By analyzing the three-phase circuit between the grid-side converter and the power system as shown in Figure 2, the three-phase mathematical model of the grid-side converter system can be written as follows: U a b c − E a b c = I a b c R + L d I a b c d t (1) where U a b c and E a b c represent the three-phase voltage of the grid-side converter and the power system respectively. R and L are the resistor and inductor of the filter. I a b c represents the three-phase grid current flowing into the power grid from the grid-side converter.

The three-phase mathematical model (1) of the grid-side converter can be transformed to a mathematical model in dq synchronously rotating reference frame, which can be expressed as follows. L d i d d t = − R i d + ω L i q + u d − e d L d i q d t = − R i q − ω L i d + u q − e q (2) e d = e e q = 0 (3) where i d and i q , u d and u q , e d and e q are the grid current, converter voltage, grid voltage in dq-axis. e and ω are the amplitude and angular frequency of the grid voltage, which are uncertain and varying parameters. The active and reactive power flowing into the power grid can be given by P = 3 2 e i d Q = 3 2 e i q (4)

It can be seen that the nonlinearities exist in the grid-side converter’s mathematical model (2) since it contains the nonlinear terms e and ω . In this paper, an inverse system is designed and connected in series to the control loop to cope with the nonlinearity existing in the grid-side converter’s mathematical model. The inverse system uses real time state feedback to compensate the control variables v d and v q , which the compensation law can be expressed as follows.

It is worth mentioning that, due to the need to solve the optimization model, the sampling interval of an MPC controller cannot be set as a small value, while the sampling interval of an inverse system can be set to very small, so the inverse system can sample the state variables (i _d and i _q ), amplitude e and angular frequency ω in real time to compensate the control variables v d and v q . The real time system states (i _d and i _q ) can be obtained by measuring the real time three-phase current and making a Park’s Transformation. u d = L v d + R i d − ω L i q + e u q = L v q + R i q + ω L i d (5)

As shown in Figure 2, v d and v q are the inputs of the inverse system. u d and u q are the outputs of the inverse system and as converter control voltages to input in the grid-side converter system. The mathematical model of the composite system composed of the inverse system and the grid-side converter system can be obtained by substituting (5) into (2)–(4). d i d d t = v d d i q d t = v q (6) P = 3 2 e i d Q = 3 2 e i q (7)

Therefore, a grid-side converter composite system is structed which inputs are v d and v q , and outputs are the active power P and reactive power Q .

The state variables and output variables of the composite system are the same as those of the grid-side converter system. Therefore, to control the composite system is essential to control the converter system grid-side converter system.

The state representation Eq. 2 of the grid-side converter system contains the nonlinear terms e and ω . If the amplitude e and angular frequency ω of the grid voltage change, the MPC controller may not achieve the expected effect of predicting and controlling the state variables. In contrast, the state representation Eq. 6 of the composite system is linear and definite, so that the state variables can be accurately predicted and controlled by the MPC controller whether the amplitude and angular frequency of the grid voltage change or not. Therefore, compared with the direct control of the grid-side converter system, the control of the composite system can obtain a more reliable control effect.

The grid-side converter composite system model (6)–(7) can be written as a normal linear state space model. x • = A x + B v y = C x x = [ i d , i q ] T ,   y = P , Q T A = 0,0 0,0 ,   B = 1,0 0,1 ,   C = 1.5 * e ,   0 0 ,   1.5 * e (8)

If the amplitude of the grid voltage is stable, the system model can accurately describe the output characteristic of the system. So that the MPC controller can accurately predict and control the outputs of the system. The system outputs will gradually reach the reference values under the control of the MPC controller.

In contrast, if the amplitude of the grid voltage changes after being measured, this means that the output characteristic of the system has changed and does not match the currently established system model during this sampling interval. The MPC controller may not achieve the expected effect of predicting and controlling the system outputs during this sampling interval. However, the system model will be corrected because the MPC controller will re-measure the grid voltage amplitude at the beginning of the next sampling interval. Based on the correct system model, the system outputs will gradually reach the reference values under the control of the MPC controller. Therefore, the change of the grid voltage amplitude will not cause the system to lose stability, but make the outputs of the system fail to reach the expected value within the current sampling interval.

The MPC algorithm is not executed continuously in the controller, but at regular interval, which is called sampling interval or control period and is denoted by T. Discretization (8) can result in x k + 1 = A d x k + B d v k y k = C d x k x k = [ i d k , i q k ] T ,   v k = v d k , v q k T y k = P k , Q k T A d = e A T ,   B d = ∫ 0 T e A t d t ⋅ B , C d = C (9) where x k , v k , y k are the states, inputs and outputs of the grid-side converter composite system in discrete time. Next, the MPC controller is designed to control the grid-side converter composite system, based on the discrete state-space model (9).

Generalized power amplitude constraint conditions include the power amplitude constraints and current amplitude constraints. Based on the discrete state-space model (9), the grid current amplitudes in the future triple control periods can be predicted as follows. x k + 1 = A d x k + B d v k x k + 2 = A d x k + 1 + B d v k + 1 = A d 2 x k + A d B d v k + B d v k + 1 x k + 3 = A d x k + 2 + B d v k + 2 = A d 3 x k + A d 2 B d v k + A d B d v k + 1 + B d v k + 2 (10)

The prediction model (10) of grid current amplitudes can be rewritten in matrix form. X = A D x k + B D V X = x k + 1 ; x k + 2 ; x k + 3 V = v k ; v k + 1 ; v k + 2 A D = A d ; A d 2 ; A d 3 B D = B d , 0 2 × 2 , 0 2 × 2 A d B d , B d , 0 2 × 2 A d 2 B d , A d B d , B d (11)

The future grid current amplitudes should not be greater than of the rated current amplitude of the grid-side converter. Then, we have. x j 2 = i d j 2 + i q j 2 ≤ i N 2 ,   j = k + 1 , . . . , k + 3 (12)

Compared to separately restricting each active current i d j and reactive current i q j amplitude such as i d min ≤ i d j ≤ i d max , i q min ≤ i q j ≤ i q max , coordinately restricting active current i d and reactive current i q j amplitudes as (12) makes the amplitude range of active current and reactive current larger.

Similarly, based on discrete state-space model (9), the power amplitudes in the future triple control periods can be predicted. y k + 1 = C d A d x k + C d B d v k y k + 2 = C d A d x k + 1 + C d B d v k + 1 = C d A d 2 x k + C d A d B d v k + C d B d v k + 1 y k + 3 = C d A d x k + 2 + C d B d v k + 2 = C d A d 3 x k + C d A d 2 B d v k + C d A d B d v k + 1 + C d B d v k + 2 (13)

The prediction model (12) of the power amplitudes can be rewritten in matrix form. Y = C D x k + D D V Y = y k + 1 ; y k + 2 ; y k + 3 V = v k ; v k + 1 ; v k + 2 C D = C d A d ; C d A d 2 ; C d A d 3 D D = C d B d , 0   2 × 2 , 0 2 × 2 C d A d B d , C d B d , 0 2 × 2 C d A d 2 B d , C d A d B d , C d B d (14)

The future apparent power amplitudes of the grid-side converter should not be greater than its rated apparent power amplitude. Then, we have. y j 2 = P j 2 + Q j 2 ≤ S N 2 , j = k + 1 , . . . , k + 3 (15)

Compared to separately restricting each active power P j and reactive power Q j amplitude such as P min ≤ P j ≤ P max , Q min ≤ Q j ≤ Q max , coordinately restricting active power P j and reactive power Q j amplitudes as (15) makes the amplitude range of active power and reactive power larger.

Based on the state space model (6)–(9), we can see that the climbing of active power and reactive power depends on the control variables v d and v q . To restrict the maximum climbing of apparent power, the coordinately restricting climbing of active and reactive power can be set as v d j 2 + v q j 2 ≤ v max 2 ,   j = k , . . . , k + 2 (16)

Compared to separately restricting each control input such as v d min ≤ v d j ≤ v d max , v q min ≤ v q j ≤ v q max , coordinately restricting v d and v q as (16) makes the climbing range of active and reactive power larger.

In order to protect the grid-side converter and dignify the output voltage waveform, the amplitude coordinated restriction and climbing coordinated restriction between grid-side converter voltages u d and u q are structed in this sub-section. The variation characteristic of the converter voltage u d and u q can be analyzed as follow and is shown as Figure 3.

(1) The variation characteristic of the control variables v d and v q

As mentioned above, The MPC algorithm is not executed continuously, but at regular control period T. At the starting point of each control period T, the MPC controller solves the MPC algorithm and outputs a new round of control variables v d and v q . Then, the outputs of the MPC controller will remain unchanged until the next control period.

Therefore, during a control period T, the control variables v d and v q remain unchanged. At the moments of two control period junctures, the MPC controller will give a new round of control variables v d and v q , so that the control variables v d and v q will suddenly change at these moments. The variation characteristic of the control variables v d and v q can be seen in Figure 3.

(2) The variation characteristic of the current i d and i q

According to mathematical model (6), it can be seen that the change rates of the current i d and i q are the control variables v d and v q , respectively. During a control period T, the control variables v d and v q remain unchanged. Therefore, the current i d and i q will monotonically increase or decrease. The variation characteristic of the current i d and i q can be seen in Figure 3. The variation characteristics of the power P and Q are consistent with those of the current i d and i q .

(3) The variation characteristic of the converter voltage u d and u q .

Based on inverse system model (5), the derivative of the converter voltage u d and u q can be calculated as d u d / d t = R v d − ω L v q and d u q / d t = R v q + ω L v d . It can be seen that the derivatives of the converter voltage u d and u q are constant, so they vary monotonically during a control period T.

At the moments of two control period junctures (such as t = kT…t=(k+3)T), the MPC controller will give a new round of control variables v d ; v q . According to mathematical model (5), the converter voltage u d and u q will suddenly change at these moments due to the sudden change of the control variables v d and v q . The variation characteristic of the converter voltage u d and u q can be seen in Figure 3.

Based on the inverse system model (5), the future converter voltage u j + , j = k . . . k + 2 in Figure 3 can be calculated as u k + = L v k + R j x k + e j u k + 1 + = = L v k + 1 + R j x k + 1 + e j u k + 2 + = L v k + 2 + R j x k + 2 + e j u k + = u d k + u q k + , R j = R , − L ω 0 L ω 0 , R , e j = e 0 (17)

The prediction model (17) of converter voltage can be rewritten in matrix form. U + = L V + R J W + e J U + = u k + ; u k + 1 + ; u k + 2 + W = x k ; x k + 1 ; x k + 2 V = v k ; v k + 1 ; v k + 2 e J = e j ; e j ; e j R J = d i a g R j , R j , R j (18)

Based on the inverse system model (5), the future converter voltage u j − , j = k + 1 . . . k + 3 in Figure 3 can be calculated as u k + 1 − = = L v k + R j x k + 1 + e j u k + 2 − = L v k + 1 + R j x k + 2 + e j u k + 3 − = L v k + 2 + R j x k + 3 + e j u k − = u d k − u q k − ,   R j = R , − L ω 0 L ω 0 ,   R , e j = e 0 (19)

The prediction model (19) of converter voltage can be rewritten in matrix form. U − = L V + R J X + e J U − = u k + 1 − ; u k + 2 − ; u k + 3 − X = x k + 1 ; x k + 2 ; x k + 3 V = v k ; v k + 1 ; v k + 2 e J = e j ; e j ; e j R J = d i a g R j , R j , R j (20)

The future voltage amplitudes of the grid-side converter should not be greater than its rated voltage amplitude. Then, we have. u j + 2 = u d j + 2 + u q j + 2 ≤ u N 2 , j = k , . . . , k + 2 u j − 2 = u d j − 2 + u q j − 2 ≤ u N 2 , j = k + 1 , . . . , k + 3 (21)

As shown in Figure 3, at the moments of two control period T junctures (such as t = kT…t=(k+3)T), the output converter voltage u = u d , u q T will suddenly change due to the suddenly change of control input v = v d , v q T . The climbing of the converter voltage depends on the change of the control input which is denoted by Δ v = Δ v d , Δ v q T . Δ v d and Δ v d are coordinated restricted in order to avoid excessive transient climbing of converter voltage. Δ v j 2 = Δ v d j 2 + Δ v q j 2 ≤ Δ v max 2 ,   j = k , . . . , k + 2 Δ v k = v k − v k − 1 Δ v k + 1 = v k + 1 − v k Δ v k + 2 = v k + 2 − v k + 1 (22)

The square of the current amplitude is i 2 = i d 2 + i q 2 and the square of the converter voltage amplitude is u 2 = u d 2 + u q 2 . Based on d i d / d t = v d and d i q / d t = v q , the second derivative of i 2 can be calculated as d 2 i 2 / d t 2 = i d v d + 2 i q v q . Similarly, based on d u d / d t = R v d − ω L v q and d u q / d t = R v q + ω L v d , the second derivative of u 2 can be calculated as d 2 u 2 / d t 2 = 2 R v d − ω L v q 2 + 2 R v q + ω L v d 2 .

It can be seen that the second derivatives of both i 2 and u 2 are greater than or equal to 0. This means that during a control period T, the curves of both i 2 and u 2 are concave downward. The maximum values of i 2 and u 2 during a control period T will appear at the beginning and end instants of the control period. The square of the apparent power amplitude S 2 and the square of the current amplitude i 2 have the same characteristics. Therefore, it is only necessary to restrict the amplitude square of converter voltage, current and power at the beginning and end instants of each control period T such as constraint conditions (12), (15), (21). Even without the above reasons, since the MPC controller is discrete, it can only carry out discrete constraints on voltage, current and power.

The optimization objective is to minimize the deviations between the output values and reference values of the grid-side converter composite system’s active and reactive power. min ⁡ J = Δ Y T R Δ Y Δ Y = Y r e f − Y Y = y k + 1 ; y k + 2 ; y k + 3 Y r e f = y k + 1 r e f ; y k + 2 r e f ; y k + 3 r e f y k r e f = P k r e f , Q k r e f T ,   y k = P k , Q k T r = r P , 0 0 , r Q ,   R = d i a g r , r , r (23)

When the apparent power reference of the grid-side converter composite system lesser than its rated apparent power, the output values of active and reactive power can reach their reference values. If the apparent power reference is greater than rated apparent power, the priority of active and reactive power must be set and the party with lower priority cannot reach its reference.

This paper sets the priority of active and reactive power by setting the deviation coefficients r P and r Q . When r P is greater than r Q , it means that the active priority is higher. On the contrary, when r P is less than r Q , reactive power priority is higher. The party with higher priority can achieve greater amplitude and climbing.

According to the National standard of China “Technical Regulations for Wind Farm Access to Electric Power System, GB/T 19963.1-2021”, when the grid voltage change is in the domain of e < 0.9 e N or e > 1.1 e N , the wind farm should provide reactive power support for the grid voltage recovery, and when the grid voltage change is in the domain of 0.9 e N < e < 1.1 e N , the wind farm should withdraw reactive power support.

Therefore, in the proposed control strategy, according to the situation of the power grid and the PMSG wind turbine, the deviation coefficients r P and r Q . are automatically adjusted so that the proposed control strategy can adapt to different grid support scenarios. For example, when the grid voltage change is in the domain of 0.9 e N < e < 1.1 e N , the active power priority is set higher ( r P > r Q ), so that the PMSG wind turbine can carry out maximum wind energy capture and frequency support. When the grid voltage change is in the domain of e < 0.9 e N or e > 1.1 e N , the priority task of the PMSG wind turbine is to provide reactive power support for the grid voltage recovery, and of cause the reactive power priority is set higher ( r P < r Q ). The priority of active and reactive power can also be set according to other conditions, such as grid frequency or rotor speeds of the PMSG wind turbine.

The optimization problem of the MPC controller can be sort out as follows min ⁡ J V = Δ Y T R Δ Y s . t .   8 − 23 c i V ≤ 0 ,   i = 1 , ⋯ , m h j V = 0 ,   j = 1 , ⋯ , n (24) where c i V and h j V represent the inequality constraints and equality constraints in (8–23). The optimization variables V of the optimization problem (24) are V = v k ; ⋯ ;   v k + N C .

The optimization problem (25) is a convex optimization problem with a convex quadratic objective function and multiple convex quadratic constraints which can be solved in many ways. Specifically, a convex optimization problem can be sort out as the following general form. min ⁡ f x k s . t .   g i x k ≤ 0 ,   i = 1 , ⋯ , m h j x k = 0 ,   j = 1 , ⋯ , n (27) where x k is the set of optimization variables, and f x k is the objective function of the convex optimization problem. g i x k and h j x k represent inequality constraints and equality constraints of the convex optimization problem, respectively. The Lagrange function is defined as: L x k , λ i , μ j = f x k + ∑ i = 1 m λ i g i x k + ∑ j = 1 n μ j h j x k (28) where λ i and μ j are called Lagrange multipliers. The optimal solution of convex optimization problem (27) can be obtained by solving the KKT conditions (Xu et al., 2001). as follows. ∂ L ∂ x k = 0 ,   k = 1 , ⋯ , K ∂ L ∂ μ j = 0 ,   j = 1 , ⋯ , J λ i g i x k = 0 ,   i = 1 , ⋯ , m λ i ≥ 0 ,   i = 1 , ⋯ , m g i x k ≤ 0 ,   i = 1 , ⋯ , m (29)

In (29), equality constraints are used to solve the optimal solution, and inequality constraints are used to verify the optimal solution. It is worth mentioning that in addition to the above method, there are many solving methods (An, 2000) and mature commercial solvers for convex optimization problems. The commercial solvers (Gurobi optimization, 2023; IBM CPLEX Optimizer, 2023) can be used to solve convex optimization problems conveniently and quickly, without the need for users to write optimization programs.

In each sampling interval T, the actions of the MPC controller include measuring the system states, constructing and solving the optimization problem (8–23), and providing the optimal control variables (V_d and V_q) to the system. The flow of the MPC algorithm is shown in Figure 4.

The performance of the proposed active and reactive power coordinated control strategy is evaluated in this section by testing the tracking performance of the PMSG wind turbine to the active and reactive power step references. The references of active and reactive power are shown in Figure 5. In order to capture maximum wind energy, the active power reference remains at 2.5 MW unchanged. The grid voltage stays in the rated value at 0–0.2s and the reactive power reference is set as 0.1 MW at 0–0.2 s. While the grid voltage drops down to 50% of the rated value at 0.2 s and the duration is 0.6 s. According to the reactive current support requirements in grid codes [21], the reactive power reference is stepped from 0.1 MW to 1.35 MW at 0.2 s.

Three different scenarios are simulated in this section using MATLAB/Simulink.

S1: Active and reactive power are controlled using the MPC controller without coordinated restrictions and priority arrangement

The other conditions and parameters in the three simulated scenarios are the same. The parameters of the grid-side converter system are indicated in Table 1 (Yaramasu and Wu, 2014). The prediction horizon is set as five times control period T and the control horizon is set as four times control period T when simulating.

Figures 6–8 depict the power reference tracking results of the PMSG wind turbine in the three different scenarios. Due to the grid voltage droping down to 50% of the rated value at 0.2 s, the maximum apparent power of the PMSG wind turbine change from 3MW to 1.5 MW at 0.2 s. In Scenario S1, the active and reactive power coordinated restrictions and priority decisions are not considered. Regardless of the power grid status, the amplitude range and climbing range of active and reactive power are fixed and do not interfere with each other. Therefore, the PMSG wind turbine cannot guarantee reactive power output by reducing the active power output. Therefore, when the grid voltage drop, the reactive power of the PMSG wind turbine cannot meet the 1.35 MW reference which is the reactive power support requirement.

Amplitude coordinated restrictions and priority decisions of active and reactive power are considered in Scenario S2. When the grid voltage drops down to 50% of the rated value at 0.2s, the priority task of the PMSG wind turbine is to provide reactive power support for the grid voltage recovery, and of cause the reactive power priority is set higher. As shown in Figure 6, by reducing the amplitude of active power, the PMSG wind turbine can output 1.35 MW reactive power to meet the reactive power support requirements of the grid. That is why we say it is very necessary and meaningful to coordinately control the active and reactive power amplitude of the wind turbine under the background of grid support.

The proposed control strategy in this paper is simulated in Scenario 3 which considers amplitude and climbing coordinated restrictions and priority decisions between active and reactive power. Similarly to Scenario 2, the PMSG wind turbine can meet the reactive power support requirements of the grid when the grid voltage drops. The difference between Scenario 2 and Scenario 3 is that, the PMSG wind turbine shows a faster response speed in Scenario 3, which the dynamic time in Scenario 3 is 20 ms and it is 40 ms in Scenario 2. This demonstrates the superiority of the control strategy proposed in this paper.

Figures 9, 10 show the current climbing of the PMSG wind turbine in Scenario 2 and Scenario 3. It can be found that the active and reactive current climbing limit value of the PMSG wind turbine in Scenario 3 is larger than that in Scenario 2. The greater ability to climb allows the PMSG wind turbine to show faster response speed in response to a step change in the power reference value. The results explain why the PMSG wind turbine shows a faster response speed in Scenario 3. The simulation results verify that under the given apparent power/current climbing constraint, active and reactive power/current climbing coordinated restrictions allow PMSG wind turbines to perform a larger range of active and reactive power/current climbing.

The voltage of the grid-side converter is shown in Figure 11 when the PMSG wind turbine executes the proposed control strategy in Scenario 3. It is easy to see that the voltage amplitude does not exceed its maximum allowed value in the whole process. In addition, there are no sharp climb and spike in the voltage waveform, which can protect the grid-side converters and improve the electricity quality of the PMSG wind turbine. Hence, The voltage amplitude and climbing constraint model proposed in this paper is effective.

The three-phase current of the grid-side converter is shown in Figure 12 when the PMSG wind turbine executes the proposed control strategy in Scenario 3. The rated peak value of single-phase current is 0.816 kA. It is easy to see that the amplitudes of the three-phase current do not exceed the rated peak value 0.816 kA in the whole process. In addition, there are no sharp climb and spike in the three-phase current waveforms, which can protect the grid-side converters and improve the electricity quality of the PMSG wind turbine. Hence, The current amplitude and climbing constraint model proposed in this paper is effective.

Figure 13 shows the result of the PMSG wind turbine tracking a 3 MW step active power reference, which is simulated with different prediction horizons. As can be seen from Figure 13, when the prediction horizon is short (Np = 1), the output of the PMSG wind turbine exists the overshoot. This is because the MPC model in this paper contains constraints on the power climbing change. The active power output of the PMSG wind turbine has a large climbing in the early stage, and the climbing cannot be changed quickly after approaching the active power reference value, so overdrive occurs. When the prediction horizon is long, the MPC controller can predict the corresponding future multi-step power output under different control variables, and select the optimal control variable to avoid overshoot. It is worth mentioning that the longer the prediction horizon, the better the control effect. In the scenario, the control effect is exactly the same when Np = 5 as when Np = 9. It is worth mentioning that as the prediction horizon increases, the control effect will not get better. In the current scenario, the control effect is exactly the same when Np = 5 and Np = 9.

In the proposed MPC based control strategy, the priority of active and reactive power can be flexibly arranged by setting the deviation coefficients r P and r Q in the objective function. The steady-state amplitude of active and reactive power at 0.2–0.4s in Scenario 3 are displayed in Table 2, which is simulated with different deviation coefficients r P and r Q . Due to the grid voltage drops of 50% at 0.2 s, the maximum apparent power of the PMSG wind turbine changes from 3MW to 1.5 MW. Under the given 1.5 MW apparent power constraint, different priority settings will result in different active and reactive power outputs. So that the PMSG wind turbine can operate in different modes such as giving priority to the active power support/output, giving priority to the reactive power support/output, and giving the same/close priority to the active power support and the reactive power support. The MPC controller can flexibly set the priority of active and reactive power, so that the proposed control strategy can be flexibly applicated in different grid support scenarios.

Figures 14, 15 depict the power reference tracking results and the grid-side converter voltage of the PMSG wind turbine when the PMSG wind turbine is controlled by a PI controller in Scenario 4. It can be seen in Figure 14 that there are overshoots and steady-state errors existing when the PMSG wind turbine tracks the active power references. It is worth mentioning that increasing the integral parameter in the PI controller can eliminate steady-state errors, but can lead to larger overshoots. As can be seen in Figure 15, the grid-side converter voltage may exceed its rated value during the dynamic process, which may cause damage to the grid-side converter and degrade the power quality. In addition, the amplitudes of output power and the grid-side converter voltage continue to fluctuate during the steady state period. This means that the power quality of the PMSG wind turbine output is lower.

As shown in Figures 8–13, the MPC based active and reactive power coordinated control strategy proposed in this paper can enable one of active power and reactive power (the one with higher priority) to track its references perfectly with zero steady-state error, zero overshoot and transient dynamic process. The steady-state power curve and the steady-state voltage curve are smooth straight lines. The power amplitude constraint, power climbing constraint, power priority arrangement, voltage amplitude constraint and voltage ramp constraint set in the proposed control strategy have achieved the expected results. That is because the MPC controller is good at dealing with multi-input and multi-output control problems with complex constraints and specific objectives. The above complex constraints and specific objectives are difficult to implement by PI controllers.