flying capacitor inverter.inverter. Figure 5. Three-level capacitor clamped/flying capacitor inverter. 2.3.2.3. CascadedCascaded H-BridgeH-Bridge InverterInverter 2.3. Cascaded H-Bridge Inverter There are minimum three voltage levels for a multilevel inverter using cascaded topologies. In ThereThere are are minimum minimum three three voltage voltage levels levels for for a multilevel a multilevel inverter inverter using using cascaded cascaded topologies. topologies. Inorder In order to attain a three-level waveform, a single full-bridge or H-bridge inverter is considered. Each to attainorder to a three-levelattain a three-level waveform, waveform, a single full-bridgea single full-bridge or H-bridge or H-bridge inverter isinverter considered. is considered. Each inverter Each is inverter is provided with a separate DC source. A three-level cascaded inverter is shown in Figure 6. providedinverter with is provided a separate with DC a source.separate A DC three-level source. A cascaded three-level inverter cascaded is shown inverter in is Figure shown6. in Figure 6. By using different combinations of the four switches, Sa, Sb, Sc and Sd, each inverter level can ByBy using using different different combinations combinations ofof thethe fourfour switches,switches, Sa,,S Sbb, ,SSc candand S Sd,d each, each inverter inverter level level can can produceproduce threethree differentdifferent outputs outputs of of voltage, voltage, i.e., i.e., V V, 0, and0 and− V−−Vby byconnecting connecting the the dc sourcedc source to theto the ac produce three different outputs of voltage, i.e., Vdcdcdc, 0 and Vdcdcdc by connecting the dc source to the output. −V −can be obtained by turning on switches S and S whereas for obtaining V , switches S ac output. dc V− can be obtained by turning on switchesb cSb and Sc whereas for obtainingdc V a, ac output. Vdcdc can be obtained by turning on switches Sb and Sc whereas for obtaining Vdc , dc and Sd can be turned on. However, for achieving the output voltage on 0 level either Sa and Sb or Sc switchesswitches S aS anda and S dS dcan can be be turned turned on.on. However,However, forfor achievingachieving the the output output voltage voltage on on 0 level0 level either either Sa Sa and Sd can be turned on. The different full-bridge inverters must be connected in series in the way that andand Sb S orb or S cS andc and S dS dcan can be be turned turned on.on. TheThe different full-bridgfull-bridgee inverters inverters must must be be connected connected in seriesin series the ﬁnally produced voltage waveform should be the sum of the inverter outputs. Multilevel cascaded in inthe the way way that that the the finally finally produced produced voltagevoltage wavefowaveformrm should should be be the the sum sum of of the the inverter inverter outputs. outputs. inverters are proposed for the applications such as static VAR generation (reactive power control), MultilevelMultilevel cascaded cascaded invertersinverters areare proposedproposed forfor thethe applicationsapplications such such as as static static VAR VAR generation generation an interface with renewable energy sources and for battery-based applications. The main reasons (reactive(reactive power power control),control), anan interfaceinterface with rerenewablenewable energyenergy sourcessources and and for for battery-based battery-based for preferring a cascaded multilevel H-bridge inverter are the availability of possible output levels applications.applications. The The mainmain reasonsreasons forfor preferring aa cascadedcascaded multilevelmultilevel H-bridge H-bridge inverter inverter are are the the more than twice the number of dc sources [42–44]. The series of H-bridges enables the manufacturing availabilityavailability of of possible possible output output levelslevels more than twicetwice the the number number of of dc dc sources sources [42–44]. [42–44]. The The series series of of and packaging process more easy, quick and economical. However, the requirement of a separate dc H-bridgesH-bridges enables enables the the manufacturingmanufacturing and packaging processprocess more more easy, easy, quick quick and and economical. economical. source for each H-bridge constrains the applications of these inverters to the products having multiple However,However, the the requirement requirement of of aa separateseparate dc source forfor eacheach H-bridge H-bridge constrains constrains the the applications applications of of separate DC sources already or readily available. thesethese inverters inverters to to the the products products havinghaving multiple seseparateparate DC DC sources sources already already or or readily readily available. available.

Sa Sc Sa Sc Sa Sc Sa Sc Sa Sc Sa Sc C1 C2 C3 C A B C2 A B C A B 1 A B A B 3 A B

Sb Sd Sb Sd Sb Sd Sb Sd Sb Sd Sb Sd

FigureFigure 6. 6.Cascaded Cascaded H-bridge multilevel multilevel inverter. inverter. Figure 6. Cascaded H-bridge multilevel inverter.

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2.4. Two-Level Three Phase VSI with an Output Filter 2.4. Two-Level Three Phase VSI with an Output Filter A simple two-level inverter is used to convert dc to ac output. It consists of six switches, IGBTs A simple two-level inverter is used to convert dc to ac output. It consists of six switches, IGBTs and and MOSFETs are the two most suitable switching components for these inverters. Due to simplicity MOSFETs are the two most suitable switching components for these inverters. Due to simplicity in in their structure and ability to handle the voltage by keeping the system stable, they are preferred their structure and ability to handle the voltage by keeping the system stable, they are preferred utmost in the industry and for commercial purpose due to their support in uninterruptible power utmost in the industry and for commercial purpose due to their support in uninterruptible power supply applications. These are usually connected to the load or the grid by using LC or LCL filter. supply applications. These are usually connected to the load or the grid by using LC or LCL ﬁlter. Various types of control systems are implemented by the researchers to improve their performance, Various types of control systems are implemented by the researchers to improve their performance, robustness and stabilization, compensating the power losses and lowering the THD value. SPWM or robustness and stabilization, compensating the power losses and lowering the THD value. SPWM SVPWM are mostly applied to these types of inverters for getting appropriate values. Two level three or SVPWM are mostly applied to these types of inverters for getting′ appropriate′ values. Two level phase VSI is shown in Figure 7. In Figure 7, the S1 to S3 and S1 to0 S3 0shows the switches of the three phase VSI is shown in Figure7. In Figure7, the S1 to S3 and S1 to S3 shows the switches of the inverter.inverter. Whereas, Whereas, uuccrepresents represents the the voltage voltage across across the the capacitors, capacitors, C. C.

S1 S2 S3

LC Filter + u 1 i Vdc u L Three-Phase - 2 L Load u3 S′ S′ S′ 1 2 3 Uc

FigureFigure 7. 7. Two-levelTwo-level three three phase phase VSI VSI with with an an output output LC LC filter. ﬁlter.

2.5. Three Phase Four-Leg VSI with an Output Filter 2.5. Three Phase Four-Leg VSI with an Output Filter Nowadays, a growing interest in using the three-phase four-leg inverters is observed from the Nowadays, a growing interest in using the three-phase four-leg inverters is observed from researchers’ due to their ability to handle the unbalanced loads efficaciously in four-wire systems the researchers’ due to their ability to handle the unbalanced loads efficaciously in four-wire [45,46]. In this topology, the neutral point is proposed by connecting the neutral path to the mid-point systems [45,46]. In this topology, the neutral point is proposed by connecting the neutral path to of the additional fourth leg, as shown in Figure 8. In Figure 8, u represents the output voltage of the mid-point of the additional fourth leg, as shown in Figure8. Ino Figure8, uo represents the output ′ thevoltage LC filter, of the whereas LC filter, M whereas represents M represents the point theneutral point point neutral between point betweentwo switches, two switches, SM andSM SandM . 0 EvenSM. Even though though the configuration the configuration in this in this topology topology do doeses not not need need expensive expensive and and large large capacitors capacitors and and producesproduces lower lower ripple ripple on on the the DC DC link link voltage, voltage, however, however, using using two two extra extra switches switches lead lead to to a a complex complex controlcontrol system system [47]. [47]. Additionally, Additionally, the the split split DC-link DC-link voltage voltage is is about about 15% 15% less less as as compared compared to to the the AC AC voltagevoltage in in this this configuration configuration [48]. [48]. AnotherAnother topology topology can can be be using using split split DC DC link, link, which which is isthe the most most common common way way of ofproviding providing a neutrala neutral point point to tothree-phase three-phase VSIs. VSIs. This This configuration configuration can canbe provided be provided by using by using two twocapacitors capacitors i.e., splittingi.e., splitting the DC-bus the DC-bus into two into parts two by parts using by a using pair of a paircapacitors of capacitors and by andconnecting by connecting a neutral a path neutral to thepath mid-point to the mid-point of these ofcapacitors, these capacitors, as shown as in shown Figure in 9. Figure Both9 these. Both configurations these configurations have several have advantagesseveral advantages and disadvantages, and disadvantages, however, however, the spli thet splitdc-link dc-link is found is found unsuitable unsuitable for for handling handling the the unbalancedunbalanced loads, loads, whereas, whereas, three-phase three-phase four four leg leg in inverterverter is is found found most most appropriate appropriate for for handling handling the the non-linearnon-linear and and unbalanced unbalanced load load conditions. conditions. A A compar comparisonison of of different different types types of of VSIs VSIs with with respect respect to to theirtheir characteristics, characteristics, control control contents contents an andd complexity complexity is described in Table 1 1..

Electronics 2018, 7, 18 9 of 37 ElectronicsElectronics 2018 2018, 7,, x7 ,FOR x FOR PEER PEER REVIEW REVIEW 9 of9 37of 37

+ + S S S S1 S 2 S 3 SM M S1 2 3 I Load I Load LCLC Filter Filter M u1 M u1 Three-Phase C i iL Three-Phase C u2 L u2 Load L L Load Vdc u3 Vdc u3 U Uo ′ ′S′ ′S′ S′ o ′SM S 1 S 2 S′ 3 Uc SM 1 2 3 Uc

- - C C

NeutralNeutral Wire Wire

Figure 8. Three-phase four-leg inverter with an output LC ﬁlter. FigureFigure 8. Three-phase8. Three-phase four-leg four-leg inverter inverter with with an an output output LC LC filter. filter.

a a + + C1 C1 Three-phaseThree-phase four four leg inverter in b VVdc leg inverter in b dc standstand alone alone mode mode

C C2 c - - 2 c

FigureFigure 9. Schematic9. Schematic of of a Three-phasea Three-phase four-leg four-leg inverter inverter withwith with splitsplit split DC-link.DC-link. DC-link.

TableTable 1. Comparison1. Comparison of of different different types types of VSIofVSI VSI inin termsinterms terms ofof design,ofdesign, design, implementationimplementation implementation && complexity.&complexity. complexity. Cascaded H- NP-Diode Flying Characteristic CascadedCascaded H- NP-DiodeNP-Diode FlyingFlying 2L-VSI CharacteristicCharacteristic 2L-VSI2L-VSI BridgeH-BridgeBridge VSI VSI VSI ClampedClampedClamped VSI VSI CapacitorCapacitorCapacitor VSI VSI VSI Design & implementation DesignDesign & implementation & implementation HighHighHigh Low LowLow MediumMediumMedium LowLowLow complexitycomplexitycomplexity SeparateSeparate DC DC DC AdditionalAdditionalAdditional SpecificSpecificSpeciﬁc Requirements Requirements Requirements ClampingClampingClamping diodes diodes IGBTs/MOSFETsIGBTs/MOSFETsIGBTs/MOSFETs sourcessourcessources capacitorscapacitorscapacitors Voltage/currentVoltage/currentVoltage/current ControlControlControl Concerns Concerns Power Power Sharing SharingSharing Voltage Voltage Voltage balancing balancing balancing Voltage Voltage Voltage Setup Setup Setup regulationregulationregulation ModularityModularityModularity High HighHigh Low Low Low High High High LowLowLow FaultFaultFault tolerance tolerance tolerance ability abilityability Easy Easy Easy Difficult Difﬁcult Difficult Easy Easy Easy Easy Easy Easy ReliabilityReliabilityReliability Medium Medium Medium MediumMedium Medium-HighMedium-HighMedium-High HighHighHigh ConverterConverter Complexity Medium Medium Medium Medium Low-Medium Low-Medium High High ConverterController Complexity Complexity Medium-High Medium Medium-High Medium Medium-High Low-Medium Medium High ControllerControllerPower Complexity Complexity Quality Medium-High Medium-High Good Medium-High Medium-High Good Medium-High GoodMedium-High Medium Medium Medium OperationalPowerPower Quality Quality Power (MW) Good Good 3–6 Good 3–7 Good 3–6 Good Good 3Medium Medium MV-IGBT, OperationalOperationalSwitching Power Power devices (MW) (MW) MV-IGBT, 3–6 3–6 IGCT MV-IGBT, 3–7 3–7 IGCT 3–6 3–6 LV-IGBT 3 3 IGCT SwitchingSwitching devices devices MV-IGBT, MV-IGBT, IGCT IGCT MV-I MV-IGBT,GBT, IGCT IGCT MV-IGBT, MV-IGBT, IGCT IGCT LV-IGBT LV-IGBT

3. Characteristics of Control Systems 3. 3.Characteristics Characteristics of of Control Control Systems Systems There are several parameters and characteristics through which a particular control system is ThereThere are are several several parameters parameters and and characteristics characteristics through through which which a particulara particular control control system system is is identiﬁed. Mainly, there are two characteristics of a control system are found i.e., analog or digital identified.identified. Mainly, Mainly, there there are are two two characteristics characteristics of ofa controla control system system are are found found i.e., i.e., analog analog or or digital digital control systems. Both are having some advantages and disadvantages, described as follows: controlcontrol systems. systems. Both Both are are having having some some advant advantagesages and and disadvantages, disadvantages, described described as as follows: follows:

3.1.3.1. Analog Analog Control Control System System

Electronics 2018, 7, 18 10 of 37

3.1. Analog Control System The control systems in which the input and output are designed and analyzed by continuous time analysis or Laplace transform (in s-domain) using state-space formulations. In analog control systems, the representation of the time domain variable is assumed to have inﬁnite precision. Hence, the equations of state space model are differential equations. These systems can be designed without using a computer, microcontrollers or a programmable logic control (PLC). Implementation of analog signals is generally done by using Op-amps, capacitors etc. Robustness against crash or breakdown, having a wide dynamic range, analytical composition accessibility and continuous processing indicate numerous advantages of the analog control systems. However, slow processing speed, interference, complicated implementation in comparative logic, intelligent control systems, neural networks and MIMO are several disadvantages of analog control systems.

3.2. Digital Control System In digital control systems, modeling, designing, implementation and analysis is carried out in discrete-time or z-transformation domain. In digital control systems, as the name depicts that digital signals are analyzed. Therefore, time is sampled and quantized for state space equations. Additionally, as a digital computer has finite precision, extra attention is needed to ensure that error in coefficients, i.e., A/D conversion, D/A conversion etc. are not producing any disturbances or inadequate effects. In a digital controller, the output is a weighted sum of current as well as previous input and output samples, therefore, its implementation requires the storage of relevant values in a digital controller. Mostly, a digital controller is implemented via a computer, so, found most economical to control the plants. Moreover, it is relatively easier to constitute and reconstitute through software. Likewise, programs can be leveled to the confines of storage without any additional cost. Correspondingly, digital controllers are compliant with constraints of the program can be changed. Furthermore, the digital controllers are less responsive to the changes in environmental conditions, unlike the analog controllers. Flexibility, swift expansion, uncomplicated implementation in comparative logic, intelligent systems and MIMO, high accuracy as well as robustness against interference are several advantages of these systems. Though, low processing speed, low dynamic range and non-user-friendly interface are the several drawbacks of the digital control systems. The digital controllers are implemented with various technologies which are classified into three categories expressed as follows:

1. Microcontroller Based implementation (MC) [49–51] 2. Digital Signal processing-based implementation (DSP) [52–54] 3. Field programmable gate array-based implementation (FPGA) [55–57]

In reliable scientific research, generally, DSP is used. Fixed point arithmetic and floating-point algorithms are mostly used in implementing the digital control technique by DSP. A traditional slow microprocessor is used normally in slow applications. However, an FPGA is found adequate in fast controllers, due to its abilities of bug fixing and to be reprogrammed in complex structures. A general structure of a closed loop grid connected digital control system, with an inner current loop and an outer voltage loop, is depicted in Figure 10. In this figure, a voltage source inverter with an output filter is considered. An AC bus is connected to point of common coupling, PCC. Moreover, coordinates transformation from abc to dq is achieved by a phase angle, PH. However, PLL represents 0 0 0 the phase locked loop. The symbols S1, S2, S3, S1, S2 and S3 represents the switches, responsible for positive and negative sequences of the inverter output. The vdre f . and vqre f . represents the reference voltages in dq frame. SVPWM shows the space vector pulse width modulation technique for generating drive signals for a voltage source inverter. The voltage across capacitors, uc and current across inductors, iL are measured and transformed into a synchronized dq reference frame. The input voltage is computed in the dq frame on the basis of vre f . in the three-phase reference frame. The computed data is then transformed from rotating dq to abc reference frame. Afterward, the PWM technique would be selected accordingly. Electronics 2018, 7, x FOR PEER REVIEW 11 of 37

on the basis of v in the three-phase reference frame. The computed data is then transformed from Electronics 2018, 7, 18 ref . 11 of 37 rotating dq to abc reference frame. Afterward, the PWM technique would be selected accordingly.

S S1 2 S3

LCL Filter

i AC Bus + u1 L P Vdc u - 2 L C u3 C

S′ S′ S′ ia i ic 1 2 3 b Uc

C vvvabc,, abc dq id iq

idref . vdref . + + Rd ˆ ˆ v PLL PH i + v d dq ˆ abc d dc + Vref . Digital Digital SVPWM current voltage dq abc Controller Controller PH R + + q ˆ vˆqc vq iq + + iq vq ref . ref . FigureFigure 10. 10.Schematic Schematic diagram diagram ofof aa controlledcontrolled three-phase grid grid connected connected VSI VSI with with a digital a digital controller. controller.

4. Reference Frames 4. Reference Frames Control systems are implemented in either a single phase or a three-phase synchronous Control systems are implemented in either a single phase or a three-phase synchronous reference reference frame. These frames are synchronized with each other through special formulation in order frame. These frames are synchronized with each other through special formulation in order to to be compatible for facilitating the modeling, design, analysis and transformation of one phase and be compatible for facilitating the modeling, design, analysis and transformation of one phase and three phase systems into other systems. Complex structures, especially for multi-level converters, can threebe simplified phase systems by using into these other referenc systems.e frames Complex describes structures, as follows especially [1,58]. for multi-level converters, can be simplified by using these reference frames describes as follows [1,58]. 4.1. abc Reference Frame 4.1. abc Reference Frame A general three-phase system is said to be applied to abc frame without any transformation. An individualA general controller three-phase is to be system used for is each said phase to be appliedcurrent in to abcabc frameframe but without Delta and any star transformation. connection Anhas individual to be considered controller for is designing to be used a for control each phasesystem. current Non-linear in abc controllersframe but are Delta used and in star this connection system hasdue to beto their considered rapid dynamic for designing response. a control system. Non-linear controllers are used in this system due to their rapid dynamic response. 4.2. dq Reference Frame 4.2. dq Reference Frame This frame is used in three-phase systems. Park’s Transformation is used for transforming the abcThis frame frame into is dq used frame. in three-phase This transformation systems. Park’s causes Transformation the current and is usedvoltage for transformingwaveforms to the beabc frameconverted into dq intoframe. a frame This that transformation rotates synchronously causes the with current the grid and voltag voltagee. As waveforms a result, the to variables be converted are intoconverted a frame into that DC rotates variables synchronously and they can with easily the be grid controlled voltage. and As afiltered result, if the required. variables are converted into DC variables and they can easily be controlled and filtered if required. 4.3. αβ Reference Frame 4.3. αβ Reference Frame This frame is used in three-phase systems and sometimes sensationally in single phase systems too.This Grid frame current is used is transformed in three-phase into systemsa stationary and reference sometimes frame sensationally from abc frame in single or single-phase phase systems too.frame Grid by current using Clark’s is transformed transformation. into a Therefore, stationary by reference using this frame transformation from abc frame control or variable single-phase can framebe transformed by using Clark’s into sinusoidal transformation. quantities. Therefore, by using this transformation control variable can be transformed into sinusoidal quantities. 5. The Control Strategy in Decoupled dq Frame 5. TheIn Control a digital Strategy control inscheme Decoupled in dq reference dq Frame frame, decoupling is the most important issue to be discussed.In a digital Generally, control a schemebalanced in and dq interrupted reference frame, sinusoidal decoupling waveform is the can most be obtained important by adopting issue to be discussed.ac voltage Generally, control in aan balanced inverter andstation. interrupted Therefor sinusoidale, the fundamental waveform requirement can be obtained is to simplify by adopting the ac voltage control in an inverter station. Therefore, the fundamental requirement is to simplify the control design [59]. The controller in an inverter station is based on a mathematical steady-state model in the synchronous reference frame. Moreover, during a balanced network state, the direction of the Electronics 2018, 7, x FOR PEER REVIEW 12 of 37 control design [59]. The controller in an inverter station is based on a mathematical steady-state model in the synchronous reference frame. Moreover, during a balanced network state, the direction of the current injected into the loads is assumed as the reference direction. The mathematical representation of a steady-state model is expressed as following: Electronics 2018, 7, 18 =+ω 12 of 37 uLiubd sq sd  (1) uLiu=−ω + current injected into the loads is assumed bq as the reference sd direction. sq The mathematical representation of a steady-state model is expressed as following: In Equation (1), the terms u and u represents the voltages in dq frame under balanced bd ( bq ubd = ωLisq + usd network conditions. Likewise, kp and ki represents the proportional and integrated controllers(1) ubq = −ωLisd + usq and the equation by using aforementioned coefficients represents a PI controller. Correspondingly, u u usd Inand Equation usq represents (1), the terms the busbd voltagesand bq representsin dq axis. However, the voltages isd in and dq frame isq represents under balanced the active network and conditions. Likewise, k and k represents the proportional and integrated controllers and the equation reactive current respectively.p iCommonly, the d-axis is fixed to the voltage source space vector, i.e., by using aforementioned coefficients represents a PI controller. Correspondingly, usd and usq represents the amplitude of the desired ac voltage space vector is kept constant and the value of usq = 0 . Then the bus voltages in dq axis. However, isd and isq represents the active and reactive current respectively. EquationCommonly, (1) thecand be-axis simplified is fixed toas: the voltage source space vector, i.e., the amplitude of the desired ac voltage space vector is kept constant and the=+ valueω of usq = 0. Then Equation (1) can be simplified as: uLiubd sq sd ( (2) uLiubd=−= ωLisq + usd  bq sd (2) ubq = −ωLisd According to Equation (2), the control structure of the inverter station is shown in Figure 11, According to Equation (2), the control structure of the inverter station is shown in Figure 11, where a PI controller is employed in the ac voltage control [60]. Moreover, usref . is the reference where a PI controller is employed in the ac voltage control [60]. Moreover, usre f . is the reference voltage whichvoltage can which be set can accordingly be set accordingly for the desirable for the desirable amplitude amplitude of AC bus of voltage.AC bus voltage.

u sd- bd K u udc + + i ref . KP usref . s + +

isd ωL SVPWM isq ωL - Ki + PLL 0 K + + P bq - s uref . usq

Figure 11. The decoupling control strategy in dq reference frame.

6. Time Delay Sampling Scheme for VSI Time samplingsampling for for digital digital controllers controllers is doneis done by usingby using a discrete a discrete time-domain time-domain analysis, analysis, i.e., z-domain. i.e., z- Twodomain. fundamental Two fundamental advantages advantages of using of z-domain using z-domain analysis analysis over s-domain over s-domain(continuous (continuous time domain) time domain)analysis foranalysis designing for designing a current a current controller controller are: First are: First thecontrol the control implementation implementation is achieved is achieved on ona computer-based a computer-based system, system, i.e., the i.e., control the control calculation, calculation, sampling sampling measurements measurements and PWM and signals PWM sequence signals sequenceare updated are in updated discrete in time discrete steps. time Although, steps. Although this sample, this and sample hold feature and hold is a feature characteristic is a characteristic of a control ofsystem a control and effects system its and dynamics effects as it pers dynamics the referred as samplingper the referred frequency. sampling Secondly, frequency. the multiple Secondly, time delays the multiplecan be modeled time delays by using can abe backshift modeled operator, by using which a backshift affords operator, no simplifications which affords in linear no simplifications control design, inunlike linear continuous control timedesign, domain, unlike where continuous the multiple time time domain, delays where were sampled the multiple usingan time exponential delays were term, whichsampled is approximatedusing an exponential generally term, by applying which is Taylor-series approximated expansion. generally The by sampling applying effect Taylor-series is a most expansion.critical requirement The sampling to handle effect model is a most uncertainties, critical requirement issues in power to handle supplies model and uncertainties, relative disturbances. issues in Therefore,power supplies in order and to dealrelative with disturbances. aforementioned Therefore, issues, zero in order order to hold, deal ZOH with should aforementioned be incorporated issues, in zerothe control order system.hold, ZOH In ZOH, should a polebe incorporated or a zero is added in the intocontrol the existedsystem. controller In ZOH, througha pole or the a zero compensator. is added Theinto fundamentalthe existed controller advantage through of this technique the compensator. is its uncomplicated The fundamental structure advantage to be implemented of this technique on a system, is though, it only affects a limited share of the overall delay. There are two basic sampling routines generally employed in the digital control systems, i.e., single updated sampling and double updated sampling [61]. A single-update sampling method comprises of the measurement samplings, in which calculated modulation indexes are updated once in every Electronics 2018, 7, x FOR PEER REVIEW 13 of 37

its uncomplicated structure to be implemented on a system, though, it only affects a limited share of the overall delay. There are two basic sampling routines generally employed in the digital control systems, i.e., Electronics 2018, 7, 18 13 of 37 single updated sampling and double updated sampling [61]. A single-update sampling method comprises of the measurement samplings, in which calculated modulation indexes are updated once switchingin every switching period. Whereas, period. Whereas, a double-update a double-upd samplingate sampling concept conferred concept conferred to a PWM to concept a PWM in concept which thein which measurement the measurement sampling and sampling therefore, and the therefore, calculated the modulation calculated index modulation are updated index twice are inupdated every switchingtwice in every period switching [61]. The detailedperiod [61]. single-update The detailed and single-update double-update and sampling double-update are shown sampling in Figure are12, where,shown T(k)in Figure represents 12, where, the switching T(k) represents period ofthe the sw presentitching timeperiod slot. of However,the present T(k time− 1) slot. and However, T(k − 2) showsT(k − 1) the and switching T(k − 2) periodshows ofthe the switching former timeperiod slots. of the former time slots. AA single-updatesingle-update PWM-technique PWM-technique with wi samplingth sampling at the at beginning the beginning of a switching of a switching period is period depicted is indepicted Figure 12in a.Figure In this 12a. technique, In this technique, the modulation the mo indexdulation is updated index is once updated in beginning once in ofbeginning a switching of a period.switching A time period. domain A time of onedomain sampling of one time sampling is introduced time is inintroduced the control in loops.the control This effectloops. is This modeled effect withis modeled a backshift with operator a backshift while operator taking while discrete taki timeng discrete domain time into domain the account. into the account. FigureFigure 1212bb showsshows anotheranother schemescheme ofof aa single-updatesingle-update PWMPWM samplingsampling inin whichwhich thethe modulationmodulation indexindex isis updatedupdated inin middlemiddle ofof aa switchingswitching period.period. Therefore,Therefore, thethe timetime delaydelay duedue toto samplingsampling andand updatingupdating routine routine is is the the mean mean value value of theof twothe two converter converter voltage voltage reference reference values, values, i.e., actual i.e., andactual former and controlformer cycles.control Therefore, cycles. Therefore, the transfer the function transfer of function a single-update of a single-upd PWM techniqueate PWM with technique sampling with in middlesampling of ain switching middle of period a switching is determined. period is determined. InIn thethe double-updatedouble-update samplingsampling concept,concept, samplingsampling andand updatingupdating occursoccurs twicetwice inin eacheach samplingsampling period.period. In thisthis technique,technique, the modulationmodulation index isis updatedupdated onon thethe basisbasis ofof formerformer controlcontrol cycle’scycle’s measurements.measurements. According According to to this this behavior, behavior, the the time time-delay-delay is is one one control control cycle. cycle. The The pattern pattern of of a adouble-update double-update sampling sampling is is presented presented in in Figure Figure 12c. 12c.

FigureFigure 12.12. Time delay model model of of a a VSI VSI (a ()a )single-update single-update time time delay delay model model (sampling (sampling at beginning) at beginning) (b) (single-updateb) single-update time time delay delay model model (sampling (sampling at at middle) middle) (c ()c )double-update double-update time time delay delay model model for for a a VSI. VSI.

7.7. OutputOutput FiltersFilters forfor InvertersInverters TheThe harmonicsharmonics reductionreduction isis thethe foremostforemost prioritypriority ofof thethe researchersresearchers whilewhile designingdesigning aa powerpower electronicselectronics oror anan electricalelectrical system.system. Therefore,Therefore, anan outputoutputfilter filteris isused used forfor thisthis purpose.purpose. AnAn outputoutput filterfilter usesuses thethe controlledcontrolled phenomenonphenomenon ofof switchingswitching thethe semiconductorsemiconductor devicesdevices forfor harmonicsharmonics reduction.reduction. ThereThere areare numerousnumerous topologiestopologies ofof suchsuch filtersfilters introducedintroduced inin thethe literatureliterature byby combiningcombining thethe inductorinductor (L)(L) andand capacitorcapacitor (C) (C) i.e., i.e., L, L, LC LC and and LCL LCL filters filters unified unified with with the the inverters inverters to to their their output. output.

7.1.7.1. L-FilterL-Filter InIn highhigh switchingswitching frequencyfrequency inverters,inverters, thethe firstfirst orderorder L-filterL-filter isis consideredconsidered asas thethe mostmost suitablesuitable filter.filter. However,However, inductance inductance decreases decreases the the dynamics dynamics of of the the whole whole system. system.

7.2.7.2. LC-FilterLC-Filter AnAn LCLC filterfilter isis aa second-ordersecond-order filterfilter havinghaving substantiallysubstantially sophisticatedsophisticated dampingdamping behaviorbehavior asas comparedcompared to to an an L-filter. L-filter. This This filter filter topology topology is relatively is relatively easier easier to design to design and it is and a compromise it is a compromise between thebetween values the of values inductance of inductance and capacitance. and capacitance. The cut-off The frequencycut-off frequency needs the needs relatively the relatively higher higher value ofvalue inductance of inductance whereas whereas the voltage the qualityvoltage can quality be improved can be throughimproved the through higher valuethe higher of capacitance. value of The value of resonant frequency is dependent on the impedance of the grid when the system is connected to the grid supply. An LC-filter is mostly preferred in standalone mode. The three-phase Electronics 2018, 7, x FOR PEER REVIEW 14 of 37 Electronics 2018, 7, x FOR PEER REVIEW 14 of 37 capacitance. The value of resonant frequency is dependent on the impedance of the grid when the Electronicscapacitance.2018 ,The7, 18 value of resonant frequency is dependent on the impedance of the grid when14 ofthe 37 system is connected to the grid supply. An LC-filter is mostly preferred in standalone mode. The system is connected to the grid supply. An LC-filter is mostly preferred in standalone mode. The three-phase two-level and three-phase four legs voltage source inverters with an integrated LC filter three-phase two-level and three-phase four legs voltage source inverters with an integrated LC filter are shown in Figures 7 and 8 respectively. two-levelare shown and in Figures three-phase 7 and four 8 respectively. legs voltage source inverters with an integrated LC filter are shown in Figures7 and8 respectively. 7.3. LCL-Filter 7.3. LCL-Filter 7.3. LCL-Filter An LCL filter is a third order filter, mostly used for the grid-tied inverters. The lower frequency An LCL filter is a third order filter, mostly used for the grid-tied inverters. The lower frequency is preferableAn LCL in filter presence is a third of orderaforementioned filter, mostly filter useds. This for thefilter grid-tied supports inverters. the comparatively The lower frequency healthier is preferable in presence of aforementioned filters. This filter supports the comparatively healthier decouplingis preferable between in presence the filter of aforementioned and the grid impedanc filters. Thise. This filter filter supports should the be comparatively precisely designed healthier by decoupling between the filter and the grid impedance. This filter should be precisely designed by takingdecoupling into betweenconsideration the filter the andparameters the grid of impedance. the inverters. This Otherwise filter should even be preciselythe smaller designed values byof taking into consideration the parameters of the inverters. Otherwise even the smaller values of inductancetaking into can consideration bring resonance the parameters and unstable of states the inverters. into the system. Otherwise However, even the the smaller smaller inductance values of inductance can bring resonance and unstable states into the system. However, the smaller inductance caninductance provide can optimized bring resonance current andripple unstable diminishing states intovalues. the system.A three-phase However, VSI the with smaller an LCL inductance filter is can provide optimized current ripple diminishing values. A three-phase VSI with an LCL filter is showncan provide in Figure optimized 13. Where, current V rippleand Z diminishing represents values. the Thevenin A three-phase voltage and VSI Thevenin with an LCL impedance filter is shown in Figure 13. Where, Vth and Zth represents the Thevenin voltage and Thevenin impedance shown in Figure 13. Where, Vth and Z threpresents the Thevenin voltage and Thevenin impedance respectively. However, the complexith tyth of the control system inflated significantly and the dynamic respectively. However, the complexitycomplexity of the controlcontrol system inflatedinflated significantlysignificantly and the dynamicdynamic performance of the inverter can perhaps be affected when relatively complex filter structures are performance of the inverter can perhaps be affected when relatively complex filterfilter structures are employed. Thus, these topologies are most suitable for high power applications, which employ low employed. Thus, these topologies are most suitable for high power applications, which employ low switching frequencies. However, Figures 14 and 15 show the one-leg block diagram of a single-phase switching frequencies. However, FiguresFigures 1414 andand 15 show the one-leg block diagram of a single-phase and three-phase grid-connected systems, respectively. Where, K represents the pulse width and three-phase grid-connected systems, respectively. Where, K pwm represents the pulse width and three-phase grid-connected systems, systems, respectively. respectively. Where, Where, KKpwmpwm representsrepresents thethe pulsepulse width modulation characteristic of the system, whereas, u , u , u , L , L , i and i represents the modulation characteristic of the system, whereas,whereas, uugg, ,u iu, iu,c , uLcg,, LLig, ,i i Landi , igi representsand ig represents the grid side the modulation characteristic of the system, whereas, ug , ui , uc , Lg , Li , ii and ig represents the voltage,grid side inverter voltage, side inverter voltage, side voltage voltage, across voltage capacitor, across gridcapacitor, side inductance, grid side inductance, inverter side inverter inductance, side grid side voltage, inverter side voltage, voltage across capacitor, grid side inductance, inverter side inductance,inverter side inverter current side and current grid side and current grid side respectively. current respectively. inductance, inverter side current and grid side current respectively.

S S S S1 S2 S3 S1 S2 S3 LCL Filter + u LCL Filter + u1 LCL Filter Vdc+ u1 IL Vdc- u2 IL dc u L Zth - 2 u L Z u3 L th V u3 Vth Vth ′ ′ ′ U S1′ S2′ S3 c S′ S′ S′ Uc 1 2 S3 c C C

Figure 13. A Three-phase voltage source inverter in grid-connected mode. Figure 13. A Three-phase voltage source inverterinverter in grid-connected mode.

- ug - - ug i u - - g ref . i i + uc ig i u 1 i + u + 1 i ref . i ii + 1 uc + ig K pwm + Σ 1 i Σ 1 c + Σ 1 K Σ Lis 1Cs Lg s K pwm + Σ Ls Σ Σ L s Li s Cs Lg s - -

Figure 14. One-leg block diagram of a single-phase grid-connected system. Figure 14. One-leg block diagram of a single-phase grid-connected system.

u - - - ug - - - ug - u - ig iref . i uk ii ic u c i i ui u 1 i i 1 u 1 ig ref . Σ Gs() i Σ K()s K uk ΣΣ1 ii c c Σ 1 + Σ + pwm + 1Ls + 1 Lsg + Σ Gs() + Σ K()s K pwm ΣΣi + Cs Σ Ls + + pwm + Lis + Cs Lsg - - i Cs - -

Figure 15. One-leg block diagram of a dual-loop current control strategy for VSI. Figure 15. One-leg block diagram of a dual-loop cu currentrrent control strategy for VSI.

Electronics 2018, 7, x FOR PEER REVIEW 15 of 37 Electronics 2018, 7, 18 15 of 37 8. Damping Techniques for Grid-Connected VSIs 8. DampingIn the grid-connected Techniques for applications, Grid-Connected LCL filter VSIs is highly preferred due to its harmonic suppressing capability.In the grid-connectedIn this case, the applications, voltage across LCL filterthe point is highly of common preferred duecoupling to its harmonicPCC is controlled suppressing in capability.synchronism In with this the case, current. the voltage Therefore, across it thebeco pointmes possible of common to regulate coupling the PCC active is controlledand reactive in synchronismpower injected with into the the current. grid according Therefore, to the it becomes requirement. possible The to LCL regulate filter theoffers active a resonance and reactive frequency power injectedwhich can into be the a gridsource according of instability to the requirement.in the closed-loop The LCL system. filter This offers problem a resonance is stated frequency by various which canresearchers be a source in the of instability literature inand the numerous closed-loop dampin system.g Thisstrategies problem are is proposed stated by to various solve researchersit [62–65]. inDamping the literature methods and can numerous be classified damping into strategiestwo groups. are (i) proposed Passive todamping solve it [and62–65 (ii)]. Active Damping damping. methods can be classified into two groups. (i) Passive damping and (ii) Active damping. 8.1. Passive Damping 8.1. Passive Damping Passive damping is to inserting passive elements in the filter for reduction of the resonant peak in thePassive system damping[32]. Generally, is toinserting passive damping passive elementsschemes never in the desire filter any for amendments reduction of in the the resonant control peakstrategy. in the Though, system these [32]. Generally,approaches passive change damping attenuat schemesion of the never filter, desire as a any result amendments of which losses in the controlincreases strategy. [18,32,34]. Though, The passive these approaches damping techniques, change attenuation presented of generally the filter, in as the a result literature, of which results losses in increasesthe addition [18 ,of32 ,a34 simple]. The passiveresistor dampingin series techniques,with the filter presented capacitor generally [63]. The in major the literature, drawback results of this in thetechnique addition is a of reduction a simple in resistor filter attenuation, in series with increasing the filter power capacitor losses [63 ].and The large major filter drawback volume [62]. of this A techniquegeneral schematic is a reduction of passive in filter damping attenuation, control increasingstrategy for power a grid losses connected and largeVSI is filter shown volume in Figure [62]. A16. general schematic of passive damping control strategy for a grid connected VSI is shown in Figure 16.

- - 1 ug + i u Cs u g iref . i u i + ic c Σ Gs() k 1 i 1 + K pwm + ΣΣ Σ Σ L s Lis g - R +

Figure 16. One-leg block diagram of a passive damping control strategy for a grid-connected VSI.

8.2. Active Damping The active damping methods are proposed to overcome the drawbacks associated with the passive damping techniques. techniques. Active Active damping damping techniques techniques offer offer modifications modifications in inthe the control control policy policy in inorder order to toafford afford closed closed loop loop damping damping [65,66]. [65,66 ].The The active active damping damping techniques techniques are are classified classified into into 3 3groups, groups, i.e., i.e., single single loop, loop, multi-loop multi-loop and and complex complex controllers. controllers. Single Single loop loop methods methods are incorporated to damp the LCL filter filter resonance, without supplementarysupplementary measurement. These methods comprise of low pass filter-based filter-based method, virtual flux flux estimationestimation method, sensor-less method, splitting capacitor method, notch-filter notch-filter method method and and grid grid current current feedback feedback method. method. Generally, Generally, single-loop single-loop methods methods are arefound found relatively relatively robust robust during during uncertainty uncertainty in inpa parametersrameters and and variation variation in in grid grid inductance inductance [62]. [62]. Multiloop methods explore additional measurements.measurements. This This group comprises of capacitor current feedback, capacitor capacitor voltage voltage feedback feedback and and weighted weighted average average current current control control techniques. techniques. However, However, the thethird third group group of active of active damping damping meth methodsods is based is based on complex on complex control control structures. structures. This outcome This outcome of these of thesetechniques techniques is usually is usually a suitable a suitable and and a robust a robust dynamic dynamic response response [67]. [67]. These These techniques techniques include predictive control, state-space controllers, adaptive controllers, sliding mode controller and vector control. Additionally,Additionally, when when LCL LCL filter filter is selected,is selected there, there are twoare optionstwo options for current for current control: control: grid current grid orcurrent converter or converter current. current. Various techniquesVarious techniques are proposed are proposed but there but exists there a disagreement exists a disagreement in the literature in the aboutliterature the about suitable the solution suitable of solution these issues of these and issues it is agreed and it thatis agreed the current that the control current strategy control should strategy be carefullyshould be selected. carefully An selected. active An damping active techniquedamping technique with a damping with a resistancedamping resistance as well as as a harmonicwell as a compensatorharmonic compensator are described are described in [65]. A generalin [65]. A schematic general schematic of active damping of active controldamping strategy control for strategy a grid connectedfor a grid connected VSI is shown VSI inis Figureshown 17in. Figure 17.

Electronics 2018, 7, 18 16 of 37 Electronics 2018, 7, x FOR PEER REVIEW 16 of 37

u - - - g i u u i i u ig ref . Σ i k 1 i c 1 c 1 + Gs() + ΣΣK()s K pwm Σ + Σ Ls + Lsi Cs g - -

Figure 17. One-leg block diagram of an active damping control strategy for a grid-connected VSI.

9. Grid Synchronization Techniques The grid voltage must must be be synchronized synchronized with with the the injected injected current current in in a autility utility network network for for a asignificant signiﬁcant output. output. In In synchronization synchronization algorithm, algorithm, phase phase of of the the grid grid voltage voltage vector vector is is considered and control variables i.e., grid voltages and grid currents are synchronized by using it. Various methodsmethods are introducedintroduced in in literature literature for for extracting extracting the the phase phase angle angle [68]. [68]. Some Some commonly commonly used techniquesused techniques found infound credible in credible research research articles articles are discussed are discussed as: as:

9.1. Zero-Crossing Technique The simplest method to implement is Zero-Crossing method. However, it is not considered on a largerlarger scale scale due due to poorto poor performances performances reported reported in the literature.in the literature. Especially, Especially, during voltage during variations, voltage amplevariations, values ample of harmonics values of andharmonics notches and are notches observed. are observed.

9.2. Filtering of Grid Voltages The grid voltages voltages can can be be filtered filtered in in the the dq dqframeframe as aswell well as in as the in theαβ referenceαβ reference frame. frame. The Theperformance performance of zero-crossing of zero-crossing method method is improved is improved by byvoltage voltage filtering filtering [68]. [68 ].However, However, it itis isa acomplicated complicated process process to to extract extract the the phase phase angle angle out out of of utility utility voltage, voltage, especially during a fault condition. This method uses the arctangent function to realize the phase angle. Generally, a delay is observed in processing a signal whilewhile usingusing thethe filteringfiltering method.method. Therefore, designing of the filterfilter must be considered critically.

9.3. Phase Locked Loop Technique The phase locked locked loop, loop, PLL PLL technique technique is isconsidered considered as asthe the state-of-the-art state-of-the-art method method to obtain to obtain the thephase phase angle angle of the of grid the gridvoltages. voltages. The PLL The is PLL implem is implementedented in dq-synchronous in dq-synchronous reference reference frame. In frame. this In this case, the coordinates transformation from abc to dq is preferred and reference voltage, uˆd case, the coordinates transformation from abc to dq is preferred and reference voltage, uˆd would be would be set to zero for realizing the lock. A general schematic of PLL technique is depicted in set to zero for realizing the lock. A general schematic of PLL technique is depicted in Figure 18. A PI Figure 18. A PI regulator is generally used to control the reference variable. Afterward, the grid regulator is generally used to control the reference variable. Afterward, the grid frequency is frequency is integrated in the system and utility voltage angle is acquired after passing through integrated in the system and utility voltage angle is acquired after passing through a voltage- a voltage-controlled oscillator, VCO. This voltage angle is then fed into the αβ to dq transformation controlled oscillator, VCO. This voltage angle is then fed into the αβ to dq transformation module for module for transforming into the synchronous reference frame. transforming into the synchronous reference frame. This technique is found the most suitable for rejecting notches, grid harmonics and other This technique is found the most suitable for rejecting notches, grid harmonics and other disturbances. However, additional improvements are needed to handle the unsymmetrical voltage disturbances. However, additional improvements are needed to handle the unsymmetrical voltage faults. Especially, filtering techniques to filter the negative sequence should be proposed in case of faults. Especially, filtering techniques to filter the negative sequence should be proposed in case of unsymmetrical voltage faults, as second-order harmonics are propagated by the PLL system and unsymmetrical voltage faults, as second-order harmonics are propagated by the PLL system and reflected in the obtained phase angle. Moreover, it should be assured to estimate the phase angle of the reflected in the obtained phase angle. Moreover, it should be assured to estimate the phase angle of positive sequence of the grid voltages during unbalanced grid voltages [68]. the positive sequence of the grid voltages during unbalanced grid voltages [68].

Electronics 2018, 7, 18 17 of 37 Electronics 2018, 7, x FOR PEER REVIEW 17 of 37

PLL Controller Loop filter ω + r ω VCO uˆd + + 1 θ PI s -

Transformation Module αβ

ud abc uα ua dq

αβ ub u uβ q uc

FigureFigure 18. 18.General General schematic schematic of of a a three-phase three-phase PLL PLL technique. technique.

10.10. Modulation Modulation Schemes Schemes InIn power power electronics electronics converters, converters, the the major major problem problem is is the the reduction reduction in in harmonics. harmonics. PWM PWM control control techniquestechniques provide provide the the most most suitable suitable solution solution for for harmonics harmonics reduction. reduction. A A sinusoidal sinusoidal output output having having controlledcontrolled values values of of frequency frequency and and magnitude magnitude is is the the core core purpose purpose for for using using these these PWM PWM techniques. techniques. Primarily,Primarily, PWM PWM techniques techniques are are classiﬁed classified into into three th majorree major categories categories i.e., Triangular i.e., Triangular Comparison-based Comparison- PWMbased (TC-PWM), PWM (TC-PWM), Space Space Vector-based Vector-based PWM PWM (SV-PWM) (SV-PWM) and and Voltage Voltage look-up look-up table-based table-based PWM PWM (VLUT-PWM).(VLUT-PWM).

10.1.10.1. Triangular Triangular Comparison Comparison Based Based PWM PWM InIn Triangular Triangular Comparison Comparisonbased based PWMPWM (TC-PWM) techniques, techniques, PWM PWM waves waves are are produced produced by by the thecombination combination of ofan anordinary ordinary triangular triangular carrier carrier and and a fundamental a fundamental modulating modulating reference reference signal. signal. The Thetriangular triangular carrier carrier signal signal has has relatively relatively very very higher higher frequency frequency than that ofof aafundamental fundamental modulating modulating referencereference signal. signal. The The magnitude magnitude and and frequency frequency of the of fundamental the fundamental modulating modulating reference reference signal control signal thecontrol magnitude the magnitude and frequency and frequency of the central of the module central inmodule the grid in the side. grid PWM side. and PWM Synchronous and Synchronous PWM (SPWM)PWM (SPWM) are the coreare the techniques core techniques to be mentioned to be mentioned in TC-PWM in TC-PWM [69]. [69].

10.2. Space Vector Based PWM 10.2. Space Vector Based PWM In SVPWM techniques, the revolving reference vectors provide the reference signals. In SVPWM techniques, the revolving reference vectors provide the reference signals. The The magnitude and frequency of central module in grid side are controlled by the frequency and magnitude and frequency of central module in grid side are controlled by the frequency and magnitude of the revolving reference vectors respectively. This technique was first introduced to magnitude of the revolving reference vectors respectively. This technique was first introduced to generate vector based PWM in the three-phase inverters. However, nowadays it is expanded to various generate vector based PWM in the three-phase inverters. However, nowadays it is expanded to other newly introduced inverters. SV-PWM is considered to be the more advanced technique for PWM various other newly introduced inverters. SV-PWM is considered to be the more advanced technique generation for getting qualified sinusoidal output with low THD values [69]. for PWM generation for getting qualified sinusoidal output with low THD values [69]. 10.3. Voltage Look-Up Table-Based PWM 10.3. Voltage Look-Up Table-Based PWM In VLUT-PWM, a new method is introduced to obtain the voltage reference based on the current In VLUT-PWM, a new method is introduced to obtain the voltage reference based on the current reference for an inverter. The major advantage of this technique is its compatibility and simplicity with reference for an inverter. The major advantage of this technique is its compatibility and simplicity the load conditions. The switching frequency in this technique is usually taken significantly lower as with the load conditions. The switching frequency in this technique is usually taken significantly compared to various other presented techniques [52]. lower as compared to various other presented techniques [52]. 11. Control Techniques 11. Control Techniques Connecting the grid to the distributed generation system plays a key role and if bit negligence is shownConnecting in implementing the grid to this the procedure, distributed a numbergeneration of problemssystem plays can arisea key i.e.,role the and grid if bit uncertainty negligence andis shown disturbance, in implementing so in order this to overcome procedure, this a situation,number of a problems suitable controller can arise musti.e., the be grid designed uncertainty for it. Inand this disturbance, section, the mostso in order appropriate to overcome control this techniques situation, are a suitable described controller according must to their be designed applications. for it. VariousIn this section, single loop the most and multiloopappropriate control control systems techniques are discussed are described in the according literature to fortheir power applications. droop Various single loop and multiloop control systems are discussed in the literature for power droop control, voltage and current control. In which inner loop is for current regulation and outer loop is

Electronics 2018, 7, 18 18 of 37

Electronics 2018, 7, x FOR PEER REVIEW 18 of 37 control, voltage and current control. In which inner loop is for current regulation and outer loop isfor for voltage voltage regulation regulation [13,70,71]. [13,70,71 ].In In Figure Figure 19, 19 ,th thee categorization categorization of of classical classical an an advanced control technique is depicted clearly.

Inverters Control Schemes

Predictive Sliding Mode Intelligent Hysteresis Linear Control Control Control Control Control

Artificial Neural Hysteresis Model Current Current Network Based Predictive Control Control Control Voltage (ANN) Control Control (MPC) Control Direct Field Trajectory MPC with Fuzzy Power Oriented Based finite control Control Control Control Control set (FCS) Current (DPC) (FOC) Control Fuzzy- Deadbeat ANN Direct Voltage MPC with Control based Torque Oriented continuous Control Control Control control set (DTC) (VOC) (CCS)

Classical Control Advance Control Techniques Techniques

Figure 19. ClassificationClassiﬁcation of control techniques for VSIs.

11.1. Classical Control Techniques The classicalclassical controllers controllers include include the categorythe category of controllers of controllers for adding for oradding subtracting or subtracting a proportion a andproportion adjusting and the adjusting system accordingly.the system accordingly. These controllers Theseinvolve controllers proportional involve proportional (P), proportional (P), integrationproportional (PI), integration proportional (PI), proportional integral derivative integral (PID) derivative and proportional (PID) and proportional derivative (PD) derivative controllers. (PD) Thesecontrollers. controllers These arecontrollers considered are asconsidered the most as fundamental the most fundamental controllers incontrollers the industry in the for industry controlling for linearcontrolling systems linear and systems considered and considered as the base ofas controlthe base theory. of control Lot oftheory. work Lot in literatureof work in is literature being done is onbeing these done controllers on these [49 controllers–52,72–78 ].[49–52,72–78]. The fundamental The benefitsfundamental of implementing benefits of theseimplementing controllers these are theircontrollers ability are to tunetheir themselvesability to tune according themselves to the a requirementccording to the of therequirement plant and theirof the simple plant and structure. their Moreover,simple structure. they are Moreover, the most they commonly are the usedmost controllerscommonly onused commercial controllers levels, on commercial so easily available.levels, so However,easily available. their tracking However, ability, their response tracking timeability, and response ability to time handle and stable ability error to handle are relatively stable error lower are as comparedrelatively lower to modern as compared state-of-the-art to modern controller. state-of-t The schematiche-art controller. of a digital The PI schematic controller of for a controlling digital PI controller for controlling a three-phase VSI with an LC filter in stand-alone mode is shown in Figure a three-phase VSI with an LC filter in stand-alone mode is shown in Figure 20. In Figure 20, ia f , 20. In Figure 20, i , i and i represents the filter current across phase a, b and c respectively. ib f and ic f representsaf thebf filter currentcf across phase a, b and c respectively. Likewise, va, vb and vc characterizes the voltage across phase a, b and c respectively. Likewise, i and i represents the current Likewise, va , vb and vc characterizes the voltage across phase a, b dand c respectively.q Likewise, across the d and q axis respectively. Moreover, Sa, Sb and Sc represents the switching commands across id and iq represents the current across the d andd q axisq respectively. Moreover, Sa , Sb and Sc phase a, b and c respectively. Correspondingly, Vre f . and Vre f . symbolizes the reference voltages along d drepresentsand q axis the respectively. switching commands across phase a, b and c respectively. Correspondingly, Vref . and q Vref . symbolizes the reference voltages along d and q axis respectively.

Electronics 2018, 7, 18 19 of 37 Electronics 2018, 7, x FOR PEER REVIEW 19 of 37 Electronics 2018, 7, x FOR PEER REVIEW 19 of 37

vdc + - vdc + - LC Filter d implementationof PI control scheme Sa i Three-Phase

SVPWM L v LC Filter ref .+ rd + vd L Load d implementationofPI PIPI control scheme SSa i Three-Phase v SVPWM b L ref-.+ rd + vd L Load PI - PI S U + + Sb c q - PI PI c iaf ibf icf rq - v U vref . + +- q S c q - PI PI c iaf ibf icf C rq v vref . - q - i i i

df qf a C

i i

i i b a

df qf dq

f f

i v v v

i a b c

c b

dq Analogue to

f f

i va vb vc c Digital abc v v Analogue to iq f a ConverterDigital abc

v v iq v a b Converter v vid v b c

vid v

Figure 20. Schematic of a PI control algorithm for a VSI. Figure 20. Schematic of of a a PI PI control control algorithm algorithm for for a aVSI. VSI.

11.2.11.2. PR PR Controllers Controllers PRPR controllers controllers are are thethe the combinationcombinationcombination ofof proportionalproportional and andand resonant resonantresonant controllers. controllers.controllers. The The frequencies frequencies closercloser to to to resonant resonant resonant frequency frequency are are are integrated integrated integrated by by thethe the inintegrator.tegrator. integrator. Therefore, Therefore, Therefore, phase phase phaseshift shift or shift orstationary stationary or stationary error error errordodo not not do occur. notoccur. occur. This This Thiscontroller controller controller cancan canbebe applied be applied inin bothboth in both ABCABCABC and andand αβ αβ αβframes. frames.frames. Due Due Due to tohigh to high high gain gain gain near near resonantresonant frequencies, frequencies, this this controllercontroller has the ability ability to to eliminate eliminate the the steady-state steady-state errors errors of ofelectrical electrical quantities.quantities. The The resonant resonant controller controller maintains maintains the the nene networktworktwork frequency frequency frequency equal equal equal to to tothe the the resonant resonant resonant frequency. frequency. frequency. It isIt iscapable capable of of adjusting adjusting adjusting thethe the frequency frequencyfrequency according according toto changes changes changes in in in grid grid grid frequency. frequency. frequency. However, However, an anaccurate accurate tuningtuning is is always always needed needed for for optimaloptioptimalmal results and and this this technique technique is is found found sensitive sensitive to to the the frequency frequency variationsvariations [[30,31].30 [30,31].,31]. These These controllers controllers are are relatively better better than than PI PI controllers controllers in interms terms of oftheir their tracking tracking ability and response time. If used with a harmonic compensator, they can optimally handle THD. ability and response time. If If used used with with a a harmonic compensator, compensator, they they can can optimally handle handle THD. THD. Their capability to handle current in grid-connected inverters is also remarkable. However, damping Their capability to handle current in grid-connected inverters is also remarkable. However, damping issues still exist. The active and passive damping adjustments and integration in a system with a issues still exist. The The active active and and passive passive damping damping adjustments adjustments and and integration integration in in a asystem system with with a harmonic compensator are somehow, the complicated issues. Moreover, they do not have aharmonic harmonic compensator compensator areare somehow, somehow, the complicatedthe complicated issues. issues. Moreover, Moreover, they do notthey have do outstanding not have outstanding ability to handle stable error and phase shift. The limitation to handle specific abilityoutstanding to handle ability stable to errorhandle and stable phase shift.error Theand limitationphase shift. to handle The limitation speciﬁc frequencies to handle i.e., specific closer frequenciesfrequencies i.e., i.e., closer closer to to resonant resonant frequenciesfrequencies isis alsoalso a a drawback drawback of of these these controllers. controllers. A PRA PR controller controller towith resonant a harmonic frequencies compensator, is also HC, a drawback in stand-alone of these mo controllers.de for a VSI is A shown PR controller in Figure with 21. Structures a harmonic with a harmonic compensator, HC, in stand-alone mode for a VSI is shown in Figure 21. Structures compensator,of a simple PR HC, controller in stand-alone and a discrete mode PR for cont a VSIroller is are shown shown in in Figure Figures 21 22. Structuresand 23, respectively. of a simple PRof a controllersimple PR and controller a discrete and PRa discrete controller PR cont areω shownroller are in shown Figures in 22 Figures and 23 22, respectively.and 23, respectively. Where, Where, Ts represents the sampling period, ω represents the grid angular frequency. However, Where,Ts represents Ts represents the sampling the sampling period, ω period,represents represents the grid angular the grid frequency. angular frequency. However, KHowever,p and Kr K and K denotes the proportional and resonant coefficients respectively. The PR controller with denotesp the proportionalr and resonant coefﬁcients respectively. The PR controller with a harmonic K p and Kr denotes the proportional and resonant coefficients respectively. The PR controller with compensatora harmonic compensator is proposed inis [proposed65]. in [65]. a harmonic compensator is proposed in [65].

vdc + - vdc Implementation of PR control technique + - LC Filter d S dq v Implementation of PR control technique SVPWM a iL Three-Phase ref .+ + vˆd vˆα LC Filter d PR S L Load dq v SVPWM S a iL Three-Phase ref .+ - + vˆd vˆα HC b - PR L Load + + αβ U PR Sb c q HC Sc i i i - af bf cf v - vˆ ref+. + - q αβ vˆ U - β PR c q Sc i i i C v ˆ af bf cf ref .v v -i vi q id iq df qf vˆβ i

- a

f C i

v v b

i i dq f

id iq df qf i a

i va vb vc c

f Analogue to

i b dq

f Digital v abc

i v v v

a a b c

c AnalogueConverter to f v

b Digital v abc v a c Converter v b v FigureFigure 21. 21.General General schematicschematic of a a PR PR Controllerc Controller and and HC HC for for a athree-phase three-phase VSI. VSI. Figure 21. General schematic of a PR Controller and HC for a three-phase VSI.

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Electronics 2018, 7, 18 20 of 37 Electronics 2018,, 7,, xx FORFOR PEERPEER REVIEWREVIEW 20 of 37 KP + Output KP ++ K  + Referencevalue r   − Output ++Output K r  Referencevalue r   − 

 Figure 22. General structure of a PR Controller.

FigureFigure 22. 22. GeneralGeneral structure structure of a PR Controller. Kp

Kp + + −1 + Kr  Ts z  Output Referencevalue − + + + + −1 + K  Ts z  Output Referencevalue r −1 − + z +  + ω 2 −1  Ts z + + − ω 2 1  Ts z +

−1 Figure 23. Structurez of a discrete PR Controller.

Figure 23. 11.3. LQG Control Technique Figure 23. StructureStructure of of a a discrete discrete PR Controller.

11.3.The LQG LQG integration Control Control Technique of Kalman filter with an LQR controller gives rise to an LQG controller. In this technique, Kalman Filter, as well as an LQG controller, can be designed independently of each other. This controlThe integration scheme is of valid Kalman for bothfilter ﬁlter linear with an time-invariant LQR controller systems gives as rise well to asan forLQG linear controller. time-varying In this systems.technique, LQG Kalman Kalman control Filter, Filter, technique as as well well as asfacilitates an an LQG LQG contro controller,the deller,signing can can be beof designed designeda linear independently independentlyfeedback controller of of each each for other. other. an uncertainThis control nonlinear scheme controlis valid system for both [79–81]. linear time-invariantAn LQG control systems structure as well with as afor Kalman linear time-varyingestimator is systems. LQGLQG controlcontrol technique technique facilitates facilitates the designingthe designing of a linearof a feedbacklinear feedback controller controller for an uncertain for an shownsystems. in LQG Figure control 24. techniqueWhere, ufacilitates represents the dethesigning known of ainput linear and feedback y is controller the estimated for an uncertainnonlinear nonlinear control system control [79 system–81].e An[79–81]. LQG An control LQG structurecontrol structure with a Kalmanwith ac Kalman estimator estimator is shown is noise/disturbance.in Figure 24. Where, The Kalmanu represents estimator the provides known inputthe optimal and y solutionis the estimatedto the continuous noise/disturbance. or discrete shown in Figure 24. eWhere, ue represents the knownc input and yc is the estimated estimationThe Kalman problems. estimator provides the optimal solution to the continuous or discrete estimation problems. noise/disturbance. The Kalman estimator provides the optimal solution to the continuous or discrete estimation problems.

Kalman ue -K estimator xˆ Output y Kalman uce -K estimator xˆ Output y Figure 24. Structure of an LQG controller. c Figure 24. Structure of an LQG controller. Figure 24. Structure of an LQG controller. 11.3.1.11.3.1. Linear Linear Quadratic Quadratic Regulator Regulator 11.3.1.TheThe Linear linear linear Quadratic quadratic quadratic Regulator regulator regulator (LQR) (LQR) technique technique is is found found optimal optimal for for steady steady as as well well as as transient transient states [82–84]. As the name depicts, this control technique is a combination of linear and quadratic statesThe [82 linear–84]. Asquadratic the name regulator depicts, (LQR) this control technique technique is found is aoptimal combination for steady of linear as well and as quadratic transient functions,functions, where where the the dynamics dynamics of of the the system system are are desc describedribed by by a set a set of oflinear linear equations equations and and the the cost cost of thestates system [82–84]. is aAs quadratic the name function. depicts, thisThe controlcost function technique parameters is a combination are considered of linear critically and quadratic while functions,of the system where is athe quadratic dynamics function. of the system The cost are functiondescribed parameters by a set of linear are considered equations criticallyand the cost while of designingdesigning the controller.controller. LQR LQR algorithm algorithm is anis automatican automatic approach approach for ﬁnding for finding a suitable a suitable state-feedback state- feedbackthe system controller. is a quadratic Pole placement function. with The statecost feedfunctionback parameterscontroller provides are considered the system critically with a whilehigh controller. Pole placement with state feedback controller provides the system with a high degree of degreedesigning of freedom the controller. and makes LQR it simpleralgorithm to implement.is an automatic This methodapproach is characteristicallyfor finding a suitable steady state- and feedbackfreedom andcontroller. makes Pole it simpler placement to implement. with state This feed methodback controller is characteristically provides the steady system and with it cana high be degree of freedom and makes it simpler to implement. This method is characteristically steady and

Electronics 2018, 7, 18 21 of 37 Electronics 2018, 7, x FOR PEER REVIEW 21 of 37 itemployed can be employed even if some even of if thesome system of theparameters system parameters are unknown. are unknown. However, However, exertion exertion in ﬁnding in thefinding exact weightingthe exact weighting factors limits factors the applicationslimits the applicatio of LQR controlns of LQR scheme. control Moreover, scheme. it hasMoreover, a discrepancy it has a of discrepancytracking accuracy of tracking during accuracy load changes during [ 83load–85 changes]. [83–85].

11.3.2. Linear Linear Quadratic Quadratic Integrator Integrator In linear linear quadratic quadratic integrator integrator (LQI) (LQI) scheme, scheme, cost costminimization minimization is considered is considered critically. critically. This techniqueThis technique is implemented is implemented for nullifying for nullifying the stea thedy-state steady-state error errorbetween between actual actual grid voltage grid voltage and referenceand reference grid gridvoltage voltage during during load loadvariations variations [82]. [An82]. integral An integral term termused usedwith withLQ control LQ control is for is minimizingfor minimizing the thetracking tracking error error produced produced by byunce uncertainrtain disturbances disturbances in in instantaneous instantaneous reference reference voltage. Optimal Optimal gains gains for for providing providing adequate adequate tracki trackingng with with zero zero steady-state steady-state error error are are relatively relatively simpler to to attain attain by by using using this this technique. technique. The The rapid rapid dynamic dynamic response, response, accurate accurate tracking tracking ability ability and relativelyand relatively simpler simpler designing designing procedure procedure provide provide this this technique technique a benefit a beneﬁt over over other other techniques. techniques. However, complications in in extracting extracting the the model model and and phase phase shift shift in in voltage voltage tracking tracking even even in in normal normal operative condition are the major drawbacks of of this this scheme. scheme.

11.4. Hysteresis Hysteresis Control Control Technique Technique Hysteresis control control is is considered as as a a nonlinea nonlinearr method method [86–93]. [86–93]. The The hysteresis hysteresis controllers controllers are are used to track the the error error between between the the referred referred and and measured measured currents. currents. Therefore, Therefore, the the gating gating signals signals are are generated on the the basis basis of of this this re referenceference tracking. tracking. Hysteresis Hysteresis bandwidth bandwidth is is adjusted adjusted for for error error removal removal in reference tracking. This This is is an an uncomplicated uncomplicated concept concept and and has has been been used used since since analog analog control control platforms werewere intensively intensively used. used. This This technique technique does does not requirenot require a modulator; a modu therefore,lator; therefore, the switching the switchingfrequency frequency of an inverter of an is inverter dependent is dependent on the hysteresis on the hysteresis bandwidth bandwidth operating operating conditions conditions and ﬁlter andparameters filter parameters [94]. The major[94]. The drawback major drawback of hysteresis of hysteresis controller controller is its uncontrolled is its uncontrolled switching switching frequency; frequency;however, researchers however, researchers are working are on working improving on this improving controller this and controller several works and several are presented works are and presentedseveral techniques and several are techniques proposed inare the proposed literature. in the Main literature. advances Main in thisadvances technique in this are technique direct torque are directcontrol torque (DTC) control [87,88, 95(DTC),96] and [87,88,95,96] direct power and control direct power (DPC) [control97–99]. (DPC) In DPC, [97–99]. active In and DPC, reactive active powers and reactiveare directly powers controlled, are directly however, controlled, in DTC however, torque and in DTC ﬂux oftorque the system and flux are of controlled. the system Error are controlled. signals are Errorproduced signals by are hysteresis produced controllers by hysteresis and drive controllers signals and are drive generated signals by are the generated look-up accordingby the look-up to the accordingmagnitude to of the the magnitude error signals. of Hysteresisthe error signals. controllers Hysteresis require controllers very high frequencyrequire very for high constraining frequency the forvariables constraining in hysteresis the variables band limits, in hysteresis whenever band implemented limits, whenever on a digital implemented platform ason showna digital in platform Figure 25 . asMoreover, shown switchingin Figure losses25. Moreover, are very highswitching in this losses type of ar controllers.e very high So, in Hysteresis this type controllers of controllers. are found So, Hysteresisinappropriate controllers for high are power found applications. inappropriate for high power applications.

vdc + - LC Filter i Three-Phase S L a L Load a + S iref . b - b + Sc U iref . i i i c - ref .+ af bf cf ic -

f i

b Analogue to f

i Digital c f Converter

Figure 25. A Hysteresis control technique for VSI. Figure 25. A Hysteresis control technique for VSI. 11.5. Sliding Mode Control 11.5. Sliding Mode Control The sliding mode control is considered to be an advanced power control technique for the powerThe converters. sliding mode It ﬁts control into theis considered family of adaptiveto be an advanced control and power variable control structure technique control for the [100 power–104 ]. converters. It fits into the family of adaptive control and variable structure control [100–104]. Sliding

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mode control is a non-linear technique, whereas it can be instigated to both non-linear as well as Sliding mode control is a non-linear technique, whereas it can be instigated to both non-linear as well linear systems [100]. In Figure 26, a sliding mode control along with SVM/PWM is presented. Where, asβ linear systems [100]. Inλ Figure 26, a sliding mode control alongφ with SVM/PWM is presented. v represents the gain, is a strictly positive constant and is a trade-off between the tracking Where, βv represents the gain, λ is a strictly positive constant and φ is a trade-off between the tracking errorerror andand smoothing smoothing of theof controlthe control discontinuity. discontinuity. The sliding The sliding controller controller produces produces the voltage the references voltage inreferences a converter in a forconverter generating for generating the drive signals.the drive A si predefinedgnals. A predefined trajectory trajectory is executed is executed and the controland the variablecontrol variable is forced is to forced slide to along slide it along [102– 104it [102–104]]. The robust. The androbust stable andresponse stable response is achieved is achieved even in even the systemin the system parameters parameters variation variation or load disturbancesor load disturbances by implementing by implementing sliding mode sliding control mode technique. control Thistechnique. controller This is controller more robust is more and robust capable and of capable removing of removing the stable the error stable as compared error as compared to the classical to the controllers.classical controllers. However, However, some drawbacks some drawbacks in implementing in implementing a sliding mode a sliding control mode are control difficulty are in difficulty finding ain suitable finding slidinga suitable surface sliding and surface limitation and oflimitation sampling of ratesampling that degrades rate that thedegrades performance the performance of SMC will of beSMC degraded. will be Wheneverdegraded. tracking Whenever a variable tracking reference, a variable the chattering reference, phenomenon the chattering is another phenomenon drawback is ofanother SMC technique.drawback Asof SMC a result, technique. overall As system a result, efficacy overall is reduced system [efficacy105,106 ].is reduced [105,106]

vdc + - implementationof sliding modecontrol LC Filter Modulator S + + a iL Three-Phase λ 1 PWM L Load β + + Sb vref . β - φ - v + U + S c - - c iaf ibf icf

- - C

i b

1 b

f i

i v v v

c a b c c

f Analogue to C f

v Digital v a a Converter v β v b v b v v c c

FigureFigure 26.26. A Sliding modemode controlcontrol techniquetechnique onon aa VSI.VSI.

11.6. Partial Feedback Controllers 11.6. Partial Feedback Controllers There are several techniques presented for conversion of non-linear systems to linear systems There are several techniques presented for conversion of non-linear systems to linear systems for their uncomplicated computation. Partial feedback controllers are one of the most effective and for their uncomplicated computation. Partial feedback controllers are one of the most effective and forthright techniques for transforming the non-linear systems into the linear ones. By this technique, forthright techniques for transforming the non-linear systems into the linear ones. By this technique, a system can be converted either partially or fully into a linear system, depends on the system a system can be converted either partially or fully into a linear system, depends on the system constraints. Linearity in a system is attained by the cancellation of the nonlinearities inside the constraints. Linearity in a system is attained by the cancellation of the nonlinearities inside the system. system. So, these systems can be controlled by using the linear controllers whenever a non-linear So, these systems can be controlled by using the linear controllers whenever a non-linear system is fully system is fully transformed into a linear system i.e., exact feedback linearization method. However, transformed into a linear system i.e., exact feedback linearization method. However, if it is partially if it is partially converted into a linear system then it is known to be partial feedback linearization. converted into a linear system then it is known to be partial feedback linearization. PFL controller is PFL controller is implemented in [104,106–109]. In PFL, it is difficult to ensure the stability of implemented in [104,106–109]. In PFL, it is difﬁcult to ensure the stability of complicated renewable complicated renewable energy system applications. However, an independent subsystem can be energy system applications. However, an independent subsystem can be obtained from PFL for obtained from PFL for constraining the extensive use of this method. Moreover, in order to deal with constraining the extensive use of this method. Moreover, in order to deal with these problems, these problems, exact feedback linearization (EFL) is a forthright and model-based technique for exact feedback linearization (EFL) is a forthright and model-based technique for scheming nonlinear scheming nonlinear control techniques. EFL receipts the built-in nonlinearity characteristic of the control techniques. EFL receipts the built-in nonlinearity characteristic of the system under deliberation system under deliberation and consents the conversion of a nonlinear structure into a linear one, and consents the conversion of a nonlinear structure into a linear one, algebraically. EFL removes algebraically. EFL removes nonlinearities of a system through nonlinear feedback, as a result, the nonlinearities of a system through nonlinear feedback, as a result, the transformed system is not reliant transformed system is not reliant on an operating point on an operating point.

11.7.11.7. RepetitiveRepetitive ControlControl TheThe plug-inplug-in schemescheme (PIS)(PIS) andand internalinternal modelmodel (IM)(IM) principleprinciple areare thethe basicbasic conceptsconcepts ofof repetitiverepetitive controlcontrol (RC).(RC). RCRC uses uses an an IMP IMP which which is is in in correspondence correspondence to to the the model model of of a periodica periodic signal. signal. In orderIn order to deriveto derive this this model, model, trigonometric trigonometric Fourier Fourier series series expansion expansion is used. is used. If the If modelthe model of reference of reference is fed is into fed theinto closed the closed loop path,loop path, optimal optimal reference reference tracking tracki canng be can obtained. be obtained. Moreover, Moreover, it is found it is robust found against robust against disturbances and has the ability to reject them. RC mostly deals with periodic signals. Closed

Electronics 2018, 7, 18 23 of 37

Electronics 2018, 7, x FOR PEER REVIEW 23 of 37 disturbances and has the ability to reject them. RC mostly deals with periodic signals. Closed loop loopbehavior behaviorElectronics of the2018 ofsystem, the7, x FOR system PEER and andREVIEW Magnitude Magnitude response response of the of IMthe areIM theare the core core factors factors used used for for analyzing 23analyzing of 37 the theperformance performance of the of the repetitive repetitive controller controller in case in case offrequency of frequency variation variation or anyor any other other uncertainty uncertainty inthe in thesystem. system.loop Both behavior Both these these of factors the factors system indicate indicateand Magnitude the the performance performanc response sagging ofe thesagging IM in are casein the case core of variationof factors variation used or uncertaintyorfor uncertaintyanalyzing in thein thereference referencethe performance signal. signal. In presence ofIn the presence repetitive of a of periodic controller a periodic disturbance, in casedist urbance,of frequency RC intends RC variation intends to attain orto any attain zero other trackingzero uncertainty tracking error in whenerror whena periodicthe a periodic system. or a constantBoth or a these constant command factors command indicate is referred the is performancreferred to it. RCtoe it. hassagging RC an has ability in ancase ability toof locatevariation to locate an or error, uncertainty an aerror, time-period ain time- the reference signal. In presence of a periodic disturbance, RC intends to attain zero tracking error periodbefore andbefore ﬁne-tunes and fine-tunes the next commandthe next accordingcommand toaccording the feedback to the control feedback system control for eliminating system for the when a periodic or a constant command is referred to it. RC has an ability to locate an error, a time- observed error. However, it lacks the ability to handle physical noise. For this purpose, an LPF can be eliminatingperiod beforethe observed and fine-tunes error. thHowever,e next command it lacks accordingthe ability to tothe handle feedback physical control noise.system Forfor this used. Kalman’s ﬁltering approach is also noticeable to remove this noise [27,110–113]. The general purpose,eliminating an LPF the can observed be used. error. Kalman’s However, filtering it lacks approach the ability is alsoto handle noticeable physical to noise.remove For this this noise [27,110–113].structurepurpose, of a Thean repetitive LPF general can controllerbe structure used. Kalman’s is of shown a repe filtering intitive Figure controller approach 27. is alsoshown noticeable in Figure to remove27. this noise [27,110–113]. The general structure of a repetitive controller is shown in Figure 27. Repetitive Controller + Repetitive Controller + Time delay Low-pass Stabilizing functionTime delay filterLow-pass ControllerStabilizing Disturbance + function filter Controller Disturbance Reference + + Reference + values + + + Output values + Nominal + Nominal Plant + Output + Controller Plant + Controller - -

FigureFigureFigure 27. 27. 27. BlockBlock Block diagram diagram diagram of of RepetitiveRepetitive Repetitive control control control algorithm. algorithm. algorithm.

11.7.1.11.7.1.11.7.1. Fuzzy Fuzzy Fuzzy Control Control Control ThisThis Thiscontrol control control technique technique technique belongs belongs belongs to toto the the family family family of of intelligent intelligent control control control systems. systems. systems. The The PI The controller PI PIcontroller controller is is replaced by a fuzzy logic controller in this technique as shown in Figure 28. Where, v fz. is the replacedis replaced by bya fuzzy a fuzzy logic logic controller controller in inthis this technique technique as as shown shown in in Figure Figure 28. 28 .Where, Where, vvfzf. z . isis the the fuzzified output voltage. However, its block diagram is shown in Figure 29. In a fuzzy controller, the fuzzifiedfuzziﬁed output output voltage. voltage. However, However, its its block block diagram diagram is shown is shown in Figure in Figure 29. 29In .a Infuzzy a fuzzy controller, controller, the the trackingtracking errorerror of load current current and and its its derivative derivative are are given given as asthe the input. input. This This controller controller design design is is trackingdependent error ofon loadthe awareness, current and knowle its dge,derivative skills and are experience given as of the the input.converter This designer controller in terms design of is dependent on the awareness, knowledge, skills and experience of the converter designer in terms of dependentfunctions on involvement.the awareness, Due knowle to non-lineardge, skillsnature and of the experience power converters, of the converter the system designer can be stabilized in terms of functionsfunctionsin case involvement. involvement. of parameters Due Due variation to to non- non-linear evenlinear if naturethe nature exact of of modelthe the power power of the converters, converters, converter isthe the unknown. system system can canFuzzy be be stabilizedlogic stabilized inin case casecontrollers of of parameters parameters are also variation variationcategorized even even as non-linear if if the exact controllers model andof theprobably converter the best is unknown.controllers amongstFuzzy Fuzzy logic logic controllerscontrollersthe repetitive are also controllers categorizedcategorized [113–116]. asas non-linear non-linear However, controllers controllers strong andassumptions and probably probably and the the adequate best best controllers controllers experience amongst amongst are the therepetitive repetitiverequired controllers incontrollers fuzzification [113– 116[113–116]. of]. However,this controller. However, strong As assumptionsst itrong is dependent assumptions and on adequate theand system adequate experience input experienceand are requireddraw are in requiredfuzziﬁcationconclusions in fuzzification of thisaccording controller. toof the this As set it controller.of is rules dependent assigned As onit to the isthem dependent system during input the on process and the draw systemof their conclusions modelinginput and according and draw designing. conclusionsto the set of according rules assigned to the to set them of rules during assigned the process to them of their during modeling the process and designing. of their modeling and designing. vdc + - implementationof fuzzycontrol technique LC Filter vdc vref +. Sa i SVPWM Three-Phase + - L implementationof+ fuzzycontrol techniquevfz. S L Load Fuzzy b LC Filter v + iref . S ref . Controller a Uc i + SVPWM L Three-Phase ddt Sc i i i v af bf cf L + Fuzzy fz. S Load i - b C ref . i U + Controller a c f S

i c i i i

ddt i af bf cf

- df b

f i

i va vb vc c qf Analogue to - f C

abc Digital

v i

v a a

iq Converter f v

i i df v

- b b dq

id f

v i

i v v v

c a b c c

qf Analogue to f

abc Digital v v a

iq Converter v v Figure 28. A Fuzzy controlb algorithm topology on a VSI. id v

Figure 28. A Fuzzy controlc algorithm topology on a VSI.

Figure 28. A Fuzzy control algorithm topology on a VSI.

Electronics 2018, 7, 18 24 of 37 Electronics 2018, 7, x FOR PEER REVIEW 24 of 37

Reference values i(t) Output Electronics 2018Fuzzification, 7, x FOR PEER REVIEW Defuzzification 24 of 37

Reference values i(t) Output Fuzzification Defuzzification Fuzzy Rule base Controller decision

Fuzzy Rule base Controller decision Figure 29. Block diagram of Fuzzy control algorithm.

11.7.2. Artificial Neural Network Control 11.7.2. Artificial Neural NetworkFigure Control 29. Block diagram of Fuzzy control algorithm. The Artificial neural network (ANN) controllers are the fundamental form of the controllers The11.7.2. Artificial Artificial neural Neural network Network (ANN) Control controllers are the fundamental form of the controllers based based on the human-thinking mode. It consists of a number of artificial neurons to behave as a on the human-thinkingThe Artificial neural mode. network It consists (ANN) of controllers a number are of artificialthe fundamental neurons form to behave of the controllers as a biological biological human brain. The reference tracking error signals are given through a suitable gain or a humanbased brain. on Thethe human-thinking reference tracking mode. error It consists signals areof a given number through of artificial a suitable neurons gain to or behave a scaling as a factor scaling factor (S) as input to the ANN for generating the switching signals into the power converters. (S) asbiological input to thehuman ANN brain. for generatingThe reference the tracking switching error signals signals into are given the power through converters. a suitable This gain approachor a This approach is used for achieving the constant switching operation in power converters. ANN can is usedscaling for achieving factor (S) as the input constant to the switchingANN for generati operationng the in switching power converters. signals into ANNthe power can beconverters. used in both be used in both online as well offline modes while operating it on system control. It has high tolerance onlineThis as approach well offline is used modes for achieving while operating the constant it on switching system control. operation It in has power high converters. tolerance ANN level tocan faults level to faults because of its ability to estimate the function mapping. Its topology is shown in Figure 30. becausebe used of its in abilityboth online to estimate as well offline the function modes while mapping. operating Its topologyit on system is control. shown inIt has Figure high 30tolerance. Fuzzylevel to faultsand ANNbecause can of its be ability combined to estimate to theachieve function an mapping. optimal Its control topology performance is shown in Figure in a30. power Fuzzy and ANN can be combined to achieve an optimal control performance in a power converterFuzzy [113–115]. and ANN ANN can does be combined not need to aachieve conv erteran optimal model control for its performance operation, in however, a power the converter [113–115]. ANN does not need a converter model for its operation, however, the operational operationalconverter behavior [113–115]. of aANN power does converter not need should a conv be preciselyerter model known for its to operation,the designer/operator however, the while behavior of a power converter should be precisely known to the designer/operator while designing designingoperational the ANN behavior control of a system.power converter should be precisely known to the designer/operator while the ANNdesigning control the system.ANN control system.

vdc +vdc - + - implementationof ANN control technique LC Filter implementationof ANN control technique S LC Filter d Sa iL Three-Phase d SVPWM a iL Three-Phase vref .+v + SVPWM L ref .+ + S L Load Load k k Sbb - - - - U U + + c c + + SScc i i i ii i q q k k af afbf bfcf cf v vref . - -

ref . - - C C

i v a

vid iq idf iqf i f

vid viq idf iqf a

b i

f b

i v v v dq f a b c

c Analogue to i f va vb vc c Analogue to f Digital v abc

a Digital v

abc Converter v a

b Converter v v b c v c FigureFigure 30. 30.Schematic Schematic of of Artificial Artificial Neural Network Network control control for forVSIs. VSIs. Figure 30. Schematic of Artificial Neural Network control for VSIs. 11.8. Robust Controllers 11.8. Robust Controllers In robust control theory, a control system vigorous against uncertainties and disturbances is Inoffered. robustrobust The control control basic theory,aim theory, is to a controlattaina control the system stability system vigorous in vigo caserous againstof inadequate against uncertainties uncertaintiesmodeling. and All disturbances theand descriptions, disturbances is offered. is Theoffered. basiccriteria The aim and basic is limitations to attainaim is theto should attain stability be the appropriately in stability case of inadequatein defined case of in inadequate order modeling. to get robust Allmodeling. the control. descriptions, All This the controller descriptions, criteria and limitationscriteriaguarantees and should limitations the bestability appropriately should and high be appropriatelyperformance defined in orderof closdefineded-loop to get in robust system order control. evento get in robust multivariable This controller control. systems This guarantees controller[117]. the stability and high performance of closed-loop system even in multivariable systems [117]. guarantees11.8.1. theH-Infinity stability Controllers and high performance of closed-loop system even in multivariable systems [117]. 11.8.1. H-Infinity Controllers 11.8.1. H-InfinityThe expression Controllers H∞ control originates from the term mathematical space on which the Theoptimization expression takes H place:∞ control H∞ is originates considered from as a thespace term of mathematicalmatrix-valued functions space on that which are the The expression H∞ control originates from the term mathematical space on which the optimizationinvestigative takes and place: confined H∞ inis consideredthe open right-half as a space of the of complex matrix-valued plane. In functions this type of that control are investigative system, optimizationfirst of all, takes the control place: problem H∞ is is formulatedconsidered and as thena space mathematical of matrix-valued optimization functionsis implemented that are and confined in the open right-half of the complex plane. In this type of control system, first of all, investigativei.e., selection and ofconfined the best in element the open according right-half to criterion of the complex from the plane. set of Inobtainable this type alternatives. of control system,H- the control problem is formulated and then mathematical optimization is implemented i.e., selection first ofinfinity all, the control control techniques problem are is generally formulated pertinent and thenfor the mathematical multivariable optimization systems. The isimpact implemented of a of the best element according to criterion from the set of obtainable alternatives. H-infinity control i.e., selectionperturbation of thecan bebest reduced element by usingaccording H-infinity to criterion control techniques from the in set a closed of obtainable loop system alternatives. subject to H- infinity control techniques are generally pertinent for the multivariable systems. The impact of a perturbation can be reduced by using H-infinity control techniques in a closed loop system subject to

Electronics 2018, 7, 18 25 of 37 techniques are generally pertinent for the multivariable systems. The impact of a perturbation can be reduced by using H-infinity control techniques in a closed loop system subject to the problem formulation. The impact can be measured either in terms of performance or stabilization of the system.Electronics However, 2018, 7, x modeling FOR PEER REVIEW of the system should be well-defined for implementation of these25 of 37 control techniques.the problem Moreover, formulation. H-infinity The impact control can techniques be measured have either another in terms discrepancy of performance of high or stabilization computational complications.of the system. In However, case of non-linear modeling systemsof the system limitations, should be the well-defined control system for implementation cannot handle of these them well and responsecontrol techniques. time also increasesMoreover, [118H-infinity]. However, control these techniques controllers have are another implemented discrepancy and of well high defined in [111computational,112,119]. complications. In case of non-linear systems limitations, the control system cannot handle them well and response time also increases [118]. However, these controllers are implemented 11.8.2.andµ -Synthesiswell defined Controllers in [111,112,119].

11.8.2.Mu-synthesis μ-Synthesis isbased Controllers on the multivariable feedback control technique, which is used to handle the structured as well as unstructured disturbances in the system. Where µ mentions the singular Mu-synthesis is based on the multivariable feedback control technique, which is used to handle value that is reciprocal of the multivariable stability margin. The basic purpose is to mechanize the the structured as well as unstructured disturbances in the system. Where μ mentions the singular synthesis of multivariable feedback controllers that are insensitive to uncertainties of the plant and be value that is reciprocal of the multivariable stability margin. The basic purpose is to mechanize the ablesynthesis to attain theof multivariable anticipated feedback performance controllers objectives. that are This insensitive method to is uncertainties well described of the in plant [120, 121and]. be able to attain the anticipated performance objectives. This method is well described in [120,121]. 11.9. Adaptive Controllers 11.9.An adaptiveAdaptive Controllers controller is designed to have the ability of self-tuning, i.e., to regulate itself spontaneouslyAn adaptive according controller to variations is designed in the to systemhave the parameters. ability of self-tuning, It does not i.e., require to regulate initial conditions,itself systemspontaneously parameters according or limitations to variations for itsin the implementation system parameters. due It does to its not ability require to initial modify conditions, the control law accordingsystem parameters to system or limitations requirements. for its Recursive implementa leasttion due squares to its and ability Gradient to modify descent the control are two law most commonlyaccording known to system technique requiremen forts. parameters Recursive estimationleast squares in and adaptive Gradient controllers. descent are two The most structure commonly known technique for parameters estimation in adaptive controllers. The structure of a of a typical adaptive controller is shown in Figure 31. In the literature, some credible research typical adaptive controller is shown in Figure 31. In the literature, some credible research articles and articles and state-of-the-art techniques for adaptive controllers are found in [14,37,53,55,113,122–125]. state-of-the-art techniques for adaptive controllers are found in [14,37,53,55,113,122–125]. These Thesecontrollers controllers are are applicable applicable for forboth both dynamic dynamic as well as well as static as static processes. processes. However, However, the complicated the complicated computationalcomputational process process leads leads to to exertion exertion in in itsits implementation.implementation.

Parameters tuning Controller Control Parameters Signal Reference values Output Controller Plant

FigureFigure 31. 31.Block Block diagramdiagram of of Adaptive Adaptive control control algorithm. algorithm.

11.10.11.10. Predictive Predictive Controllers Controllers Predictive controllers are commenced as a propitious control technique for electronics inverters. Predictive controllers are commenced as a propitious control technique for electronics inverters. The system model is considered critically and then imminent behavior of the control variables is The systempredicted model conferring is considered to the specified critically criterion. and thenIt is an imminent uncomplicated behavior technique of the and control can variableshandle is predictedmultivariable conferring systems to theefficiently. speciﬁed Moreover, criterion. it can It handle is an the uncomplicated system with several technique limitations and or can non- handle multivariablelinearities. systemsIt is generally efﬁciently. preferred Moreover, due to its prompt it can handlestatic as thewell systemas dynamic with response several and limitations ability or non-linearities.to handle stable It is errors. generally However, preferred its computational due to its prompt analysis static is complex as well as ascompared dynamic to responseclassical and abilitycontrollers. to handle It stableis further errors. categorized However, into its Deadbeat computational control and analysis Model is Predictive complex ascontrol. compared It can to refer classical controllers.to literature It is further[105,125–127] categorized for predictive into Deadbeat controllers. control A comparison and Model of predictive Predictive control control. techniques It can refer to literatureon basis [105 of, 125their– 127pros.] forand predictive cons. is described controllers. in Table A 2. comparison of predictive control techniques on basis of their pros. and cons. is described in Table2. 11.10.1. Deadbeat Control Deadbeat control technique is the most authentic, competent and attractive technique in terms of low THD value, frequency as well as rapid transient response. Differential equations are derived

Electronics 2018, 7, 18 26 of 37

11.10.1. Deadbeat Control Deadbeat control technique is the most authentic, competent and attractive technique in terms Electronics 2018, 7, x FOR PEER REVIEW 26 of 37 of low THD value, frequency as well as rapid transient response. Differential equations are derived and discretizedand discretized in thisin this type type of of controlcontrol system system for for controlling controlling the dynamic the dynamic behavior behavior of the system. of the The system. The controlcontrol signalsignal is predicted for for the the new new sampling sampling period period for for attaining attaining the thereference reference value. value. Its effective Its effective Electronics 2018, 7, x FOR PEER REVIEW 26 of 37 dynamicdynamic performance performance and and high high bandwidth bandwidth simplifysimplify the the current current contro controll for forthisthis type type of controller. of controller. Error compensation is a specialty of a deadbeat controller. However, its major discrepancy is its Error compensationand discretized in is this a specialty type of control of a system deadbeat for controlling controller. the dynamic However, behavior its major of the system. discrepancy The is its sensitivitysensitivitycontrol for signal for network network is predicted parameters parameters for the new and sampling accurate accurate period ma mathematicalthematical for attaining filter the ﬁlter modeling reference modeling [13,54,56,128–135]. value. [Its13 effective,54,56,128 Its– 135]. topology is shown in Figure 32, where a disturbance observer, a state estimator and a digital deadbeat Its topologydynamic is performance shown in Figureand high 32 band, wherewidth a simplify disturbance the current observer, control afor state this estimatortype of controller. and a digital ˆ deadbeatcontrollerError controller compensation are used are to used iscontrol a specialty to control the voltageof thea deadbeat voltageand current controller. and of current a However,VSI. ofThe a VSI.coefficientits major The discrepancy coefﬁcient d represents disˆ representsits the sensitivity for network parameters and accurate mathematical filter modeling [13,54,56,128–135].ˆ Its the outputoutput ofof disturbancedisturbance observer observer compri comprisesses of current of current and andvoltage. voltage. However, However, vd andvˆ andvˆ representsvˆ represents topology is shown in Figure 32, where a disturbance observer, a state estimator and a digitald q deadbeatq the controlledthe controlled voltage voltage across acrossd-axis d-axis and andq -axisq-axis respectively. respectively. controller are used to control the voltage and current of a VSI. The coefficient dˆ represents the output of disturbance observer comprises of current and voltage. However, vˆ and ˆ represents d vq implementationof deadbeat control scheme vdc the controlled voltage across d-axis and q-axis respectively. + - S LC Filter d SVPWM a vα iL Three-Phase v Deadbeat v vˆd dq ref . + implementationofd deadbeat control scheme vdc Controller L Load −1 Sb + - State z αβ U q S c LC Filter S c iaf ibf icf v d - estimator v v SVPWM a ref . q vˆ vαβ iL Three-Phase Deadbeat vˆ dq vref . + vd qd Controller C L Load

−1 Sb i αβ i ˆ a State df

z f U q d c i S c i i i

dq b v - estimator v i vβ af bf cf ref . q vˆ qf f

q i va vb vc c v Analogue to f C id

abc Digital

v i i v ˆ a

a f

d iq Converter i v Observer

dq b i

b qf f

Disturbance Disturbance i

v va vb vc c v Analogue to

c f id

abc Digital v v a

iq Converter v Observer b Disturbance Disturbance Figure 32. Deadbeat control topology for VSIs. Figure 32. v Deadbeatc control topology for VSIs.

11.10.2. Model Predictive Control 11.10.2. Model Predictive ControlFigure 32. Deadbeat control topology for VSIs. As the name depicts, a model of the system is used to predict the behavior of the system in model 11.10.2. Model Predictive Control Aspredictive the name control depicts, (MPC) a modeltechnique. of the A cost system function is used criterion to predict is defined the behaviorin this type of of the control system system, in model predictivewhich controlAscan the be name (MPC)minimized depicts, technique. fora model optimal of A the cost control system function actions. is used criterion toThe predict controller is the deﬁned behavior adapts in of this thethetype systemoptimal of in control switching model system, whichstates canpredictive according be minimized control to (MPC)the forcost technique. optimal function A control criterion.cost function actions. Forecast criterion The error is controller defined can be in lessened this adapts type forof the control current optimal system, tracking switching statesimplementing. accordingwhich can be to Moreover,minimized the cost functionforsystem optimal limitations criterion. control actions.and Forecast non- Thelinearities, errorcontroller can asadapts be well lessened theas multipleoptimal for currentswitching inputs trackingand implementing.outputstates systems, according Moreover, are to handled the system cost well function limitations by MPC. criterion. Control and Forecast non-linearities, actions error of the can present asbe welllessened state as multiple arefor consideredcurrent inputs tracking in and order output implementing. Moreover, system limitations and non-linearities, as well as multiple inputs and systems,to predict are handled the control well actions by MPC. of the Control system in actions the next of state. the presentLike deadbeat state arecontrol, considered it is also infound order to sensitiveoutput systems,to system are parameter handled well variations by MPC. [136–147]. Control ac Thetions topology of the present for implementation state are considered of MPC in order on VSI predictto the predict control the control actions actions of the of systemthe system in in the the next next state.state. Like Like deadbeat deadbeat control, control, it is also it isfound also found is shown in Figure 33, whereas, its control schematic is depicted in Figure 34. sensitivesensitive to system to system parameter parameter variations variations [ 136[136–147].–147]. The The topology topology for forimplementation implementation of MPC of on MPC VSI on VSI is shownis shown in Figure in Figure 33, whereas, 33, whereas, its its control control schematic schematic is is depicted depicted in Figure in Figure 34. 34. vdc + - implementationof MPC control scheme vdc + - LC Filter d S implementationof MPC controlvˆ schemeSVPWM a i Three-Phase vref . d L + LC FilterL Load q d Model Predictive S vˆ SVPWM ba i Three-Phase v vref . d L ref . - + L Load ControllerModel Predictive S Uc q Sb i i i vref . - c af bf cf Controller vˆq U dˆ S c c iaf ibf icf C ˆ vˆq

Disturbanced i a C

Observer f i i

Disturbance i b

df a

f f

Observer i v v v

i i a b c

i c b

qf Analogue to

df f

f i v v v

i Digital a b c c v abc

qf Analogue to f a v ConverterDigital iq v v abc b a v v Converter v iq v id c b v v id c

FigureFigure 33. 33.Model Model Predictive Predictive Control topology topology for for VSIs. VSIs. Figure 33. Model Predictive Control topology for VSIs.

Electronics 2018, 7, 18 27 of 37 Electronics 2018, 7, x FOR PEER REVIEW 27 of 37

MODEL PREDICTIVE CONTROLLER predicted control variables Predictor

Reference values - + Output + Optimizer Plant Reference values -

Cost Function Constraints

Figure 34. Block Diagram of Model Predictive Control algorithm.

11.11. Iterative Learning Scheme Iterative Learning Learning Scheme Scheme (ILS) (ILS) is isa complicat a complicateded but butauthentic authentic technique technique for attaining for attaining zero zerotracking tracking error. error. In this In thisscheme, scheme, each each control control comma commandnd is isexecuted executed and and the the system system is is examined examined and then adjusted accordingly before each repetition. HighlyHighly accurate modeling of the system is essential for the implementation of ILS; therefore, its designing technique is relatively more complicated than other schemes. schemes. ILS ILS is is capable capable of ofremoving removing the the tracking tracking error error caused caused by the by periodic the periodic disturbances. disturbances. The Thenext next cycle cycle is predicted is predicted by byconsidering considering the the learning learning gain, gain, system system adjustment adjustment in in z-transform, z-transform, tracking error at each repetition, control function of the designed controller and the error function between two consecutive iterations.

12. Comparative Analysis and Future Research Goals VSIs are specially designed for converting DC to three-phase AC, therefore, control strategies must be according to thethe three-legthree-leg three-phasethree-phase powerpower inverters.inverters. However, for MLIs, the control strategies must must be be inherited inherited from from three-leg three-leg threethree-phasephase power power inverters. inverters. The Thecontrol control policies policies of VSIs of VSIsin stand-alone in stand-alone mode mode can be can categorized be categorized into intonumerous numerous categories categories depending depending upon upon similar similar and anddissimilar dissimilar considerations. considerations. Considering Considering the PWM, the PWM, VSIs VSIscan be can classified be classified into intotwo twocategories categories i.e., i.e.,carrier-based carrier-based modulation modulation and andcarrier-less carrier-less modula modulation.tion. The carrier-based The carrier-based modulation modulation schemes schemes such suchas Selective as Selective Harmonic Harmonic Elimination Elimination (SHE), (SHE),3D SVPWM, 3D SVPWM, Sinusoidal Sinusoidal Pulse Width Pulse Modulation Width Modulation (SPWM) (SPWM)and Minimum-Loss and Minimum-Loss Discontinuous Discontinuous PWM PWM(MLDPWM) (MLDPWM) based based PWM PWM techniques techniques have have attained significantsignificant consideration due to their constantconstant switchingswitching frequency.frequency. SPWM offers constant switching frequency and fl flexibleexible control schemes; nevertheless, one major disadvantage ofof this this technique technique is theis the compact compact efficacy efficacy of the of DC the voltage DC voltage [148]. The[148]. 3D-SVPWM The 3D-SVPWM delivers andelivers adequate an adequate DC bus utilization DC bus utilization and a standardized and a standa loadrdized harmonic load curvatureharmonic ascurvature compared as tocompared the SPWM to technique.the SPWM However,technique. it isHowever, complex init is nature complex to be in implemented nature to be on implemented the digital devices. on the Correspondingly, digital devices. theCorrespondingly, SHE-PWM suggests the SHE-PWM a flexible controller suggests bya flexible considering controller the switching by considering angle. However, the switching the real-time angle. enactmentHowever, the of thisreal-time carrier-based enactment modulation of this carrier-ba is quitesed difficult. modulation The capability is quite ofdifficult. the MLDPWM The capability under nonlinearof the MLDPWM and unbalanced under conditionsnonlinear isand found unbalanced relatively conditions admissible; is however, found itsrelatively real-time admissible; execution ishowever, found very its real-time much circuitous. execution However, is found very the carrier-lessmuch circuitous. modulation However, approaches the carrier-less such as modulation flux vector andapproaches hysteresis such provide as flux a vector rapid-dynamic and hysteresis response provide [149]. a But,rapid-dynamic they suffer response from variable [149]. switchingBut, they frequencysuffer from [91 variable]. Additionally, switching they frequency require [91]. composite Additionally, switching they tables require for theircomposite implementation. switching tables for theirThe implementation. conventional PI controllers encounter problems to eliminate the steady-state error. In order to solveThe this conventional problem, a PR PI controllercontrollers is encounter commonly problems used in the to eliminate stationary the reference steady-state frame error. for regulating In order theto solve output this voltages problem, of thea PR VSIs controller due to its is sophisticatedcommonly used explication in the stationary in eliminating reference the steady-state frame for error,regulating while the controlling output voltages sinusoidal of the signals. VSIs due Additionally, to its sophisticated it is competent explication in eliminating in eliminating selective the harmonicsteady-state uncertainties. error, while controlling sinusoidal signals. Additionally, it is competent in eliminating selective harmonic uncertainties.

Electronics 2018, 7, 18 28 of 37

It is also taken into consideration that the PR controller perceives the resonant frequency to offer gains at specific frequencies. Thus, the resonant frequency should be synchronized with the frequency of the microgrid. Hence, it can be said that it is very sensitive with respect to the variations in system frequency. The PI controller is also extensively used in the dqo frame and performs robustly with pure DC signals. Though, in order to allocate the control variables from the abc to the dqo frame, the phase angle of the microgrid should be known. Likewise, using cross-coupling and voltage feedforward terms are the secondary problems in implementing this method. In the stand-alone operating mode, VSIs primarily controls the power transfer, voltage and frequency of the system. Nevertheless, power quality can be enhanced by offering a suitable control technique in the inverter-based type DGs. As in VSIs, the auxiliary services for improvement in power quality embedded in the control assembly. In case of VSIs, compensation of unbalanced voltage, a lower value for total harmonic distortion, harmonic power-sharing schemes, power sharing between active/reactive powers, imbalance power, active/reactive power control and augmentation in power quality are critically considered and embedded in control schemes. VSIs are also applied on several applications in microgrid systems, extensively, for improving the power quality. This power control strategy is presented in [38]. However, a comprehensive review of various control strategies for microgrids is described in [150]. Moreover, using modular multilevel inverters can improve the modularity and scalability to meet reference voltage levels, efficiency in high power applications, reduction in harmonics in high voltage applications and size of passive filters as well as no requirement for dc-link capacitors [151]. In Table3, different types of filters are suggested by various researchers based on the control systems. However, it is significant to use L-filters for low power applications having a simple design, nevertheless, L-filters are not found suitable in resonance state as well as for high power applications. So, LCL-filter is highly preferred in aforementioned system characteristics. The designing of this filter is comparatively complicated due to a few constrictions related to the system stability. The accuracy in designing and modeling of the system leads to better performance against resonance and harmonics. Nevertheless, the choice should be made according to the customer’s demand. The prime parameters should be chosen on the basis of system condition and intended tasks to be performed by the system. Afterward, the designing of power system and control system parameters should be finalized. This corresponding study incorporates the advantages and disadvantages of each controller in terms of stability, rapid response time, harmonic elimination, the nonlinearity of the system, unbalanced compensation and robustness against parameter variation. Various suitable control schemes for different types of VSIs are documented in this paper. However, their implementations for power generation and power quality improvement are still not perfect simultaneously. Moreover, each controller has its own benefits and obstructions. Therefore, it is not easy to decide that which control scheme is better than the others. These are significant subjects for the future research. On the basis of the analysis of former publications, appended research is suggested to be carried out in the aforementioned area. Regardless of the several investigations in this field, none of the proposed control techniques can be selected as an immaculate solution to meet al.l the requirements of power quality, i.e., harmonic/reactive/imbalance power-sharing and voltage unbalanced/harmonic/swell/sag and Interruption compensation at the same time. Therefore, further research should be focused on the novel power-electronics topologies to fulfill all aforementioned necessities simultaneously. Three-phase three-wire VSIs are now a well-developed and mature research topic with respect to their hierarchical control. But on the other hand, control hierarchies are not as well established for ML-VSIs, as for three-phase three-wire VSIs. It may be beneficial to consider ML-VSI system, as well as the primary, secondary and tertiary stages, whenever a control scheme is to be designed. Substantially, a lot of work is to be done for exploiting the new control approaches for ML-VSIs. In order to achieve enhanced performance, it is compulsory to use some innovative techniques such as robust, MPC and LQR control techniques. Electronics 2018, 7, 18 29 of 37

It is also observed through a number of studies that coupling among the phases is neglected whenever controlling an ML-VSI by means of a conventional PI controller, which results in a reduction of the system’s robustness. Hence, it can also be beneﬁcial to implement decoupled phase voltage control to realize the referred response in time domain. A comparison of the credible research articles found in literature with respect to their control techniques, modulation schemes, control parameters, loop characteristics, employed ﬁlters and applications is described in Table3.

13. Conclusions On the basis of research, conventional multilevel inverter topologies given in the previous sections, general and asymmetrically constituted ML-VSIs have been also reviewed in this paper. Several new hybrid topologies can be designed through the combinations of three main MLI topologies. Besides the combination of topologies, the trade-offs in MLI structures can be dealt by using H-MLIs that is formed using different DC source levels in inverter cells. PWM strategies that generate switching frequency at fundamental frequency are also introduced for H-MLIs for the switching devices of the higher voltage modules to operate at high frequencies only during some inverting instants. Due to numerous applications of conventional MLIs and ﬂexibility to design the hybrid MLI topologies, this paper cannot cover all utilizations with MLIs but the authors intend to provide a useful basis to deﬁne the most proper control schemes and applications. In addition to these, the fundamental design and control principles of MLIs have been introduced as a result of a detailed literature survey. This paper has been destined to provide a reference to readers and the results given in this paper can also be extended with experimental studies.

Table 2. Description of predictive controllers on the basis of their pros. & cons.

Deadbeat Control • -Modulator required • -Fixed switching frequency • -Low Computations • -Limitations not undertaken

Trajectory Based control • -Modulator not required • -Variable frequency • -No cascaded structure

Predictive Hysteresis Based predictive control Control • -Modulator not required • -Variable frequency • -Uncomplicated structure

Model Predictive Control • -Modulator required in case of continuous control set (CCS) and not required in case of ﬁnite control set (FCS). • -Likewise, ﬁxed switching frequency (CCS) and variable switching frequency exists in (FCS). • -Online optimization and simple designing is included in case of FCS. • -Constraints are considered in both cases Electronics 2018, 7, 18 30 of 37

Table 3. Digital control system characteristics in numerous credible scientiﬁc proposals.

Application Controller Filter Ref. Frame Feedback Modulation Ctrl. Parameter Ref. General adaptive LCL Single Phase Multi-loop SPWM V, I [51] General Classic, PR LCL Single Phase Multi-loop PWM I [152] General Adp., Rpt. L Single Phase Single-loop SPWM I [105] UPS DB LC Single Phase Multi-loop PWM V, I [153] General Rpt. LC Single-Phase Single-loop PWM V [101] General Rpt C LCL Single Phase Single-loop PWM I [104] DG Classic LCL abc, αβ Single-loop PWM V, P [47] DG Classic LC abc, αβ Multi-loop SVPWM V, I [48] DG Classic LC abc, αβ Multi-loop SPWM V, I [49] DG Classic L abc, αβ Single-loop VLUT V [50] General DB L abc, αβ Single-loop PWM I [52] APF Adp., Rpt. LC abc, dq Multi-loop SVPWM I [53] General DB LCL abc, dq Multi-loop PWM I [54] DG Adp., MPC LCL abc, αβ Multi-loop SVPWM I [55] General LQG LCL abc, dq Single-loop PWM I [66] PV PR, LQG L abc, αβ Single-loop SVPWM I [64] General Adp. L abc, αβ Multi-loop PWM I [107] UPS Pred. LC abc, dq Single-loop SVPWM V [109] PV, APF Pred., Fuzzy L abc, αβ Multi-loop PWM P [108] PV, APF SMC, Pred. L abc, αβ Multi-loop PWM P [111] General DB L abc, dq Single-loop SVPWM I [113] General Adp., DB L abc, dq Single-loop PWM I [112] DG DB L abc, dq Single-loop SVPWM I [116] UPS DB, Rpt. LC abc, αβ Single-loop PWM V [115] General MPC LCL abc, abc Single-loop PWM V, I [122] General MPC L abc, αβ Single-loop PWM I [125] General MPC L abc, dq Single-loop SVPWM I [128] PV MPC L abc, dq Single-loop SVPWM I [130] PV Classic, Rpt. L abc, dq Single-loop SVPWM I [97]

Acknowledgments: The National Natural Science Foundation of China supported this research work under Grant No. 61374155. Moreover, the Specialized Research Fund for the Doctoral Program of Higher Education PR China under Grant No. 20130073110030 is highly acknowledged. Author Contributions: Sohaib proposed the idea for writing the manuscript. Wang suggested the literature and supervised in writing the manuscript. Mazhar helped Sohaib in writing and formatting. Sarwar helped in modifying the figures and shared the summary of various credible articles to be included in this manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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