Random model predictive control method suitable for wind power participating in grid frequency modulation

Abstract

The application relates to a random model predictive control method suitable for wind power participation in power grid frequency modulation, and belongs to the technical field of double-fed wind turbine participation in power grid frequency modulation control. The application aims to convert opportunity constraints into deterministic constraints according to distribution information of random disturbance, and finally obtains an optimal control law of fan additional power control of a system at a current time by solving the model, so that the random model predictive control method suitable for wind power participation in power grid frequency modulation is suitable for double-fed wind turbines to participate in power grid frequency modulation. The application is based on a frequency response model of a wind power grid-connected system to establish a predictive control state space model, and a CCSMPC controller applied to a double-fed wind turbine power reference value is designed on the basis, the controller obtains an optimal control law of a fan additional power increment of the system at the current time by solving a CCSMPC optimization model. The application provides a scientific and reasonable, highly applicable, good and random model predictive control (CCSMPC) method suitable for double-fed wind turbines to participate in power grid frequency modulation.

Description

Technical Field

[0001] This invention belongs to the field of doubly fed wind turbine generators participating in grid frequency regulation control technology. Background Technology

[0002] With the significant increase in installed wind power capacity, wind farm control and its impact on grid security and stability have become key research areas. Doubly fed induction generators (DFIGs) are one of the main types of wind turbines currently in use. They are connected to the grid via back-to-back converters, decoupling the generator speed from the grid frequency, preventing their output power from autonomously responding to grid frequency changes. As wind farms gradually replace traditional thermal power units, the system inertia decreases, reducing the overall grid's frequency regulation capability and seriously jeopardizing grid frequency stability. Therefore, how to adopt effective control strategies to enable DFIGs to participate in grid frequency regulation has attracted widespread attention from scholars and technicians.

[0003] The widely used frequency regulation strategy is virtual inertia integrated control, also known as proportional-derivative (PD) control. This strategy can effectively increase the minimum frequency of the system under constant wind speed and when a single frequency event occurs. However, the frequency regulation effect of this method is limited by the fixed gain coefficient. Therefore, some scholars have proposed a variable coefficient virtual inertia integrated control strategy to improve the control effect of doubly-fed induction generators (DFIGs) participating in grid frequency regulation. Compared with the steady PD control strategy, these improved control strategies have improved the frequency regulation capability of DFIGs to a certain extent. However, under the condition of random fluctuations in wind speed and load, they cannot quickly track changes in system power, and will produce large control deviations during the frequency regulation process. Summary of the Invention

[0004] The purpose of this invention is to transform chance constraints into deterministic constraints based on the distribution information of random disturbances, and finally obtain the optimal control law for the additional power control of the wind turbine at the current moment by solving the model, so as to enable the doubly fed wind turbine to participate in grid frequency regulation. This is a stochastic model predictive control method applicable to wind power participation in grid frequency regulation.

[0005] The steps of this invention are: S1. Establish the frequency response model of the wind power grid-connected system. The doubly fed wind turbine model is shown in equation (1). (1) In the formula: P m Capture mechanical power for the wind turbine; C p Wind energy capture factor; C p,n This is the rated wind energy capture factor; v This refers to the actual wind speed; v n Rated wind speed; The tip speed ratio; This is the rated tip speed ratio; β The pitch angle; oh r This refers to the fan speed; oh r,n This refers to the rated speed of the fan. v , oh r Real-time fluctuations are analyzed by performing a first-order Taylor expansion at the initial stable operating point of the wind turbine, yielding the small-signal increment form of the wind turbine's captured mechanical power as follows: (2) In the formula: ∆P m To capture changes in mechanical power of the wind turbine; ∆C p This represents the change in the wind energy capture coefficient. ∆v This represents the change in wind speed. v 0 Initial wind speed; C p,0 This is the initial wind energy capture factor; The final small-signal increment of the mechanical power captured by the fan in the integrated (2) formula is as follows: (3) In the formula: I see. r This represents the change in fan speed; k ω , k v After integration I see. r , ∆v Corresponding coefficients; The wind turbine generator section is equivalent to a first-order inertial element, and the asynchronous generator model is shown in equation (4): (4) In the formula: P e To output electromagnetic power to the fan; P ref The power setting value for the electrical components of the wind turbine; α p It is the first-order inertial constant; P MPPT The MPPT active power reference value is calculated based on rotational speed; ∆P Add active power to the wind turbine; K c This is the scaling factor for the maximum power tracking curve of the wind turbine; According to equation (4), the small-signal increment form of the wind power output electromagnetic power is obtained: (5) In the formula: ∆P e This refers to the change in the electromagnetic power output of the fan. The transmission chain adopts a single-mass model: (6) In the formula: H m Let be the inertial time constant of the mass; T m This refers to the mechanical torque of the asynchronous generator; T e The electromagnetic torque of the asynchronous generator; F The mass self-damping coefficient; According to equation (6), the small-signal increment form of the fan speed is obtained: (7) According to the frequency response model: (8) In the formula: M The inertial time constant of the synchronous machine; D This is the load damping coefficient; R For speed controller factor; The time constant of the speed controller; T t The turbine time constant; or This is the per-unit conversion factor for switching from wind turbines to thermal power units; ∆f It is the change in frequency; This represents the change in turbine output. For speed governor increment; ∆P L This refers to the change in load disturbance. S2. Constructing the CCSMPC frequency control prediction model Selecting the system frequency change ∆f Changes in turbine output Speed ​​governor increment Fan speed change I see. r Changes in wind power output electromagnetic power ∆P e As a state variable, the wind turbine's additional active power increment ∆P As a system control input, load disturbance change ∆P L and wind speed fluctuations ∆v As a random disturbance term of the system, the following state-space expression is established: (9) (10) (11) (12) In the formula: x ( t ), u ( t ), w ( t These are, respectively, the state variables, the control inputs, and the random disturbance terms; A f B f , G f The coefficient matrix of the continuous system model; Discretizing equation (9) using the forward Euler method yields the following prediction model: (13) In the formula: k+i|k Indicates the first k The sampling time for the future... k+i Make predictions at all times; A d , B d G d This is the transformed prediction model coefficient matrix; S3, State Feedback Control Law The expression for the state feedback control law is as follows: (14) In the formula: K This is the state feedback coefficient matrix; h For decision variables; N For prediction in the time domain; S4. Constructing the CCSMPC frequency control optimization model Construct the desired objective function as shown in equation (15): (15) In the formula: E [∙] indicates the expectation operation; J S The objective function is... P N For terminal penalty matrix; This is the weight matrix of the state variables; R u To control the input weight matrix; Consider the following deterministic constraints: (16) In the formula: ∆P emin ,∆P emax The upper and lower limits for adjusting the output power of the wind turbine; System frequency change ∆f Fan speed change I see. r System control input u The constraints are given in the form of chance constraints: (17) In the formula: ∆f min , ∆f max These are the upper and lower limits of frequency deviation; I see. rmin , I see. rmax These are the upper and lower limits of the rotational speed deviation; u min , u max To control the upper and lower limits of quantity changes; e f This is a parameter for the risk of system frequency deviation. e ωr For wind turbine speed deviation risk parameters; e u To control the risk parameters; Construct the following CCSMPC frequency control optimization model: (18) S5. Transform opportunity constraints into deterministic equivalences. When wind speed and load follow a normal distribution, i.e. ∆P L ~ N (0, s L 2 ), ∆v ~ N (0, s v 2 ), s L , s v These are the standard deviations of load disturbance and wind speed disturbance, respectively. Based on the distribution information of wind speed and load fluctuations, the inverse function of the distribution function can be used to calculate the rotational speed deviation. I see. r and system frequency deviation ∆f The opportunity constraint is transformed into a deterministic constraint through the following steps: First, the state variable chance constraints are integrated into the following form: (19) In the formula: T This is the state constraint coefficient matrix; t This is the state constraint matrix; z k+i|k This refers to the deterministic part of the predicted state; e k+i|k The uncertainty part of the predicted state follows a normal distribution with a mean of 0; State variable constraints are represented in the form of a normal distribution function: (20) In the formula: You k+i|k -t Let be a random variable that follows a normal distribution; Ф represents the normal distribution function; e u Risk parameters for the integrated state variables; Based on the monotonicity of the normal distribution function, the chance constraint is transformed into the following deterministic constraint: (twenty one) In the formula: Ф -1 This represents the inverse function of the normal distribution function; The control quantity will be determined through the above steps. u The opportunity constraint is transformed into a deterministic constraint: (twenty two) In the formula: D is the control constraint coefficient matrix; d is the control constraint matrix; Finally, based on the prediction model, the expected objective function and the deterministic equivalence after the chance constraint transformation, the final format of the CCSMPC optimization model as shown in Equation (18) is formed, and the quadprog function is called in Matlab to solve the optimization model to obtain the optimal control law of the wind turbine additional power increment at the current moment.

[0006] This invention provides a scientifically sound, highly applicable, and effective stochastic model predictive control (CCSMPC) method suitable for doubly-fed wind turbine units participating in grid frequency regulation. Attached Figure Description

[0007] Figure 1 This is a diagram of the grid-connected structure of a doubly fed wind turbine provided by the present invention; Figure 2 The frequency response model diagram of the wind power grid-connected system provided by this invention; Figure 3 The simulation system model diagram provided by this invention; Figure 4 The present invention provides a normally distributed random wind speed map; Figure 5The diagram shows the control effect of system frequency, wind turbine speed, and wind power when the wind speed follows a normal distribution and the load does not fluctuate, as provided by the present invention. Figure 6 The normal distribution load fluctuation diagram provided by this invention; Figure 7 The diagram shows the control effect of system frequency, wind turbine speed, and wind power when both wind speed and load follow a normal distribution, as provided by this invention. Detailed Implementation

[0008] The objective of this invention is achieved through the following technical solution: a stochastic model predictive control method suitable for doubly-fed induction generator (DFIG) wind turbines participating in grid frequency regulation. The method is characterized by establishing a stochastic predictive control state-space model based on the frequency response model of the wind power grid-connected system; constructing a CCSMPC stochastic optimization model with the minimum system frequency change as the control objective, considering system frequency, turbine speed, and chance constraints of control variables; transforming chance constraints into deterministic constraints based on the distribution information of random disturbances; and finally, obtaining the optimal control law for the additional power control of the turbine at the current moment by solving the model, thereby enabling the DFIG wind turbines to participate in grid frequency regulation.

[0009] This invention provides a stochastic model predictive control method for the additional power of doubly-fed induction generator (DFIG) wind turbines participating in grid frequency regulation. Based on the frequency response model of the wind power grid-connected system, a predictive control state-space model is established. On this basis, a CCSMPC controller is designed for the power reference value of the DFIG wind turbine. The controller obtains the optimal control law for the incremental additional power of the wind turbine at the current moment by solving the CCSMPC optimization model. The technical solution provided by this invention can suppress wind power fluctuations and improve system frequency stability under scenarios of random wind speed fluctuations, and can also effectively improve the frequency regulation performance of DFIG wind turbines under scenarios of random load fluctuations.

[0010] The further beneficial effects of this invention compared to the closest prior art are as follows: 1) CCSMPC can solve optimization problems with multiple objectives simultaneously and can explicitly handle input and output constraints. Furthermore, CCSMPC no longer makes decisions solely based on the system's current state information, but also considers the prediction time domain. N The prediction information within the time domain is based on the prediction time domain. N The CCSMPC can effectively suppress wind power fluctuations and reduce the system frequency standard deviation during the period when the doubly fed wind turbine participates in grid frequency regulation, making it more suitable for doubly fed wind turbines to participate in grid frequency regulation.

[0011] 2) CCSMPC adopts a state feedback control law, determines the optimal state feedback coefficient matrix through the LQR algorithm, and transforms the stochastic optimization model into a deterministic optimization model based on the distribution function information of random disturbances. Finally, it obtains the optimal control law for the wind turbine's additional active power increment at the current moment. This strategy can make full use of the probability information of random disturbances to make the optimal decision for the current moment of the system. It is sensitive to random disturbances of wind speed and load, can effectively track changes in grid power, and provide frequency support for the system.

[0012] 3) Simulation analysis results verified the effectiveness of the stochastic model predictive control method for additional power in grid frequency regulation of doubly-fed induction generator (DFIG) wind turbines. This strategy can effectively suppress wind power fluctuations and reduce the system frequency standard deviation in scenarios where wind speed follows a normal distribution and wind speed and load fluctuate simultaneously, thus improving system frequency stability. It is scientifically sound, highly applicable, and effective.

[0013] The present invention will be described in detail below: 1) Establish a frequency response model for wind power grid-connected systems To control the doubly-fed induction generator (DFIG) wind turbine using CCSMPC, a state-space model needs to be established based on the frequency response model of the wind power grid connection system. All models in this paper are built under a per-unit system, and the DFIG wind turbine model is shown in equation (1): (1) In the formula: P m Capture mechanical power for the wind turbine; C p Wind energy capture factor; C p,n This is the rated wind energy capture factor; v This refers to the actual wind speed; v n Rated wind speed; l The tip speed ratio; l n This is the rated tip speed ratio; β The pitch angle; oh r This refers to the fan speed; oh r,n This is the rated speed of the fan.

[0014] When the wind turbine operates below its rated speed, the blade pitch angle does not change, and the wind turbine is affected by random wind speed. v , oh r Real-time fluctuations are analyzed by performing a first-order Taylor expansion at the initial stable operating point of the wind turbine, yielding the small-signal increment form of the wind turbine's captured mechanical power as follows: (2) In the formula: ∆P m To capture changes in mechanical power of the wind turbine; ∆C p This represents the change in the wind energy capture coefficient; ∆v This represents the change in wind speed. v 0 Initial wind speed; C p,0 This represents the initial wind energy capture factor.

[0015] The final small-signal increment of the mechanical power captured by the fan in the integrated (2) formula is as follows: (3) In the formula: I see. r This represents the change in fan speed; k ω , k v After integration I see. r , ∆v Corresponding coefficient.

[0016] The wind turbine generator section is equivalent to a first-order inertial element, and the asynchronous generator model is shown in equation (4): (4) In the formula: P e To output electromagnetic power to the fan; P ref The power setting value for the electrical components of the wind turbine; α p It is the first-order inertial constant; P MPPT The MPPT active power reference value is calculated based on rotational speed; ∆P Add active power to the wind turbine; K c This is the scaling factor for the maximum power tracking curve of the wind turbine.

[0017] According to equation (4), the small-signal increment form of the electromagnetic power output by wind power can be obtained: (5) In the formula: ∆P e This represents the change in the electromagnetic power output of the fan.

[0018] The transmission chain adopts a single-mass model: (6) In the formula: H m Let be the inertial time constant of the mass;T m This refers to the mechanical torque of the asynchronous generator; T e The electromagnetic torque of the asynchronous generator; F is the self-damping coefficient of the mass.

[0019] According to equation (6), the small-signal increment form of the fan speed can be obtained: (7).

[0020] according to Figure 2 The frequency response model shown yields: (8) In the formula: M The inertial time constant of the synchronous machine; D This is the load damping coefficient; R For speed controller factor; T g The time constant of the speed controller; T t The turbine time constant; or This is the per-unit conversion factor for switching from wind turbines to thermal power units; ∆f It is the change in frequency; ∆P g This represents the change in turbine output. ∆X g For speed governor increment; ∆P L This represents the change in load disturbance.

[0021] 2) Constructing a CCSMPC frequency control prediction model according to Figure 2 The frequency response model shown selects the system frequency change. ∆f Changes in turbine output ∆P g Speed ​​governor increment ∆X g Fan speed change I see. r Changes in wind power output electromagnetic power ∆P e As a state variable, the wind turbine's additional active power increment ∆P As a system control input, load disturbance change ΔPL and wind speed fluctuations ∆v As a random disturbance term of the system.

[0022] The following state-space expression can be established. (9) (10) (11) (12) In the formula: x ( t ), u ( t ), w ( t These are, respectively, the state variables, the control inputs, and the random disturbance terms; A f B f , G f This is the coefficient matrix of the continuous system model.

[0023] Discretizing equation (9) using the forward Euler method yields the following prediction model: (13) In the formula: k+i|k Indicates the first k The sampling time for the future... k+i Make predictions at all times; A d , B d G d This is the coefficient matrix of the transformed prediction model.

[0024] 3) The CCSMPC control input adopts a state feedback control law. When state feedback control is used, state variable information is directly introduced into the control input. Based on the system's state equations and the Linear Quadratic Optimal Control (LQR) algorithm, the optimal feedback coefficient matrix K is obtained by solving the Riccati differential equation. The expression of the state feedback control law is as follows: (14) In the formula: K This is the state feedback coefficient matrix; h For decision variables; N For prediction in the time domain.

[0025] 4) Constructing the CCSMPC frequency control optimization model When applying CCSMPC to a doubly-fed wind turbine, the control objective is to minimize the system frequency deviation, wind power deviation, and control cost. The desired objective function can be constructed as shown in equation (15): (15) In the formula: E [∙] indicates the expectation operation; J S The objective function is... P N For terminal penalty matrix;Q x This is the weight matrix of the state variables; R u To control the input weight matrix.

[0026] Consider the following deterministic constraints: (16) In the formula: ∆P emin , ∆P emax This sets the upper and lower limits for adjusting the output power of the wind turbine.

[0027] Due to random fluctuations in wind speed and load, the system frequency changes. ∆f Fan speed change I see. r System control input u It is directly affected by random disturbances. ∆f , I see. r , u The constraints are given in the form of chance constraints: (17) In the formula: ∆f min , ∆f max These are the upper and lower limits of frequency deviation; I see. rmin , I see. rmax These are the upper and lower limits of the rotational speed deviation; u min , u max To control the upper and lower limits of quantity changes; e f This is a parameter for the risk of system frequency deviation. e ωr For wind turbine speed deviation risk parameters; e u To control the risk parameters.

[0028] Through the above processing, the following CCSMPC frequency control optimization model can be constructed: (18).

[0029] 5) Transform opportunity constraints into deterministic equivalences When wind speed and load follow a normal distribution, i.e. ∆P L ~ N (0, s L2 ), ∆v ~ N (0, s v 2 ), s L , s v These are the standard deviations of load disturbance and wind speed disturbance, respectively. Based on the distribution information of wind speed and load fluctuations, the inverse function of the distribution function can be used to calculate the rotational speed deviation. I see. r and system frequency deviation ∆f Opportunity constraints are transformed into deterministic constraints.

[0030] The specific steps are as follows: First, the state variable chance constraints are integrated into the following form: (19) In the formula: T This is the state constraint coefficient matrix; t This is the state constraint matrix; z k+i|k This refers to the deterministic part of the predicted state; e k+i|k The uncertainty component of the predicted state follows a normal distribution with a mean of 0.

[0031] Through the above processing, state variable constraints can be represented in the form of a normal distribution function: (20) In the formula: You k+i|k -t Let be a random variable that follows a normal distribution; Ф represents the normal distribution function; e u These are the risk parameters for the integrated state variables.

[0032] Based on the monotonicity of the normal distribution function, the chance constraint can be transformed into the following deterministic constraint: (twenty one) In the formula: Ф -1 It represents the inverse function of the normal distribution function.

[0033] Similarly, the control quantity can be adjusted through the above steps. u The opportunity constraint is transformed into a deterministic constraint: (twenty two) In the formula: D is the control constraint coefficient matrix; d is the control constraint matrix.

[0034] Finally, based on the prediction model, the expected objective function and the deterministic equivalence after the chance constraint transformation, the final format of the CCSMPC optimization model as shown in Equation (16) is formed, and the quadprog function is called in Matlab to solve the optimization model to obtain the optimal control law of the wind turbine additional power increment at the current moment.

[0035] In summary, the overall steps of the additional power frequency modulation strategy based on CCSMPC are as follows: (1) Establish the prediction model as shown in equation (13) through the wind power grid connection frequency response model; (2) Predict the state variables for the next 25 sampling times and use them for rolling optimization; (3) Based on the distribution information of random disturbances, the opportunity constraints are solved by combining the state feedback control law. The specific process is shown in equation (19-22). After processing, the opportunity constraints are transformed into deterministic equivalences. (4) In Matlab, call the quadprog function to solve the prediction model shown in equation (18) to obtain the additional power increment of the wind turbine. ∆P The optimal control sequence is determined, and its first value is applied to the wind turbine. (5) Use the new prediction information to solve the problem at the next sampling time and repeat the above steps.

[0036] Example The invention will be further described in detail using a doubly-fed wind power grid-connected system, and a model will be built using Matlab / Simulink software, such as... Figure 3 The simulated wind power grid-connected system includes three 133MW thermal power units and a wind farm consisting of 70 1.5MW doubly-fed induction generator (DFIG) wind turbines. The three thermal power units have identical parameters, as shown in Table 1. The frequency response model only considers the case of a single thermal power unit; for multiple units, simply increasing the dimension of the corresponding state variables is sufficient. The following two scenarios involving DFIG wind turbines participating in grid frequency regulation are analyzed: 1) When the wind speed follows a normal distribution and the load does not fluctuate, verify the effectiveness of the proposed CCSMPC additional power frequency modulation strategy.

[0037] 2) When wind speed and load fluctuate simultaneously and both follow a normal distribution, verify the effectiveness of the proposed CCSMPC additional power frequency modulation strategy.

[0038] The CCSMPC control method is compared with RMPC, MPC, and proportional-derivative control to verify its superior performance. In both cases, the weight matrices of each strategy are... Q x , R u They are all the same.Q x Frequency change on the main diagonal ∆f The weighting coefficient is 1, and the change in rotational speed is... I see. r Changes in wind power output electromagnetic power ∆P e The weight coefficient for is 0.01, and the weights for all other elements are 0. R u Set the value to 0.0001. Prediction time domain for each strategy. N The risk parameters for the SMPC control quantity are set to 25, with a unit sampling step size of 0.01s. e u Take 0.01 as the speed deviation risk parameter. e ωr Take 0.05 as the frequency deviation risk parameter. e f Take 0.05.

[0039] When wind speed fluctuates randomly while the load remains constant, a normally distributed white noise signal is used to simulate wind speed fluctuations. Figure 4 The wind speed sequence is a normally distributed random sequence with an average value of 9.5 m / s and a turbulence intensity of [missing value]. s v =1, simulation results are as follows Figure 5 As shown in the figure, when proportional-derivative (PD) control, MPC, RMPC, and CCSMPC are used in grid frequency regulation, the standard deviations of the system frequency are 0.006025, 0.004683, 0.004029, and 0.003483, respectively; and the standard deviations of wind turbine output are 0.009284, 0.007245, 0.006233, and 0.005380, respectively. These data indicate that compared with RMPC and MPC strategies, CCSMPC reduces both the system frequency and the mean wind turbine output, with the system frequency standard deviation decreasing by 13.55% and 25.62%, respectively, and the wind turbine output standard deviation decreasing by 13.69% and 25.74%, respectively. The system frequency curve shows that when the wind turbine adopts a PD control strategy, its frequency regulation effect is poor. This is because PD control is limited by a fixed gain coefficient, making it difficult to fully utilize the frequency regulation capability of the wind turbine. This also illustrates that proportional-derivative control is not an optimal strategy. When designing wind power frequency regulation strategies, the highly malleable nature of wind power output should be utilized to achieve rational utilization of wind power frequency regulation capabilities. Figure 4During periods of low wind speed fluctuation, the system frequency curves show that RMPC, MPC, and CCSMPC have comparable frequency regulation performance. However, as wind speed fluctuations intensify, CCSMPC begins to demonstrate its frequency regulation advantage. Observing the wind turbine output curve at this time reveals that the wind turbine using CCSMPC effectively smooths out wind power fluctuations during periods of severe wind speed fluctuations and reduces the impact of wind power randomness on the system frequency better than RMPC and MPC strategies. This is because CCSMPC considers the random uncertainty of wind speed in its design, and can use the probability distribution information of wind speed to process opportunity constraints, thereby improving the frequency regulation capability of the wind turbine. In contrast, traditional MPC does not consider the impact of random disturbances in its modeling, and its frequency regulation performance is slightly worse than RMPC and CCSMPC. RMPC only considers the worst-case scenario when random disturbances occur, and its control strategy design is more conservative than CCSMPC, reducing the frequency regulation performance of the wind turbine.

[0040] Even when wind speed and load fluctuate simultaneously, the following method is still adopted. Figure 4 The random wind speed sequence shown, while load fluctuations are... Figure 6 The simulation was performed using the normally distributed signal shown, with a load mean of 238MW. The simulation results are as follows: Figure 7 As shown, when the wind turbine employs proportional-derivative (PD) control, MPC, RMPC, and CCSMPC, the system frequency standard deviations are 0.01277, 0.009707, 0.008735, and 0.008087, respectively. These data indicate that the MPC, RMPC, and CCSMPC strategies significantly improve the frequency standard deviation compared to the PDR control strategy, with CCSMPC reducing the frequency standard deviation by 7.42% and 16.67% compared to RMPC and MPC, respectively. Combined with... Figure 6 and Figure 7 It can be seen that when the local load amplitude is too large or too small, the wind turbines under the CCSMPC strategy can always provide timely support for the system frequency, improving system frequency stability compared to other strategies. It should be noted that when wind speed and load fluctuate simultaneously, the system frequency deviation... ∆f Directly affected by random load fluctuations ∆P L Due to the impact of [the situation], the constraints are replaced with opportunity constraints, and the opportunity constraints are appropriately tightened by handling them. ∆f The constraints on the deterministic part of the predicted state can improve the frequency regulation performance of the unit.

[0041] Finally, to investigate the impact of CCSMPC risk parameters on the frequency regulation capability of wind turbines, 10 simulations were conducted for comparative analysis under the condition that wind speed and load fluctuate simultaneously and follow a normal distribution, controlling the risk parameters. e u Always set to 0.01, speed deviation risk parameter e ωrAlways set to 0.05, while the frequency deviation risk parameter e f The frequency standard deviations of the ten simulations were set to 0.05, 0.04, 0.03, 0.02, 0.01, 0.005, 0.004, 0.003, 0.002, and 0.001, respectively. The simulation results are shown in Table 2. Table 2 shows that an excessively small risk parameter actually reduces the frequency regulation performance of the wind turbine. The risk parameter can be appropriately increased, but it should not be too large, otherwise there may be a high probability of constraint violations, which is detrimental to the safety of the wind turbine. Therefore, it is necessary to appropriately select the risk parameter to improve the frequency regulation effect. Table 2 shows that a frequency deviation risk parameter of 0.005 has a better frequency regulation effect.

[0042] Table 1 Simulation Model Parameters

[0043] Table 2. Frequency Standard Deviation for Different Risk Parameters .

Claims

1. A stochastic model predictive control method suitable for wind power participation in grid frequency regulation, characterized in that: The steps are as follows: S1. Establish the frequency response model of the wind power grid-connected system. The doubly fed wind turbine model is shown in equation (1). （1） In the formula: P m Capture mechanical power for the wind turbine; C p Wind energy capture factor; C p,n This is the rated wind energy capture factor; v This refers to the actual wind speed; v n Rated wind speed; The tip speed ratio; This is the rated tip speed ratio; β The pitch angle; ω r This refers to the fan speed; ω r,n This refers to the rated speed of the fan. v , ω r Real-time fluctuations, when subjected to a first-order Taylor expansion at the initial stable operating point of the wind turbine, yield the following small-signal increment form of the wind turbine's captured mechanical power: （2） In the formula: ∆P m To capture changes in mechanical power of the wind turbine; ∆C p This represents the change in the wind energy capture coefficient. ∆v This represents the change in wind speed. v 0 Initial wind speed; C p,0 This is the initial wind energy capture factor; The final small-signal increment of the mechanical power captured by the fan in the integrated (2) formula is as follows: （3） In the formula: ∆ω r This represents the change in fan speed; k ω , k v After integration ∆ω r , ∆v Corresponding coefficients; The wind turbine generator section is equivalent to a first-order inertial element, and the asynchronous generator model is shown in equation (4): （4） In the formula: P e To output electromagnetic power to the fan; P ref The power setting value for the electrical components of the wind turbine; α p It is the first-order inertial constant; P MPPT The MPPT active power reference value is calculated based on rotational speed; ∆P Add active power to the wind turbine; K c This is the scaling factor for the maximum power tracking curve of the wind turbine; According to equation (4), the small-signal increment form of the wind power output electromagnetic power is obtained: （5） In the formula: ∆P e This refers to the change in the electromagnetic power output of the fan. The transmission chain adopts a single-mass model: （6） In the formula: H m Let be the inertial time constant of the mass; T m This refers to the mechanical torque of the asynchronous generator; T e The electromagnetic torque of the asynchronous generator; F The mass self-damping coefficient; According to equation (6), the small-signal increment form of the fan speed is obtained: （7） According to the frequency response model: （8） In the formula: M The inertial time constant of the synchronous machine; D This is the load damping coefficient; R For speed controller factor; The time constant of the speed controller; T t The turbine time constant; η This is the per-unit conversion factor for switching from wind turbines to thermal power units; ∆f It is the change in frequency; This represents the change in turbine output. For speed governor increment; ∆P L This refers to the change in load disturbance. S2. Constructing the CCSMPC frequency control prediction model Selecting the system frequency change ∆f Changes in turbine output Speed ​​regulator increment Fan speed change ∆ ω r Changes in wind power output electromagnetic power ∆P e As a state variable, the wind turbine's additional active power increment ∆P As a system control input, load disturbance change ∆PL and wind speed fluctuations ∆v As a random disturbance term of the system, the following state-space expression is established: （9） （10） （11） （12） In the formula: x ( t ), u ( t ), w ( t These are, respectively, the state variables, the control inputs, and the random disturbance terms; A f B f , G f The coefficient matrix of the continuous system model; Discretizing equation (9) using the forward Euler method yields the following prediction model: （13） In the formula: Indicates the first k The sampling time for the future... k+i Make predictions at all times; A d , B d G d This is the transformed prediction model coefficient matrix; S3, State Feedback Control Law The expression for the state feedback control law is as follows: （14） In the formula: K This is the state feedback coefficient matrix; h For decision variables; N For prediction in the time domain; S4. Constructing the CCSMPC frequency control optimization model Construct the desired objective function as shown in equation (15): （15） In the formula: This represents the expectation operation; J S The objective function is... P N For terminal penalty matrix; This is the weight matrix of the state variables; R u To control the input weight matrix; Consider the following deterministic constraints: （16） In the formula: ∆P emin , ∆P emax The upper and lower limits for adjusting the output power of the wind turbine; System frequency change ∆f Fan speed change ∆ω r System control input u The constraints are given in the form of chance constraints: （17） In the formula: ∆f min , ∆f max These are the upper and lower limits of frequency deviation; ∆ω rmin , ∆ω rmax These are the upper and lower limits of the rotational speed deviation; u min , u max To control the upper and lower limits of quantity changes; ε f This is a parameter for the risk of system frequency deviation. ε ωr For wind turbine speed deviation risk parameters; ε u To control the risk parameters; Construct the following CCSMPC frequency control optimization model: （18） S5. Transform opportunity constraints into deterministic equivalences. When wind speed and load follow a normal distribution, i.e. ∆P L ~ N (0, σ L 2 ), ∆v ~ N (0, σ v 2 ), σ L , σ v These are the standard deviations of load disturbance and wind speed disturbance, respectively. Based on the distribution information of wind speed and load fluctuations, the inverse function of the distribution function is used to calculate the rotational speed deviation. ∆ω r and system frequency deviation ∆f The opportunity constraint is transformed into a deterministic constraint through the following steps: （19） In the formula: T This is the state constraint coefficient matrix; t This is the state constraint matrix; This refers to the deterministic part of the predicted state; The uncertainty part of the predicted state follows a normal distribution with a mean of 0; State variable constraints are represented using a normal distribution function: （20） In the formula: Let be a random variable that follows a normal distribution; Ф represents the normal distribution function; ε u Risk parameters for the integrated state variables; Based on the monotonicity of the normal distribution function, the chance constraint is transformed into the following deterministic constraint: （21） In the formula: Ф -1 This represents the inverse function of the normal distribution function; The control quantity will be determined through the above steps. u The opportunity constraint is transformed into a deterministic constraint: （22） In the formula: D is the control constraint coefficient matrix; d is the control constraint matrix; Finally, based on the prediction model, the expected objective function and the deterministic equivalence after the chance constraint transformation, the final format of the CCSMPC optimization model as shown in Equation (18) is formed, and the quadprog function is called in Matlab to solve the optimization model to obtain the optimal control law of the wind turbine additional power increment at the current moment.

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