# Variable Speed Pump Storage for the Mitigation of SSR in Power System with Wind Generation

Authors: Ye Fengchun; Girmaw Teshager Bitew; Han Minxiao; Sun Yao; Zhang Hanhua
Journal: Complexity
 (2019)

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## Abstract

Subsynchronous resonance (SSR) can bring significant negative effects on the grid system like stability, security, and even generator shaft damage. This work presents a new method of using a doubly-fed induction machine (DFIM) based system of variable speed pumped storage plant (VSPS) to mitigate SSR in the power system with high penetration of wind generation. The mitigation is reached based on the principle of balanced shaft mechanical input power and electromagnetic power. The fundamental concepts and phenomena of SSR with wind farm are discussed in brief in this work. For the sake of analysis and verification of performance of the proposed system, the network model including wind farm, VSPS, HVDC, and synchronous machine is built based on Ningxia grid for the SSR study using PSCAD platform. The result shows that VSPS brings significant effect to dampen the SSR in the power system with high penetration of wind generation.


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## Body

## 1. Introduction

Subsynchronous resonance (SSR) in a power system is an electromechanical instability occurrence when the interaction exists between the torsional modes of generator shafts and effect of series-compensated transmission line running with less than the nominal grid frequency [1]. The studies have also confirmed that the wind farms constructed with doubly-fed induction generator (DFIG) and connected to series capacitor compensated transmission lines are quite vulnerable to subsynchronous interaction (SSI) and cause the escalation of SSR in the power system. SSR brings significant negative effects on the grid system like stability, security, and even generator shaft damage [2, 3]. So, the analysis and mitigation for SSR is imperative.There are two categories in practice to mitigate SSR: one is primary machine parameters modification and the other one is the secondary control loop [4, 5]. The typical examples for the first one are pole-face amortisseur windings at the generator rotor, blocking filter, TCSC, NGH damper, phase shifters, static var compensator (SVC), etc. The most typical example of the second one is using generator excitation regulator. In addition, different supplementary damping measures of FACTS have been put forward in [6–8]. Besides, to mitigate SSR, a new method of using a doubly-fed induction machine (DFIM) based system of variable speed pumped storage plant (VSPS) is proposed based on the principle of balanced shaft mechanical input power and electromagnetic power. Electromagnetic power can be calculated by the power flow of DFIM terminal to the grid, and thus controlled by the converters connected to the DFIM. By regulating injecting or absorbing active power of DFIM according to the generator speed deviation, the balance of the shaft power will be maintained smooth; therefore, VSPS can provide damping for SSR and suppress transient torque amplification effect. Regulating the absorbing or generating reactive power by the converters of the VSPS also keeps the AC voltage oscillations damped quickly. To analyse SSR and validate the performance of the proposed system, the network model including wind farm, VSPS, HVDC, and synchronous machine is built based on Ningxia grid for the study of SSR using PSCAD platform.


## 2. Problem Description Associated with Wind Generation

The SSR of DFIG originates from the resonance of the inductance-capacitance (L-C) of the components, but is reinforced by the converter control of DFIG. The latter, by greatly enlarging the negative resistance at the slip frequency, serves as the primary reason for the self-excitation of SSR, even under the context of a very low series compensation. This has been explained by theoretical analysis and confirmed by field observations [6]. It would significantly increase the absolute value of the negative resistance and thus contribute a lot to an unstable oscillation [2]. Consequently, DFIG is made much more vulnerable to the subsynchronous control interaction (SSCI)-type SSR. SSCI is emerged that there is a growing risk of SSR caused by the interaction between DFIGs and series compensated transmission line due to the increasing applications of wind power energy and series compensation.In the SSR event, the frequency at different locations is identical, meaning all wind turbine generators (WTGs) and the network are engaged in the same SSR mode. But its value is not fixed and keeps changing over time as well as the variation of the factors such as the network topology and number of online generators [6].According to the study of [7], many SSR phenomena have been detected in Guyuan, Hebei in 2010. The current of both DFIG of the wind farm and transmission line oscillates with large magnitude at the subsynchronous frequency.The proposed system in this paper is designed based on the IEEE second benchmark model of SSR so that the SSR can be well analysed. This wind generator model is shown in (Figure1). An equivalent lumped machine is provided to represent a behaviour of a group of wind turbines. As many studies [11, 12] support this assumption, the aggregation of a wind farm provides a reasonable approximation for system interconnection studies. According to system studies [13–16], simulations of bulk system dynamics using a single machine equivalent is adequate for most planning studies.Figure 1
The PSCAD circuit diagram model of wind farm built based on IEEE second benchmark circuit model.Based on this lumped wind machine model, the system shown in (Figure2) is considered for the case study for Ningxia grid that consists of large penetration of wind and PV generation with HVDC sending out. The synchronous machine mechanical system of the model consists of exciter, generator, low-pressure (LP) and high-pressure (HP) turbine sections. PSCAD model is built for Figure 2 for the case study and the detailed analysis is presented in the following section.Figure 2
The structure of the power grid to study SSR, its effect, characteristics.The effect of SSR is also distributed into the grid. The following Figures including Figures3–5 show the effect of SSR on the voltage, power flow and speed responses of wind farm, and HVDC operations.Figure 3
The wind farm machine terminal AC voltage characteristics.Figure 4
Electrical torque characteristics due to SSR in the wind farm.Figure 5
Effect of SSR in the grid. (a) Power flow in one of the wind farm turbines. (b) DC voltage and current responses in the HVDC.
(a)
(b)While the synchronous generator is connected to the infinite bus AC-source, the operation is responding very well. But, when the infinite bus AC-source is shunted by RL components, the SSR starts due to the dominant effect of the series capacitor which is interacted with the torsional shaft mode of operation of the generator.The transition time is made att=1.5 seconds. The RL remains connected for 0.2 s. However, even if the RL is disconnected, the resonance and the disturbance continue as in Figure 4.The effects of SSR in the power grid considered in Figure5 are presented in the simulated waveforms shown in the following Figures.It can be concluded that the SSR has significant effect on the quality of voltage and power flow of the grid. It is more pronounced on the proximity where SSR is emerged. It leads to system failure and is a threat of power security. Thus, it needs to be suppressed by the appropriate method or technique. Some methods used so far have been presented in the introduction section in this paper. Besides, a new method of using a doubly-fed induction machine (DFIM) based system of variable speed pumped storage plant (VSPS) to mitigate SSR is proposed in this paper and discussed in the following section.


## 3. VSPS for the Mitigation of the SSR

The VSPS plays important roles in the power grid for its energy management, stability control and renewable energy resources smoothening. If it deploys a DFIM topology, it is very suitable in independent and fast active and reactive power controls. Another advantage includes that the speed of the machine is no longer locked to system frequency. Thus, in the steady state, the controls select the optimum relationship between gate position and speed to get the desired power. Hence, the efficiency and the operation flexibility of the conventional pumped storage running at constant speed can be noticeably increased by using variable speed groups. The VSPS, in general, has an immense advantages and benefits for wind power fluctuation compensation and other renewable energy smoothening, stability control, frequency control, and AC voltage control among others. Thus, it is suitable and verified that this new method of using a doubly-fed induction machine (DFIM) based system of variable speed pumped storage (VSPS) is capable of mitigating the SSR based on the principle of power balance between the machine shaft power and electromagnetic power, which is regulated by the VSPS control strategy. The electromagnetic power can be calculated by the equivalent power flow of the VSPS in to the grid, and thus regulated by the converters connected to in the DFIM. The structure of the recommended system is illustrated with a single-line diagram shown in (Figure6). The VSPS power is defined by (1) under d−q frame.(1)Ps=32vqsiqs+vdsids,Qs=32vqsids−vdsiqs,wherePs, Qs, vdqs and idqs, are, respectively, active power, reactive power, dq-axis voltages, and dq-axis currents of the stator terminal of the DFIM.Figure 6
Structure of the proposed system to mitigate the effects of SSR in the power system.According to [12], the VSPS is very effective for regulating grid frequency and AC voltage, stability control and wind power compensation as it is proved and verified with the case study end experimental results. By regulating injecting or absorbing active power of DFIM, the balance of the power in the grid will be maintained. Regulating the absorbing or generating reactive power by the converters of the VSPS also keeps the AC voltage oscillations damped quickly. Therefore, this principle brings a balanced shaft mechanical input power and electromagnetic power, which is able to suppress the SSR very quickly. Hence, VSPS can provide damping for SSR and suppress transient torque amplification effect. To analyse SSR and validate the performance of the proposed system, IEEE second benchmark model of SSR is used.Based on the basic theoretical description of the VSPS DFIM presented in (1), (2), and (3), flexible and fast control strategy is likely possible to design for mitigating the SSR in the power system. Since VSC allows the DFIM more versatile and flexible for controlling, the VSC system is a preferable option and used in this study. Basically, two main methods including voltage-mode control and current-mode control exist for controlling active and reactive power in the VSC system. In a voltage-mode control, there is no control loop closed on the VSC line current. As a result, the VSC is not protected against over-currents, whereas, in the current-mode control, the VSC line current is tightly regulated by a dedicated current-control scheme. In this study, thus, current-mode control strategy is employed for controlling the real and reactive power that each VSC system exchanges with the corresponding AC system. The VSC also allows to adopt the droop control mounted on the PQ-control. The control design is presented in the following section.


## 4. Control Design of the VSPS

### 4.1. VSC Based DFIM Control

The hierarchical control structure (the current controllers in the inner loops and the active/reactive power control in the outer loops) of VSC based DFIM topology is implemented in this study for its effectiveness. To minimize the excursions of the grid frequency and AC voltage deviations caused by the contingencies, the outer loop control of the rotor side converter (RSC) is supported by the droop control. (Figure7) illustrates the control structure proposed in this study. The droop control scheme is vested on the control strategy. Direct power control is an extension of direct torque control, which is a vector control family. In the implementation of direct power control, control of the instantaneous real and reactive power is independent, simple, and direct. In the application of VSPS, this type of control scheme attempts to assure having lower computational complexity and machine model dependency, direct controllability of active and reactive powers, very good transitory response, and lower overall implementation complexity than field-oriented control scheme. It is also characterized by its fast-dynamic response against parameter variations and it does not utilize a rotor current control loop. The estimation of active and reactive powers is carried out using current measurements, and directly controlled with hysteresis controllers and a switching table. However, the frequency and voltage control are considered as open loop control. Thus, they need feedback signals to track the frequency and voltage fluctuations very quickly for damping accordingly. The parameters determined and used in the VSPS plant are listed in Appendix.Figure 7
Overall structure of control strategy used in this paper implemented in the VSPS plant.


### 4.2. Control of RSC

Starting with the dynamics model of the three-phase induction machine based on the synchronous reference frame, the electrical equations of the DFIM are expressed by.(2)dΨdsdt=Vds−Rsids+ωsΨqs,dΨqsdt=Vqs−Rsiqs−ωsΨds,dΨdrdt=Vdr−Rridr+ωs−ωrΨqr,dΨdsdt=Vqr−Rsiqr−ωs−ωrΨdr,(3)
Ψ
d
s
=
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s
i
d
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+
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m
i
d
r
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Ψ
q
s
=
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i
q
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+
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i
q
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=
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+
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=
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L
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,where;Ψdqr: dq-axis rotor fluxes, Ψdqs: dq-axis stator fluxes, idqr: dq-axis rotor currents, idqs: dq-axis stator currents, Vdqs: dq-axis stator voltages, Vdqr: dq-axis rotor voltages, Lm: magnetizing reactance, Llr: rotor leakage reactance, Lls: stator leakage reactance, Rr: rotor resistance, Rs: stator resistance, ωr: electrical angular speed, ωs: synchronous angular speed.Based on [13], with the implementation of the vector control method, the stator flux is aligned with the d-axis. Taking the stator flux equations in (3), one can deduce that Ψqs=0,andΨds=Ψs. Thus, from equations in (3), the following are obtained.(4)
i
d
s
=
Ψ
s
L
s
−
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m
L
s
i
d
r
,
i
q
s
=
−
L
m
L
s
i
q
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.Taking the assumption that the voltage drop across stator resistor is very small compared to the grid voltage, stator resistance can be neglected. Thus,vds=0,andvqs=vs. Hence, substituting these and the values of iqs=0,andids in (4) to (1), the following hold.(5)Ps=32VsLmLsiqr,Qs=32VsΨsLs−LmLsidr.Equation (5) explains that the active power and reactive power are independently controlled. This reveals that RSC offers a proper AC excitation for the windings of the rotor that provides the stator windings proper active power and used for controlling the turbine output power and the reactive power which is measured at the terminals of the stator of the machine [12]. The active power is regulated so as to follow a relationship of power and speed of the turbine of the DFIM.The model used to control the currents is presented as under.Taking the equation of (4) and differentiating the rotor flux leakage equation of the d-axis component with respect to time, the equation (6) holds.(6)dΨdrdt=Lrdidrdt+Lmdidsdt.Substituting the derivative value ofiqs in (4) to (2), equation (7) is derived.(7)dΨdrdt=Lrdidrdt+Lm−LmLsdidsdt.Substituting the value ofdΨdr/dt in (7) to the d-axis rotor equation of (2), equation (8) is derived.(8)Vdr=Rridr+Lr∗didrdt−ωs−ωrLriqr+Lmiqs.Following the same procedures to the q-axis, equation (9) holds.(9)Vqr=Rriqr+Lr∗diqrdt+ωs−ωrLridr+Lmids,whereLr∗=Lr−Lm2/Ls.Equations of (8) and (9) are helpful to develop the inner current control loops. But, due to the presence of Lrωs−ωr terms in (8) and (9), the dynamics of iqrand idr are coupled. To decouple the dynamics, one can determine mqrand mdr. Taking into account the theory of VSC, mVdc/2 is the gain of the VSC. Thus, the computed signals VqrandVdr are divided by Vdc/2 to give, respectively, mqrandmdr signals. The modulated signals of mqrandmdr are defined by(10)mdr=2Vdcudr−ωs−ωrLriqr+Lmiqs,mqr=2Vdcuqr−ωs−ωrLridr+Lmids.The two new control inputs are defined as(11)udr=Lr∗didrdr+Rridr,uqr=Lr∗diqrdr+Rriqr.Thus, the rotor electrical dynamics model is determined and representing two decoupled, first-order subsystems.The plant transfer function is given by(12)Gris=IdqrsUdqrs=1Lr∗s+Rr.These subsystems are the rotor-current control loops. Feedforward terms predictingVqrandVdr are provided on both inner loops. The loops can now control iqrandidr with the PI compensators. The PI compensator with kpri as proportional gain and kiri as integral gain of the compensator is defined by(13)Kris=kpris+kiris.Based on these mathematical models of (12) and (13), the control structure is built and illustrated in Figure 8.The outer loops are developed to generate the reference currentidqr−ref to the inner loops. From Figure 8, the closed loop transfer function of q-axis current can be defined by(14)iqrs=KriGri1+KriGriiqr−refs.Based on (5) and substituting the value of iqrs in (14) to it (5), the active power is expressed by (15).(15)Ps=32LmLsVsKriGri1+KriGriiqr−refs=Grpsiqr−refs.Figure 8
The PI current control (inner loop) structure of the RSC.Therefore, the plant function of active power in (15) can be controlled by PI compensator. The control structure is shown in Figure 9.Figure 9
The PI active power control (outer loop) structure of the RSC.Where the PI-control is denoted by.(16)Krps=kprps+kirps,withkprp and kirp are, respectively, proportional and integral gains of the controller. The refence value of Ps−ref is determined from the optimization of the hydraulic turbine.Moreover, controlling of active power can ensure controlling of grid frequency. But, in the above model, frequency is controlled in a mode of open loop scheme. Thus, the frequency could not be fully regulated and leads to more excursions. Hence, the frequency needs to be designed in such a way that the frequency closed loop circuit is added to the above active power control loop as a concept of droop control. The droop control can compensate if some excursions of a grid frequency occur due to contingencies including SSR. The control structure is illustrated in Figure10. The droop constant Kf is computed by (17).(17)Kf=−Δf/fΔP/P,where,Δf is allowable deviation of grid frequency, ΔP is and P is the maximum power carried by the converter.Figure 10
Droop-based direct power vector control structure for RSC of the VSPS (active power control loop).The reactive power control design is presented as follow. From (5) and Figure8, the equation (18) holds.(18)Ps=−32LmLsVsKriGri1+KriGriidr−refs+32ΨsLsVs=GrQsiqr−refs+32ΨsLsVs.Thus, the dynamics of (18) can be controlled by applying PI control and the control structure is depicted in Figure 11.In this model, the AC voltage is controlled through controlling reactive power but the reference of reactive is set to a fixed value. This leads to deviations and instability when contingencies occur. The reference value of the reactive value should be determined through the proportional value of change of AC voltage. This process is effective by providing the droop control loop to add with the above reactive power control loop. The control structure of this new idea is shown in the Figure12.The constant of the droop loop is determined based on the concept emerged from Figure13.Figure 11
The PI reactive power control loop structure of the RSC.Figure 12
Droop‐based direct power vector control structure for RSC of the VSPS (reactive power control loop).Figure 13
Block diagram of voltage‐control units connected in parallel for briefing voltage droop control.From Figure13, we can have (19).(19)Vt−SG=eSG+kSGRSG+jXSGiSG,Vt−SG=eSG+kSGRSG+jXSGiSG.Equation (19) states that with the voltage control units connected in parallel, the load compensation is likely made.


### 4.3. Control of GSC

The objective of the active/reactive power controller of the VSC system is to regulate the active/reactive power exchange between the converter and the AC grid. Active power is controlled by controlling the DC voltage that ensures the converter operation at unity power factor. The VSC based model also allows the GSC to absorb or generate reactive power. So, since there is no reactive power exchange initially, the reactive power control can be handled only by inner loop of current control. The control design is presented in the following.Based on Figure14, the voltage equations across the coupling inductor in dq-frame are determined. The same procedure as done in the RSC is followed for developing the inner loops (current controllers). The equations are expressed by(20)Vdg=Rids+Ldidsdt−ωsLiqs+Vds,(21)Vqg=Riqs+Ldiqsdt−ωsLids+Vqs,whereR and L are resistance and inductance of the coupling inductor.Figure 14
A simplified GSC equivalent circuit.To decouple the dynamics ofidg and iqg, the modulated signals of mdg and mqg are determined as.(22)mdg=2Vdcudg−ωsLiqg+Lmiqs,(23)mdg=2Vdcudg−ωsLiqg+Lmiqs.Thus, the two new control inputs for the inner current loops are defined in (24) and (25) and supported by feed forward terms predicting Vdg and Vqg.(24)udg=Ldidgdt+Ridg,(25)uqg=Ldiqgdt+Riqg.The compensator can be a simple proportional-integral (PI) compensator,Kgis to enable tracking of a respective reference signal. The compensator is defined by(26)Kgis=kpgis+kigis.Thus, based on the plant function,Ggis=1/Ls+R and considering the compensator Kgis in (26), the closed-loop desired transfer function becomes(27)IdqgsIdqg−refs=Ggis=1τgis+1,if and only ifkpgi=L/τgi and kigi=R/τgi.Wherekpgi and kpgi are proportional and integral gains. The gains are determined and then tuned based on the control stability theory until the better result is achieved. The control loop is illustrated in Figure 15.Figure 15
The control structure for the GSC current control (inner loops).Thed-axis is, for control design purposes, supposed to be set in phase with the voltage across the resistor, and neglecting the harmonics and losses due to switching in the converter, the active power balance equation is given by:(28)VdcIdc=1.5vdgidg=Pr,∵vqg=0,and on the output side, thedc current is (29)Idc=Cdvdcdt+iL,whereVdc and Idc are dc output voltage and current respectively.Thus, the d-component of the voltages ind-q coordinates becomes vdg and zero that of vqg. So, the active and reactive power equations are deduced by (30) and (31) respectively.(30)Pg=1.5vdgidg,(31)Qg=−1.5vdgiqg.These equations prevail that active power is likely controlled byidg and reactive power by iqg. Based on (32), the real power balance equation on the grid side can be given by:(32)Pg=1.5vdgiqg=VdcIdc.Equation (32) implies that the active power can be controlled by controlling the DC-bus voltage and in such a way that independently the DC voltage is controlled by controlling the d-axis current idg. In this controller, for the sake of mathematical formulation, it is supposed to be the DC side of the VSC is connected to an ideal DC voltage source that dictates the DC-bus voltage as shown in Figure 14. Thus, the DC-voltage Vdc of the grid port requires proper regulation.The current controller as described earlier is ensured that the output current tracks the reference values generated by an additional external control loop, which performs the output active power regulation. This power regulation is confirmed by implementing the dc voltage control. The DC link dynamics of Figure14 is given by(33)Cdvdcdt=32VdgVdcidg−iL.The minimum value of required DC side voltage [15] is given by the inverter output voltage as,(34)Vdc=223VLL,rms=2Vpeak,ph.whereVpeak,ph is peak phase voltage at the ac side and VLL,rms is the line-line rms voltage.Since the DC-link dynamics of (33) is a nonlinear equation, the PI control parameters are to be determined by linearizing the operating point of the system model. For linearization of the system model, the input value Vdc−ref is specified as a reference and it yields the transfer function as.(35)ΔVdcsΔidgs=32Vdg,0Vdc−ref1sC.To analyse this control loop, the inner current control closed loop is approximately defined as first order system with time constantTeq which is about to be 2Ta [14]. Ta is the time constant of the inner current loop plant function. Thus, the control structure of the DC voltage control is depicted in (Figure 16).Figure 16
The control structure of the DC voltage control of the DC link in the VSCs.The capacitor current in dc link is controlled by the DC voltage controller to maintain the power balance between the grid and the converter. Thus, in balanced conditions,ic=0 and Idc=IL. Hence, the current reference value of Idg should ensure exact compensation for load variation. The complete block diagram of dc-link voltage controller is represented as in Figure 10 as the system equations are analysed in per unit [14], where Kpdc and Kidc are PI controller parameters, and C is per unit capacitance of DC link.The load variation can be greatly reduced if feed-forward method is used. Otherwise, to reduce the large error, the large gain of voltage controller which is important from stability viewpoint is not necessarily deployed.


## 4.1. VSC Based DFIM Control

The hierarchical control structure (the current controllers in the inner loops and the active/reactive power control in the outer loops) of VSC based DFIM topology is implemented in this study for its effectiveness. To minimize the excursions of the grid frequency and AC voltage deviations caused by the contingencies, the outer loop control of the rotor side converter (RSC) is supported by the droop control. (Figure7) illustrates the control structure proposed in this study. The droop control scheme is vested on the control strategy. Direct power control is an extension of direct torque control, which is a vector control family. In the implementation of direct power control, control of the instantaneous real and reactive power is independent, simple, and direct. In the application of VSPS, this type of control scheme attempts to assure having lower computational complexity and machine model dependency, direct controllability of active and reactive powers, very good transitory response, and lower overall implementation complexity than field-oriented control scheme. It is also characterized by its fast-dynamic response against parameter variations and it does not utilize a rotor current control loop. The estimation of active and reactive powers is carried out using current measurements, and directly controlled with hysteresis controllers and a switching table. However, the frequency and voltage control are considered as open loop control. Thus, they need feedback signals to track the frequency and voltage fluctuations very quickly for damping accordingly. The parameters determined and used in the VSPS plant are listed in Appendix.Figure 7
Overall structure of control strategy used in this paper implemented in the VSPS plant.


## 4.2. Control of RSC

Starting with the dynamics model of the three-phase induction machine based on the synchronous reference frame, the electrical equations of the DFIM are expressed by.(2)dΨdsdt=Vds−Rsids+ωsΨqs,dΨqsdt=Vqs−Rsiqs−ωsΨds,dΨdrdt=Vdr−Rridr+ωs−ωrΨqr,dΨdsdt=Vqr−Rsiqr−ωs−ωrΨdr,(3)
Ψ
d
s
=
L
s
i
d
s
+
L
m
i
d
r
,
Ψ
q
s
=
L
s
i
q
s
+
L
m
i
q
r
,
Ψ
d
r
=
L
s
i
d
r
+
L
m
i
d
s
,
Ψ
q
r
=
L
s
i
q
r
+
L
m
i
q
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,
L
r
=
L
l
r
+
L
m
,
L
s
=
L
l
s
+
L
m
,where;Ψdqr: dq-axis rotor fluxes, Ψdqs: dq-axis stator fluxes, idqr: dq-axis rotor currents, idqs: dq-axis stator currents, Vdqs: dq-axis stator voltages, Vdqr: dq-axis rotor voltages, Lm: magnetizing reactance, Llr: rotor leakage reactance, Lls: stator leakage reactance, Rr: rotor resistance, Rs: stator resistance, ωr: electrical angular speed, ωs: synchronous angular speed.Based on [13], with the implementation of the vector control method, the stator flux is aligned with the d-axis. Taking the stator flux equations in (3), one can deduce that Ψqs=0,andΨds=Ψs. Thus, from equations in (3), the following are obtained.(4)
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=
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−
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L
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i
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q
r
.Taking the assumption that the voltage drop across stator resistor is very small compared to the grid voltage, stator resistance can be neglected. Thus,vds=0,andvqs=vs. Hence, substituting these and the values of iqs=0,andids in (4) to (1), the following hold.(5)Ps=32VsLmLsiqr,Qs=32VsΨsLs−LmLsidr.Equation (5) explains that the active power and reactive power are independently controlled. This reveals that RSC offers a proper AC excitation for the windings of the rotor that provides the stator windings proper active power and used for controlling the turbine output power and the reactive power which is measured at the terminals of the stator of the machine [12]. The active power is regulated so as to follow a relationship of power and speed of the turbine of the DFIM.The model used to control the currents is presented as under.Taking the equation of (4) and differentiating the rotor flux leakage equation of the d-axis component with respect to time, the equation (6) holds.(6)dΨdrdt=Lrdidrdt+Lmdidsdt.Substituting the derivative value ofiqs in (4) to (2), equation (7) is derived.(7)dΨdrdt=Lrdidrdt+Lm−LmLsdidsdt.Substituting the value ofdΨdr/dt in (7) to the d-axis rotor equation of (2), equation (8) is derived.(8)Vdr=Rridr+Lr∗didrdt−ωs−ωrLriqr+Lmiqs.Following the same procedures to the q-axis, equation (9) holds.(9)Vqr=Rriqr+Lr∗diqrdt+ωs−ωrLridr+Lmids,whereLr∗=Lr−Lm2/Ls.Equations of (8) and (9) are helpful to develop the inner current control loops. But, due to the presence of Lrωs−ωr terms in (8) and (9), the dynamics of iqrand idr are coupled. To decouple the dynamics, one can determine mqrand mdr. Taking into account the theory of VSC, mVdc/2 is the gain of the VSC. Thus, the computed signals VqrandVdr are divided by Vdc/2 to give, respectively, mqrandmdr signals. The modulated signals of mqrandmdr are defined by(10)mdr=2Vdcudr−ωs−ωrLriqr+Lmiqs,mqr=2Vdcuqr−ωs−ωrLridr+Lmids.The two new control inputs are defined as(11)udr=Lr∗didrdr+Rridr,uqr=Lr∗diqrdr+Rriqr.Thus, the rotor electrical dynamics model is determined and representing two decoupled, first-order subsystems.The plant transfer function is given by(12)Gris=IdqrsUdqrs=1Lr∗s+Rr.These subsystems are the rotor-current control loops. Feedforward terms predictingVqrandVdr are provided on both inner loops. The loops can now control iqrandidr with the PI compensators. The PI compensator with kpri as proportional gain and kiri as integral gain of the compensator is defined by(13)Kris=kpris+kiris.Based on these mathematical models of (12) and (13), the control structure is built and illustrated in Figure 8.The outer loops are developed to generate the reference currentidqr−ref to the inner loops. From Figure 8, the closed loop transfer function of q-axis current can be defined by(14)iqrs=KriGri1+KriGriiqr−refs.Based on (5) and substituting the value of iqrs in (14) to it (5), the active power is expressed by (15).(15)Ps=32LmLsVsKriGri1+KriGriiqr−refs=Grpsiqr−refs.Figure 8
The PI current control (inner loop) structure of the RSC.Therefore, the plant function of active power in (15) can be controlled by PI compensator. The control structure is shown in Figure 9.Figure 9
The PI active power control (outer loop) structure of the RSC.Where the PI-control is denoted by.(16)Krps=kprps+kirps,withkprp and kirp are, respectively, proportional and integral gains of the controller. The refence value of Ps−ref is determined from the optimization of the hydraulic turbine.Moreover, controlling of active power can ensure controlling of grid frequency. But, in the above model, frequency is controlled in a mode of open loop scheme. Thus, the frequency could not be fully regulated and leads to more excursions. Hence, the frequency needs to be designed in such a way that the frequency closed loop circuit is added to the above active power control loop as a concept of droop control. The droop control can compensate if some excursions of a grid frequency occur due to contingencies including SSR. The control structure is illustrated in Figure10. The droop constant Kf is computed by (17).(17)Kf=−Δf/fΔP/P,where,Δf is allowable deviation of grid frequency, ΔP is and P is the maximum power carried by the converter.Figure 10
Droop-based direct power vector control structure for RSC of the VSPS (active power control loop).The reactive power control design is presented as follow. From (5) and Figure8, the equation (18) holds.(18)Ps=−32LmLsVsKriGri1+KriGriidr−refs+32ΨsLsVs=GrQsiqr−refs+32ΨsLsVs.Thus, the dynamics of (18) can be controlled by applying PI control and the control structure is depicted in Figure 11.In this model, the AC voltage is controlled through controlling reactive power but the reference of reactive is set to a fixed value. This leads to deviations and instability when contingencies occur. The reference value of the reactive value should be determined through the proportional value of change of AC voltage. This process is effective by providing the droop control loop to add with the above reactive power control loop. The control structure of this new idea is shown in the Figure12.The constant of the droop loop is determined based on the concept emerged from Figure13.Figure 11
The PI reactive power control loop structure of the RSC.Figure 12
Droop‐based direct power vector control structure for RSC of the VSPS (reactive power control loop).Figure 13
Block diagram of voltage‐control units connected in parallel for briefing voltage droop control.From Figure13, we can have (19).(19)Vt−SG=eSG+kSGRSG+jXSGiSG,Vt−SG=eSG+kSGRSG+jXSGiSG.Equation (19) states that with the voltage control units connected in parallel, the load compensation is likely made.


## 4.3. Control of GSC

The objective of the active/reactive power controller of the VSC system is to regulate the active/reactive power exchange between the converter and the AC grid. Active power is controlled by controlling the DC voltage that ensures the converter operation at unity power factor. The VSC based model also allows the GSC to absorb or generate reactive power. So, since there is no reactive power exchange initially, the reactive power control can be handled only by inner loop of current control. The control design is presented in the following.Based on Figure14, the voltage equations across the coupling inductor in dq-frame are determined. The same procedure as done in the RSC is followed for developing the inner loops (current controllers). The equations are expressed by(20)Vdg=Rids+Ldidsdt−ωsLiqs+Vds,(21)Vqg=Riqs+Ldiqsdt−ωsLids+Vqs,whereR and L are resistance and inductance of the coupling inductor.Figure 14
A simplified GSC equivalent circuit.To decouple the dynamics ofidg and iqg, the modulated signals of mdg and mqg are determined as.(22)mdg=2Vdcudg−ωsLiqg+Lmiqs,(23)mdg=2Vdcudg−ωsLiqg+Lmiqs.Thus, the two new control inputs for the inner current loops are defined in (24) and (25) and supported by feed forward terms predicting Vdg and Vqg.(24)udg=Ldidgdt+Ridg,(25)uqg=Ldiqgdt+Riqg.The compensator can be a simple proportional-integral (PI) compensator,Kgis to enable tracking of a respective reference signal. The compensator is defined by(26)Kgis=kpgis+kigis.Thus, based on the plant function,Ggis=1/Ls+R and considering the compensator Kgis in (26), the closed-loop desired transfer function becomes(27)IdqgsIdqg−refs=Ggis=1τgis+1,if and only ifkpgi=L/τgi and kigi=R/τgi.Wherekpgi and kpgi are proportional and integral gains. The gains are determined and then tuned based on the control stability theory until the better result is achieved. The control loop is illustrated in Figure 15.Figure 15
The control structure for the GSC current control (inner loops).Thed-axis is, for control design purposes, supposed to be set in phase with the voltage across the resistor, and neglecting the harmonics and losses due to switching in the converter, the active power balance equation is given by:(28)VdcIdc=1.5vdgidg=Pr,∵vqg=0,and on the output side, thedc current is (29)Idc=Cdvdcdt+iL,whereVdc and Idc are dc output voltage and current respectively.Thus, the d-component of the voltages ind-q coordinates becomes vdg and zero that of vqg. So, the active and reactive power equations are deduced by (30) and (31) respectively.(30)Pg=1.5vdgidg,(31)Qg=−1.5vdgiqg.These equations prevail that active power is likely controlled byidg and reactive power by iqg. Based on (32), the real power balance equation on the grid side can be given by:(32)Pg=1.5vdgiqg=VdcIdc.Equation (32) implies that the active power can be controlled by controlling the DC-bus voltage and in such a way that independently the DC voltage is controlled by controlling the d-axis current idg. In this controller, for the sake of mathematical formulation, it is supposed to be the DC side of the VSC is connected to an ideal DC voltage source that dictates the DC-bus voltage as shown in Figure 14. Thus, the DC-voltage Vdc of the grid port requires proper regulation.The current controller as described earlier is ensured that the output current tracks the reference values generated by an additional external control loop, which performs the output active power regulation. This power regulation is confirmed by implementing the dc voltage control. The DC link dynamics of Figure14 is given by(33)Cdvdcdt=32VdgVdcidg−iL.The minimum value of required DC side voltage [15] is given by the inverter output voltage as,(34)Vdc=223VLL,rms=2Vpeak,ph.whereVpeak,ph is peak phase voltage at the ac side and VLL,rms is the line-line rms voltage.Since the DC-link dynamics of (33) is a nonlinear equation, the PI control parameters are to be determined by linearizing the operating point of the system model. For linearization of the system model, the input value Vdc−ref is specified as a reference and it yields the transfer function as.(35)ΔVdcsΔidgs=32Vdg,0Vdc−ref1sC.To analyse this control loop, the inner current control closed loop is approximately defined as first order system with time constantTeq which is about to be 2Ta [14]. Ta is the time constant of the inner current loop plant function. Thus, the control structure of the DC voltage control is depicted in (Figure 16).Figure 16
The control structure of the DC voltage control of the DC link in the VSCs.The capacitor current in dc link is controlled by the DC voltage controller to maintain the power balance between the grid and the converter. Thus, in balanced conditions,ic=0 and Idc=IL. Hence, the current reference value of Idg should ensure exact compensation for load variation. The complete block diagram of dc-link voltage controller is represented as in Figure 10 as the system equations are analysed in per unit [14], where Kpdc and Kidc are PI controller parameters, and C is per unit capacitance of DC link.The load variation can be greatly reduced if feed-forward method is used. Otherwise, to reduce the large error, the large gain of voltage controller which is important from stability viewpoint is not necessarily deployed.


## 5. Simulation Results and Discussion

Figures17–19 show the responses of the proposed system and the analysis is compared with the simulated results presented in chapter two. The time duration for the case study is set as the same duration as the above discussion and description shown in Figures 3–5. This is for arguing and verifying the hypothesis of the proposed system.Figures17 and 18 show the response of machine terminal voltage and torque characteristics where the SSR model is in effect on the wind farm. Comparing with the responses shown in Figure 5, the oscillations in the torque characteristics are significantly reduced. This is because the control strategy designed on the VSPS is capable of balancing the mismatch power between the shaft power and electromagnetic power and in turn to reduce the torque oscillations and the regulated electromagnetic power to cancel the effect of shaft torque resonance interaction with series capacitor.The voltage responses become improved from the oscillations due to SSR. It is the reason that the SSR is compensated by the VSPS reactive power control strategy. The VSPS is capable of generating and absorbing the reactive power and hence regulating the AC voltage oscillations based on the required and given reference voltage value using the AC droop controller.Additionally, because of the SSR effects on the system frequency and power flow, the effects were elongated on the power flow in to HVDC system. However, due to the SSR reduction by the VSPS with its control strategy, the oscillation effects on the wind farm, HVDC and synchronous hydropower plant are being minimal. These results are shown in Figure19.Figure 17
Voltage characteristics on the machine terminal voltage of the wind farm.Figure 18
The electrical torque characteristics of the wind farm.Figure 19
Evolution of the proposed network to demonstrate the SSR effect reduction on. (a) Power flow characteristics in the wind farm. (b) DC voltage and current response in the HVDC.
(a)
(b)


## 6. Conclusion

This paper presents a study on the mitigation method of SSR in the power system using VSPS plant. This new method is deployed to mitigate the effects of SSR with the implementation of VSPS plant based on the principle of balanced shaft mechanical input power and electromagnetic power of the VSPS. The droop-based direct power control strategy on the bases ofdq-coordinate technique is designed. For the sake of implementation, IEEE second benchmark model is used and its effect by simulation with the PSCAD platform discussed. A case of Ningxia power grid area is taken for the realization of the proposed system.The results show that the proposed VSPS system along with its appropriate control strategy achieves well-regulated power flow and AC voltage so as to reduce the effects of SSR spreading in the power system. Hence, VSPS plant ensures to mitigate SSR which causes instability and security problem in the power grid.



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*Source: 3765821-2019-12-10.xml*