Coordinated Control of Transient Voltage Support in Doubly Fed Induction Generators

Abstract

The large-scale integration of wind power significantly alters the voltage dynamic characteristics of power systems. Wind turbines have a weak ability to withstand grid disturbances and have difficulty in providing effective reactive power support during transient periods. The sensitivity of wind turbines to the grid voltage significantly increases the probability of large-scale, cascading off-grid events. This paper proposes a coordinated control strategy to enhance the transient reactive power support capability of doubly fed wind farms. The additional stator current demagnetization control reduces the risk of a crowbar protection action after a fault and ensures that the unit power is controllable. Based on the voltage–reactive power coupling relationship, each unit can produce reactive power according to the voltage–reactive power sensitivity matrix during the transient period. After the reactive power output of the unit reaches the limit, transient active and reactive combined control is further adopted to reduce the active power output of the unit to a certain extent and improve the reactive power support capability. Finally, two cases are built in the PSCAD to verify the effectiveness of the proposed control strategy. The results show that the proposed control strategy can enable the wind farm to output more reactive power to the grid during the transient period, effectively supporting the system voltage during the transient process and avoiding further deterioration of the fault.

1. Introduction

In the global context of sustainable energy development, the transition toward renewable power sources, particularly wind energy, is a crucial component of achieving long-term environmental and energy security goals [1]. As governments worldwide focus on reducing carbon emissions and enhancing energy security, wind farms featuring doubly fed induction generators (DFIGs) become pivotal [2]. However, the integration of DFIGs into power grids introduces complex challenges, especially in maintaining stability during grid disturbances like voltage dips or faults [3]. Therefore, enhancing the transient voltage support capabilities of DFIGs is critical for ensuring the reliability of power grids and the efficient operation of wind farms [4].

DFIGs are vulnerable to grid disturbances due to their stator windings being directly connected to the grid and the limited capacity of their converters [5]. These factors can lead to rotor overcurrents, DC link overvoltages, and fluctuations in active and reactive power outputs during grid faults, potentially compromising the turbines’ operational stability and safety [6]. Effective support for the terminal voltage of the wind turbine is conducive to smoothing the transient component of the magnetic flux, ensuring the safety of the converter and the low-voltage ride-through (LVRT) capability of the wind turbine without disconnecting from the grid [7].

The active voltage support of doubly fed wind power systems under large current disturbances is mostly achieved through external auxiliary devices [8] and wind power self-control [9]. Voltage support based on auxiliary devices includes crowbar protection [10], dynamic voltage restorer [11], and topology change [12]. However, these devices would increase the operational risk of multidevice interactions, while also increasing the operational costs. Therefore, in recent years, implementing voltage active support based on wind power self-control has been an important measure to maintain voltage stability in new power systems with wind power as the core power source.

For a single wind turbine, the reactive power limit of the unit is affected by its output active power, terminal voltage, and the voltage and current of the rotor-side and grid-side converters [13]. The rotor voltage compensation term of the doubly fed wind turbine is used to suppress the rotor overcurrent and coordinate the reactive output of the rotor-side and grid-side converter of the unit in [14]. A dynamic coordinated control of the doubly fed wind turbine is proposed in [15], which calculates the reactive power reference value of the wind turbine based on adaptive proportional integral control. It is directly used for the outer loop of the rotor-side converter control to adjust the reactive output of the wind turbine stator circuit. A joint wind farm power control method based on MPC (model predictive control) is proposed in [16]. The active and reactive power of the wind turbine are decoupled and controlled to achieve the goal of preventing a reactive power shortage. However, the control of a single wind turbine cannot meet the transient voltage support requirements of the grid-connected system. To provide more voltage support for grid-connected systems, it is important to study the control strategy of coordinated voltage support for multiple wind turbines in wind farms.

From the perspective of transient voltage support at the wind farm level, the reactive power compensation device equipped in the wind farm can play a significant supporting role in its transient voltage [17]. However, it may also cause problems such as transient overvoltage [18] or synchronous instability [19]. Therefore, some scholars have studied how to improve the transient voltage support capability of the wind farm itself. Adaptive Q/IQ-V control and variable droop gain control of doubly fed wind farms are proposed in [20,21,22]. An active control strategy for wind turbines to improve the low-through capability of wind farms is proposed in [23]. Transient voltage support for wind farms was performed with the minimum number of actively cut off wind turbines. A three-level sequential coordinated control of wind farms is proposed in [24]. For different voltage disturbance scenarios, the voltage control target of each unit was determined in real time. However, these studies did not consider the impact of grid faults on the available reactive power capacity of the units, which may lead to the units operating beyond their limits during the fault period. Meanwhile, there is a lack of verification regarding the loss of active power output and the overall stability of wind farm operation.

This paper proposes a coordinated control of transient voltage support in doubly fed induction generators. The proposed method considers the operational differences of each unit within the wind farm and achieves active voltage support for the grid-connected system by jointly optimizing the output of each unit within the wind farm. First, stator current additional demagnetization control is used to ensure that more units have reactive power output capacity during transient periods. Secondly, each doubly fed unit coordinates reactive power output based on voltage-reactive sensitivity during the transient period. Finally, transient active and reactive joint control is adopted to further expand the transient reactive capacity of the unit. A model is built in the PSCAD simulation platform to verify the effect of the proposed coordinated control strategy.

The rest of this paper is arranged as follows. Section 2 introduces the transient operation characteristics of the DFIG, which includes the characteristic modeling and control objectives of the DFIG during transient operation. Section 3 investigates the mathematical derivation process of the proposed method and explains the control objectives and implementation methods of the coordinated control strategy. Section 4 introduces the implementation process of the proposed coordinated control strategy. Section 5 verifies the effectiveness of the proposed method based on PSCAD. Section 6 gives the conclusion of this paper.

2. Transient Operation Analysis of DFIG Grid Connection

2.1. Transient Operation Characteristics of DFIG

When there is a failure in the power grid, the operation of DFIGs (doubly fed induction generators) is directly affected due to their weak ability to handle overcurrents, leading to voltage drops. This results in a transient overcurrent that impacts the rotor circuit. In severe cases, this may trigger the activation of crowbar protection.

Assuming the stator voltage of the wind turbine is U_s0 in the steady state, a symmetrical fault occurs in the power grid at moment t₀, which causes the grid voltage to fall to U_s+. The transient voltage U_s can be represented by Equation (1).

$$U_{\mathrm{s}}=\left\{\begin{array}{cc}{U}_{\mathrm{s}0}{\mathrm{e}}^{\mathrm{j}{\omega }_{1}t}& ,t<t_0\\ U_{\mathrm{s}+}{\mathrm{e}}^{\mathrm{j}{\omega }_{1}t}& ,t\ge t_0\end{array}\right.$$

(1)

Combining the DFIG voltage and flux linkage equations, the stator flux linkage Ψ_s before and after the fault can be obtained as follows:

$${\psi }_{\mathrm{s}}=\left\{\begin{array}{cc}{\displaystyle \frac{U_{\mathrm{s}0}}{1/{\tau }_{\mathrm{s}}+\mathrm{j}{\omega }_1}}{\mathrm{e}}^{\mathrm{j}{\omega }_{1}t}& ,t<t_0\\ {\displaystyle \frac{U_{\mathrm{s}+}}{1/{\tau }_{\mathrm{s}}+\mathrm{j}{\omega }_1}}{\mathrm{e}}^{\mathrm{j}{\omega }_{1}t}+{\displaystyle \frac{U_{\mathrm{s}0}-U_{\mathrm{s}+}}{1/{\tau }_{\mathrm{s}}+\mathrm{j}{\omega }_1}}{\mathrm{e}}^{\mathrm{j}{\omega }_1{t}_0}{\mathrm{e}}^{-t/{\tau }_{\mathrm{s}}}& ,t\ge t_0\end{array}\right.$$

(2)

where τ_s is the stator time constant, τ_s = L_s/R_s. L_s and R_s are the stator inductance and resistance. ω₁ is the synchronous speed in the synchronous rotation coordinate system.

The rotor flux linkage Ψ_r is calculated as follows:

$${\psi }_{\mathrm{r}}={\displaystyle \frac{L_{\mathrm{m}}}{L_{\mathrm{s}}}}{\psi }_{\mathrm{s}}+\left(L_{\mathrm{r}}-{\displaystyle \frac{L_{\mathrm{m}}^2}{L_{\mathrm{s}}}}\right)I_{\mathrm{r}}$$

(3)

where L_r and L_m are the rotor inductance and mutual inductance. I_r is the rotor current vector.

The rotor voltage U_r is calculated as follows:

$$U_{\mathrm{r}}={\displaystyle \frac{L_{\mathrm{m}}}{L_{\mathrm{s}}}}\left({\displaystyle \frac{\mathrm{d}{\psi }_{\mathrm{s}}}{\mathrm{d}t}}+\mathrm{j}{\omega }_{\mathrm{slip}}{\psi }_{\mathrm{s}}\right)+\left(R_{\mathrm{r}}{I}_{\mathrm{r}}+\sigma L_{\mathrm{r}}\left({\displaystyle \frac{\mathrm{d}{I}_{\mathrm{r}}}{\mathrm{d}t}}+\mathrm{j}{\omega }_{\mathrm{slip}}{I}_{\mathrm{r}}\right)\right)$$

(4)

where ω_slip is the differential electrical angular velocity. σ is the transient leakage inductance factor, σ = 1 − L_m²/L_sL_r.

Combining Equations (2) and (4), the post-fault rotor-induced electromotive force is obtained using the following equation:

$$E_{\mathrm{r}}\approx {\displaystyle \frac{L_{\mathrm{m}}}{L_{\mathrm{s}}}}s{U}_{\mathrm{s}+}{\mathrm{e}}^{\mathrm{j}{\omega }_{1}t}-{\displaystyle \frac{L_{\mathrm{m}}}{L_{\mathrm{s}}}}\left(1-s\right)\left(U_{\mathrm{s}0}-U_{\mathrm{s}+}\right){\mathrm{e}}^{-t/{\tau }_{\mathrm{s}}}$$

(5)

The rotor’s transient induced electromotive force consists of two parts: the steady state component and the transient component. Among them, the amplitude of the transient component decaying with τ_s is proportional to the degree of fault voltage drop and is affected by the size of the turndown rate, which is the fundamental cause of the rotor overcurrent in the DFIG during the transient period.

During grid voltage dips, the rotor winding resistance will be shorted by the crowbar device to protect the safety of the converter. The transient operation mode of the DFIG with crowbar protection is shown in Figure 1.

Figure 1a,b show the sub-synchronous and super-synchronous operation modes when crowbar protection of the DFIG is not operated. In this case, the turbine reactive power is controllable and can output reactive power to support the grid voltage by setting the reactive power reference value. And Figure 1c,d are the sub-synchronous and super-synchronous operation modes after the crowbar protection is operated. The turbine absorbs excitation power from the grid, and the reactive power is not controllable.

2.2. Transient Operational Control Objectives

According to the requirements of China’s wind power grid connection guidelines: when the voltage at the grid point falls to 0.2 p.u., the wind turbines in the wind farm can ensure that they do not go off-grid and run continuously for 0.625 s. If the voltage fall is lower than 0.2 p.u., the wind turbines are allowed to go off-grid. In addition, if the voltage at the grid point can be restored to 0.9 p.u. within 2 s after the dip, the units are required to be able to operate continuously without going off-grid during the voltage restoration period [25], as shown in Figure 2.

V_h and V_l are the upper and lower limits of the LVRT transient voltage for wind turbines that have not entered the LVRT. The turbine enters the LVRT operation interval when the voltage at the grid connection point falls between V_l and V_c. When the grid point voltage falls to less than V_c, the turbine will be allowed to go off-grid. Therefore, the transient voltage control target for each wind turbine is set to 0.9 p.u. (rated voltage at the machine end as a reference) based on the provisions of the grid connection guidelines.

$$V_{\mathrm{ref}}=V_{\mathrm{l}}=0.9 \mathrm{p}.\mathrm{u}.$$

(6)

In addition, the wind power grid integration guidelines provide for the recovery of active power from the unit after a fault. It is required that the output active power of a wind turbine that is not off-grid is restored to its pre-fault state at a rate of change of at least 0.1 p.u. per second.

3. Cooperative Control Method for Transient Voltage Support

The different control methods in the proposed coordinated control are illustrated in this section, including additional stator current demagnetization control, unit output control based on voltage reactive power sensitivity matrix, and unit transient active and reactive power joint control.

3.1. Additional Stator Current Demagnetization Control

To enhance the reactive power support of the unit during the transient period, it is necessary to minimize the possibility of the operation of crowbar protection while ensuring the safety of the unit’s converter.

The post-fault stator current expression is as follows:

$$I_{\mathrm{s}}={\displaystyle \frac{U_{\mathrm{s}+}}{L_{\mathrm{s}}\left(1/{\tau }_{\mathrm{s}}+\mathrm{j}{\omega }_1\right)}}{\mathrm{e}}^{\mathrm{j}{\omega }_{1}t}+{\displaystyle \frac{U_{\mathrm{s}0}-U_{\mathrm{s}+}}{L_{\mathrm{s}}\left(1/{\tau }_{\mathrm{s}}+\mathrm{j}{\omega }_1\right)}}{\mathrm{e}}^{-t/{\tau }_{\mathrm{s}}}$$

(7)

Crowbar protection is usually based on the amount of rotor current as the threshold for determining operation. From Equations (5) and (7), the stator current transient component after a fault has a similar form to the rotor-induced electromotive force transient component.

Therefore, the demagnetization current, which is proportional to the stator current in magnitude, can be input to the rotor current control loop to directly suppress the rotor current. At the same time, the rotor-induced electromotive force is suppressed by decreasing the reference value of the input voltage control loop. The block diagram of additional stator current demagnetization control is shown in Figure 3.

K is the demagnetization current coefficient; the coefficient K (K > 0) directly affects the size of the stator time constant, and K is positive so that the stator flux linkage transient component decays faster.

The critical value of the demagnetization coefficient K_max is as follows:

$$K_{\max }=L_{\mathrm{s}}/L_{\mathrm{m}}$$

(8)

The improper setting of parameter K may lead to instability in the DFIG (doubly fed induction generator). In practice, it is important to select a value slightly less than the maximum permissible K [26]. By employing additional stator current demagnetization control in the DFIG, it is possible to make the power of as many units as possible in the wind farm controllable during the transition process. This is the foundation for fully exploiting the reactive power support capability of the units during the transition process.

3.2. DFIG Reactive Power Control Based on Voltage Reactive Power Sensitivity Matrix

After a grid fault occurs, let the machine-end voltage of DFIG j on feeder i fall to U_Gi,j+; then, its machine-end voltage target increment ΔU_Gi,j can be expressed as follows:

$$\Delta U_{\mathrm{G}i,j}=0.9-U_{\mathrm{G}i,j+}$$

(9)

The DFIG’s reactive power output is different from the optimal allocation of reactive power during steady-state operation, and the reactive power output of each unit should be calculated according to its target voltage increment at the end of the machine. Based on Equation (9), the relationship between the target voltage increment at the machine end and the reactive power output of the unit is as follows:

$$\Delta U_{\mathrm{G}i,j}=\mathbf{S}\Delta Q_{\mathrm{G}i,j}$$

(10)

where S is the voltage–reactive power sensitivity matrix for doubly fed wind farms. The elements of the matrix can be obtained by offline calculation.

$$\mathbf{S}={\left[\begin{array}{ccccccc}{\displaystyle \frac{\partial U_{\mathrm{G}1,1}}{\partial Q_{\mathrm{G}1,1}}}& {\displaystyle \frac{\partial U_{\mathrm{G}1,1}}{\partial Q_{\mathrm{G}1,2}}}& \cdots & {\displaystyle \frac{\partial U_{\mathrm{G}1,1}}{\partial Q_{\mathrm{G}1,\mathrm{n}}}}& {\displaystyle \frac{\partial U_{\mathrm{G}1,1}}{\partial Q_{\mathrm{G}2,1}}}& \cdots & {\displaystyle \frac{\partial U_{\mathrm{G}1,1}}{\partial Q_{\mathrm{G}\mathrm{m},\mathrm{n}}}}\\ {\displaystyle \frac{\partial U_{\mathrm{G}1,2}}{\partial Q_{\mathrm{G}1,1}}}& {\displaystyle \frac{\partial U_{\mathrm{G}1,2}}{\partial Q_{\mathrm{G}1,2}}}& \cdots & {\displaystyle \frac{\partial U_{\mathrm{G}1,2}}{\partial Q_{\mathrm{G}1,\mathrm{n}}}}& {\displaystyle \frac{\partial U_{\mathrm{G}1,2}}{\partial Q_{\mathrm{G}2,1}}}& \cdots & {\displaystyle \frac{\partial U_{\mathrm{G}1,2}}{\partial Q_{\mathrm{G}\mathrm{m},\mathrm{n}}}}\\ ⋮& ⋮& \ddots & ⋮& ⋮& \ddots & ⋮\\ {\displaystyle \frac{\partial U_{\mathrm{G}1,\mathrm{n}}}{\partial Q_{\mathrm{G}1,1}}}& {\displaystyle \frac{\partial U_{\mathrm{G}1,\mathrm{n}}}{\partial Q_{\mathrm{G}1,2}}}& \cdots & {\displaystyle \frac{\partial U_{\mathrm{G}1,\mathrm{n}}}{\partial Q_{\mathrm{G}1,\mathrm{n}}}}& {\displaystyle \frac{\partial U_{\mathrm{G}1,\mathrm{n}}}{\partial Q_{\mathrm{G}2,1}}}& \cdots & {\displaystyle \frac{\partial U_{\mathrm{G}1,\mathrm{n}}}{\partial Q_{\mathrm{G}\mathrm{m},\mathrm{n}}}}\\ {\displaystyle \frac{\partial U_{\mathrm{G}2,1}}{\partial Q_{\mathrm{G}1,1}}}& {\displaystyle \frac{\partial U_{\mathrm{G}2,1}}{\partial Q_{\mathrm{G}1,2}}}& \cdots & {\displaystyle \frac{\partial U_{\mathrm{G}2,1}}{\partial Q_{\mathrm{G}1,\mathrm{n}}}}& {\displaystyle \frac{\partial U_{\mathrm{G}2,1}}{\partial Q_{\mathrm{G}2,1}}}& \cdots & {\displaystyle \frac{\partial U_{\mathrm{G}2,1}}{\partial Q_{\mathrm{G}\mathrm{m},\mathrm{n}}}}\\ ⋮& ⋮& \ddots & ⋮& ⋮& \ddots & ⋮\\ {\displaystyle \frac{\partial U_{\mathrm{G}\mathrm{m},\mathrm{n}}}{\partial Q_{\mathrm{G}1,1}}}& {\displaystyle \frac{\partial U_{\mathrm{G}\mathrm{m},\mathrm{n}}}{\partial Q_{\mathrm{G}1,2}}}& \cdots & {\displaystyle \frac{\partial U_{\mathrm{G}\mathrm{m},\mathrm{n}}}{\partial Q_{\mathrm{G}1,\mathrm{n}}}}& {\displaystyle \frac{\partial U_{\mathrm{G}\mathrm{m},\mathrm{n}}}{\partial Q_{\mathrm{G}2,1}}}& \cdots & {\displaystyle \frac{\partial U_{\mathrm{G}\mathrm{m},\mathrm{n}}}{\partial Q_{\mathrm{G}\mathrm{m},\mathrm{n}}}}\end{array}\right]}_{\left(\mathrm{m}\times \mathrm{n}\right)\times \left(\mathrm{m}\times \mathrm{n}\right)}$$

(11)

The doubly fed wind farm contains m feeders with n doubly fed units per feeder. Then, this sensitivity matrix’s row–column dimension is (m × n) × (m × n). Combining Equations (10) and (11), the reactive power output increment of doubly fed turbines during the transient period is as follows:

$$\left[\begin{array}{c}\Delta Q_{\mathrm{G}1,1}\\ ⋮\\ \Delta Q_{\mathrm{G}\mathrm{m},\mathrm{n}}\end{array}\right]={\mathrm{S}}^{-1}\left[\begin{array}{c}\Delta U_{\mathrm{G}1,1}\\ ⋮\\ \Delta U_{\mathrm{G}\mathrm{m},\mathrm{n}}\end{array}\right]={\left[\begin{array}{ccc}{\displaystyle \frac{\partial U_{\mathrm{G}1,1}}{\partial Q_{\mathrm{G}1,1}}}& \cdots & {\displaystyle \frac{\partial U_{\mathrm{G}1,1}}{\partial Q_{\mathrm{G}\mathrm{m},\mathrm{n}}}}\\ ⋮& \ddots & ⋮\\ {\displaystyle \frac{\partial U_{\mathrm{G}\mathrm{m},\mathrm{n}}}{\partial Q_{\mathrm{G}1,1}}}& \cdots & {\displaystyle \frac{\partial U_{\mathrm{G}\mathrm{m},\mathrm{n}}}{\partial Q_{\mathrm{G}\mathrm{m},\mathrm{n}}}}\end{array}\right]}^{-1}\left[\begin{array}{c}\Delta U_{\mathrm{G}1,1}\\ ⋮\\ \Delta U_{\mathrm{G}\mathrm{m},\mathrm{n}}\end{array}\right]$$

(12)

The DFIG normally operates at a unit power factor during steady-state conditions. During the fault period, then, the reference value of the reactive power output Q_refi,j of feeder i unit j is set to the calculated reactive power increment ΔQ_Gi,j for the reactive power output.

$$Q_{\mathrm{ref}i,j}=\Delta Q_{\mathrm{G}i,j}$$

(13)

3.3. Transient Active and Reactive Power Joint Control

If the grid fault voltage drops deeply, the reactive power output of the DFIG will reach its limit due to capacity constraints. When the reactive power output reaches the limit, the lift amount obtained by calculating the terminal voltage of each unit ΔU_Gi,j^f is as follows:

$$\Delta {Q_{\mathrm{G}\max i,j}}^{\mathrm{f}}={\mathrm{S}}^{-1}\Delta {U_{\mathrm{G}i,j}}^{\mathrm{f}}$$

(14)

To further explore the reactive power support capability of the DFIG, the DFIG in which crowbar protection is not activated during the transient period can be allowed to weaken the active output. The maximum overcurrent of the rotor is allowed to increase by 0.1~0.2 p.u. in a short period of time to obtain more reactive power capacity. At this stage, the target increment of terminal voltage of DFIG i and j is as follows:

$$\Delta {U_{\mathrm{G}i,j}}^{\mathrm{s}}=\Delta U_{\mathrm{G}i,j}-\Delta {U_{\mathrm{G}i,j}}^{\mathrm{f}}$$

(15)

Taking the PCC point voltage dropping to 0.75 p.u. as an example, the method of active power reduction to obtain additional reactive capacity is shown in Figure 4. To avoid the interaction between the additional demagnetization current on the rotor side and the active power reduction rotor d-axis current, the P-V droop characteristic can be used to directly control the active power reference value.

By changing the transient power operating point of the doubly fed fan from point A to point B, the additional reactive power capacity ΔQ_G^s is obtained. According to Figure 4, the wind turbine active power reference value after active power reduction is as follows:

$${P_{\mathrm{ref}i,j}}^{\mathrm{s}}=K_{\mathrm{cut}}{U}_{\mathrm{G}i,j+}$$

(16)

The value of the P-V droop coefficient K_cut is 0.75~1.0, which changes according to the degree of voltage drop. The reactive power output in the active power reduction control stage can still be calculated through the sensitivity matrix as follows:

$$\Delta {Q_{\mathrm{G}i,j}}^{\mathrm{s}}={\mathrm{S}}^{-1}\Delta {U_{\mathrm{G}i,j}}^{\mathrm{s}}$$

(17)

Currently, the DFIG reactive power reference value is as follows:

$$Q_{\mathrm{ref}i,j}=\Delta {Q_{G\max i,j}}^{\mathrm{f}}+\Delta {Q_{Gi,j}}^{\mathrm{s}}$$

(18)

4. Doubly Fed Wind Farm Transient Voltage Support Coordination Control Process

The implementation process of the proposed transient voltage support coordinated control strategy is as follows. The proposed control has three steps after a grid failure. They are additional stator current demagnetization control, unit reactive power output control, and active and reactive combined control.

(1)

Step 1: When a power grid failure occurs, the voltage at the wind farm connection point drops. The additional stator current demagnetization control acts first to suppress the rotor current, reducing the number of units that trigger the crowbar protection action and ensuring that the power of as many units as possible is controllable during the transient process.

Afterward, if the crowbar protection is activated, the unit will still be unable to provide corresponding reactive power support, and the unit will be uncontrollable during the transient period. If crowbar protection does not operate, the control strategy proceeds to step 2.

(2)

Step 2: The computer terminal voltage control target increment is calculated according to Equation (9). Next, the sensitivity matrix is calculated offline according to Equations (11) and (12) to obtain the reactive output increment of the DFIG during the transient period. If the current unit does not reach the reactive power output limit, the reactive power output increment is calculated, and the reactive power output is formed proportionally to achieve transient support. If the current unit reaches the reactive power output limit, the control strategy proceeds to step 3.

(3)

Step 3: When the reactive power output of the unit does not reach its limit, the voltage at the computer terminal rises as shown in Equation (13). When the reactive power output of the unit reaches the limit, voltage support is carried out according to the joint control of active and reactive power. At this time, the reactive power output of the unit can be calculated according to Equations (14)–(17).

Taking feeder i and unit j as an example, the proposed transient voltage support coordinated control implementation process is shown in Figure 5.

5. Simulation

5.1. Case I

The doubly fed wind farm simulation model built in PSCAD4.6 is shown in Figure 6. The doubly fed wind farm had a rated capacity of 60 MW and contained three feeders. Each feeder was connected to 15 2 MW doubly fed wind turbines, with a spacing of 1 km between units. The parameters are shown in

Table 1. Wind farm model parameters.

Parameters	Value
Baseline capacity	150 MVA
DFIG rated capacity	5 MVA
Rated frequency	60 Hz
Feeder reference voltage	33 kV
AC grid rated voltage	138 kV
Collector circuit resistance	0.0034 p.u./km
Collector line reactance	0.0048 p.u./km
Spacing between units	1 km

. The rated voltage of the machine terminal was 690 V. The rated voltage of the power collection system was 33 kV. The rated voltage of the AC system was 230 kV. The rated frequency was 60 Hz. The simulated wind farm had 200 km of overhead lines. In the simulation, random wind speed was used to fluctuate up and down 0.6 m/s from 11 m/s.

To verify the effect of the transient coordinated control strategy of the doubly fed wind farm proposed in this article, a three-phase short-circuit ground fault was simulated at the PCC point. The PCC point voltage was set to drop to three typical transient simulation scenarios: 0.35 p.u., 0.5 p.u., and 0.75 p.u., and the fault lasted 0.4 s and was cleared.

The comparative control performed reactive power support during the transient period in accordance with the grid-connection guidelines. The maximum limit of the transient rotor current under the original control was 1.0 p.u., while the control in this paper increased it to 1.2 p.u. The crowbar protection threshold of DFIG was set to 1.3 p.u.

5.1.1. The PCC Point Voltage Dropped to 0.35 p.u.

The voltage at the grid connection point was dropped to 0.35 p.u., which may trigger the crowbar protection action of the DFIG. The simulation results of the PCC point voltage, active power, and reactive power output of the doubly fed wind farm in this scenario are shown in Figure 7.

Each unit operated stably in a sub-synchronous state, and the wind farm absorbed about 30 Mvar reactive power from the power grid. After the fault occurred, the voltage at the PCC instantly dropped to about 0.35 p.u. Under the original control, the fault caused the rotor overcurrent of each unit to exceed the standard, triggering the crowbar protection action.

Taking units 1–15 at the end of feeder 1 as an example, Figure 8 shows the waveform of their rotor current during the transient period. After the crowbar protection action, the DFIG lost the ability to control the power output, and the overall active output of the wind farm dropped to 31 MW. During this period, the wind farm absorbed about 9 Mvar more reactive power than during steady-state operation, causing the voltage drop at the grid connection point to worsen.

After each unit adopted demagnetization control and unit transient reactive power output control, the voltage drop depth at the PCC point increased by nearly 0.07 p.u. compared with the original control. Because the rotor overcurrent of each unit is suppressed after the fault, reactive power can be output during this period to support the grid-connection point voltage. Compared with the steady-state operation, the wind farm can generate nearly 30 Mvar reactive power. And it can output about 51 MW of active power to the grid.

Complete coordinated control allowed the PCC point voltage to rise to 0.44 p.u. during a fault. Compared with steady-state operation, the wind farm could generate nearly 44.7 Mvar of reactive power, and the active output was reduced by 13 MW compared with demagnetization and reactive output control. In addition, although the coordinated control in this paper reduced the active power output, it sped up the recovery of the active power of the wind farm in this transient scenario.

5.1.2. The PCC Point Voltage Dropped to 0.5 p.u.

①

Transient voltage support verification

In this transient scenario, the active and reactive power output of the wind farm that can be adjusted was greater than the scenario in Section 5.1. The proposed coordinated control increased the voltage drop depth at the PCC by about 0.02 p.u., as shown in Figure 9. The active power of the wind farm decreased by 20 MW (0.17 p.u.) compared with the original control during the transient period, but more active power was also absorbed for fault removal. The reactive power output increased by 16.7 Mvar (0.14 p.u.) during the transient period.

The voltage at the PCC dropped to the lowest value when the fault that occurred under the two controls was almost the same. The reason is that, after the additional transient active and reactive power joint control, the PI parameters of the rotor-side converter power control loop are not adjusted accordingly. This leads to power fluctuations when active power reduction and reactive power addition control are enabled. This causes short-term fluctuations in the voltage at the PCC point. After the active and reactive power output is stabilized, the PCC voltage support effect is more obvious.

②

Coordinated reactive power control verification

In this transient scenario, the effect of coordinating the reactive power output of each unit based on the voltage and reactive power sensitivity matrix was verified. The simulation results of units 1, 5, 9, and 15 of feeder 1 are shown in Figure 10.

The farther the unit is from the grid-connected point, the greater the influence of its terminal voltage increment on the reactive power increment of its own unit and that of the more remote units on the feeder. The increment of own reactive power has a greater impact on the increment of terminal voltage of more remote units. The coordinated reactive power output of each unit obtained according to the sensitivity matrix is more reasonable. During the transient period, the reactive power output of the head-end unit of feeder 1 was about 0.03 p.u. higher than that of the terminal unit.

5.1.3. The PCC Point Voltage Dropped to 0.75 p.u.

①

Transient voltage support verification

The simulation results of the PCC voltage and the wind farm active and reactive power output are shown in Figure 11.

The proposed coordinated control in this transient scenario increased the PCC voltage drop depth by approximately 0.02 p.u. The active power output of the wind farm decreased by approximately 17 MW (0.14 p.u.) compared with the original control during the transient period. After the reactive power output of each unit reached its limit for the first time, the investment in joint active and reactive power control caused large active power fluctuations in the wind farm. It brought a slight secondary drop in the PCC point voltage, as shown in the figure at 0.07 s. The reactive power output of the wind farm was effectively increased by about 18.5 Mvar (0.15 p.u.) during the transient period.

②

Influence of P-V droop active power reduction coefficient

In mild transient fault scenarios, the active and reactive power output range of wind farms that can be used for coordinated control was relatively large. The value of the sag coefficient K_cut was 0.95, which is greater than the sag coefficient in Section 5.1.2. Although the wind farm can obtain more reactive power support under mild faults, changes in the active power output have a greater impact on the voltage of the PCC. If the active power is reduced too much, it will aggravate the PCC voltage drop. In this scenario, the droop coefficient K_cut was set to 0.75 for comparison, and the results are shown in Figure 12. When K_cut was 0.75, the voltage drop at the PCC point deepened, and the PCC voltage had a serious secondary drop below 0.70 p.u.

5.2. Case II

A simulation model of IEEE 39 nodes with wind farms was built in PSCAD, as shown in Figure 13. The number represents the node name. The arrow indicates that there is a load at this node. The wind farm was connected to node 22, and its parameters were set as in Section 5.1. In this section, comparative simulations are designed for symmetrical faults and asymmetrical faults of power grid. At the same time, the simulation effects of the original PI control, demagnetization control, and the proposed control are compared to verify the effectiveness of the proposed control.

5.2.1. The PCC Point Voltage Dropped Symmetrically to 0.9 p.u.

A three-phase short circuit fault occurred when the PCC point was set for 3.5 s, with a duration of 0.2 s and a grounding resistance of 1 Ω. The fault caused the PCC point voltage to drop symmetrically to 0.9 p.u. Considering that the threshold for crowbar protection activation was 1.5 p.u. and comparing the proposed control with PI control and demagnetization control, the output terminal voltage and power are shown in Figure 14.

The proposed control can effectively improve the terminal voltage of the DFIG under power grid faults. Its dynamic response process shows that the proposed control enhances the voltage support capability by setting the reactive power reference value during the fault period and can achieve active support of wind farms for grid voltage.

When the DFIG adopts PI control and demagnetization control, the available reactive power capacity of the wind farm in this scenario is not fully utilized due to the limitation of reactive power command values. The proposed control has a high reactive power support capability and can inject a large amount of reactive power into the grid-connected system during symmetrical faults in the power grid. Under the three control actions, the transient active power output waveform was similar, and it quickly decreased due to the influence of the fault before recovering during the fault clearing stage.

5.2.2. The PCC Point Voltage Dropped Symmetrically to 0.6 p.u.

A three-phase short circuit fault was set up at the grid connection point, with a starting time of 3.5 s. After 0.2 s, the fault was cleared, and the grounding resistance was 10 Ω. During the fault period, the grid voltage dropped symmetrically by 0.6 p.u. In this scenario, the voltage and power responses of PI control, demagnetization control, and the proposed control are shown in Figure 15.

The dynamic response process of the DFIG voltage under different control effects is shown in Figure 15a. The proposed control of combined active and reactive power adjustment and the given control reactive power reference values can fully utilize the reactive power capacity of the DFIG, improve the terminal voltage of wind turbines under grid faults, and lay the foundation for achieving active voltage support technology in wind farms.

Under the three control effects, the active output performance of the DFIG was basically the same, and the active output fluctuation caused by the voltage drop at the grid connection point gradually recovered and stabilized after the fault was cleared. The reactive power output waveform of the DFIG under fault is shown in Figure 15c. Compared with the other three controls, the proposed control can effectively improve the reactive power support capacity of the wind farm to the grid during faults, that is, the ability to inject reactive power into the grid, so that the available reactive capacity of a single wind farm can be fully utilized.

5.2.3. Asymmetric Voltage Drop of PCC

This scenario assumed that an asymmetric grounding fault occurred in the power grid at 3.5 s, with a fault duration of 0.2 s. In this case, the dynamic response of voltage and power using PI control, demagnetization control, and the proposed control are shown in Figure 16.

The dynamic process of reactive power output shows that the proposed control can enable the unit to reliably output reactive power based on the station control command value, enabling the wind turbine to provide reactive power support to the grid-connected system during asymmetric faults in the power grid, improving its own terminal voltage, and optimizing the reactive voltage operating environment of the wind farm.

6. Conclusions

Aiming at the problem of reactive power and voltage support during the transient period of wind farms, a coordinated control strategy that can enhance the transient reactive power support capabilities of doubly fed wind farms is proposed. By adding stator current demagnetization control, the risk of crowbar protection action after a fault is reduced and the unit power is guaranteed to be controllable. Secondly, based on the voltage–reactive power coupling relationship, the reactive power of each unit is adjusted according to the voltage–reactive power sensitivity matrix during the transient period. After the unit’s reactive power output reaches the limit, transient active and reactive power joint control is used to further increase the reactive power output. The simulation results show that the proposed voltage active support coordinated optimization control has good control effects in scenarios of symmetrical and asymmetrical voltage drops at the grid connection point and can cope with various working conditions. Future work could explore the adaptability and robustness of control strategies under different grid conditions, as well as how to integrate these strategies into a wider range of grid management systems.