Enhancement of Power System Transient Stability by Active and Reactive Power Control of Variable Speed Wind Generators

Abstract

This paper proposes a novel control method for enhancing transient stability by using renewable energy sources (RES). The kinetic energy accumulated in a rotor of variable speed wind generator (VSWG) is proactively used as the active power source, which is controlled according to the frequency measured at the wind farm. In addition, coordinated reactive power control according to the grid voltage is also carried out to more effectively use the kinetic energy of the VSWG. The effects of the proposed control system were evaluated by simulation analyses performed using a modified IEEE nine-bus power system network made up of synchronous generators (SGs), a photovoltaic (PV) system and a VSWG-based wind farm. Furthermore, the coordinated reactive power control between the VSWG and PV system was also demonstrated.

1. Introduction

As a result of the need to minimize environmental impacts and diversify the electricity mix, the number of grid-connected renewable energy sources (RES), such as wind generators (WGs) and photovoltaic (PV) systems, has been steadily growing. The global cumulative capacity of installed WGs reached 651 GW at the end of 2019, of which 60 GW were installed in 2019 [1]. On the other hand, the global cumulative capacity of installed PV systems reached 627 GW [2]. In Japan, the cumulative capacities of WGs and PV systems reached 3.9 GW and 63 GW, respectively. In particular, the PV market has been growing at a rapid rate. The annual installed PV capacity in 2019 reached 7 GW.

With the increase in the number of the grid-connected RES, the number of thermal units composed of synchronous generators (SGs) needs to be reduced to maintain the electricity demand–supply balance. This leads to lower synchronizing power and power system inertia, and thus the transient stability may be negatively affected [3,4,5]. In addition, when disturbances occur in the grid, some parts of the power sources without implemented fault ride through (FRT) capability may be disconnected from the grid owing to the voltage drop. The disconnection of the power sources causes a decline of power generation, and thus a further voltage drop may be induced. Ultimately, a large number of power sources may be disconnected from the grid. In this case, due to the decline of power supply caused by the disconnection of many power sources, the conventional SGs may go out-of-step in the decelerating direction [6,7,8].

Therefore, this paper proposes a novel control method for enhancing the power system transient stability by using a variable speed wind generator (VSWG). The power converter of a VSWG can individually control the active power and the reactive power. If the active power reference is set to larger value than the mechanical power from the wind turbine, the active power injected from the generator to the grid is compensated for by rotational energy (i.e., kinetic energy). As the response of the energy conversion from the kinetic energy into the electric power is fast, the control strategy using the kinetic energy of the VSWG may be effective for enhancing the stability. On the other hand, the reactive power injected from the VSWG to the grid increases the load voltage and thus the power demand. This leads to enhanced transient stability and reduced release of the kinetic energy of the VSWG.

Several control schemes for transient stability enhancement using the active power or both the active and reactive power of a fixed speed WG (FSWG) or VSWG have been suggested [8,9,10,11]. In [8], coordinated control of the active power of doubly fed induction generator (DFIG)-based wind farms and SG tripping was demonstrated. In [9], possible improvements in voltage stability and transient stability resulting from active and reactive power control were investigated. However, a VSWG modeled as a negative load was used for the simulation analysis, and hence the dynamics in the VSWG may have been neglected. In [10], wide area control using both a DFIG and SG to enhance the transient stability was demonstrated. In [11], the active and reactive power of an FSWG were controlled based on a unified inter-phase power controller (UIPC), which was installed between the FSWG and the grid.

In this study, the kinetic energy of a VSWG equipped with a full power converter was actively used for transient stability enhancement. Although the rotational speed was adjusted over a large range by using the full power converter, as mentioned above, the speed variation during the control mode could be reduced by the reactive power support. This means that the proposed method can handle more severe disturbances and offer increased reliability as a power system stabilization device. As the proposed control works based on local information, power producers can easily use the proposed control as an ancillary service. The kinetic energy accumulated in the rotor of VSWG is used as the active power source, which is controlled according to the frequency measured in the wind farm. As the frequency response is equivalent to the collective dynamic response of all generators in the power system, the dynamic stability of SGs can be controlled effectively by using the frequency response as the input signal for the control system. On the other hand, the reactive power of the VSWG is controlled according to the response of the grid voltage. To decide the appropriate value of reactive power, we referred a reactive power characteristic of the static VAR compensator (SVC). As the disconnection of many power sources owing to the voltage drop may cause the SGs to be out-of-step and thus a blackout, we gave the reactive power control higher priority than the kinetic energy control. Therefore, if the residual capacity of the power converter is insufficient, the active power delivered from the VSWG to the grid is regulated.

To verify the effectiveness of the proposed control method, simulation analyses were carried out by using a modified IEEE nine-bus power system network with a VSWG-based wind farm and PV system. Furthermore, the effect of the coordinated reactive power control with the VSWG and PV system on transient stability enhancement was also demonstrated. PSCAD/EMTDC software was used for the simulation analyses.

2. Scheme of Proposed Control Model

Figure 1 illustrates the proposed control scheme of the VSWG used to enhance the transient stability. The permanent magnet synchronous generator (PMSG) is connected to the grid through a power converter and a transformer. The power converter has a general control structure through which the active power and the reactive power are controlled according to each corresponding reference value. When the absolute value of deviation of the grid frequency, |Δf|, becomes less than or equal to 0.2 Hz, which is the target value of the frequency deviation limit in Japan, ΔP_ref is set to 0, and hence the active power reference, P_ref, is equal to P_mppt, which is calculated according to the maximum power point tracking (MPPT) algorithm. When |Δf| becomes greater than 0.2 Hz, P_ref is equal to the sum of –ΔP_ref and P_mppt. ΔP_ref is determined by multiplying Δf by two variable proportional gains K_p1 and K_p2 as shown in Figure 2. To prevent the VSWG operation from stopping due to the extreme release of the kinetic energy, K_p1 is set to 0 when the rotor speed, ω_r, is less than 0.5 pu.

When the absolute value of deviation of grid voltage, |ΔV |, becomes less than or equal to 1% of pre-fault voltage (the appropriate value for the voltage fluctuation in an extra-high-voltage system in Japan is within 1–2%), the reactive power reference, Q_ref, is set to 0. When |ΔV | becomes greater than 1 %, Q_ref is calculated as follows [12]:

$$Q_{ref}=VA\left\{{\left(\frac{V}{V_o}\right)}^2-{\left(\frac{V}{V_o}\right)}^{12}\right\}$$

(1)

where $VA$ is the rated apparent power of the VSWG and $V_o$ is pre-fault voltage (1.04 pu). The voltage–reactive power characteristic drawn based on Equation (1) and considering the dead band is shown in Figure 3.

As described above, the reactive power control has higher priority than the active power control. Therefore, the maximum value of P_ref is calculated by the following equation:

$$P_{ref lim}=\sqrt{V{A}^2-Q_{ref}^2}$$

(2)

3. Simulation Model

3.1. Power System Model and Simulation Conditions

Figure 4 illustrates the power system model [13] used for the simulation analysis. It consists of the power sources of the VSWG and three conventional SGs (SG1, SG2 and SG3). Simulation analysis using the power system model with the PV system installed instead of SG3 was also carried out. The line impedances (R + jX (jB/2)) and the initial power flows are described in per unit values on the system base (1000 MVA). The static load models with the constant impedance characteristic were used as the power demand load. The parameters of each SG are listed in

Table 1. SG parameters.

		SG1	SG2, 3			SG1	SG2, 3
Ra	(pu)	0.003	0.004	Xd”	(pu)	0.171	0.134
Xl	(pu)	0.102	0.078	Xq”	(pu)	0.171	0.134
Xd	(pu)	1.651	1.22	Tdo’	(s)	5.9	8.97
Xq	(pu)	1.59	1.16	Tqo’	(s)	0.535	1.5
Xd’	(pu)	0.232	0.174	Tdo”	(s)	0.033	0.033
Xq’	(pu)	0.38	0.25	Tqo”	(s)	0.078	0.141
H	(s)	3.0	3.0

. Figure 5 illustrates the models of the automatic voltage regulator (AVR) [14] and governor system, which are included in each SG model.

We assumed that a symmetrical three-line-to-ground (3LG) fault occurs at each fault location (F1, F2 and F3) in the grid model. After the 3LG fault occurs at 0.1s, the circuit breakers on the faulted lines are opened at 0.17 s and then reclosed at 1.17 s.

In these simulations, the effects of three control methods shown below on the transient stability enhancement are demonstrated.

• Case 1: Active power control of the VSWG;
• Case 2: Active and reactive power control of the VSWG;
• Case 3: Active and reactive power control of the VSWG and reactive power control of the PV system.

3.2. PV System Model

Figure 6 illustrates the model of the 250 MW PV system made up of an inverter and a PV module. The voltage source converter is used as a PV inverter. The active power and the reactive power injected to the grid are controlled by the inverter at the reference set points (Cases 1 and 2: $P_{ref}=0.225 \mathrm{pu}, Q_{ref}=0$; Case 3: $P_{ref}=\sqrt{{0.225}^2-Q_{ref}^2}$, $Q_{ref}=Equation \left(1\right):$ $VA$ in the equation is the rated apparent power of the PV system). We assumed that the active and reactive power are constant under the steady state, based on the assumption that irradiation and PV cell temperature do not change dramatically within the simulation period. We also assumed that the PV inverter has FRT capability and hence that the PV inverter maintains connection to the grid after the fault.

The time constants of the control system are set to slightly larger values than those of the control system of the VSWG in order to avoid the instability (hunting) of the reactive power injected to the grid [15,16].

3.3. VSWG Model

A VSWG model made up of a three-phase current source [17], as shown in Figure 7, was used in this work. The current source model has sufficient accuracy in the analysis of the power system with a great number of WGs, which cannot be simulated by using the detailed generator model. In this work, the wind farm is composed of 100 VSWGs each rated at 5 MW. The VSWG parameters [17] are listed in

Table 2. VSWG parameters.

VSWG
Wind Turbine			PMSG
R	(m)	60	Ps	(MW)	5
Vw	(m/s)	8.8	Vs	(kV)	1
ωr	(rad/s)	1.2	Rs	(Ω)	0.004
Cp opt		0.48	Lsd	(mH)	1.528
λopt		8.2	Lsq	(mH)	1.21
ρ	(kg/m3)	1.225	ψm	(Wb)	11.255
Jt	(kgm2)	49.5 × 106	Cdc	(μF)	2500
			Vdc	(kV)	1.75
			Rc	(Ω)	0.45

.

The wind turbine power output, $P_w$, can be calculated as follows [18]:

$$P_w = \frac{1}{2}{\rho \pi R}^2{V}_w^3{C}_p\left(\lambda , \beta \right)$$

(3)

$$C_p\left(\lambda , \beta \right) = 0.5176\left(\frac{116}{{\lambda }_i}-0.4\beta -5\right)e^{-21/{\lambda }_i} +0.0068\lambda$$

(4)

$$\frac{1}{{\lambda }_i} = \frac{1}{\lambda -0.08\beta } - \frac{0.035}{{\beta }^3+1}$$

(5)

$$\lambda = \frac{{\omega }_{r}R}{V_w}$$

(6)

where $\rho$ is the air density, $R$ is the radius of rotor blade, $V_w$ is the wind speed, $C_p$ is the performance coefficient, $\lambda$ is tip speed ratio and $\beta$ is blade pitch angle.

From Equation (3), the maximum power point, which changes according to the rotor speed, is calculated as follows [18]:

$$P_{mppt} = \frac{1}{2}\rho \pi R^2{\left(\frac{{\omega }_{r}R}{{\lambda }_{opt}}\right)}^3{C}_{p opt}$$

(7)

where ${\lambda }_{opt}$ and $C_{p opt}$ are the optimal values of the tip speed ratio and the power coefficient, respectively. The wind turbine parameters are also listed in Table 2. In this case study, we assumed that $V_w$ is kept constant at 8.8 (m/s) at which the active power reference of the VSWG is 0.45 pu (VSWG capacity base) within the simulation period.

The equation of motion of the drive train is expressed as follows:

$$T_m-T_e = J_t\frac{\mathrm{d}{\omega }_r}{\mathrm{dt}}$$

(8)

where $T_m, T_e, J_t$ and ${\omega }_r$ are mechanical torque, electrical torque, moment of inertia and rotor speed of the wind turbine, respectively.

The dynamic model of the PMSG in the d-q rotating reference frame is expressed as follows:

$$V_{sd} = R_s{I}_{sd}+L_{sd}\frac{\mathrm{d}{I}_{sd}}{\mathrm{dt}}-{\omega }_e{L}_{sq}{I}_{sq}$$

(9)

$$V_{sq} = R_s{I}_{sq}+L_{sq}\frac{\mathrm{d}{I}_{sq}}{\mathrm{dt}}+{\omega }_e{L}_{sd}{I}_{sd}+{\omega }_e{\psi }_m$$

(10)

where $V_{sd}$ and $V_{sq}$ are stator voltages, $R_s$ is the stator winding resistance, $I_{sd}$ and $I_{sq}$ are stator currents, ${\omega }_e$ is the rotor speed, $L_{sd}$ and $L_{sq}$ are the synchronous inductances of stator winding and ${\psi }_m$ is the flux of permanent magnet.

Active and reactive power of the PMSG are expressed as follows:

$$P_s = V_{sd}{I}_{sd}+V_{sq}{I}_{sq}$$

(11)

$$Q_s = V_{sq}{I}_{sd}-V_{sd}{I}_{sq}$$

(12)

The electrical torque of the PMSG can be expressed as follows;

$$T_e = p\left\{{\psi }_m{I}_{sq}+\left(L_{sd}-L_{sq}\right)I_{sd}{I}_{sq}\right\}$$

(13)

where $p$ is the number of pole pairs. The dynamic behavior of DC capacitor voltage $V_{dc}$ is expressed as follows:

$$\frac{\mathrm{d}{V}_{dc}}{\mathrm{dt}} = \frac{1}{C_{dc}{V}_{dc}}\left(P_s-P_g-P_{rc}\right)$$

(14)

$$P_{rc} = \left\{\begin{array}{cc}\frac{V_{dc}^2}{R_c}& \left(V_{dc}\ge 1.05 \mathrm{pu}\right)\\ 0& (V_{dc}<1.05 \mathrm{pu})\end{array}\right.$$

(15)

where $C_{dc}$ is the DC-link capacitance, $P_g$ is the active power injected to the grid and $P_{rc}$ is the consumed power in the resistance, $R_c$, which is installed in the DC-link circuit in order to protect the circuit during the fault as illustrated in Figure 7d [19]. When the DC-link voltage becomes larger than or equal to the pre-defined limit (1.05 pu), the DC-link voltage is applied to $R_c$.

4. Simulation Results

4.1. Transient Stability Analysis in the Case with SG3 Installed

First, the simulation results for the power system model with SG3 installed, in which it is assumed that 3LG fault occurs at F1, are presented. Figure 8 shows the deviation of the kinetic energy of each SG, $\Delta W$, which is the per unit value on the summation of the steady state kinetic energy of each SG. It can be seen that the oscillations of all of SGs in Cases 1 and 2 are restrained compared with those of “No control”. In particular, the oscillations in Case 2 are greatly restrained.

Figure 9 shows the deviation of the summation of the kinetic energy of each SG, $\Delta W_{total}$. As $\Delta W_{total}$ is the collective dynamic response of all generators, we can evaluate the stability of the overall power system from the response of $\Delta W_{total}$. It can be seen from the figure that the oscillation of $\Delta W_{total}$ in Case 2 is restrained, hence the enhanced transient stability.

Figure 10 shows the power system frequency. It can be seen from the figure that the frequency fluctuations are smaller in Cases 1 and 2, and hence the frequency fluctuations are restrained in these cases. In Case 2, |Δf| becomes less than or equal to 0.2 Hz after 6.13 s, and hence P_ref of the VSWG is equal to P_mppt after this time. In other words, the active power control of the VSWG is returned to the steady state mode at 6.13 s. The control mode in Case 1 is not returned to the steady state mode within 20 s.

Figure 11 shows the grid voltage at bus 7. As the VSWG has FRT capability, the grid voltage is gradually returned to the pre-fault value after the fault clearing. It can be seen that the voltages in Cases 1 and 2 after the fault clearing rise up slightly faster than that in “No control”. In Case 1, however, a larger overshoot occurs. The overshoot in Case 2 is suppressed more than that in Case 1, and the subsequent fluctuation is also suppressed more than those in other cases. In Case 2, |ΔV| becomes less than or equal to 1% of pre-fault voltage after 11.2 s, and hence the reactive power control is also returned to the steady state mode at this time.

Figure 12, Figure 13 and Figure 14 show the active power, the reactive power and the apparent power of the VSWG, respectively. As the power capacity of the VSWG is 0.5 pu (power system base), it can be seen from Figure 14 that the apparent power of the VSWG is controlled in the range of 0 to about 0.5 pu. As can be seen from Figure 12, the active power of the VSWG in Cases 1 and 2 decreases due to the increase in frequency when the fault occurs. As a result, in these cases, the power loads of SGs increase, and thus the accelerating power acting on rotors of SGs is decreased. On the other hand, when the frequency decreases, the decelerating powers acting on the rotors are decreased because the active power of the VSWG increases. Thus, as the power loads of the SGs are controlled by the active power of the VSWG, the rotor speed variations of the SGs can be restrained. Furthermore, the effect of the active power control on transient stability enhancement may be improved by the grid voltage control. This is because the voltage control changes the power demands in the grid loads. As can be seen from Figure 13, the reactive power in Case 2 rises up quickly more than that in Case 1 after the fault clearing. After that, the reactive power drops down significantly to suppress the overshoot voltage. As a result, as the power demand–supply balance in the grid is improved more than that in Case 1, and the kinetic energy released from the rotor of the VSWG becomes smaller than that in Case 1. The kinetic energy released from the rotor to the grid in each case is depicted in

Table 3. Released energy from the rotor of the VSWG in case with SG3 installed.

(s)*
Case 1	Case 2
1.31	0.32

*time-integral of active power [W × s] divided by the system base power [VA].

(e.g., 1.31 s in the table means the released energy is 1.31 × 1000 MVA, the system base power).

Figure 15 shows the rotor speed of the VSWG. It can be seen that the deceleration of the rotor in Case 2 is far less than that in Case 1. However, the rotor speed in Case 1 also certainly increases toward to the pre-fault value.

Figure 16 shows the DC-link voltage of the VSWG. The maximum values of the DC-link voltages in Cases 1 and 2 are suppressed more than that in “No control”.

4.2. Transient Stability Analysis in the Case with PV System Installed

This section represents the simulation results for the power system model with the PV system installed instead of SG3. As described above, the PV system also has FRT capability, the same as the VSWG. The results of Case 3, the coordinated reactive power control with the VSWG and PV system, are also shown in this section.

Figure 17 shows $\Delta W_{total}$. It can be seen that the oscillations of $\Delta W_{total}$ in Cases 2 and 3 are significantly restrained. In particular, the oscillation in Case 3 is greatly restrained and quickly converged.

Figure 18 shows the power system frequency. It is clear that the frequency fluctuations are smaller in Cases 2 and 3. In these cases, each value of |Δf| is maintained less than or equal to 0.2 Hz after 10.0 and 6.8 s, respectively.

Figure 19 shows the grid voltage at bus 7. It can be seen that the voltage fluctuations in Cases 2 and 3 are effectively restrained. In particular, the overshoot voltage in Case 3 is suppressed. Each value of |ΔV| in Cases 2 and 3 is maintained less than or equal to 1% of pre-fault voltage after 11.1 and 8.3 s, respectively.

Figure 20, Figure 21 and Figure 22 show the active power, the reactive power and the apparent power of the VSWG, respectively. In Case 1, although the kinetic energy released from the rotor of the VSWG to the grid increases more than that in case with SG3 installed, both oscillations of $\Delta W_{total}$ and Δf are not sufficiently restrained as shown in Figure 17 and Figure 18. On the other hand, in Cases 2 and 3, both oscillations of $\Delta W_{total}$ and Δf are sufficiently restrained in spite of the smaller release of the active power than that in Case 1. The kinetic energy released from the rotor of the VSWG to the grid in each case is depicted in

Table 4. Released energy from rotor of the VSWG in case with PV system installed.

(s)*
Case 1	Case 2	Case 3
1.68	0.77	0.65

*time-integral of active power [W × s] divided by the system base power [VA].

. As can be seen from Figure 21, the amount of reactive power absorbed by the VSWG in Case 3 is less than that in Case 2. This is because the PV system also absorbs the reactive power to suppress the overshoot voltage after the fault clearing.

Figure 23 shows the rotor speed of the VSWG. It can be seen that the deceleration of the rotors in Cases 2 and 3 is far less than that in Case 1. This is because, as can be clearly seen from Table 4, the kinetic energy released from the rotor in Cases 2 and 3 is smaller than that in Case 1.

Figure 24 shows the DC-link voltage of the VSWG. The DC-link voltage fluctuation in Case 3 converges relatively faster than those in other cases.

Figure 25 and Figure 26 show the active and reactive power outputs of the PV system. It can be seen that the reactive power in Case 3 is controlled based on the voltage–reactive power characteristic as shown in Figure 3. However, as described above, as the time constants of the control system of the PV system were set to larger values than those of the VSWG to avoid the hunting of the reactive power output, the response of the reactive power of the PV system in Case 3 is slower than that of the VSWG. Therefore, as can be seen from Figure 19 and Figure 26, the reactive power control of the PV system mainly contributes to the suppression of the overshoot and the fluctuation of the voltage after the fault clearing.

Finally, the results of the simulations performed under the various conditions are summarized.

Table 5. Integrated value of absolute value of $\Delta W_{total}$.

(s)*
System Configuration	With SG3 Installed			With PV System Installed
Fault Location	F1	F2	F3	F1	F2	F3
No control	0.775	0.564	0.623	1.429	1.175	1.122
Case 1	0.441	0.328	0.375	1.021	1.034	0.892
Case 2	0.114	0.103	0.107	0.345	0.212	0.193
Case 3	-	-	-	0.233	0.172	0.146

*time-integral of absolute value of $\Delta W_{total}$ [J × s] divided by the pre-fault value [J]

shows the integrated value from 0 to 20 s of the absolute value of $\Delta W_{total}$, divided by pre-fault value. A low value represents small oscillation and hence better transient stability [20]. It is clear that the transient stability can be enhanced in all of the simulation cases by using the proposed method. In particular, the control methods of Cases 2 and 3 effectively enhance the transient stability.

5. Conclusions

In this paper, a novel control method for transient stability enhancement using the active and reactive power control of a VSWG is presented. In addition, the effect of the coordinated reactive power control between the PV system and the VSWG on the stability enhancement is demonstrated. The effects of the control methods were evaluated by transient simulations performed using a modified IEEE nine-bus power system network. The conclusions obtained through the case studies can be summarized as follows:

• The transient stability can be enhanced by releasing the kinetic energy accumulated in the rotor of the VSWG. In this work, the kinetic energy injected to the grid is controlled according to the frequency measured in the local area.
• The transient stability can be further enhanced by combining the reactive power control of the VSWG. In this work, the reactive power injected to the grid was controlled according to the grid voltage. As the frequency fluctuations are restrained, the kinetic energy released to the grid can be reduced, and hence the deceleration of the rotor of the VSWG can be suppressed.
• The transient stability can be further enhanced by combining the reactive power control of the PV system with the VSWG control. In this work, the reactive power output of the PV system was also controlled based on the same control scheme as that of the VSWG.

As the proposed method is based on the local control strategy, it is not optimized as a closed-loop system. As the proposed method does not require wide-area measurement technologies such as a phasor measurement unit (PMU), however, power producers can easily use it as an ancillary service. As the system frequency is used as the control input, the effect of the control method on the transient stability enhancement may, in principle, be significant as use of VSWG systems implemented with control units increases. Further analysis of the proposed method considering the capacity and the location of the VSWG and PV system in a more realistic grid model (IEEJ standard model possessing the distinctive characteristics of the Japanese power system [21]) will be conducted in future work.