energies
Article Strategies to Increase the Transient Active Power of Photovoltaic Units during Low Voltage Ride Through
Xiangwu Yan 1, Baixue Liang 1,* , Jiaoxin Jia 1, Waseem Aslam 2 , Chenguang Wang 1, Shizheng Zhang 1 and Hongbin Ma 1
1 Key Laboratory of Distributed Energy Storage, Micro-Grid of Hebei Province, North China Electric Power University, No.619 Yonghua Road, Baoding 071003, China; [email protected] (X.Y.); [email protected] (J.J.); [email protected] (C.W.); [email protected] (S.Z.); [email protected] (H.M.) 2 Department of Electrical Engineering, University of Sargodha, Sargodha 40100, Pakistan; [email protected] * Correspondence: [email protected]
Abstract: Due to a limitation in the magnitude of the three-phase output inverter currents, the output active power of the photovoltaic (PV) unit has been de-rated during low voltage ride through, which brings great instability risk to the power system. With the increase in the penetration rate of new energy, the impact of the power shortage on the system transient stability increases. It is of great significance to analyze the impact of this transient power shortage on system stability. This article explores methods to improve the active power output capability of photovoltaic units during low-breakthrough periods. A transient simulation model of a grid-connected PV generator with low- voltage ride-through (LVRT) capability is presented, under the condition of meeting the overcurrent capacity of the PV inverter and the requirement of dynamic reactive power support supplied by the Citation: Yan, X.; Liang, B.; Jia, J.; PV generator specified in the China grid codes (GB/T 19964-2012) during grid fault. An example Aslam, W.; Wang, C.; Zhang, S.; Ma, H. Strategies to Increase the Transient system with high PV penetration is built. The change principle and influencing factors of PV transient Active Power of Photovoltaic Units active power output are analyzed. The simulation model is designed in PowerFactory/DIgSILENT, during Low Voltage Ride Through. and several types of three-phase voltage sags are performed in simulation to assess the impact of Energies 2021, 14, 5236. the active current reference calculation method and the maximum inverter output current (Imax) https://doi.org/10.3390/en14175236 limit value on the PV active power output. According to the three indexes, namely the maximum active power of PV unit during the fault, the power improvement gradient and the power surge after Academic Editor: Surender Reddy the fault is cleared. Simulation results showed that using the orthogonal decomposition method Salkuti to calculate the active current reference can make full use of the current capacity of the converter.
Setting Imax to 1.1 rated current of photovoltaic inverter (IN) can reduce the cost-effectiveness ratio of Received: 26 July 2021 the transient active power output of the PV unit. Therefore, we aim to improve the unit’s transient Accepted: 13 August 2021 active power output capacity and realize the optimal effect of improving the transient active power Published: 24 August 2021 shortage of the system.
Publisher’s Note: MDPI stays neutral Keywords: voltage sags; grid-connected photovoltaic system; low voltage ride through; transient with regard to jurisdictional claims in published maps and institutional affil- active power iations.
1. Introduction
Copyright: © 2021 by the authors. With the deterioration of the current environment and the exhaustion of traditional Licensee MDPI, Basel, Switzerland. fossil energy, clean and efficient renewable energy, especially solar energy, has been used This article is an open access article on a large scale. Photovoltaic (PV) generation has shown a large-scale grid-connection distributed under the terms and trend, with increasing installed capacity and an increasing penetration rate [1–5]. PV array conditions of the Creative Commons needs to be converted from DC to AC by an inverter to access the grid, but the overcurrent Attribution (CC BY) license (https:// capacity of the inverter is limited. When the grid suffers from fault, there may be transient creativecommons.org/licenses/by/ overcurrent and overvoltage through the PV inverter. The instantaneous peak value will 4.0/).
Energies 2021, 14, 5236. https://doi.org/10.3390/en14175236 https://www.mdpi.com/journal/energies Energies 2021, 14, 5236 2 of 14
exceed the maximum limit value of the inverter, which leads to the triggering of the PV system’s overcurrent protection and the disconnection from the utility grid [6–9]. Therefore, in order to reduce the risk of PV systems going off the grid when the grid fails, and to improve the transient performance of the systems, these systems must remain connected to the grid within a certain voltage drop range and supply reactive power to support the grid, namely low-voltage ride-through (LVRT) capability [10]. If the PV array works at the maximum power point, the active power injected into the grid will be de-rated below the operating value no matter the DC bus voltage increases or decreases, which is conducive to the realization of low-voltage ride-through [11–13]. The national standard specifies the requirements for dynamic reactive power support capacity for the grid but does not specify the active power of PV units. During grid faults, the voltage of the PV parallel node decreases. The active power injected into the grid has been de-rated to avoid exceeding the inverter’s capacity and assure injection of reactive power’s priority for providing support to the grid voltage [14,15]. Thus, the active power shortage is inevitable in the system, affecting the system’s transient stability. The Australian power grid accounts for 48.36% of new sources. Some new energy units are disconnected from the grid after extreme weather conditions because the present number of low-voltage ride-through (LVRT) is less than the number of failures, resulting in the continuous active power shortage of the system. At the same time, although some new energy units have successfully passed through the fault, they do not immediately recover to the output power level before the interference. It takes hundreds of milliseconds to recover, which leads to the transient active power shortage of new energy units. The active power shortage of these two parts makes the power flow of the line increase instantaneously, which leads to the overload of the tie line and the system jumping off, and the system becomes an isolated network operation and then collapses [16–18]. Therefore, it is important to study the transient active power changes during low-voltage ride-through and recovery of photovoltaic units in a high permeability system. Scholars have done a lot of research on the LVRT of PV generation systems. In [3], the various possible fault current characteristics for solar photovoltaic generators considering low-voltage ride-through are established. However, this paper aims to discuss the per- formance of overcurrent relays, not the transient system stability. In [19], a study of a PV generator and its LVRT capability was carried out when voltage faults were introduced to the utility grid. However, this paper evaluates PV inverter behavior and influence on the grid regarding voltage support during grid fault. In light of the power grid current imbal- ance and power grid oscillation during low-voltage ride-through, a method for modeling and parameter optimization of grid-connected photovoltaic (PV) systems is proposed [20]. A new control strategy of active and reactive power is proposed to improve the reactive power support capability to provide a full range of voltage regulation for grid-connected PV systems during grid faults [21]. The article studies the control of PV inverters with the low-voltage ride-through capability to ensure the PV system remains connected during grid faults [14]. The improvement of the LVRT capability for a two-stage grid-connected inverter of a three-phase PV generator can be observed in [22]. The control of modular multilevel converters with LVRT capability is proposed [23]. However, as far as the authors are concerned, from decreasing transient active power shortage and improving system transient stability, the control strategies have not been commonly studied in the scientific literature. This paper will deal with this current lack of knowledge. Compared with the existing work, this paper’s contribution includes: (i) The characteristic and influence factors of active power supplied from the PV system in the fault are analyzed. (ii) Under the premise of ensuring the safety of equipment overcurrent and meeting the reactive power support requirements in the Chinese grid, the PV inverter control strategies corresponding to different active current calculation formulas are estab- lished. The LVRT control block is added to the current and voltage loops in a grid- connected PV system’s rotating orthonormal dq axes. The added LVRT control-block Energies 2021, 14, x FOR PEER REVIEW 3 of 14
Energies 2021, 14, 5236 lished. The LVRT control block is added to the current and voltage loops3 ofin 14 a grid-connected PV system’s rotating orthonormal dq axes. The added LVRT con- trol-block regulates the reference for the quadrature q component of the output three-phase inverter currents (iq_ref) according to the depth of the voltage sag, which regulatesattains an theeffective reference performance for the quadrature for reactive q (Q) component powers support of the output during three-phase fault condi- invertertions. Meanwhile, currents (i q_refthe )reference according for to the depthquadrature of the d voltage component sag, whichof the attainsoutput anthree-phase effective performanceinverter currents for reactive(id_ref) is (Q)regulated powers by support differen duringt active fault current conditions. calcula- Meanwhile,tion formulas, the obtaining reference different for the quadrature active power d component output. of the output three-phase (iii) inverterA three-phase currents single-stage (id_ref) is regulated large power by different grid-connected active current PV system calculation is analyzed formulas, and obtainingtested under different several active grid powerfaults in output. PowerFactory/DIgSILENT. The influence of the d (iii) A three-phase single-stage large power grid-connected PV system is analyzed and component of inverter currents (id) calculation formulas and the limitation of the testedinverter’s under output several currents grid faults on inthe PowerFactory/DIgSILENT. inverter’s reactive power Theoutput influence is analyzed of the d component of inverter currents (i ) calculation formulas and the limitation of the through simulation results. d inverter’s output currents on the inverter’s reactive power output is analyzed through
simulation results. The paper is organized as follows: Section 2 presents the LVRT capability of a PV systemThe paperfollowing is organized the recommendations as follows: Section described2 presents in the the LVRT Chinese capability grid of acodes PV system(GB/T19964-2012). following the This recommendations section also describes described the in inverter the Chinese control grid model. codes Section (GB/T19964- 3 pre- 2012).sents the This simulation section also results describes (using the PowerFactory/DIgSILENT) inverter control model. of Section the system3 presents under the in- simulationvestigation. results The conclusion (using PowerFactory/DIgSILENT) of the system performance of is the presented system in under Section investigation. 4. The conclusion of the system performance is presented in Section4. 2. Grid-Connected PV System Model with LVRT Capability 2. Grid-Connected PV System Model with LVRT Capability 2.1.2.1. PV PV SystemSystem ModelModel FigureFigure1 1shows shows the the block block diagram diagram of of the the three-phase three-phase single-stage single-stage grid-connected grid-connected PV PV systemsystem presented presented in in this this article. article. The The modeling modeling of of the the PV PV power power station station mainly mainly includes includes threethreeparts: parts: PVPV batteries, inverters inverters and and th theireir control control systems systems [2 [4].24]. In In Figure Figure 1,1 p, andp and q areq arethethe active active and and reactive reactive power power supplied supplied to the to thegrid, grid, respectively. respectively. Us andUs and δs areδs arethe theam- plitude and phase angle of the AC grid voltage, respectively. Cd and ud are the DC capac- amplitude and phase angle of the AC grid voltage, respectively. Cd and ud are the DC capacitanceitance and andDC DCvoltage, voltage, respectively. respectively. SPWM SPWM is isthe the acronym acronym of of sinusoidal pulsepulse widthwidth PV modulation.modulation.L Lis is the the abbreviation abbreviation of of filter filter inductance. inductance.u uPV is is the the operating operating voltage voltage of of the the PVPV array. array.i PViPV isis thethe operatingoperating currentcurrent ofof thethe PVPV array.array.
FigureFigure 1. 1.Structure Structure of of the the proposed proposed single-stage single-stage grid-connected grid-connected PV PV system. system.
TheThe PV PV generator generator does does not not have have the the same same strong strong excitation excitation function function as as a a synchronous synchronous generator.generator. DuringDuring faultyfaulty operationoperation ofof thethe grid,grid, severesevere voltage voltage fault fault happens. happens. AtAt the the same same time,time, thethe instantaneousinstantaneous active current current has has not not changed, changed, and and thus thus the the active active power power could could not notbe bedelivered delivered to the to the grid, grid, which which makes makes DC DC volt voltageage increase. increase. According According to tothe the PV PV curve curve for forMPP, MPP, the the operation operation point point of ofPV PV array array will will shift shift from from the the maximum maximum power power point point to tothe the left leftside side of ofthe the maximum maximum power power point. point. When When the the MPPT MPPT algorithm isis deactivated,deactivated, thethe active active power injected into the grid can be calculated according to active current and grid voltage during the fault. It determines the active power delivered by the PV generator and adjust DC voltage to balance the active power, to realize the low-voltage ride-through [25]. Energies 2021, 14, x FOR PEER REVIEW 4 of 14
power injected into the grid can be calculated according to active current and grid voltage Energies 2021, 14, 5236 4 of 14 during the fault. It determines the active power delivered by the PV generator and adjust DC voltage to balance the active power, to realize the low-voltage ride-through [25].
2.2.2.2. OverallOverall ControlControl ModelModel TheThe LVRTLVRT capability capability of of a PVa PV system system requires requires the the distributed distributed generation generation (DG) (DG) systems sys- totems remain to remain connected connected to the gridto the within grid within a certain a certain voltage voltage sag and sag time and interval time interval during griddur- faults.ing grid The faults. Chinese The gridChinese codes grid (GB/T19964-2012) codes (GB/T19964-2012) are shown are in shown Figure in2. Figure 2.
FigureFigure 2.2. LVRTLVRT (low–voltage–ride–through)(low–voltage–ride–through) curves curves in in Chinese Chinese grid grid code. code.
TheThe PVPV generatorgenerator deliversdelivers thethe maximummaximum powerpower toto the the utility utility grid grid during during the the normal normal operation.operation. WhenWhen thethe gridgrid operatesoperates underunder faultyfaulty conditions,conditions,the theDC DCvoltage voltage decreases decreasesand and activeactive powerpower isis de-ratedde-rated belowbelow thethe operatingoperating valuevalue toto achieveachieve low-voltagelow-voltage ride-through.ride-through. Thus,Thus, photovoltaicphotovoltaic unitsunits cancan obtainobtain LVRTLVRT capabilitycapability byby improvingimproving thethe inverterinverter controlcontrol strategystrategy withoutwithout additionaladditional hardwarehardware overhead.overhead. ItsIts controlcontrol goalgoal isis mainlymainly toto regulateregulate thethe activeactive (P)(P) and and reactive reactive (Q) (Q) powers powers solely solely with with the inverterthe inverter currents’ currents’ dq components dq components to meet to the requirements of the PV systems and provide dynamic reactive power support specified meet the requirements of the PV systems and provide dynamic reactive power support by the national standard. It also provides the limitation of the inverter currents to avoid its specified by the national standard. It also provides the limitation of the inverter currents automatic disconnection from the utility grid, avoiding the inverter failure. to avoid its automatic disconnection from the utility grid, avoiding the inverter failure. Figure3 shows the control block diagram of PV inverter with LVRT capability pre- Figure 3 shows the control block diagram of PV inverter with LVRT capability pre- sented in this paper [26]. During the normal operating conditions of the grid, a typical sented in this paper [26]. During the normal operating conditions of the grid, a typical voltage and current double closed-loop inverter control strategy are adopted. As the voltage and current double closed-loop inverter control strategy are adopted. As the conventional mode in Figure3 displays, the outer voltage control loop tracks the DC conventional mode in Figure 3 displays, the outer voltage control loop tracks the DC side side voltage, which corresponds to the maximum power and generates the active current voltage, which corresponds to the maximum power and generates the active current reference as the active current command input of the current inner loop. Reactive current reference as the active current command input of the current inner loop. Reactive current reference of the inner current control loop is set to zero in order to achieve a unity power factorreference to enhance of the inner the utilizationcurrent control factor loop of solaris set energy.to zero in During order gridto achieve faults, a tounity avoid power the PVfactor system’s to enhance automatic the utilization disconnection factor from of solar the energy. utility grid, During the grid PVinverter faults, to quits avoid the the con- PV ventionalsystem’s automatic operation logicdisconnection and enters from the low-voltagethe utility grid, ride-through the PV inverter operation quits logic, the conven- which istional mainly operation divided logic into and two enters modes, the namely low-voltage fault ride-through ride-through mode operation and recovery logic, which mode. is Frommainly the divided moment into the two voltage modes, of the namely PV grid-connected fault ride-through point dropsmode toand 90% recovery of the normal mode. value,From the moment inverter entersthe voltage the fault of the ride-through PV grid-connected stage, adopting point drops fault to ride-through 90% of the normal mode. Thevalue, inverter the inverter control enters structure the fault switches ride-throu from thegh stage, fault ride-through adopting fault mode ride-through to the recovery mode. modeThe inverter when the control voltage structure returns switches to 90% of from the normalthe fault value, ride-through but the active mode power to the doesrecovery not restoremode when to normal the voltage levels immediately. returns to 90% The of inverter the normal switches value, back but tothe the active conventional power does mode not whenrestore the to active normal power levels climbs immediately. to the pre-fault The in level,verter as switches the fault back ride-through to the conventional mode and conventionalmode when the mode active in Figure power3 climbsdisplays, to the respectively pre-fault [level,27]. as the fault ride-through mode and conventional mode in Figure 3 displays, respectively [27].
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FigureFigure 3. 3. ControlControl block diagramdiagram ofof PV PV inverter inverter considering considering LVRT LVRT capability. capability.
2.2.1.2.2.1. Inverter Inverter Reactive CurrentCurrent in in Fault Fault Ride-Through Ride-Through Mode Mode and and Recovery Recovery Mode Mode A reactivereactive power power priority priority strategy strategy is adopted is adopted to supply to supply reactive reactive power for power supporting for sup- portingthe voltage the recoveryvoltage recovery within the within limit ofthe the limit total of current. the total Priority current. is givenPriority to regulateis given theto reg- ulatereactive the current reactive output current according output to according the depth ofto the the voltage depth sag,of the and voltage then the sag, active and current then the activeoutput current of the inverter output is of regulated. the inverter No reactiveis regula currentted. No injection reactive is requiredcurrent injection in the China is required grid U ≤ U ≤ U incodes the asChina long asgrid the codes gridvoltage as long stays as the in thegrid dead-band voltage stays region in (i.e., the0.9 dead-bandT S region1.1 T ).(i.e., On the other hand, if the grid voltage drops below 90% of the nominal value, reactive 0.9UT ≤ US ≤ 1.1UT). On the other hand, if the grid voltage drops below 90% of the nominal current injection is required (see Equation (1)). value, reactive current injection is required (see Equation (1)). 1.5 × (0.9 − U )I (0.2 ≤ U ≤ 0.9) 1.5×− (0.9TUITN ) N (0.2 ≤≤ UT T 0.9) Iq = 1.05 × IN (UT < 0.2) (1) Iq= 1.05×
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where P0 is the active power output before the fault; that is, the PV maximum active power output, and Imax is the allowable maximum inverter current. It can be seen from Figure4 that compared with the method of recovery active current rising according to the specified slope or parabola, the immediate recovery method can quickly restore the inverter active current output and thus attain the best performance for active powers support. Therefore, this paper focuses on regulating active current output by an immediate recovery in the recovery stage. P0/Us represents the maximum active Energies 2021, 14, x FOR PEER REVIEWcurrent output supplied by PV array. Its value is substantial that the active current during6 of 14 the fault period will not exceed. Thus, the active current is mainly determined by the selected calculation formulas and Imax value under the same reactive current value.
FigureFigure 4. 4.Transient Transient active active current current response response of of PV PV unit unit with with LVRT LVRT function. function.
2.3. Control of p and q − Based on the field-oriented vectorIPUIId0smaxq=min( control, / the , q components ) of the grid voltages are(2) set to zero. According to the instantaneous power theory, the p and q powers delivered to 22 the utility grid can be expressed as:IPUIId0smaxq=min( / ,− ) (3) 3 where P0 is the active power output beforep = 2 e dtheid fault; that is, the PV maximum active 3 (4) power output, and Imax is the allowable qmaximum= 2 ediq inverter current. It can be seen from Figure 4 that compared with the method of recovery active cur- where e is the d component of the grid voltage, and i is the dq components of the rent risingd according to the specified slope or parabola,dq the immediate recovery method inverter currents. can quickly restore the inverter active current output and thus attain the best perfor- In conclusion, during grid faults, the amount of active power delivered by the inverter mance for active powers support. Therefore, this paper focuses on regulating active cur- depends on the depth of the voltage sag, active current calculation formulas and the rent output by an immediate recovery in the recovery stage. P0/Us represents the maxi- maximum allowable current. Because the fault type determines the depth of the system’s mum active current output supplied by PV array. Its value is substantial that the active voltage sag and fault location, it is impossible to control it in advance. Therefore, this paper current during the fault period will not exceed. Thus, the active current is mainly deter- focuses on the influence of active current calculation formulas and the maximum allowable mined by the selected calculation formulas and Imax value under the same reactive current current on PV units’ transient active power characteristics. value. 3. Results and Discussion 2.3. Control of p and q Based on a standard 3-machine 9-node example system, a simulation model of a grid- connectedBased PV on generation the field-oriented system withvector high control, penetration the q components (50%) is built of uponthe grid the voltages PowerFac- are tory/DIgSILENTset to zero. According simulation to the platform,instantaneous as shown power in theory, Figure the5. In p orderand q powers to keep delivered the active to powerthe utility injected grid by can each be expressed node in the as: original system unchanged, the synchronous generator (G2) is directly turned off, and the photovoltaic power station (PV) with the same output is = 3 used to replace it at the same location. The p capacityeidd and active power output during the normal operation of each generator in the system2 are shown in Table1. The parameters of (4) the established PV generator are listed in Table23. qei= dq The simulation set up three-phase short-circuit 2 faults at different locations. The fault occurred at 1 s. The duration of the fault was 150 ms, and the fault was cleared without disconnectingwhere ed is the the d component line. As indicated of the grid in Figurevoltage,5, aand three-phase idq is the dq short-circuit components fault of the was in- verter currents. In conclusion, during grid faults, the amount of active power delivered by the in- verter depends on the depth of the voltage sag, active current calculation formulas and the maximum allowable current. Because the fault type determines the depth of the sys- tem’s voltage sag and fault location, it is impossible to control it in advance. Therefore, this paper focuses on the influence of active current calculation formulas and the maxi- mum allowable current on PV units’ transient active power characteristics.
3. Results and Discussion Based on a standard 3-machine 9-node example system, a simulation model of a grid-connected PV generation system with high penetration (50%) is built upon the
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Energies 2021, 14, 5236 7 of 14 PowerFactory/DIgSILENT simulation platform, as shown in Figure 5. In order to keep the active power injected by each node in the original system unchanged, the synchro- nous generator (G2) is directly turned off, and the photovoltaic power station (PV) with simulatedthe same output in Bus7, isBus8 used andto replace A location. it at the The same corresponding location. The voltage capacity of PV and parallel active pointpower wasoutput 1%, during 30% and the 50%normal of the operation normal of value. each ge Innerator each fault in the scenario, system are the shown simulation in Table was 1. conductedThe parameters with eight of the cases, established as Table PV3 displays. generator are listed in Table 2.
FigureFigure 5. 5.Simulink Simulink model model of of Power Power system system with with high high PV PV penetration. penetration.
TableTable 1. 1.The The capacity capacity and and active active power power output output of of each each power power source source during during normal normal operation. operation.
GeneratorGenerator PP(MW)(MW) SSNN (MVA)(MVA) G01G01 73.273.2 247.5 247.5 G02G02 163163 192 192 G03G03 8585 128 128 PVPV 163.1163.1 182 182 The capacity of each generator (SN), The active power output of each generator (P). The capacity of each generator (SN), The active power output of each generator (P).
Table 2. Parameters of the established PV generator. Table 2. Parameters of the established PV generator.
ParameterParameter SymbolSymbol Value Value Deadband forDeadband AC voltage for support AC voltage [p.u.] support deadband[p.u.] deadband 0.1 0.1 Static for ACStatic voltage for support AC voltage [-] support [-] droopdroop 1 1 MPP voltage of module in STC [V] Umpp0 35 MPP currentMPP of module voltage in STCof module [A] in STC [V] Impp0 Umpp0 4.58 35 InitialMPP DC voltage current [V] of module in STC [A] Udc0 Impp0 700 4.58 Initial DC voltage [V] Udc0 700 Table 3. Working conditions corresponding to different types of three-phase short-circuit fault. The simulation set up three-phase short-circuit faults at different locations. The faultFault occurred Location at 1 s. The Working duration Condition of the faultid Calculationwas 150 ms, Formula and the faultI maxwas(I Ncleared) without disconnecting the line. As1 indicated in Figure 5, a three-phase short-circuit1 fault 2 1.1 was simulated in Bus7, Bus8 and A location. The correspondingEquation (2) voltage of PV parallel point was 1%, 30% and 50% of 3the normal value. In each fault scenario, the 1.2simulation 4 1.3 wasLine5/Bus7/Bus8 conducted with eight cases, as Table 3 displays. 5 1 6 1.1 Table 3. Working conditions corresponding to different typesEquation of three-phase (3) short-circuit fault. 7 1.2 Fault Location Working8 Condition id Calculation Formula 1.3Imax (IN) Line5/Bus7/Bus8 1 Equation (2) 1 As shown in Figure6, the voltage sag of the PV parallel node is mainly determined by the fault location, having little effect on active currents. In combination with Figure2, the PV system should remain connected to the grid during grid faults and supply reactive
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2 1.1 3 1.2 4 1.3 5 1 6 1.1 Equation (3) 7 1.2 8 1.3
Energies 2021, 14, 5236 As shown in Figure 6, the voltage sag of the PV parallel node is mainly determined8 of 14 by the fault location, having little effect on active currents. In combination with Figure 2, the PV system should remain connected to the grid during grid faults and supply reac- powertive power to support to support the grid the ingrid these in these 24 simulation 24 simulation scenarios. scenarios. Take Take the the fault fault at at Bus8 Bus8 as as anan example; example; increasing increasingImax Imaxcan can decrease decrease the the voltage voltage surge surge at the at momentthe moment of fault of fault clearing, clear- whiching, which smooths smooths voltage voltage recovery recovery and reduces and reduces the impact the impact on the grid.on the In grid. this case,In this the case, total the recoverytotal recovery time remains time remains unchanged. unchanged. When Bus7When or Bus7 Line5 or faults, Line5 itfaults, has the it has same the rule. same rule.
FigureFigure 6. 6.PV PV parallel parallel node node voltage voltage in in each each simulation simulation scenario. scenario.
3.1. Three-Phase Short-Circuit Fault on a Location Energies 2021, 14, x FOR PEER REVIEW 3.1. Three-Phase Short-Circuit Fault on a Location 9 of 14
TheThe results results of of the the working working condition condition (1) (1) of of the the fault fault on on location location A A are are seen seen below below in in FigureFigure7. 7.
(a) (b)
Figure 7. SimulationFigure 7. Simulationresults in case results (1) of in the case fault (1) ofon the location fault onA: location(a) active A: output (a) active of PV output generator; of PV generator; (b) reactive( boutput) reactive of PV output generator. of PV generator.
The voltageThe of voltagethe PV ofparallel the PV node parallel dropped node to dropped 0.497 p.u. to 0.497at 1.11s, p.u. which at 1.11 is s, around which is around 0.199 kV (the0.199 base kV is (the 0.4 basekV). Before is 0.4 kV). and Beforeafter the and fault, after both the buses fault, obtain both buses values obtain close valuesto close nominal (1.002 p.u.). Considering these values, the following simple calculations can be performed:
dUs=−− U s before fault U s deaband U s during the fault =−−=1.002 0.1 0.497 0.405p.u. (5)
The PV generator in a non-fault state supplies the LV bus with 0 p.u. reactive cur- rent, and since the droop parameter is 1.5 (Table 2) the reactive current injected from the PV generator (iq during the fault) is 0.608, which leads to qUiduring the fault=⋅=×= s during the fault q during the fault 0.497 0.608 0.302p.u. (6) According to the reactive current during a fault (0.608 p.u.) and the calculation formula (2), it can be concluded that the active current during the fault is 0.392 p.u, which leads to pUiduring the fault=⋅=×= s during the fault d during the fault 0.497 0.392 0.195p.u. (7) The above theoretical calculations are in accordance with simulation results shown in Figure 7, which indicates the effectiveness of the simulation model of the PV genera- tor with LVRT capability and verifies the relationship between the transient active pow- er, the voltage drop degree, the calculation method of the active current and the maxi- mum allowable current of the inverter. The results of the other working conditions are the same. The results of working conditions (1)–(8) when the fault occurs are shown below in Figures 8 and 9 and Table 4.
(a) (b) Figure 8. Simulation results in cases (1)–(4) of the fault on location A: (a) active current; (b) active output.
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to nominal (1.002 p.u.). Considering these values, the following simple calculations can be performed:(a) (b) Figure 7. Simulation results in case (1) of the fault on location A: (a) active output of PV generator; dUs = Usbeforefault − Usdeaband − Usduringthefault = 1.002 − 0.1 − 0.497 = 0.405 p.u. (5) (b) reactive output of PV generator. The PV generator in a non-fault state supplies the LV bus with 0 p.u. reactive current, The voltageand since of the the PV droop parallel parameter node dropped is 1.5 (Tableto 0.4972) thep.u. reactiveat 1.11s, currentwhich is injected around from the PV 0.199 kV (thegenerator base is 0.4 (iq kV). during Before the fault)and after is 0.608, the fault, which both leads buses to obtain values close to nominal (1.002 p.u.). Considering these values, the following simple calculations can be performed: qduringthefault = Usduringthefault·iqduringthefault = 0.497 × 0.608 = 0.302 p.u. (6)
dUs=−− U s before fault U s deaband U s during the fault =−−=1.002 0.1 0.497 0.405p.u. According to the reactive current during a fault (0.608 p.u.) and(5) the calculation The PVFormula generator (2), in it a can non-fault be concluded state supp thatlies the the active LV current bus with during 0 p.u. the reactive fault is cur- 0.392 p.u, which rent, and sinceleads the to droop parameter is 1.5 (Table 2) the reactive current injected from the PV generator (iq during the fault) is 0.608, which leads to pduringthefault = Usduringthefault · idduringthefault = 0.497 × 0.392 = 0.195 p.u. (7) qUiduring the fault=⋅=×= s during the fault q during the fault 0.497 0.608 0.302p.u. (6) The above theoretical calculations are in accordance with simulation results shown Accordingin Figure to the7, whichreactive indicates current the during effectiveness a fault (0.608 of the simulationp.u.) and the model calculation of the PV generator formula (2),with it can LVRT be concluded capability andthat verifiesthe active the current relationship during between the fault the is transient0.392 p.u, active power, which leadsthe to voltage drop degree, the calculation method of the active current and the maximum allowablepUiduring the currentfault=⋅=×= s ofduring the the inverter. fault d during The the fault results0.497 of the 0.392 other working0.195p.u. conditions(7) are the same. The results of working conditions (1)–(8) when the fault occurs are shown below in The aboveFigures theoretical8 and9 and calculations Table4. are in accordance with simulation results shown in Figure 7, which indicates the effectiveness of the simulation model of the PV genera- It can be seen from Figures8 and9, during grid faults, increasing Imax value can not tor with LVRTonly capability improve and the activeverifies current the relationship but also have between little influencethe transient on theactive voltage pow- sag and thus er, the voltagereduce drop the degree, active the power calculation shortage. method However, of the the active active current current and and the active maxi- power increase mum allowablesharply, current accompanied of the inverter. by small-amplitude The results of oscillationthe other working at the recovery conditions stage. are As shown in the same. Figure9, when Imax increases to 1.2, the active current during grid faults can be restored The resultsto the of pre-fault working level.conditions However, (1)–(8) because when the the fault voltage occurs has are not shown yet recovered, below in there is still Figures 8 anda shortage 9 and Table of active 4. power during the fault period.
Energies 2021, 14, x FOR PEER REVIEW (a) (b) 10 of 14
Figure 8. SimulationFigure 8. resultsSimulation in cases results (1)–(4 in cases) of the (1)–(4) fault of on the location fault on A: location (a) active A: ( acurrent;) active current;(b) active (b ) active output. output.
(a) (b)
Figure 9. SimulationFigure results 9. Simulation in cases results (5)–(8 in) of cases the (5)–(8) fault on of thelocation fault onA: location(a) active A: current; (a) active (b current;) active ( b) active output. output.
Table 4. Active power index in cases (1)–(8) of the fault on location A.
Pfrtmax Δpfrt Prsmax Working Condition (p.u.) (p.u.) (p.u.) 1 0.189 - 0.905 2 0.233 0.044 0.985 3 0.275 0.042 1.035 4 0.313 0.038 1.073 5 0.351 - 0.870 6 0.389 0.038 0.934 7 0.418 0.029 0.979 8 0.436 0.018 1.011 The maximum active power during the fault (Pfrtmax), The increment of PV active power output corresponding to Imax increasing by 0.1 IN (Δp), The power surge after the fault is cleared (Prsmax).
It can be seen from Figures 8 and 9, during grid faults, increasing Imax value can not only improve the active current but also have little influence on the voltage sag and thus reduce the active power shortage. However, the active current and active power increase sharply, accompanied by small-amplitude oscillation at the recovery stage. As shown in Figure 9, when Imax increases to 1.2, the active current during grid faults can be restored to the pre-fault level. However, because the voltage has not yet recovered, there is still a shortage of active power during the fault period. It can be seen from the maximum power during the fault in Table 4, when Formula (3) is used to calculate the active current (corresponding cases 5–8), the PV active power output during the fault is greater than that of formula (2) (corresponding cases 1–4). Us- ing Formula (3) to control the active current output during the fault can make greater use of the current capacity of the power conversion device and improve the active pow- er shortage during the fault period. It can be seen from the power surge in Table 4, within the limits of the same value of Imax, applying the orthogonal decomposition method to calculate the active current (namely using Formula (3)) can reduce the active power surge after fault clearing and the impact on the power grid. It can be seen from the power improvement gradient in Table 4, when Imax is increased from 1 IN to 1.1 IN, the improvement effect of active power during fault is the most significant. With the con- tinuous rise in Imax, the active power improvement gradient becomes smaller; that is, the improvement effect on fault active power becomes smaller. The higher the limit value of the maximum output current of the inverter, the higher the cost is. The Imax is set to 1.1 IN. Therefore, the simulation results of this fault condition verify that setting the max- imum output current limit (Imax) of the photovoltaic inverter proposed in this paper as 1.1 IN, and adjusting the active current output according to the orthogonal decomposi- tion method during the fault period and the immediate recovery method during the re- covery period, is the most effective control strategy.
Energies 2021, 14, 5236 10 of 14
Table 4. Active power index in cases (1)–(8) of the fault on location A.
P ∆p P Working Condition frtmax frt rsmax (p.u.) (p.u.) (p.u.) 1 0.189 - 0.905 2 0.233 0.044 0.985 3 0.275 0.042 1.035 4 0.313 0.038 1.073 5 0.351 - 0.870 6 0.389 0.038 0.934 7 0.418 0.029 0.979 8 0.436 0.018 1.011
The maximum active power during the fault (Pfrtmax), The increment of PV active power output corresponding to Imax increasing by 0.1 IN (∆p), The power surge after the fault is cleared (Prsmax).
It can be seen from the maximum power during the fault in Table4, when Formula (3) is used to calculate the active current (corresponding cases 5–8), the PV active power output during the fault is greater than that of formula (2) (corresponding cases 1–4). Using Formula (3) to control the active current output during the fault can make greater use of the current capacity of the power conversion device and improve the active power shortage during the fault period. It can be seen from the power surge in Table4, within the limits of the same value of Imax, applying the orthogonal decomposition method to calculate the active current (namely using Formula (3)) can reduce the active power surge after fault clearing and the impact on the power grid. It can be seen from the power improvement gradient in Table4, when Imax is increased from 1 IN to 1.1 IN, the improvement effect of active power during fault is the most significant. With the continuous rise in Imax, the active power improvement gradient becomes smaller; that is, the improvement effect on fault active power becomes smaller. The higher the limit value of the maximum output current of the inverter, the higher the cost is. The Imax is set to 1.1 IN. Therefore, the simulation results of this fault condition verify that setting the maximum output current limit (Imax) of the photovoltaic inverter proposed in this paper as 1.1 IN, and adjusting the active current output according to the orthogonal decomposition method during the fault period and the immediate recovery method during the recovery period, is the most effective control strategy.
3.2. Three-Phase Short-Circuit Fault of Bus8 The results of working conditions (1)–(8) of the three-phase short-circuit fault of Bus8 are seen below in Figures 10 and 11 and Table5. The change rule is similar to the three-phase short circuit fault on location A. Using Formula (3) to control the active current output during the fault can make greater use of the current capacity of the inverter. Increasing Imax can improve the active current and reduce the active power shortage. It can be seen from Table5 that with the increase in Imax, the degree of power improvement is decreasing. Comprehensively considering the improvement of active power and the increase of economic cost corresponding to the increase in Imax, Imax is still selected as 1.1 IN. Since the depth of voltage sag is greater than the three-phase short-circuit on location A, the PV output active power is less than the corresponding PV output active power at the three-phase short-circuit on location A. The simulation results of this fault condition also verify that setting the maximum output current limit (Imax) of the photovoltaic inverter proposed in this paper as 1.1 IN, and adjusting the active current output according to the orthogonal decomposition method during the fault period and the immediate recovery method during the recovery period is the most effective control strategy. Energies 2021, 14, x FOR PEER REVIEW 11 of 14
Energies 2021, 14, x FOR PEER REVIEW 11 of 14
3.2. Three-Phase Short-Circuit Fault of Bus8 3.2. Three-PhaseThe results Short-Circuit of working Faultconditions of Bus8 (1)–(8) of the three-phase short-circuit fault of Bus8The are seenresults below of working in Figures conditions 10 and 11 (1)–(8) and Table of the 5. three-phaseThe change short-circuitrule is similar fault to the of Bus8three-phase are seen short below circuit in Figures fault on 10 location and 11 A.and Using Table Formula 5. The change(3) to control rule is the similar active to cur- the rentthree-phase output duringshort circuit the fault fault can on make location greater A. Using use of Formula the current (3) to capacity control ofthe the active inverter. cur- Increasingrent output I maxduring can improvethe fault canthe activemake greatercurrent use and of reduce the current the active capacity power of the shortage. inverter. It canIncreasing be seen I maxfrom can Table improve 5 that the with active the increasecurrent andin Imax reduce, the degree the active of power power improvement shortage. It canis decreasing. be seen from Comprehensively Table 5 that with considering the increase the in improvementImax, the degree of of active power power improvement and the increaseis decreasing. of economic Comprehensively cost corresponding considering to the the increase improvement in Imax, Iofmax active is still power selected and as the1.1 IincreaseN. Since ofthe economic depth of costvoltage corresponding sag is greater to thanthe increase the three-phase in Imax, I maxshort-circuit is still selected on location as 1.1 IA,N. theSince PV the output depth active of voltage power sag is isless greater than thethan corresponding the three-phase PV short-circuit output active on power location at theA, the three-phase PV output short-circuit active power on islocation less than A. the corresponding PV output active power at the three-phaseThe simulation short-circuit results ofon this location fault A.condition also verify that setting the maximum outputThe current simulation limit results(Imax) of of the this photovoltaic fault condition inverter also proposedverify that in setting this paper the maximum as 1.1 IN, andoutput adjusting current thelimit active (Imax) ofcurrent the photovoltaic output according inverter to proposed the orthogonal in this paperdecomposition as 1.1 IN, Energies 2021, 14, 5236 andmethod adjusting during thethe faultactive period current and output the imme accordingdiate recovery to the method orthogonal during decomposition the recovery 11 of 14 methodperiod is during the most the effective fault period control and strategy. the imme diate recovery method during the recovery period is the most effective control strategy.
(a) (b) (a) (b) Figure 10. Simulation results in cases (1)–(4) of the fault of Bus8: (a) active current; (b) active out- put.Figure 10. SimulationFigure 10. resultsSimulation in cases results (1)–(4) in casesof the (1)–(4) fault of theBus8: fault (a) of active Bus8: current; (a) active (b current;) active out- (b) active output. put.
(a) (b) (a) (b) Figure 11. SimulationFigure 11. resultsSimulation in cases results (5)–(8) in casesof the (5)–(8) fault of theBus8: fault (a) of active Bus8: current; (a) active (b current;) active out- (b) active output. put.Figure 11. Simulation results in cases (5)–(8) of the fault of Bus8: (a) active current; (b) active out- Table 5. Active power index in cases (1)–(8) of the fault of Bus8. put. Table 5. Active power index in cases (1)–(8) of the fault of Bus8. P ∆p P Working Condition frtmax frt rsmax Table 5. Active power index in cases (1)–(8) of the(p.u.) fault of Bus8. (p.u.) (p.u.) Pfrtmax Δpfrt Prsmax Working Condition 1 0.055P(p.u.)frtmax (p.u.)Δpfrt -(p.u.)Prsmax 0.959 Working Condition 1 2 0.082(p.u.)0.055 (p.u.)- 0.027 (p.u.)0.959 1.047 3 0.109 0.027 1.104 1 0.055 - 0.959 2 4 0.1340.082 0.027 0.0025 1.047 1.166 32 5 0.1450.1090.082 0.027 -1.1041.047 0.928 43 6 0.180 0.1340.109 0.00250.027 0.035 1.1661.104 0.988 54 7 0.2100.145 0.134 0.0025- 0.030 1.1660.928 1.035 5 8 0.2360.145 - 0.0260.928 1.068 The maximum active power during the fault (Pfrtmax), The increment of PV active power output corresponding to Imax increasing by 0.1 IN (∆p), The power surge after the fault is cleared (Prsmax).
3.3. Three-Phase Short-Circuit Fault of Bus7 When three phase short circuit fault occurs in Bus7, the corresponding voltage drops to 1% of the normal value. Due to the severe voltage sag, any active power strategy hardly works, and the active power shortage is larger than that of the first two faults. The simulation results of working conditions (1)–(8) of the three-phase short-circuit fault of Bus7 are seen below in Figures 12 and 13. Different active current power strategies during the fault period have little difference in the effect of transient frequency stability, but during the recovery period, with the increase in Imax, the fluctuation degree of active current and active power becomes larger. Therefore, comprehensively considering the effects of different active current control strategies under the first two fault conditions, it can be concluded that the maximum output current limit of the photovoltaic inverter (Imax) has been set to 1.1 IN and the orthogonal decomposition method been used during the fault; the strategy of adjusting the active current output according to the immediate recovery method used during the recovery period can most effectively cope with various degrees of voltage drop faults in the system and improve the transient frequency stability of the system. Energies 2021, 14, x FOR PEER REVIEW 12 of 14 Energies 2021, 14, x FOR PEER REVIEW 12 of 14
6 0.180 0.035 0.988 6 0.180 0.035 0.988 7 0.210 0.030 1.035 7 0.210 0.030 1.035 8 0.236 0.026 1.068 8 0.236 0.026 1.068 The maximum active power during the fault (Pfrtmax), The increment of PV active power output The maximum active power during the fault (Pfrtmax), The increment of PV active power output corresponding to Imax increasing by 0.1 IN (Δp), The power surge after the fault is cleared (Prsmax). corresponding to Imax increasing by 0.1 IN (Δp), The power surge after the fault is cleared (Prsmax). 3.3. Three-Phase Short-Circuit Fault of Bus7 3.3. Three-Phase Short-Circuit Fault of Bus7 When three phase short circuit fault occurs in Bus7, the corresponding voltage When three phase short circuit fault occurs in Bus7, the corresponding voltage drops to 1% of the normal value. Due to the severe voltage sag, any active power strate- drops to 1% of the normal value. Due to the severe voltage sag, any active power strate- gy hardly works, and the active power shortage is larger than that of the first two faults. gy hardly works, and the active power shortage is larger than that of the first two faults. The simulation results of working conditions (1)–(8) of the three-phase short-circuit fault The simulation results of working conditions (1)–(8) of the three-phase short-circuit fault of Bus7 are seen below in Figures 12 and 13. Different active current power strategies of Bus7 are seen below in Figures 12 and 13. Different active current power strategies during the fault period have little difference in the effect of transient frequency stability, during the fault period have little difference in the effect of transient frequency stability, but during the recovery period, with the increase in Imax, the fluctuation degree of active but during the recovery period, with the increase in Imax, the fluctuation degree of active current and active power becomes larger. current and active power becomes larger. Therefore, comprehensively considering the effects of different active current con- Therefore, comprehensively considering the effects of different active current con- trol strategies under the first two fault conditions, it can be concluded that the maximum trol strategies under the first two fault conditions, it can be concluded that the maximum output current limit of the photovoltaic inverter (Imax) has been set to 1.1 IN and the or- output current limit of the photovoltaic inverter (Imax) has been set to 1.1 IN and the or- thogonal decomposition method been used during the fault; the strategy of adjusting the thogonal decomposition method been used during the fault; the strategy of adjusting the active current output according to the immediate recovery method used during the re- Energies 2021, 14, 5236active current output according to the immediate recovery method used during the re- 12 of 14 covery period can most effectively cope with various degrees of voltage drop faults in covery period can most effectively cope with various degrees of voltage drop faults in the system and improve the transient frequency stability of the system. the system and improve the transient frequency stability of the system.
(a) (b) (a) (b) Figure 12. Simulation results in cases (1)–(4) of the fault of Bus7: (a) active current; (b) active out- Figureput. 12. SimulationFigure 12. resultsSimulation in cases results (1)–(4) in of cases the (1)–(4)fault of of Bus7: the fault (a) active of Bus7: current; (a) active (b) current;active out- (b) active output. put.
(a) (b) (a) (b) Figure 13. SimulationFigure 13. resultsSimulation in cases results (5)–(8) in of cases the (5)–(8)fault of of Bus7: the fault (a) active of Bus7: current; (a) active (b) current;active out- (b) active output. Figureput. 13. Simulation results in cases (5)–(8) of the fault of Bus7: (a) active current; (b) active out- put. 4. Conclusions 4. Conclusions 4. Conclusions In this article, a transient simulation model of a grid-connected photovoltaic (PV) In this article,generator a transient with low-voltage simulation ride-through model of a(LVRT) grid-connected capability photovoltaic is proposed. (PV) A power system In this article, a transient simulation model of a grid-connected photovoltaic (PV) generator withmodel low-voltage with a high ride-through PV penetration (LVRT) is established,capability is andproposed. several A types power of three-phasesystem voltage generator with low-voltage ride-through (LVRT) capability is proposed. A power system model with asags high are PV simulated penetration in PowerFactory/DIgSILENT. is established, and several types According of three-phase to the three volt- power indexes, model with anamely high PV the penetration maximum is active establis powerhed, of and PV several unit during types the of fault,three-phase the power volt- improvement gradient and the power surge after the fault is cleared, the impact of the active current ref- erence calculation method and the inverter allowable maximum inverter current (Imax) on the PV active power output is assessed. Additionally, methods to improve the active power
output capability of photovoltaic units during low-breakthrough periods are explored. The conclusions are as follows: (i) The active current control strategies have minimal effect on the voltage for grid- connected PV generation systems at the point of common coupling, so the PV transient active power has the same change in trend as the transient active current during grid fault. Effective performance for active power (P) support is attained by choosing the appropriate calculation method of active current and Imax value when voltage faults are introduced to the utility grid. It is carried out to meet the requirement of reactive powers (Q) support capability in China grid codes. (ii) The error between the inverter current limitation (Imax) and reactive current is com- pared to obtain the active current values within the limits of the same value of Imax. Applying the orthogonal decomposition method to calculate the active current refer- ence enhances the utilization factor of the inverter’s capacity and increase the inverter active output current. It improves the active power shortage and boosts the transient stability of the power system. (iii) Increasing Imax value can reduce the active power shortage during grid faults by increasing the active current output and improving the oscillation phenomenon in power recovery by reducing the excitation increment of active current and active power at the moment of fault clearing. However, increasing Imax value proportionally does not bring about an equal gradient of active power improvement effect, and the Energies 2021, 14, 5236 13 of 14
cost becomes larger. Considering the economic cost and transient stability, the best way to regulate active current is to set Imax value as 1.1 IN and apply the orthogonal decomposition method.
Author Contributions: Conceptualization, B.L., X.Y. and J.J.; methodology, B.L., X.Y. and J.J.; soft- ware, B.L. and J.J.; validation, B.L.; data curation, B.L.; writing—original draft preparation, B.L.; writing—review and editing, B.L., C.W., W.A., H.M., S.Z. and J.J. All authors have read and agreed to the published version of the manuscript. Funding: This paper was supported by general projects of the Beijing Natural Science Foundation (3212037); Natural Science Funding of Hebei Province (E2018502134). Acknowledgments: The authors gratefully thank the financial supports of the general projects of the Beijing Natural Science Foundation (3212037) and Natural Science Funding of Hebei Province (E2018502134). The authors of the article appreciate the referees for their valuable suggestions, which contributes to improving the paper. Conflicts of Interest: The authors declare no conflict of interest.
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