Low Frequency Damping Control for Power Electronics-Based AC Grid Using Inverters with Built-In PSS

Article Low Frequency Damping Control for Power Electronics-Based AC Grid Using Inverters with Built-In PSS

Ming Yang 1, Wu Cao 1,*, Tingjun Lin 1, Jianfeng Zhao 1 and Wei Li 2

1 School of Electrical Engineering, Southeast University, Nanjing 210096, China; [email protected] (M.Y.); [email protected] (T.L.); [email protected] (J.Z.) 2 NARI Group Corporation (State Grid Electric Power Research Institute), Nanjing 211106, China; [email protected] * Correspondence: [email protected]

Abstract: Low frequency oscillations are the most easily occurring dynamic stability problem in the power system. With the increasing capacity of power electronic equipment, the coupling coordination of a synchronous generator and inverter in a low frequency range is worth to be studied further. This paper analyzes the mechanism of the interaction between a normal active/reactive power control grid-connected inverters and power regulation of a synchronous generator. Based on the mechanism, the power system stabilizer built in the inverter is used to increase damping in low frequency range. The small-signal model for electromagnetic torque interaction between the grid-connected inverters and the generator is analyzed ﬁrst. The small-signal model is the basis for the inverters to provide damping with speciﬁc amplitude and phase. The additional damping torque control of the inverters is realized through a built-in power system stabilizer. The fundamentals and the structure of a built-in

power system stabilizer are illustrated. The built-in power system stabilizer can be realized through the active or reactive power control loop. The parameter design method is also proposed. With the

Citation: Yang, M.; Cao, W.; Lin, T.; proposed model and suppression method, the inverters can provide a certain damping torque to Zhao, J.; Li, W. Low Frequency improve system stability. Finally, detailed system damping simulation results of the universal step Damping Control for Power test verify that the analysis is valid and effective. Electronics-Based AC Grid Using Inverters with Built-In PSS. Energies Keywords: low frequency damping; grid-connected inverter; power system stabilizer; power 2021, 14, 2435. https://doi.org/ electronics-based AC power system 10.3390/en14092435

Academic Editor: Juri Belikov 1. Introduction Received: 22 March 2021 The power system has expanded and changed incessantly. There is a trend that Accepted: 22 April 2021 Published: 24 April 2021 conventional power systems are expected to be replaced by next-generation power systems. The grid-connected inverters are the crucial component that delivers renewable energy

Publisher’s Note: MDPI stays neutral and energy storage to the grid. The grid-connected inverter should play a more critical role with regard to jurisdictional claims in in the power system [1–6]. Due to the negative damping effect of the power system, the published maps and institutional afﬁl- phenomenon of low frequency oscillations (LFOs) often occurs on the transmission lines iations. with long distances, heavy loads or weak connections. The typical feature of low frequency oscillation is power swing and low frequency ranging between 0.1 and 2.5 Hz. The power regulation characteristic of inverter is different from that of synchronous generator. In the same power grid, the power regulation of inverters affects the swing characteristics of generator’s power angle. Obviously, the research of the inﬂuence mechanism of inverter Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. power regulation on generator torque, and the low frequency damping control is important This article is an open access article for the system stability. distributed under the terms and There have been many studies on the low frequency damping control. The power conditions of the Creative Commons system stabilizer (PSS) in excitation system is used to generate the damping effect. The PSS Attribution (CC BY) license (https:// suppresses LFOs through controlling electromagnetic torque variation. PSS in excitation creativecommons.org/licenses/by/ system has been proved to be the most cost-effective damping control [7–10]. In power 4.0/). electronics-based AC grid, the proportion of synchronous generator capacity decreases.

Energies 2021, 14, 2435. https://doi.org/10.3390/en14092435 https://www.mdpi.com/journal/energies Energies 2021, 14, 2435 2 of 18

The damping torque provided by the excitation system is not enough for LFOs suppression. Some power electronic devices such like unified power flow controller (UPFC), static var compensators (SVC), voltage source converter based high voltage direct current (VSC- HVDC) are researched to suppress the LFOs. The power electronic equipment can increase the system damping to inhibit oscillation [11–14]. References [15–19] analyze the impact of VSC control parameters on power system stability based on small-signal stability analysis. Reference [20] proposes a UPFC-based stabilizer that adopts a conventional PI controller and a lead-lag controller to produce the damping effect. Because of the UPFC covers active and reactive power controls with multiple time scales, the low frequency damping control parameters of UPFC are hard to design for most working condition. References [21,22] research the SVC with a damping controller. The damping control in SVC increases system damping by reactive power control. The influence of SVC’s reactive power on generator is limited by distance and area. Reference [23–26] proposes VSC-HVDC damping strategies. These strategies are realized by adding angular velocity close loop control to the basic control of inverter. The damping control and the normal inverter control both regulate the active power. But the purpose of control is different. So, the two kinds of control are easy to affect each other, and the parameters are hard to design. For the situation that the virtual synchronous generator (VSG) control changes the regulation characteristic of inverter, references [27,28] investigates extra damping control in the VSG control. The damping capacity of inverter can not be fully utilized due to the limitation of virtual inertia control. There are still some improvements as follows in the research of low frequency damping control in power electronic based AC grid. (1) The capacity proportion of the UPFC and SVC is small in the power system. The damping effect of the UPFC and SVC is limited. The low frequency damping control should focus on the grid-connected inverters which have large proportion. (2) These stability analyses mainly focus on the inverter itself. The correlation with generators in the power grid has not been considered enough. The influence of grid- connected inverter with normal active/reactive power control on the electromagnetic torque of the synchronous generator has little research. Using the mechanism of the influence to improve the dynamic safety and stability of the power system has not been fully considered. (3) The different time scales controls are directly superimposed together in the inverters based on existing research. Without the detailed model for the interaction between inverters and generators, the control parameters are hard to set. To improve the low frequency damping control and LFOs suppression, the main contributions of this paper are as follows: (1) This paper investigates how grid-connected inverter with normal active/reactive power control influences the electromagnetic torque of the synchronous generator. The small-signal model for the impact of the output of the grid-connected inverter on the electromagnetic torque of the synchronous generator is proposed. The damping torque analysis is used to evaluate the effect of inverter on low frequency damping. The mechanism of grid-connected inverter providing positive damping is found. That can also be suitable for multi grid-connected inverters with same voltage and current control. (2) The control time scale of the introduced damping control is adapted to the frequency range of LFOs. It is independent of the original fast control of the inverter. The method of introducing electromagnetic damping torque with built-in PSS to increase low frequency damping is proposed. The structure and parameter design method is also proposed. The additional electromagnetic damping control can be realized by the active power control or reactive power control of the inverter. Because of most of the inverters in power system output active power, the built-in PSS realized through the active power control are taken as the object of analysis. That is different from the excitation system’s PSS. The difference between traditional PSS in excitation system and the proposed built-in PSS in inverter can be illustrated in Figure1, where Vref is the terminal voltage control reference value for excitation system, Vt is the terminal voltage value, Efd is the excitation voltage, Energies 2021, 14, x FOR PEER REVIEW 3 of 19

Energies 2021, 14, 2435 3 of 18

in PSS in inverter can be illustrated in Figure 1, where Vref is the terminal voltage control reference value for excitation system, Vt is the terminal voltage value, Efd is the excitation voltage, Pref Pisref theis theactive active power power control control reference reference value value for inverter, for inverter, P is theP is active the active power power actual actual value,value, Qref isQ theref isreactive the reactive power power control control reference reference value value for inverter, for inverter, Q is theQ is reactive the reactive power power actualactual value, value, Gi-P(s) G isi-P the(s) isactive the active power power control, control, Gi-Q(s) G isi-Q the(s) reactive is the reactive power powercontrol, control, G(s) G(s) is the excitationis the excitation control. control.

build-in PSS

traditional PSS ref P Gi-P(s) PWM

Efd P Vref G(s) G Qref Gi-Q(s) Vt Q VSC (a) (b) Figure 1. TraditionalFigure 1. PSSTraditional in excitation PSS insystem excitation and the system proposed and the built-in proposed PSS in built-in inverter. PSS (a in) Traditional inverter. (a )PSS Traditional in excitation PSS in excitation system; (b) thesystem; proposed (b) the built-in proposed PSS in built-in inverter. PSS in inverter.

(3) To verify(3) the To above verify analysis, the above two-part analysis, simulation two-part is simulationused. One part is used. is about One dif- part is about ferent dampingdifferent torques’ damping effect torques’ on single effect grid-connected on single grid-connected inverter. The inverter. different The damping different damping torques are torquesrealized are by realized using different by using parame differentters. parameters. The other The part other is about part the is about effective- the effectiveness ness of the built-inof the built-in PSS for PSS dual for paralleled dual paralleled grid-connected grid-connected inverters. inverters. The rest of thisThe paper rest of is this organized paper is as organized follows. Section as follows. II derives Section a 2small-signal derives a small-signal model model of the impactof theof the impact grid-connected of the grid-connected inverter on inverterelectromagnetic on electromagnetic torque of synchronous torque of synchronous generator. Thegenerator. influence The of inﬂuenceinverter output of inverter on damping output on torque damping is analyzed. torque isSection analyzed. III Section3 provides a designprovides for a built-in design PSS for built-inbased on PSS the based small on signal the smallmodel. signal Section model. Ⅳ gives Section the4 gives the simulation result.simulation The conclusions result. The conclusionsof this paper of are this presented paper are in presented Section V. in Section5.

2. Modeling2. and Modeling Analysis and Analysis The study ofThe the study generator of the oscillation generator process oscillation shows process that in shows most that cases in the most generator cases the generator rotor oscillationrotor is oscillation related to is the related mechanical to the mechanicalinertia time inertia constant. time The constant. electrical The angular electrical angular ω δ velocity (Δωvelocity) and electrical (∆ ) and acceleration electrical ( accelerationΔδ) are used (to∆ describe) are used the to oscillations. describe the The oscillations. me- The mechanical inertia time constant represents lower oscillation frequency and slower attenu- chanical inertia time constant represents lower oscillation frequency and slower attenua- ation [29]. So, in the study of the process related to rotor oscillation, the fast process can be tion [29]. So, in the study of the process related to rotor oscillation, the fast process can be considered to be over. In the process of modelling, circuit impedance could be calculated considered to be over. In the process of modelling, circuit impedance could be calculated under the situation of the rated frequency of power grid. under the situation of the rated frequency of power grid. The electromagnetic torque of synchronous generator is used to increase low frequency The electromagnetic torque of synchronous generator is used to increase low fre- damping because of its fast-changing characteristics. The power regulation of the grid- quency damping because of its fast-changing characteristics. The power regulation of the connected inverters affects the electromagnetic torque of synchronous generator. So, the grid-connected inverters affects the electromagnetic torque of synchronous generator. So, influence of electromagnetic torque caused by inverter power regulation is the first problem the influence of electromagnetic torque caused by inverter power regulation is the first to be clarified. problem to be clarified. 2.1. System Description 2.1. System Description Figure2 depicts the structure of a typical structure of power electronics-based AC Figure power2 depicts system. the structure The power of electronics-baseda typical structure AC of power power system electronics-based has synchronous AC generators power system.and The multi power inverters. electronics-based The inverters AC have power a considerable system has proportionsynchronous of thegenera- transformation tors and multiand inverters. consumption The capacityinverters in have power a considerable grid. The normal proportion control of architecture the transfor- of the inverter mation and controllerconsumption is shown capacity in Figure in power3, where grid. ThePref isnormal the d-axis control control architecture reference of of the active power, inverter controllerUdcref is is the shown d-axis in Figure control 3, reference where Pref of is DCthe voltage,d-axis controlQref is reference the q-axis of active control reference power, Udcrefof is reactivethe d-axis power, controlU referenceacref is the of q-axis DC voltage, control Q referenceref is the q-axis of AC control voltage, referencei2dref is the d-axis of reactive power,reference Uacref current is the valueq-axis ofcontrol inverter, referencei2qref is of the AC q-axis voltage, reference i2dref is the current d-axis value ref- of inverter, erence currenti2d isvalue the d-axisof inverter, current i2qref value is the of q-axis inverter, referencei2q is thecurrent q-axis value current of inverter, value of i2 inverter,d is Ucd is the d-axis currentthe d-axis value component of inverter, of i system2q is the sideq-axis voltage, currentU valuecq is the of q-axisinverter, component Ucd is the of d- system side axis componentvoltage, of system∆vd is side the d-axisvoltage, component Ucq is the q-axis variation component of inverter of system side voltage, side voltage,∆vq is the q-axis Δvd is the d-axiscomponent component variation variat ofion inverter of inverter side voltage.side voltage,Fo(s) Δisv theq is the outer-loop q-axis component control function of the inverter, F(s) is the inner-loop control function of the inverter.

Energies 2021, 14, x FOR PEER REVIEW 4 of 19

Energies 2021, 14, x FOR PEER REVIEW 4 of 19 Energies 2021, 14, x FOR PEER REVIEW 4 of 19

Energies 2021, 14, 2435 variation of inverter side voltage. Fo(s) is the outer-loop control function of the inverter, 4 of 18 F(s) isvariation the inner-loop of inverter control side function voltage. of Ftheo(s) inverter. is the outer-loop control function of the inverter, variation of inverter side voltage. Fo(s) is the outer-loop control function of the inverter, F(s) is the inner-loop control function of the inverter. F(s) is the inner-loop control function of the inverter. Synchronous Generators AC BUS Filters SynchronousLx Generators AC BUS Filters Synchronous Generators AC BUS Filters Lx G Lx GG ~ DC-AC AC-DC Wind Farm LFOs ~ DC-AC AC-DC Wind Farm ~ DC-AC AC-DC Wind Farm LFOs LFOs G ~ GG ~ DC-AC DC-DC PV System ~ DC-AC DC-DC PV System DC-AC DC-DC PV System

Load DC-AC DC-DC Battery Load Grid-connected Inverters Load DC-AC DC-DC Battery Grid-connectedDC-AC Inverters DC-DC Battery Figure 2. A typical set up of powerGrid-connected electronics-based Inverters AC power system.

Figure 2. A typical set up of power electronics-based AC power system. FigureFigure 2. A 2.typicalA typical set up set of up power of power electronics-based electronics-based AC power AC power system. system.

i2dref Ucd F0(s) F(s) ref dcref i2dref Ucd P /U i2dref Ucd

P/Udc F0(s) id F(s)wL1i1q Δvd PWM Pref/Udcref F0(s) F(s) Pref/Udcref P/Udc id wL1i1q Δvd PWM P/Udc id wL1i1q Δvd PWM i2qref Ucq 0 F (s) i2qref F(s) Ucq Qref/Uacref i2qref Ucq F0(s) q F(s) q VSC Q/Uac 0 i wL1i1d Δv Qref/Uacref F (s) F(s) Qref/Uacref Q/Uac iq wL1i1d Δvq VSC Q/Uac iq wL1i1d Δvq VSC Figure 3. The typical control structure of the inverter.

FigureFigure 3. 3. TheThe typical typical control control structure structure of the inverter. TheFigure multi-inverters 3. The typical shown control in structure Figure of2 canthe inverter. be considered as a controllable voltage The multi-inverters shown in Figure2 can be considered as a controllable voltage source, connectingThe multi-inverters to the power shown grid within Figure an LCL 2 can filter be typically.considered The as multia controllable generators voltage source,The multi-inverters connecting to theshown power in Figure grid with 2 can an LCLbe considered filter typically. as a Thecontrollable multi generators voltage can can besource, equivalent connecting as a voltage to the source power with grid characteristics with an LCL filterof synchronous typically. The generator. multi generators Fig- source,be equivalent connecting as to a voltagethe power source grid with with characteristics an LCL filter of typically. synchronous The generator.multi generators Figure4 is ure 4 iscan the be equivalent equivalent two-port as a voltage network source of withthe system characteristics shown in of Figure synchronous 2, where generator. U is the Fig- can thebe equivalent equivalent as two-port a voltage network source of with the characteristics system shown of in synchronous Figure2, where generator.U is the Fig- voltage voltageure of 4 theis the generator, equivalent V is two-port the voltage network of the of inverter, the system xs is shown the contact in Figure inductive 2, where reac- U is the ure of4 is the the generator, equivalentV two-portis the voltage network of the of the inverter, systemxs shownis the contactin Figure inductive 2, where reactance, U is the x0 tance,voltage x0 is the of inductive the generator, reactance V is ofthe load, voltage r is ofthe the resistance inverter, of x sthe is theload, contact x1 and inductive x2 is the reac- voltageis the of inductive the generator, reactance V is ofthe load, voltager is theof the resistance inverter, of x thes is load,the contactx1 and inductivex2 is the inductive reac- inductivetance, reactance x0 is the of inductive LCL filter reactance for the inverter of load, andr is ythec is resistancethe admittance of the of load, LCL x filter1 and forx2 is the tance,reactance x0 is the of inductive LCL filter reactance for the inverter of load, and r isyc theis the resistance admittance of the of LCLload, filter x1 and for x the2 is inverter. the the inverter.inductive reactance of LCL filter for the inverter and yc is the admittance of LCL filter for inductive reactance of LCL filter for the inverter and yc is the admittance of LCL filter for the inverter. the inverter. xs x2 x1 xs x2 x1 i xs x2 x1 i2 r U i Vi2 i i2 U x0 r r V U yc V x0 0 x yc yc Figure 4. Two-port network for simplified power electronics-based AC power system. Figure 4. Two-port network for simplified power electronics-based AC power system. Figure 4. Two-port network for simplified power electronics-based AC power system. Figure 4. Two-port network for simplified power electronics-based AC power system. The loopThe circuit loop circuit equation equation of two-port of two-port network network is shown is shown in the infollowing: the following: The loop circuit equation of two-port network is shown in the following: The loop circuit equation of two-port0 network0 is shown0 in the0 following: u z11z 22 + z12z 32 z11z 23 + z12z 33 v = 0 0 0 0 (1) i z21z 22 + z22z 32 z21z 23 + z22z 33 i2

Energies 2021, 14, 2435 5 of 18

0 0 0 0 where z11, z12, z21, z22 and z 22, z 23, z 32, z 33 are the impedance of two-port networks 1 and 2, respectively, i and i2 are the currents of the line connected with the generator and the inverter, respectively. Then, the current of the generator in dq synchronous frame is got as:

i = y u + y u + y v + y v d 1 d 2 q 3 d 4 q (2) iq = y5ud + y6uq + y7vd + y8vq

where y1~y6 represents the correlation impedance, vd is the d-axis component of inverter side voltage, vq is the q-axis component of inverter side voltage, ud is the d-axis voltage of the generator, uq is the q-axis voltage of generator.

2.2. System Modeling Through Equation (2), the small-signal model of generator’s current and voltage is derived as shown in Equation (3).

 u = x i  ∆ d q∆ q  ∆u = ∆E0 − x0 ∆i q q d d (3)  ∆id = y1∆ud + y2∆uq + y3∆vd + y4∆vq  ∆iq = y5∆ud + y6∆uq + y7∆vd + y8∆vq

0 where x d is the d-axis transient resistance of the generator, xq is the q-axis resistance of the generator, id is the d-axis current of the generator, id is the q-axis current of generator, ud is the d-axis voltage of the generator, uq is the q-axis voltage of generator, Eq is the internal potential of the generator, ∆ represents the micro change of electrical quantities. The expression of ∆id and ∆iq could be derived by eliminating ∆ud and ∆uq and illustrated as Equation (4):

( 0 ∆id = Z1∆Eq + Z2∆vd + Z3∆vq 0 (4) ∆iq = Z4∆Eq + Z5∆vd + Z6∆vq

where Z1~Z6 are the admittance coefﬁcient which are derived through Equation (3). A series equation of electromagnetic relation of the generator is shown as the following Equation (5) [7]:   ud = xqiq  = − ( − 0 ) = 0 − 0  uq Eq xd xd id Eq xdid   Me = udid + uqiq = EQiq 0 0 (5) Eq = EQ − (xq − xd)id  dE0  q = 1 ( − )  dt T0 Ef d Eq  d0  2 2 2 u = ud + uq 0 where E q is a hypothetical potential which is proportional to the ﬂux of excitation system, Me is the electromagnetic torque of the generator, EQ is hypothetical potential behind xq, Efd is the excitation voltage, T’d0 is the time constant of the rotor when the stator is open-circuit. The small-signal model of the generator is derived as:

 0 0  ∆Me = iq0∆Eq + iq0(xq − xd)∆id + EQ0∆iq  0 0 0 (1 + Td0s)∆Eq = ∆Ef d − (xq − xd)∆id (6) u  ud0 q0 0 0  ∆u = xq∆iq + (∆E − x ∆i ) u0 u0 q d d

Δ=Δ+′′ −Δ+Δ MiEixxiEieq00 qqqdd() Qq 0  ′′ ′ (1+Δ=Δ−−ΔTs ) E E ( x x ) i  dq0 fdqdd (6)  u u ′′ Δ=d0 Δ+q0 Δ − Δ  uxiExiqq() q dd  uu00

where iq0 is the steady-state q-axis current of the generator, ud0 is the steady-state d-axis voltage of the generator, uq0 is the steady-state q-axis voltage of the generator, u0 is the steady-state voltage of the generator, EQ0 is the hypothetical steady-state potential behind xq. The small-signal model of the synchronous generator with inverter’s voltage is de- Energies 2021, 14, 2435 rived in Equation (7) by substituting Equation (4) of Δid and Δiq into Equation (6). 6 of 18

′′ Δ=Δ+Δ+ΔMKEKvKvKi =+ ixxZEZ() − − eqdqqqqdQ123100104 ′′ Δ=ΔE K E −Δ K vK-() Δ v K = i x − xZ + EZ The small-signal qfddqqqdQ model45620205 of the synchronous generator with inverter’s voltage is derived  ′′ Δ=uKEKvKv Δ++ Δ Δ K = ix ( − xZEZ ) + in Equation (7) by substituting789qdq Equation (4) of ∆id 30and qqdQ∆iq into Equation 306 (6).  Δ=EGsu() Δ   0fd ∆Me = K ∆E + K2∆v + K3∆vq  1 q d  K = i + i (x − x0 )Z − E Z  0   1 uq0 q0 quud 1′ Q0 4  ∆Eq = K4∆Ef d=− K5∆vd −1 K6∆vq  =+d0 qq000 (7) K4 ′′KxZxZ74K = i qd(x − x )-Z + E 1Z = 0 + +−+ + 2 uuuq0 q d 2 Q0 5  ∆u K7∆Eq K1(8∆xxZTsvqdd K )9∆10vq d   0000  K3 = iq0(xq − x )Z3 + EQ0Z6  E = G(s) u ′  d ∆ f d ∆=−  u uq0 ′ (7) KKxxZ54()qd 2 =−d0   1  KxZxZud0 uq0 uq0 0 K = ′ K 852= xqqdZ + − x Z  4 +  − 0=−+ 0  7 uuu0 4 u0 u0 d 1  1 (xqKKxxxd)Z1 ()ZTd0s   00u  640 qd 3 K = ud0 x Z − q0 x0 Z K5 = K xq − x Z2 8 u q 5 uu d 2 4 d ud00 q0 ′  0   =−ud0 uq0 0  K = K x − x )Z  KKxZxZ963= xqqdZ − x Z 6 4 q d 3  9 u0 6 u0 d 3  uu00 G(s)G(s) represents represents the the transfer transfer function function of of the the excitation excitation system. system. ConsiderConsider the the inverter inverter control control shown shown in in Figure Figure3 ,3, the the block block diagram diagram of of the the small-signal small-signal controlcontrol model model of of the the generator-inverter generator-inverter system system can can be be obtained obtained from from the the above above analysis analysis as Figureas Figure5. 5.

Active power control of inverter i2d Ucd i2dref Pref/Udcref F0(s) F(s)

Δvd wL1i2q P/Udc

K8 K5

ΔEfd ΔEq´ ΔMe K7 G(s) K4 K1

K9 K6

Inverter’s impact on electromagnetic torque of generator

Δvq Ucq Qref/Uacref i2qref F0(s) F(s)

wL1i2d Q/Uac i2q Reactive power control of inverter

FigureFigure 5. 5.The The small-signal small-signal model model of of the the inverter inverter output output and and the the generator generator electromagnetic electromagnetic torque. torque.

AccordingAccording to to the the control control block block diagram diagram and and the the superposition superposition principle, principle, the the transfer transfer functionsfunctions of of∆ ΔMMe/e/Δ∆Vdd andand Δ∆MMee/Δ/∆VVq qareare obtained, obtained, respectively: respectively:

 ∆M (K K −K K )GK −K K +K  e = 1 8 2 7 4 1 5 2  ∆vd 1−K7GK4 ∆Me (K1K9−K3K7)GK4−K1K6+K3 ∆v = 1−K GK (8)  q 7 4  ki+kps G(s) = s

where ki is the integral time constant, kp is the proportion coefﬁcient. The phase and amplitude difference between the output of the grid-connect inverter and the electromagnetic torque of the synchronous generator can be calculated by Equation (8). In this chapter, the small-signal model of the impact of the grid-connected inverter on electromagnetic torque of synchronous generator in power electronics-based AC power system has been deduced. The model reveals the relationship between the output power of the inverter and the generator torque. The model is the analysis basis of using the grid-connected inverter to increase low frequency damping. Energies 2021, 14, 2435 7 of 18

According to the classical power system theory, a torque can be decomposed into two components, i.e., damping torque and synchronizing torque. The positive direction of the damping torque is in phase with the angular frequency ∆ω. The positive direction of the synchronizing torque is in phase with the angle ∆δ. The inﬂuence of normal control grid-connected inverter on low frequency damping mainly depends on the ∆ω direction component of electromagnetic torque. According to the Heffron-Philips model, the relationship between terminal voltage and power angle can be present as Equation (9).

 0 ∆u = K5H−P∆δ + K6H−P∆Eq  0  ud0 xq uq0 x d K5H−P = UL cos δ0 − 0 UL sin δ0 (9) u0 xq+xl u0 x d+xl  uq0 xl  K6H−P = 0 u0 x d+xl

where ∆δ is the power angle deviation, K5H-P is the factor of ∆δ in the Heffron-Philips 0 model, K6H-P is the factor of ∆Eq in Heffron-Philips model, xl is the line impedance and UL is the voltage behind line impedance xl. According to Equation (9), ∆u occurs when there is a disturbance of power angle. The variation of the active power of grid-connect inverter ∆P can be assumed to follow ∆u. Moreover, the regulation of active power in the inverter is in the opposite direction of active power measurement variation. After a series of PI control, the phase of ∆Me produced by grid-connect inverter lags the phase of -∆u. So, the torque phasor diagram under oscillation can be shown in Figure6, where ∆u is the component related to power angle, ∆MeD is the damping torque component of ∆Me, ∆MeS is the synchronizing torque component of ∆Me, θM represents the phase difference from the phase of -∆u to the phase of ∆Me. From Figure6 , it can be seen that the damping torque component of ∆Me is negative. Energies 2021, 14, x FOR PEER REVIEW 8 of 19 The negative damping reduces the damping of the system and makes it easier for the appearance of LFOs.

Δω

-Δu ΔMeS Δu=K5H-PΔδ

θM Δδ

ΔMe ΔMeD

Figure 6. Torque phasorphasor diagramdiagram duringduring oscillation.oscillation.

3. LFOs Suppression Strategy Using Inverter with Built-In PSS 3.1. The Control Structure of the Inverte with Built-In PSSPSS In orderorder toto increaseincrease lowlow frequencyfrequency damping,damping, thethe grid-connectedgrid-connected inverterinverter needsneeds toto increase thethe torque inin the positive direction ofof the axis Δ∆ω toto increase increase the the damping damping torque. torque. An extraextra torquetorque ∆ΔTT cancan bebe introducedintroduced toto provideprovide positivepositive synchronizingsynchronizing torquetorque inin thethe frequency range ofof LFOs.LFOs. From From Figure 44 andand EquationEquation (8),(8), anan additional additional control control that that passes the the lead-lag lead-lag correction correction component component and and inve inverterrter control control loop loop can canbe introduced be introduced into intothe control the control loop loop of the of the grid-connected grid-connected invert inverterer to to make make the the inverter inverter produce positivepositive damping torque. ω To introduceintroduce thethe positivepositive directiondirection ofof thethe axisaxis ∆Δω,, the active power or electric angular velocity on the interconnection line can be taken as the input of the additional control. Active power or angular velocity signal is introducedintroduced intointo thethe grid-connectedgrid-connected inverterinverter toto produce positive damping, which is similar to the purpose of installing PSS on the excitation produce positive damping, which is similar to the purpose of installing PSS on the excita- system. So, the additional control in the grid-connected inverter can use the experience of tion system. So, the additional control in the grid-connected inverter can use the experi- the structure of PSS to restrain LFOs. The grid-connected inverter is not willing to produce ence of the structure of PSS to restrain LFOs. The grid-connected inverter is not willing to additional torque due to the normal power regulation of the generator, which will affect produce additional torque due to the normal power regulation of the generator, which will affect its output capacity. Regarding the control structure of PSS2B, the acceleration power is used as the input signal. After the acceleration power input signal passes through a series of lead-lag components, the output phase is corrected to produce positive damping to suppress LFOs. The built-in PSS structure for grid-connected inverter and application in the system is shown in Figure 7, where Pref is the d-axis control reference of active power, Udcref is the d-axis control reference of DC voltage, Qref is the q-axis control reference of reactive power, Uacref is the q-axis control reference of AC voltage. ω and Pe is the input signal, TW1 is the time constant of the first DC block component for input signal ω, TW2 is the time constant of the second DC block of input signal ω, TW3 is the time constant of the first DC block of input signal Pe, TW4 is the time constant of the second DC block for input signal Pe, KS2 is the gain coefficient of the integral component for input signal Pe, KS3 is a composite coefficient, T6 is the time constant of the integral component for input signal Pe, KS1 is gain coefficient of regulating component, T1 is the lead time constant of first lead-lag component, T2 is the lead time constant of first lead-lag component, T3 is the lead time constant of second lead-lag component, T4 is the lag time constant of second lead-lag component, VBPSS is the output of PSS for grid-connected inverter, VBPSS_max is the upper limit of VBPSS, VBPSS_min is the lower limit of VBPSS. VBPSS is superimposed on the control target of the grid- connected inverter.

Energies 2021, 14, 2435 8 of 18

its output capacity. Regarding the control structure of PSS2B, the acceleration power is used as the input signal. After the acceleration power input signal passes through a series of lead-lag components, the output phase is corrected to produce positive damping to suppress LFOs. The built-in PSS structure for grid-connected inverter and application in the system is shown in Figure7, where Pref is the d-axis control reference of active power, Udcref is the d-axis control reference of DC voltage, Qref is the q-axis control reference of reactive power, Uacref is the q-axis control reference of AC voltage. ω and Pe is the input signal, TW1 is the time constant of the first DC block component for input signal ω, TW2 is the time constant of the second DC block of input signal ω, TW3 is the time constant of the first DC block of input signal Pe, TW4 is the time constant of the second DC block for input signal Pe, KS2 is the gain coefficient of the integral component for input signal Pe, KS3 is a composite coefficient, T6 is the time constant of the integral component for input signal Pe, KS1 is gain coefficient of regulating component, T1 is the lead time constant of first lead-lag component, T2 is the lead time constant of first lead-lag component, T3 is the lead time constant of second lead-lag component, T4 is the lag time constant of second lead-lag component, VBPSS is the output of PSS for grid-connected inverter, VBPSS_max is the upper Energies 2021, 14, x FOR PEER REVIEWlimit of VBPSS, VBPSS_min is the lower limit of VBPSS. VBPSS is superimposed on the control9 of 19

target of the grid-connected inverter.

Control block

Inverter 1 G P,ω ω sTw1 sTw2 1 1+sTw1 w2 Load 1+sT 1+sT6 Control block Ks3

e Inverter n P sTw3 sTw4 Ks2 (a) 1+sTw3 1+sTw4 1+sT7

P/Udc Pref/Udcref idref vd N PI1 PI2 1+sT8 1+sT9 id optional based on the P VBPSS main output type W VBPSS_max M VBPSS iqref q 1+sT1 1+sT3 Qref/Uacref v Ks1 PI3 PI4 1+sT2 1+sT4 VBPSS_min Q/Uac iq

(b) (c) FigureFigure 7. 7. PSSPSS control control structure structure for forgrid-connected grid-connected inverter inverter and andapplication application in the in system. the system. (a) System (a) System structure; structure; (b) super- (b) positionsuperposition point of point PSS of output PSS output in the ininverter the inverter control; control; (c) PSS (c control) PSS control structure. structure.

TheThe additional additional electromagnetic electromagnetic torque torque is is real realizedized through through the the output output of of built-in built-in PSS. PSS. TheThe output ofof built-inbuilt-in PSS PSS can can be be added added with with the the reference reference of active of active power power or reactive or reactive power powerin the controlin the control of grid-connected of grid-connected inverter. inverter. The superposition The superposition position isposition shown is in shown Figure7 inb, Figurewhere 7b, The wherePref/U Thedcref PorrefQ/Urefdcref/U oracref Qrefin/U Figureacref in 7Figureb can be7b selectedcan be selected as the superimposedas the superimposed point pointaccording according to the to actual the actual needs. needs. When When the th grid-connectede grid-connected inverter inverter output output mainly mainly active ac- tivepower, power, the built-inthe built-in PSS shallPSS shall be superposed be superposed on the on corresponding the corresponding active poweractive controlpower con- loop. trolWhen loop. the When grid-connected the grid-connected inverter outputinverter mainly output reactive mainly power,reactive the power, built-in the PSS built-in shall PSSbe superposed shall be superposed on the corresponding on the corresponding reactive power reactive control power loop. control The loop. inverter The damping inverter dampingtorque control torque realized control through realized active through power active control power is control different is fromdifferent the dampingfrom the damp- control ingof PSScontrol realized of PSS through realized reactive through power reactive control power of the control generator. of the generator.

3.2. Parameters Design Guidline for Built-In PSS Different introduced extra torques have different damping effect. The angle between extra torque ΔT and Δω axis and the amplitude of ΔT are the main factor determining damping torque. For the parameter tuning of built-in PSS, the lead-lag component parameters mainly determine the angle and Ks1 determines the amplitude. Undamped natural oscillation angular velocity is taken as the compensation point. The phase which the additional torque generated by built-in PSS lag to the input of the lead-lag components can be calculated through Equation (8). Then the parameters of the lead-lag components can be set according to the phase compensation demand. The other parameters of the filters in built-in PSS can use the design method of PSS which is used in excitation system. As illustrated above, built-in PSS is superimposed on the reference of the outer-loop control. The additional control torque of built-in PSS has passed the control function Fo(s) and F(s). Then, the whole transfer function of additional torque of built-in PSS to electromagnetic torque of generator is shown as Equation (10).

 ΔΔMM ee=⋅⋅Fs() Fs () ΔΔω o  iPSSv d

Fs()= k+ k / s  0 po io (10) Fs()=+ k k / s  pi ii

Energies 2021, 14, 2435 9 of 18

3.2. Parameters Design Guidline for Built-In PSS Different introduced extra torques have different damping effect. The angle between extra torque ∆T and ∆ω axis and the amplitude of ∆T are the main factor determining damping torque. For the parameter tuning of built-in PSS, the lead-lag component parameters mainly determine the angle and Ks1 determines the amplitude. Undamped natural oscillation angular velocity is taken as the compensation point. The phase which the additional torque generated by built-in PSS lag to the input of the lead-lag components can be calculated through Equation (8). Then the parameters of the lead-lag components can be set according to the phase compensation demand. The other parameters of the ﬁlters in built-in PSS can use the design method of PSS which is used in excitation system. As illustrated above, built-in PSS is superimposed on the reference of the outer-loop control. The additional control torque of built-in PSS has passed the control function Fo(s) and F(s). Then, the whole transfer function of additional torque of built-in PSS to electromagnetic torque of generator is shown as Equation (10).

 ∆Me ∆Me = · Fo(s) · F(s)  ∆ωiPSS ∆vd F0(s) = kpo + kio/s (10)   F(s) = kpi + kii/s

where kpo is the proportion coefﬁcient of the outer-loop control, kio is the integral time constant of the outer-loop control, kpi is the proportion coefﬁcient of the inner-loop control, kii is the integral time constant of the inner-loop control. According to the Heffron-Philips model, the undamped mechanical nature angular velocity of the rotor can be obtained through Equation (11). ( p ωn = K1H−Pω0/TJ 0 xq−xd u cos δ0 (11) K1H−P = 0 iq0u sin δ0 + EQ0 xd +xs xq+xs

where ωn is the undamped mechanical nature angular velocity of the rotor, ∆0 is the steady value of generator power-angle, ω0 is the rated angular velocity, and TJ is the inertia constant of the generator. When ωn has been calculated, the phase of the whole system at the undamped mechanical nature angular velocity can be obtained through Equation (11). In order to produce positive damping torque and synchronous torque, the phase of additional damping torque should lead ∆ω with phase 0~40 degrees. Then, compensatory angle φx of the lead-lag component of built-in PSS can be deduced. The two lead-lag components of built-in PSS can adopt the same parameters. Then, T1 is equal to T3, T2 is equal to T4. As the inverter regulars very fast, the lag time constant T2 is required to correspond with the speed. So, T2 can be determined by reference to the regular time of inverter. The value of T1 can be obtained according to the requirement of compensatory angle φx through Equation (12) as follow.

φx/2 = arctanT1ωn − arctanT2ωn (12)

When lead-lag component parameters are determined, KS1 can be determined by the critical gain method. The equivalent ampliﬁcation factor of built-in PSS can be deﬁned as AP, and its calculation formula is shown as Equation (13). s 1 + T2 = 1 AP Ks1 2 (13) 1 + T2 Energies 2021, 14, 2435 10 of 18

4. Verification The classic step test of the generator terminal voltage is used to test low frequency damping. 5% step test of the generator terminal voltage is used in simulation and 3% step test of the generator terminal voltage is used in experiment. The damping effect of the built-in PSS can be observed in the process of the oscillation. The built-in PSS is a control for damping torque. So, the damping mechanism for multi-inverters with built-in PSS is same with the single inverter with built-in PSS. The simulation includes two parts. One part is about the different damping effects of different parameters of the built-in PSS. The other part is about the damping effects of dual paralleled grid-connected inverters with different built-in PSS situations. The experiment of generator-inverter system is also carried out to verify the damping control effect of the built-in PSS. The oscillation waveforms with Energies 2021, 14, x FOR PEER REVIEW 11 of 19 and without built-in PSS in setting conditions are compared. The inverter can produce corresponding power oscillation which suppress the transmission power oscillation. The correctness of the analysis above is verified by the simulation and experimental result. 4.1. System Description and Setting 4.1. System Description and Setting SimulationSimulation results results based onon PSCAD PSCAD are are provided provid toed verify to verify the analysis the analysis of built-in of PSS. built-in PSS.The The simulation simulation and and experimental experimental set up set of a up simplified of a simplified power electronics-based power electronics-based AC power AC powersystem system is established is established as Figure as Figure8. The two8. The simulation two simulation parts uses parts single uses inverter single and inverter two and twoparalleled paralleled inverters, inverters, respectively. respectively. The part The with part one with inverter one is inverter used to verify is used the dampingto verify the dampingeffects witheffects different with built-indifferent PSS built-in parameters. PSS Theparameters. part with twoThe inverters part with is used two to inverters verify is usedthe to damping verify the effect damping of multi-inverters. effect of multi- The maininverters. parameters The main are shownparameters in Table are1. shown The in Tablevoltage 1. The of DCvoltage source of isDC set source as 400V. is set as 400 V.

Grid-connected Inverters AC BUS Filter L2 L1 Lx G C inverter1 Synchronous Generators

L2 L1

Load C Topology of Inverter inverter2

FigureFigure 8. 8.SimulationSimulation and and experimental experimental setset up up on on PSCAD. PSCAD.

TableTable 1. Main 1. Main parameters parameters for for simplified simpliﬁed powerpower electronics-based electronics-based AC AC power power system. system.

ParametersParameters ValuesValues s systemsystem impedance impedance Ls L 0.10.1 mH mH r r 0.0820.082ΩΩ loadload L0 0.082 mH L0 0.082 mH DC source Vdc 400 V DC source Vdc 400 V x’d 0.0361 Ω xq 0.2238 Ω T’d0 3.55 id0 1093.7 A iq0 1803.7 A Generator ud0 285.6726 V uq0 117.17 V u0 308.77 V EQ0 361.96 V Sbase 1 MVA Utbase 20 kV kp 100 excitation system control ki 60 L1 0.2 mH LCL filter L2 0.04 mH C 15 uF kpo 4 Inverter control Fo(s) kio 20 kpi 4 Inverter control F(s) kii 100

Energies 2021, 14, 2435 11 of 18

Table 1. Cont.

Parameters Values 0 x d 0.0361 Ω

xq 0.2238 Ω 0 T d0 3.55

id0 1093.7 A

iq0 1803.7 A Generator ud0 285.6726 V

uq0 117.17 V

u0 308.77 V

EQ0 361.96 V

Sbase 1 MVA

Utbase 20 kV

kp 100 excitation system control ki 60

L1 0.2 mH

LCL ﬁlter L2 0.04 mH C 15 uF

kpo 4 Inverter control Fo(s) kio 20

kpi 4 Inverter control F(s) kii 100

4.2. Parameters Design

To make T1~T4 positive, the output of built-in PSS is multiplied by −1 before adding to the reference value of active power control in this simulation, which results in a phase ◦ shift of 180 . According to the parameters of circuit and control function, the phase of ∆Me ◦ lags the phase of ∆ωBPSS about 0~90 in the frequency range of LFOs. The output of built-in PSS is added with the output of d-axis control. The Pref and Qref of the grid-connected inverter are set to be 0.4 MW and 0 MVar. According to the parameters of circuit and control function, ωn can be calculated as 11.04 rad/s. From ◦ Figure9 the phase of ∆Me/∆ωBPSS at ωn can be got as 75.1 . ◦ Achieving ∆ωBPSS leading ∆Me with 30 , this paper set compensatory angle φx of the lead-lag component of built-in PSS as 75◦. According to the regulation time of the inverter, 0.01 can be taken as T2 value. T1 value can be derived through Equation (12). The parameters of built-in PSS are shown in Table2. For see more details of the inﬂuence of built-in PSS, the limited output of built-in PSS is set quite lager as 20% of Pref. In the actual project, the limit value should be according to the capacity of the inverter. The bode diagram of ∆Me/∆ωBPSS with and without compensation is shown in Figure9 . From the bode diagram, ∆ωBPSS leads ∆Me 30 degree at the target frequency of LFOs. As the ∆ω relevance vector is used as input, the phase of additional torque is 30 degrees lead of ∆ω axis. Energies 2021, 14, x FOR PEER REVIEW 12 of 19

4.2. Parameters Design

To make T1~T4 positive, the output of built-in PSS is multiplied by −1 before adding to the reference value of active power control in this simulation, which results in a phase shift of 180°. According to the parameters of circuit and control function, the phase of ΔMe lags the phase of ΔωBPSS about 0~90° in the frequency range of LFOs. The output of built-in PSS is added with the output of d-axis control. The Pref and Qref of the grid-connected inverter are set to be 0.4 MW and 0 MVar. According to the parameters of circuit and control function, ωn can be calculated as 11.04 rad/s. From Figure 9 the phase of ΔMe/ΔωBPSS at ωn can be got as 75.1°. Achieving ΔωBPSS leading ΔMe with 30°, this paper set compensatory angle ϕx of the lead-lag component of built-in PSS as 75°. According to the regulation time of the inverter, 0.01 can be taken as T2 value. T1 value can be derived through Equation (12). The parameters of built-in PSS are shown in Table 2. For see more details of the influence of built-in PSS, the limited output of built-in PSS is set quite lager as 20% of Pref. In the actual project, the limit value should be according to the capacity of the inverter.

Table 2. Parameters of built-in PSS of inverter.

Tw1 Tw2 Tw3 Tw4 T6 T7 M 2 2 2 2 0 10 5 N Ks2 Ks3 T8 T9 T1 T2 1 3.2 1 0.2 0.05 0.0868 0.01 T3 T4 Ks1 VBPSS_max VBPSS_max 0.0868 0.01 7.98 0.08 MW −0.08 MW

The bode diagram of ΔMe/ΔωBPSS with and without compensation is shown in Figure Energies 2021, 14, 2435 9. From the bode diagram, ΔωBPSS leads ΔMe 30 degree at the target frequency of LFOs.12 of As 18 the Δω relevance vector is used as input, the phase of additional torque is 30 degrees lead of Δω axis.

160

)

d (

140

t i

n 120

a M 100

180 Frequency (Hz): 1.75 )

g 90 Phase (deg): 75

(

e 0

s a

h Frequency (Hz): 1.75 P -90 Phase (deg): -30.4 -180 0.5 1 1.5 2 2.5 3 Frequency (Hz)

Figure 9. The bode diagram of ΔMe/ΔωBPSS with and without compensation. Figure 9. The bode diagram of ∆Me/∆ωBPSS with and without compensation.

Table4.3. Damping 2. Parameters Effects of of built-in Single PSSGrid of-Connected inverter. Inverter with Different Parameters Case I is the situation that damping torques have same ϕx with different AP. Case II T T T T T T M is the wsituation1 thatw damping2 torquesw3 have samew4 AP with different6 ϕx. The7 simulation results are2 shown in 2Figure 10. 2 2 0 10 5 x InNK case I compensatorys2 angleKs3 ϕ of lead-Tlag8 componentT 9of built-in PSST1 is fixed Tas2 75°, the damping torque diagram with different AP is shown in Figure 10a, where TBPSS0 is the 1 3.2 1 0.2 0.05 0.0868 0.01 damping torque of built-in PSS without phase compensation, TBPSS1 is the damping torque T T Ks V V when K3 s1 = 7.98, TBPSS4 2 is the damping1 torqueBPSS_max when Ks1 =BPSS_max 6, TBPSS3 is the damping torque when0.0868 Ks1 = 4. 0.01 7.98 0.08 MW −0.08 MW

4.3. Damping Effects of Single Grid-Connected Inverter with Different Parameters Case I is the situation that damping torques have same φx with different AP. Case II is the situation that damping torques have same AP with different φx. The simulation results are shown in Figure 10. ◦ In case I compensatory angle φx of lead-lag component of built-in PSS is fixed as 75 , the damping torque diagram with different AP is shown in Figure 10a, where TBPSS0 is the damping torque of built-in PSS without phase compensation, TBPSS1 is the damping torque when Ks1 = 7.98, TBPSS2 is the damping torque when Ks1 = 6, TBPSS3 is the damping torque when Ks1 = 4. In case II AP of built-in PSS is fixed as 8.04, the damping torque diagram with different φx is shown in Figure 10a. Where TBPSS0 is the damping torque of built-in PSS without ◦ phase compensation, TBPSS1 is the damping torque when φx =65 , TBPSS2 is the damping ◦ ◦ torque when φx =75 , TBPSS3 is the damping torque when φx = 85 . Figure 10b shows the active power of generator in both cases; Figure 10c shows output of built-in PSS with various φx and AP; Figure 10d shows active power of grid-connected inverter in both cases; Figure 10e shows reactive power of grid-connected inverter in both cases; Figure 10f shows terminal voltage of generator in both cases. For case I, from Figure 10b it can be seen that the bigger AP could produce lager positive damping torque. For case II, from Figure 10b the closer to the ∆ω-axis could produce a lager positive damping torque. From Figure 10c,d it can be seen that larger output of the built-in PSS corresponds larger power fluctuation of inverter and lager positive damping torque. With the appropriate setting of KS1 and φx, the system damping can be increased. Under the action of built-in PSS, the active power fluctuation of inverter provides positive damping to the system. The verification results are consistent with the above theoretical analysis. Meanwhile, from Figure 10e,f, the damping regulation has little influence on terminal voltage of generator. The reason for that is that the built-in PSS in inverter is added to the active power control and the inverter adopts active and reactive power decoupling control strategy. Energies 2021, 14, 2435 13 of 18 Energies 2021, 14, x FOR PEER REVIEW 14 of 19

Δω Δω

ϕx=85° Ks1=7.98 TBPSS1 TBPSS1 ϕx=75° TBPSS2 Ks1=6 TBPSS2

TBPSS3 BPSS3 Ks1=4 ϕx=65° TBPSS0 T TBPSS0

Δ Δδ δ

(a) (a)

no ipss Ks1=7.98 Ks1=6 Ks1=4 no ipss ϕx=85° ϕx=75° ϕx=65° 0.96 0.96

0.94 0.94

0.92 0.92 )

) 0.9 0.9

MW MW

( 0.88

P P

0.86 0.86

0.84 0.84

0.82 0.82

0.8 0.8 17.5 18 18.5 19 19.5 20 20.5 17.5 18 18.5 19 19.5 20 20.5 t(s) t(s) (b) (b)

Ks1=7.98 Ks1=6 Ks1=4 ϕx=85° ϕx=75° ϕx=65° 0.03 0.03

0.02 0.02

0.01 0.01

) )

0 0

MW (

( -0.01 -0.01 BPSS

BPSS -0.02 -0.02

V V -0.03 -0.03

-0.04 -0.04

-0.05 -0.05

-0.06 -0.06 17.5 18 18.5 19 19.5 20 20.5 17.5 18 18.5 19 19.5 20 20.5 t(s) t(s) (c) (c)

no ipss Ks1=7.98 Ks1=6 Ks1=4 no ipss ϕx=85° ϕx=75° ϕx=65° 0.45 0.45

0.44 0.44

0.43 0.43

) )

0.42 0.42

(

( m m 0.41

0.41 P P

0.4 0.4

0.39 0.39

0.38 0.38 17.5 18 18.5 19 19.5 20 20.5 17.5 18 18.5 19 19.5 20 20.5 t(s) t(s) (d) (d)

no ipss Ks1=7.98 Ks1=6 Ks1=4 no ipss ϕx=85° ϕx=75° ϕx=65° 0.2 0.2

0.15 0.15

0.1 0.1

) ) 0.05 0.05

Mvar 0

(

m Q Q -0.05 -0.05

-0.1 -0.1

-0.15 -0.15

-0.2 -0.2 17.5 18 18.5 19 19.5 20 20.5 17.5 18 18.5 19 19.5 20 20.5 t(s) t(s) (e) (e)

no ipss Ks1=7.98 Ks1=6 Ks1=4 no ipss ϕx=85° ϕx=75° ϕx=65° 1.07 1.07

1.06 1.06

1.05 1.05

1.04 1.04

)

( (

t 1.03

U U 1.02 1.02

1.01 1.01

1 1

0.99 0.99 17.5 18 18.5 19 19.5 20 20.5 17.5 18 18.5 19 19.5 20 20.5 t(s) t(s) (f) (f)

Figure 10. Simulation results of same ϕx with different AP (case I), same AP with different ϕx (case Figure 10. Simulation results of same φx with different AP (case I), same AP with different φx (case II). (a) Schematic II). (a) Schematic diagram of damping torque with different AP and ϕx; (b) active power of genera- diagram of damping torque with different AP and φx;(b) active power of generator; (c) output of built-in PSS with various tor; (c) output of built-in PSS with various ϕx and AP; (d) active power of grid-connected in- φx and AP; (d) activeverter; power (e) reactive of grid-connected power of grid- inverter;connected (e inverter;) reactive (f power) terminal of grid-connectedvoltage of generator. inverter; (f) terminal voltage of generator.

Energies 2021,, 14,, 2435x FOR PEER REVIEW 1514 of 1819

4.4. Damping Damping Effects Effects of of Dual Dual Paralleled Grid Grid-Connected-Connected Inverters More capacity of inverters to influence influence the electromagnetic torque of generator can present more damping e effect.ffect. In In this this paper the situation of two inverters is taken as an example of multi multi-inverters-inverters connected with synchronous generator. When the load is fixed, fixed, the different numbers of grid-connectedgrid-connected inverters is set to realizerealize the different distribution of ac activetive power between the inverter and the generator inin the the system shown shown in in Figure 88.. FigureFigure 1111 isis thethe simulationsimulation resultresult ofof twotwo parallelparallel grid-grid- connected inverters inverters system system with with different different built built-in-in PSS PSS situations. situations. The The Pref ofPref theof grid the- grid-con- nectedconnected inverter inverter are set are to set be to 0.4 be MW 0.4 MW and and0.2 MW 0.2 MW,, respectively. respectively. The TheQref ofQ reftheof grid the- grid-con- nectedconnected inverter inverter are set are to set be to 0 be MVar. 0 MVar. The Thebuilt built-in-in PSSPSS in both in both inverters inverters adopts adopts Ks1 =K 6s1 and= 6 sameand same value value as shown as shown in Table in Table 2 for2 thefor theother other parameters. parameters. Three built built-in-in PSS situations are simulated, c casease I: none of the inverters has built-inbuilt-in PSS; case II: only the larger output inverter has built built-in-in PSS; case III III:: both of the inverters have built-inbuilt-in PSS. PSS. Figure Figure 11 a11 showsa shows the thefluctuation fluctuation comparison comparison of generator’s of generator’s active power active powerunder under the three the cases.three cases. From From the figure the figure it can it becan seen be seen that that better better damping damping effect effect can can be beget get by by more more inverters inverters with with built-in built-in PSS. PSS. Figure Figure 11 11bb shows shows the theactive active powerpower ofof the larger output inverter under the three cases. Figure Figure 1111cc shows shows the the active power of the lower output inverter unde underr the three cases. Figure 11d shows the output of built built-in-in PSS in the invertersinverters under under the the three cases. From From Figure 11b11b–d,–d, the active power fluctuation fluctuation of the largerlarger inverter inverter can be reduced reduced when two inverters have damping effect.effect. The increasing of lowlow frequ frequencyency damping reduces the output of the built-inbuilt-in PSS ofof thethe inverter.inverter.

no ipss One inverter has ipss two inverters has ipss no ipss One inverter has ipss two inverters has ipss 0.8 0.45

0.78 0.44

0.76 0.43 0.74 ) 0.42

) 0.72 MW

0.7 ( 0.41

(

m P 0.68 P 0.4 0.66 0.39 0.64 0.38 0.62

0.6 0.37 17.5 18 18.5 19 19.5 20 20.5 17.5 18 18.5 19 19.5 20 20.5 t(s) t(s) (a) (b) no ipss One inverter has ipss two inverters has ipss One inverter has ipss two inverters has same output of ipss 0.24 0.03

0.02 0.23

0.01 )

) 0.22 0

MW (

MW -0.01

( 2

0.21 BPSS

m V P -0.02

0.2 -0.03

-0.04 0.19

-0.05 17.5 18 18.5 19 19.5 20 20.5 17.5 18 18.5 19 19.5 20 20.5 t(s) t(s) (c) (d) Figure 11. SSimulationimulation results of two parallel grid grid-connected-connected inverters system with different different built built-in-in PSS situations, case case I: I: none of the inverters has built built-in-in PSS; case II: only the larger output inverter has built-inbuilt-in PSS; case III:III: both of the inverters have built-in PSS. (a) Active power fluctuation comparison of generator under the three cases; (b) active power of the have built-in PSS. (a) Active power ﬂuctuation comparison of generator under the three cases; (b) active power of the larger larger output inverter under the three cases; (c) active power of the lower output inverter under the three cases; (d) output output inverter under the three cases; (c) active power of the lower output inverter under the three cases; (d) output of of built-in PSS in the inverters under the three cases. built-in PSS in the inverters under the three cases. 4.5. Experimental Results 4.5. Experimental Results The experimental platform is consisted of one synchronous generator, two inverters and resistances.The experimental The structure platform of isthe consisted system is of same one synchronouswith the simulation generator, system two structure inverters asand shown resistances. in Figure The 8. structure The experimental of the system platform is same is withshown the in simulation Figure 12. systemThe parameters structure as shown in Figure8. The experimental platform is shown in Figure 12. The parameters of the experimental platform are shown in Table3. The two inverters all adopt same control

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of the experimental platform are shown in Table 3. The two inverters all adopt same control and built-inand PSS. built-in The excitation PSS. The system excitation andsystem the inverters and the use inverters the same use control the same param- control parameters eters as shown inas Table shown 1. in Table1.

(a) (b) (c)

FigureFigure 12.12. ExperimentExperiment platform.platform. ((aa)) SynchronousSynchronous generator;generator; ((bb)) inverter;inverter; ((cc)) controllercontroller of of the the inverter. inverter. Table 3. The parameters of the experimental platform. Table 3. The parameters of the experimental platform. Parameters Values Parameters Values S 30 kVA Sbase base 30 kVA Utbase Utbase 400 V 400 V Generator Generator x’d x’d 0.3556 pu 0.3556 pu

xq xq 1.0825 pu 1.0825 pu T’d0 6.55 T’d0 6.55 L1 0.2 mH L1 0.2 mH LCL filter LCL ﬁlter L2 0.04 mH L2 0.04 mH C 15 uF C 15 uF load r 2.4 Ω load r 2.4 Ω DC source Vdc 400 V DC source Vdc 400 V The parameters of built-in PSS are designed as the analysis above and shown in Table 4. The parameters of built-in PSS are designed as the analysis above and shown in Table4. Table 4. Parameters of built-in PSS of inverter for experiment. Table 4. Parameters of built-in PSS of inverter for experiment. Tw1 Tw2 Tw3 Tw4 T6 T7 M

2 2 2 Tw1 2 Tw2 T0w 3 Tw4 10 T6 5 T7 M N Ks2 Ks3 2T8 2T 29 2T1 0T2 10 5 1 3.2 1 0.2 0.05 0.15 0.01 NKs2 Ks3 T8 T9 T1 T2 T3 T4 Ks1 VBPSS_max VBPSS_max 1 3.2 1 0.2 0.05 0.15 0.01 0.15 0.01 6.3 0.9 kW −0.9 kW T3 T4 Ks1 VBPSS_max VBPSS_max Three percent step0.15 of the generator 0.01 terminal 6.3 voltage 0.9test kW is used −as0.9 the kW test condition. The active power waveforms of the generator under the system with and without built-in PSS are shown in FigureThree 13. percent To illustrate step of thethe generatordamping effect terminal of the voltage built-in test PSS is used with as dif- the test condition. ferent parameters,The the active waveform power waveformsof with built-in of the PSS generator 1 uses the under parameters the system in Table with 4 and and without built-in the waveform ofPSS with are built-in shown inPSS Figure 2 adopts 13. To the illustrate parameters the damping in Table effect4 except of theT1 = built-in T3 = 0.16, PSS with different Ks1 = 7.3. The dataparameters, of active the power waveform is recorded of with by built-in controller PSS of 1 usesthe inverter. the parameters The active in Table 4 and the power waveformswaveform are obtained of with by built-inusing data PSS pr 2ocessing adopts thesoftware parameters to process in Table the recorded4 except T1 = T3 = 0.16, data. From the comparison,Ks1 = 7.3. The the data inverters of active with power built-in is PSS recorded can increase by controller the low of frequency the inverter. The active power waveforms are obtained by using data processing software to process the recorded

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data. From the comparison, the inverters with built-in PSS can increase the low frequency damping. The The low low frequency frequency damping damping can can be be controlled controlled through through the the adjusting adjusting of the of thepa- parameters.rameters. The The result result is consistent is consistent with with theoretical theoretical analysis analysis above. above.

without built-in PSS with built-in PSS 1 with built-in PSS 2 31.5

30.25

P(kW) 29.0

28.25

27.5 15.0 17.5 20.0 22.5 25.0 t(s) Figure 13. Active power waveform ofof thethe generatorgenerator underunder thethe system system with with and and without without built-in built-in PSS. PSS. The oscillation information can be obtained through the input signals of the trans- missionThe activeoscillation power information and angular can velocity. be obtained The through lead-lag the component input signals compensates of the trans- the phasemission shift active caused power by theand power angular electronics-based velocity. The lead-lag AC grid. component That makes compensates the inverter canthe providephase shift the caused corresponding by the power active electronics- power variationbased to AC suppress grid. That the oscillation.makes the inverter The simula- can providetion and the experimental corresponding result active illustrate power that variation the built-in to suppress PSS could the increaseoscillation. low The frequency simula- tiondamping and experimental with the proposed result parametersillustrate that design. the built-in The simulation PSS could and increase experimental low frequency results dampingare consistent with withthe proposed the above parameters theoretical design analysis.. The The simulation analysis and is also experimental suitable for results multi parallelare consistent grid-connected with the above inverters theoretical system inanalysis. the power The gridanalysis with is synchronous also suitable generatorfor multi parallelcharacteristics. grid-connected inverters system in the power grid with synchronous generator characteristics. 5. Conclusions 5. ConclusionsUnder the new situation that larger scale power electronics equipment and synchronous generator coexist in the power grid, making inverter participate in low frequency Under the new situation that larger scale power electronics equipment and synchro- damping control is the key to enhancing system stability. In this paper, the low frequency nous generator coexist in the power grid, making inverter participate in low frequency damping control for power electronics-based AC power system using inverters with damping control is the key to enhancing system stability. In this paper, the low frequency built-in PSS is analyzed. The model of the impact of the grid-connected inverter on the damping control for power electronics-based AC power system using inverters with built- electromagnetic torque of the synchronous generator is researched and proposed. The in PSS is analyzed. The model of the impact of the grid-connected inverter on the electro- model is the basis of increasing accurate positive low frequency damping torque through magneticthe grid-connected torque of inverter.the synchronous The built-in generato PSS ofr theis researched inverter is and used proposed. to introduce The additional model is positivethe basis dampingof increasing torque accurate for the positive system. low The frequency structure damping of the built-in torque PSSthrough is illustrated. the grid- Angularconnected velocity inverter. and The active built-in power PSS are of used the invert as inputer is signals. used to Through introduce lead-lag additional components, positive dampingthe built-in torque PSS makes for the inverter system. generate The structure positive of damping the built-in torque PSS to increaseis illustrated. low frequency Angular velocitydamping. and The active built-in power PSS controlare used can as be inpu superpositiont signals. Through to active lead-lag power control components, or reactive the powerbuilt-in control PSS makes loop inverter of the inverter. generate The positive design damping methodfor torque themain to increase parameter low offrequency built-in damping.PSS is also The proposed. built-in Finally, PSS control the correctness can be superp of theosition theoretical to active analysis power and control the effectiveness or reactive powerof the built-incontrol PSSloop is of veriﬁed the inverter. by the The simulation design method and experiment. for the main parameter of built-in PSS is also proposed. Finally, the correctness of the theoretical analysis and the effective- Authorness of Contributions:the built-in PSSConceptualization, is verified by the W.C. simulation and M.Y.; and Data experiment. curation, M.Y.; Funding acquisition, J.Z.; Methodology, M.Y. and T.L.; Software, T.L.; Validation, W.L.; Writing—original draft, M.Y. and T.L.;Author Writing—review Contributions: & Conceptualization, editing, W.C. and M.Y. W.C. All and authors M.Y.; haveData readcuration, and agreedM.Y.; Funding to the published acquisi- versiontion, J.Z.; of Methodology, the manuscript. M.Y. and T.L.; Software, T.L.; Validation, W.L.; Writing – original draft, M.Y. and T.L.; Writing – review & editing, W.C. and M.Y. All authors have read and agreed to the Funding: published Thisversion research of the was manuscript. supported in part by the National Natural Science Foundation of China (Grant Number 51877042).

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Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References 1. Chompoobutrgool, Y.; Ghandhari, M.; Vanfretti, L. Survey on power system stabilizers control and their prospective applications for power system damping using synchrophasor-based wide-area systems. Eur. Trans. Electr. Power 2011, 21, 2098–2111. [CrossRef] 2. Pogaku, N.; Prodanovic, M.; Green, T.C. Modeling, analysis and testing of autonomous operation of an inverter-based microgrid. IEEE Trans. Power Electron. 2007, 22, 613–625. [CrossRef] 3. Qi, J.; Wu, Q.; Zhang, Y.; Weng, G.; Zhou, D. Unified residue method for design of compact wide-area damping controller based on power system stabilizer. J. Mod. Power Syst. Clean Energy 2020, 8, 366–375. [CrossRef] 4. Zhong, Q.; Weiss, G. Synchronverters: Inverters that mimic synchronous generators. IEEE Trans. Ind. Electron. 2011, 58, 1259–1267. [CrossRef] 5. Alipoor, J.; Miura, Y.; Ise, T. Stability assessment and optimization methods for microgrid with multiple VSG units. IEEE Trans. Smart Grid 2018, 9, 1462–1471. [CrossRef] 6. Jiang, Q.; Li, B.; Liu, T. Large-scale power base’s impact on low frequency oscillation characteristic in UHVAC power transmission system. IEEE Access 2019, 7, 56423–56430. [CrossRef] 7. Kundur, P. Power System Stability and Control; McGraw-Hill: New York, NY, USA, 1994. 8. Zhou, J.; Shi, P.; Gan, D.; Xu, Y.; Xin, H.; Jiang, C.; Xie, H.; Wu, T. Large-scale power system robust stability analysis based on value set approach. IEEE Trans. Power Syst. 2017, 32, 4012–4023. [CrossRef] 9. Chen, H.; Yu, W.; Liu, Z.; Yan, Q.; Tasiu, I.A.; Han, Z. Low-frequency instability induced by hopf bifurcation in a single-phase converter connected to non-ideal power grid. IEEE Access 2020, 8, 62871–62882. [CrossRef] 10. Zhou, J.; Ke, D.; Chung, C.Y.; Sun, Y. A computationally efficient method to design probabilistically robust wide-area PSSs for damping inter-area oscillations in wind-integrated power systems. IEEE Trans. Power Syst. 2018, 33, 5692–5703. [CrossRef] 11. Xiong, L.; Zhuo, F.; Wang, F.; Liu, X.; Chen, Y.; Zhu, M.; Yi, H. Static synchronous generator model: A new perspective to investigate dynamic characteristics and stability issues of grid-tied PWM inverter. IEEE Trans Power Electron. 2016, 31, 6264–6280. [CrossRef] 12. Yao, W.; Jiang, L.; Wen, J.; Wu, Q.H.; Cheng, S. Wide-area damping controller of FACTS devices for inter-area oscillations considering communication time delays. IEEE Trans. Power Syst. 2014, 29, 318–329. [CrossRef] 13. Zhang, C.; Ke, D.; Sun, Y.; Chung, C.Y.; Xu, J.; Shen, F. Coordinated supplementary damping control of DFIG and PSS to suppress interarea oscillations with optimally controlled plant dynamics. IEEE Trans. Sustain. Energy 2018, 9, 780–791. [CrossRef] 14. D’Arco, S.; Suul, J.A. Equivalence of virtual synchronous machines and frequency-droops for converter-based microgrids. IEEE Trans. Smart Grid. 2014, 5, 394–395. [CrossRef] 15. Wen, B.; Boroyevich, D.; Burgos, R.; Mattavelli, P.; Shen, Z. Small signal stability analysis of three-phase AC systems in the presence of constant power loads based on measured D-Q frame impedances. IEEE Trans. Power Electron. 2015, 30, 5952–5963. [CrossRef] 16. Amin, M.; Molinas, M. Small-signal stability assessment of power electronics based power systems: A discussion of impedance- and eigenvalue-based methods. IEEE Trans. Ind. Appl. 2017, 53, 5014–5030. [CrossRef] 17. Wen, B.; Boroyevich, D.; Burgos, R.; Mattavelli, P.; Shen, Z. Analysis of D-Q small-signal impedance of grid-tied inverters. IEEE Trans. Power Electron. 2016, 31, 675–686. [CrossRef] 18. Ashabani, M.; Mohamed, Y.A.R.I. Mohamed. Integrating VSCs to weak grids by nonlinear power damping controller with self-synchronization capability. IEEE Trans. Power Syst. 2014, 29, 805–813. [CrossRef] 19. Kalcon, G.O.; Adam, G.P.; Anaya-Lara, O.; Lo, S.; Uhlen, K. Small-signal stability analysis of multi-terminal VSC-based DC transmission systems. IEEE Trans. Power Syst. 2012, 27, 1818–1830. [CrossRef] 20. Hassan, L.H.; Moghavvemi, M.; Almurib, H.A.; Muttaqi, K.M. A coordinated design of PSSs and UPFC-based stabilizer using genetic algorithm. IEEE Trans. Ind. Appl. 2014, 50, 2957–2966. [CrossRef] 21. Zhang, K.; Shi, Z.; Huang, Y.; Qiu, C.; Yang, S. SVC damping controller design based on novel modified fruit fly optimization algorithm. IET Renew. Power Gener. 2017, 12, 90–97. [CrossRef] 22. Zuo, J.; Li, Y.; Shi, D.; Duan, X. Simultaneous robust coordinated damping control of power system stabilizers (PSSs), static var compensator (SVC) and doubly-fed induction generator power oscillation dampers (DFIG PODs) in multi machine power systems. Energies 2017, 10, 565–588. 23. Ahmed, M.; Vahidnia, A.; Datta, M.; Meegahapola, A. An adaptive power oscillation damping controller for a hybrid AC/DC microgrid. IEEE Access 2020, 8, 69482–69495. [CrossRef] 24. Kerdphol, T.; Waranabe, M.; Hongesombut, K.; Mitani, Y. Self-adaptive virtual inertia control-based fuzzy logic to improve frequency stability of microgrid with high renewable penetration. IEEE Access 2019, 7, 76071–76083. [CrossRef] Energies 2021, 14, 2435 18 of 18

25. Zhou, Y.; Liu, J.; Li, Y.; Gan, C.; Li, H.; Liu, Y. A gain scheduling wide-area damping controller for the efﬁcient integration of photovoltaic plant. IEEE Trans. Power Syst. 2019, 34, 1703–1715. [CrossRef] 26. Wan, C.; Huang, M.; Tse, C.K.; Ruan, X. Effects of interaction of power converters coupled via power grid: A design-oriented study. IEEE Trans. Power Electron. 2015, 30, 3589–3600. [CrossRef] 27. Liu, J.; Miura, Y.; Ise, T. Comparison of dynamic characteristics between virtual synchronous generator and droop control in inverter based distributed generators. IEEE Trans. Power Electron. 2016, 31, 3600–3611. [CrossRef] 28. Huang, L.; Xin, H.; Wang, Z. Damping low-frequency oscillations through VSC-HVDC stations operated as virtual synchronous machines. IEEE Trans. Power Electron. 2018, 34, 5803–5818. [CrossRef] 29. Faraji, A.; Naghshbandy, A.H.; Baayeh, A.G. A hybrid coordinated design method for power system stabilizer and FACTS device based on synchro squeezed wavelet transform and stochastic subspace identiﬁcation. J. Mod. Power Syst. Clean Energy 2020, 1–10. [CrossRef]