Wind turbine generator field-level power collaborative optimization control strategy considering wake effect
By optimizing the wake effect of wind turbines through the DMPC architecture and coordinating the control of wind turbine actuators, the problems of reduced wind energy capture efficiency and increased load caused by the wake effect are solved, thereby achieving power optimization and improved economic benefits of wind farms.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-11
- Publication Date
- 2026-04-10
AI Technical Summary
The wake effect in wind farms leads to a decrease in the wind energy capture efficiency of downstream wind turbines, increases turbine load, and causes power loss and reduced economic efficiency of wind farms.
A distributed model predictive control (DMPC) architecture is adopted to establish a mathematical model of the wind turbine and a wake model, which are then linearized and discretized. A wind farm control framework and a cluster decision cost function are designed to collaboratively optimize the operation of the wind turbine actuators.
It reduces the power capture loss of downstream wind turbines due to wake effects, increases the total power capture of the wind farm, reduces the fatigue load on wind turbine actuators, and improves the economic benefits and power quality of the wind farm.
Smart Images
Figure CN121840775A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of wind farm technology, and more specifically to a wind turbine field-level power collaborative optimization control strategy that takes into account the wake effect. Background Technology
[0002] As a typical representative of clean energy in China, wind power has seen its installed capacity and power generation steadily increase year by year. A wind farm typically consists of multiple wind turbines to generate a large amount of electricity. Upstream wind turbines extract kinetic energy from the ambient wind, leading to a decrease in wind speed in the downstream area. Simultaneously, the rotational disturbances of the upstream turbines mix with the ambient wind, increasing the turbulence intensity in the downstream area and creating a "low wind speed, high turbulence" wake effect. With the continuous expansion of the scale and capacity of onshore and offshore wind farms, the distance between wind turbines is relatively smaller, and the impact of the wake effect on the wind energy capture efficiency of the turbines becomes more severe, resulting in significant power losses in the wind farm and higher loads on downstream turbines. Enhancing the suppression of the wake effect in wind farms is beneficial for improving power point tracking accuracy, reducing mechanical losses of wind turbine units, improving economic efficiency, and enhancing power quality. Therefore, how to regulate the impact of the wake effect on the power capture of downstream wind turbines and research collaborative optimization strategies for wind farms' power commands to the dispatch center is of great significance for the economic efficiency and safety of wind farm operation and maintenance. Summary of the Invention
[0003] To address the aforementioned issues, this invention proposes a wind turbine farm-level power collaborative optimization control strategy that considers wake effects, aiming to reduce the weakening effect of wake effects on wind farm power generation and meet power control requirements under rated operating conditions. This method is based on a Distributed Model Predictive Control (DMPC) architecture. First, a numerical model is established based on the mechanical characteristics of the wind turbine actuators and transmission system. Second, a wake model is established considering the radial distribution characteristics of the wind turbine wake. Next, the established model is linearized. Finally, using the DMPC framework, a wind farm control framework and a cluster decision cost function are established to control the wind turbine actuators within the farm to work collaboratively.
[0004] The technical solution adopted by this invention to solve its technical problem is:
[0005] A wind turbine field-level power collaborative optimization control strategy considering wake effects includes the following steps:
[0006] Step 1: Establish a mathematical model for the wind turbine, including modeling the transmission system, the pitch angle actuator, the aeroelastic dynamics, and the asynchronous generator;
[0007] Step 2: Establish a numerical model of the wake, considering the radial and longitudinal distribution characteristics of the wake; establish a corrected model that considers the yaw angle;
[0008] Step 3: Complete the linearization and discretization of the wind turbine model and the wake numerical model. Linearization is performed using the first-order form of Taylor expansion, and discretization is completed by combining the backward Euler method. This discretization is then used as the prediction model for the controller.
[0009] Step 4: Design a wind farm power optimization strategy, set cost functions and constraints based on model predictive control, and achieve wind farm power scheduling through multi-machine collaboration.
[0010] Furthermore, step 1 is detailed as follows:
[0011] 1.1) Modeling of the wind turbine drive system
[0012] The shaft system of the wind turbine is modeled as follows:
[0013]
[0014]
[0015] It is the rotor's equivalent moment of inertia. It is the equivalent rotational inertia of the generator. It is the mechanical torque generated by the wind acting on the fan rotor. It is low-speed shaft torque. It is the generator torque. It is the angular velocity of the wind turbine rotor. It is the generator's angular velocity. It is the gear ratio of the fan gearbox.
[0016] Considering the flexible deformation of the low-speed shaft in the wind turbine drive train, the following mathematical model is established:
[0017]
[0018]
[0019]
[0020] in, It is the torsional stiffness coefficient. It is the torsional damping coefficient. It is the relative angular displacement between the two ends of the low-speed shaft.
[0021] 1.2) Modeling of the pitch angle actuator
[0022]
[0023] It is the inertial time constant of the pitch actuator. It is the reference pitch angle output by the controller. It is the actual pitch angle output by the pitch actuator.
[0024] 1.3) Aeroelastic Dynamics Modeling
[0025]
[0026]
[0027]
[0028] Here, It is aerodynamic thrust. It is air density. It is the blade radius. It is the power capture factor. It is the thrust coefficient. For the tip speed ratio, It is the rotor angular velocity. It is the wind speed acting on the plane of the wind turbine.
[0029] 1.4) Modeling of asynchronous generators
[0030]
[0031]
[0032] It is the generator's inertial time constant. It is the reference generator torque output by the controller. It refers to power generation capacity. It refers to generator efficiency.
[0033] Furthermore, step 2 is detailed as follows:
[0034] 2.1) Wake Model
[0035] This invention employs a single-wake flow model, as shown in the attached figure. Figure 1 As shown
[0036] The cross-sectional radius of the wake generated by the upstream wind turbine is related to the longitudinal distance between the upstream and downstream wind turbines as follows:
[0037]
[0038]
[0039] It is the radius of the wake section acting on the downstream wind turbine within the wake range of the upstream wind turbine. This indicates the radius of the wind turbine rotor. It is the longitudinal distance between the upstream and downstream wind turbines. The wake expansion rate, and These are the wheel hub height and the ground surface roughness, respectively.
[0040] The effective wind speed acting on downstream wind turbine j is:
[0041]
[0042] Let be the thrust coefficient of wind turbine i.
[0043] 2.2) Establish a corrected model that considers yaw angle.
[0044] Because wind turbines involve controlling the yaw angle, this action can adjust the direction of the wake generated by upstream wind turbines, accelerating the recovery of the inflow wind speed in front of the downstream wind turbine rotor. Since this angle affects the power capture capability of the wind turbine, the aforementioned aerodynamic expression needs to be updated:
[0045]
[0046] Where 'a' is the axial induction factor of the wind turbine. It's the yaw angle.
[0047] The revised expression is:
[0048]
[0049] It is the power factor loss correction factor. It is the yaw angle correction factor.
[0050] Step 3 is described in detail below:
[0051] 3.1) Model linearization:
[0052] set up ,for Its Taylor expansion is expressed as follows:
[0053]
[0054]
[0055] Here This refers to the value of the state variable at the operation point. This refers to the increment of the state variable relative to the operation point; similarly, the output of the system can be linearized.
[0056] Combining the linearization method described above, the state variables of this system are defined as follows: The output is The details are as follows:
[0057]
[0058]
[0059] The state-space equations that can be constructed are as follows:
[0060]
[0061]
[0062] in These are system control variables and disturbance variables, respectively.
[0063] 3.2) Model Discretization:
[0064] The above equations are discretized using the Euler method.
[0065]
[0066]
[0067] These represent the values of the state variables, control variables, and disturbance variables in the system's discrete equations at time k; These are the values of the system control quantity and the output quantity at time k+1, respectively.
[0068] Furthermore, step 4 is detailed as follows:
[0069] 4.1) Cost Function
[0070] The control framework described is attached. Figure 2 As shown
[0071] In order to meet the power dispatch command Y assigned by the wind turbine dispatch center dem (k), while considering the minimization of fatigue load on wind turbine units, is the objective cost function for wind farm design. :
[0072]
[0073] N is the control range of the controller, i represents the control step size of the controller, M represents the total number of wind turbines in the wind farm, and l represents the serial number of the wind turbine. This indicates the actual output power of the wind turbine. This indicates the output power command issued by the dispatch center to the wind turbine. This indicates the rate of change of the control variables for the wind turbine generator. , These represent the weight adjustment matrices for the quadratic forms of the output quantity and the quadratic forms of the control quantity, respectively.
[0074] 4.2) Constraints
[0075] Constraints are mainly divided into output constraints and control variable change rate constraints.
[0076] Pitch control and generator speed are typically constrained by physical limitations, with limitations on amplitude or rate. Meanwhile, to prevent overly aggressive control inputs and outputs, the controller constraints are set as follows:
[0077]
[0078] Here, and These represent the minimum and maximum output limits of the wind turbine, specifically including generator speed, low-speed shaft torque, tower bending moment, and generator power. and These represent the minimum and maximum limits of the rate of change of the control quantity, respectively.
[0079] By ensuring the cost function under constraints The minimum required is sufficient to ensure that all M wind turbine generators in the wind farm can fulfill their assigned power commands. Tracking enables coordinated power scheduling at the field level under the influence of wake effects.
[0080] The technical concept of this invention is as follows:
[0081] This invention discloses a wind turbine farm-level power collaborative optimization control strategy considering wake effects to reduce the weakening effect of wake effects on wind farm power generation, optimize wind farm power capture performance, and improve the economic benefits of wind farms. The method utilizes a distributed model predictive control architecture. First, a numerical model is established based on the mechanical characteristics of the wind turbine actuators and transmission system. Second, a wake model and a correction model considering yaw angle are established for the radial distribution characteristics of the wind turbine wake. Next, the established models are linearized. Finally, using the model predictive control framework, a wind farm control framework and a cluster decision cost function are established to control the wind turbine actuators within the farm to work collaboratively.
[0082] The beneficial effects of this invention are as follows:
[0083] 1) The strategy proposed in this invention takes into account the influence of the longitudinal and radial characteristics of the wake generated by the upstream wind turbine, thereby reducing the power capture loss of the downstream wind turbine.
[0084] 2) The strategy proposed in this invention can improve the total power capture of wind farms as a whole.
[0085] 3) The strategy proposed in this invention can reduce the fatigue load on wind turbine actuators such as pitch and yaw. Attached Figure Description
[0086] Figure 1 This is a schematic diagram of the wake model established in this invention;
[0087] Figure 2 This is a schematic diagram of the DMPC power control architecture of the present invention. Detailed Implementation
[0088] The present invention will be further described below with reference to the accompanying drawings.
[0089] A wind turbine field-level power collaborative optimization control strategy considering wake effects includes the following steps:
[0090] Step 1: Establish a mathematical model for the wind turbine, including modeling the transmission system, the pitch angle actuator, the aeroelastic dynamics, and the asynchronous generator;
[0091] 1.1) Modeling of the wind turbine drive system
[0092] The transmission system of a wind turbine is responsible for transmitting mechanical energy and torque. It is also a region with highly concentrated fatigue loads and one of the most prone to failure. A failure often necessitates the costly reinstallation of the wind turbine nacelle. This paper simplifies the wind turbine transmission system into a two-mass model using the lumped mass method. First, the equivalent mechanical torque... Transformation to the transmission system:
[0093]
[0094]
[0095] It is the rotor's equivalent moment of inertia. It is the equivalent rotational inertia of the generator. It is the equivalent mechanical torque generated by the wind exerted on the fan rotor. It is low-speed shaft torque. It is the generator torque. It is the angular velocity of the wind turbine rotor. It is the generator's angular velocity. It is the gear ratio of the fan gearbox.
[0096] Secondly, considering the flexible deformation of the low-speed shaft in the wind turbine generator drivetrain, the following mathematical model is established based on the above-mentioned drivetrain:
[0097]
[0098]
[0099]
[0100] in, It is the torsional stiffness coefficient. It is the torsional damping coefficient. It is the relative angular displacement between the low-speed shaft and the high-speed shaft.
[0101] 1.2) Modeling of the pitch angle actuator
[0102] Wind turbines adjust their pitch angle using a pitch angle actuator. When the pitch angle is 0, the wind turbine's energy capture efficiency is highest. As the pitch angle increases, wind curtailment worsens, and energy capture efficiency decreases. Normally, the pitch mechanism is hydraulically driven. In this invention, the pitch angle actuator is approximated with a slightly longer response time (…). First-order inertial element:
[0103]
[0104] It is the inertial time constant of the pitch actuator. It is the reference pitch angle output by the controller. It is the actual pitch angle output by the pitch actuator;
[0105] 1.3) Aeroelastic Dynamics Modeling
[0106] The energy output of a wind turbine depends on the energy captured by the turbine blades, which is significantly related to the blade airfoil, blade radius, and inflow wind speed. In this invention, the influence of blade airfoil on the energy capture of the wind turbine is not considered, and the aeroelastic dynamics are described as follows:
[0107]
[0108]
[0109]
[0110] In the formula, It is aerodynamic thrust. It is pi. It is air density. It is the radius of the wind turbine blades. , It is the power capture factor and thrust coefficient related to the blade pitch angle and tip speed ratio. For the tip speed ratio, It is the rotor angular velocity. It is the effective wind speed acting on the plane of the wind turbine;
[0111] 1.4) Modeling of Doubly Fed Asynchronous Generator
[0112] In this embodiment, the wind turbine referenced is a doubly-fed asynchronous wind turbine generator set, which is connected to the wind turbine drive system during operation and applies a reverse torque to the drive system. This invention approximates it as having a relatively fast response speed ( The first-order model (=0.02s):
[0113]
[0114]
[0115] It is the generator's inertial time constant. It is the reference generator torque output by the controller. It refers to power generation capacity. This is the generator efficiency, which we take as 0.95 in this paper.
[0116] Step 2: Establish a numerical model of the wake, considering the radial and longitudinal distribution characteristics of the wake; establish a corrected model considering the yaw angle.
[0117] 2.1) Wake Model
[0118] As attached Figure 1 The diagram illustrates the wake model used in this invention patent, which considers the two-dimensional characteristics of the wake in both longitudinal and transverse directions. Although its accuracy is not as high as simulation models such as large eddy simulation, it is suitable for engineering applications, taking into account wake deficit, wake expansion characteristics, and computational timeliness.
[0119] The cross-sectional radius of the wake generated by the upstream wind turbine is related to the longitudinal distance between the upstream and downstream wind turbines as follows:
[0120]
[0121]
[0122] It is the radius of the wake section acting on the downstream wind turbine within the wake range of the upstream wind turbine. This indicates the radius of the wind turbine rotor. It is the longitudinal distance between the upstream and downstream wind turbines. The wake expansion rate, and These are the wheel hub height and the ground surface roughness, respectively.
[0123] The effective wind speed acting on downstream wind turbine j is:
[0124]
[0125] Let be the thrust coefficient of wind turbine i.
[0126] In this embodiment, the impact of the wind turbine layout on the wind farm's wind energy capture efficiency is not considered, so the hub height is assumed to be... and surface roughness This is a constant value, and all the wind turbines are arranged longitudinally, with the spacing between each turbine being 10 times the radius of the rotor blades. =10R.
[0127] 2.2) Yaw Angle Model Update
[0128] Because wind turbines involve controlling the yaw angle, this action can adjust the direction of the wake generated by upstream wind turbines, accelerating the recovery of the inflow wind speed in front of the downstream wind turbine rotor. Since this angle affects the power capture capability of the wind turbine, the aforementioned aerodynamic expression needs to be updated:
[0129]
[0130] Where 'a' is the axial induction factor of the wind turbine. It's the yaw angle.
[0131] The revised expression is:
[0132]
[0133] It is the power factor loss correction factor. It is the yaw angle correction factor.
[0134] In this embodiment, the yaw angle is... As one of the control variables, it participates in the process of regulating wind field power, therefore, it is necessary to consider the equivalent power of aeroelasticity. Capture and express:
[0135]
[0136] Step 3: Complete the linearization and discretization of the wind turbine model and the wake numerical model. Linearization is performed using the first-order form of Taylor expansion, and discretization is completed by combining the backward Euler method. This discretization is then used as the prediction model for the controller.
[0137] 3.1) Model linearization:
[0138] Assumption ,for Its Taylor expansion is expressed as follows:
[0139]
[0140]
[0141] Refers to the system The value at the operation point, This refers to the increment of a state variable relative to an operation point; similarly, the output of the system can be linearized.
[0142] Combining the linearization method described above, the state variables of this system are defined as follows: The output is Meanwhile, the system's control variable is defined as The disturbance amount is The details are as follows:
[0143]
[0144]
[0145]
[0146]
[0147] The state-space equations that can be constructed are as follows:
[0148]
[0149]
[0150] , All about The function.
[0151] In this embodiment;
[0152]
[0153]
[0154] It is the system state matrix. It is a control matrix. It is the state perturbation matrix. It is the output feedthrough matrix.
[0155] 3.2) Model Discretization:
[0156] Discretize the above equations using the Euler method:
[0157]
[0158]
[0159] These represent the values of the state variables, control variables, and disturbance variables in the system's discrete equations at time k; These are the values of the system control quantity and the output quantity at time k+1, respectively.
[0160] Step 4: Design a wind farm power optimization strategy, set cost functions and constraints based on model predictive control, and achieve wind farm power scheduling through multi-machine collaboration.
[0161] 4.1) Cost Function
[0162] In order to meet the power dispatch command Y assigned by the wind turbine dispatch center dem (k), while considering the minimization of fatigue load on wind turbine units, is the objective cost function for wind farm design. :
[0163]
[0164] N is the control range of the controller, i represents the control step size of the controller, M represents the total number of wind turbines in the wind farm, and l represents the serial number of the wind turbine. This represents the actual output of the wind turbine. This indicates the output command sent from the dispatch center to the wind turbine. This indicates the rate of change of the control variables for the wind turbine generator. , These represent the weight adjustment matrices for the quadratic forms of the output and control quantities, respectively.
[0165] The instruction only includes the actual output power of the wind turbine. The command only contains the output power instruction sent by the dispatch center to the wind turbine. In this embodiment, the rated power of a single wind turbine is 5MW.
[0166] This represents the control quantity of the wind turbine. The rate of change during the operation of wind turbine generator sets.
[0167] 4.2) Constraints
[0168] Constraints include output constraints and control variable change rate constraints;
[0169] Due to practical physical limitations, pitch control and generator speed are typically subject to amplitude or rate constraints. Furthermore, to prevent overly aggressive control inputs and outputs, the controller constraints are set as follows:
[0170]
[0171] Here, and These represent the minimum and maximum output limits of the wind turbine, respectively, and only include the generator's output power; and These represent the minimum and maximum limits of the rate of change of the control quantity, respectively.
[0172] like Figure 2 The diagram shows the control framework proposed in this invention. This invention addresses the issue of cost functions. The rate of change of control variables was added, and constraints were imposed on them. The cost function was guaranteed under these constraints. The minimum required ensures that the pitch actuators, yaw angles, and generator torques of the M wind turbine generators within the wind farm can smoothly execute the allocated power commands within the execution constraints. The tracking of this data allows for the simultaneous maximization of coordinated power scheduling at the field level under the influence of wake effects, as described in this paper, while suppressing fatigue loads on actuators caused by severe fluctuations.
[0173] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the technical solutions of the present invention. Any technical solution that can be implemented based on the above embodiments without creative effort should be considered to fall within the scope of protection of the patent of the present invention.
Claims
1. A wind turbine field-level power collaborative optimization control strategy considering wake effect, characterized in that, Includes the following steps: Step 1: Establish a wind turbine model, including modeling the transmission system, the pitch angle actuator, the aeroelastic dynamics, and the asynchronous generator; Step 2: Establish a numerical model of the wake, considering the radial and longitudinal distribution characteristics of the wake; and based on the yaw angle between the rotor plane and the inflow wind speed, establish a modified model that considers the yaw angle. Step 3: Complete the linearization and discretization of the wind turbine model and the wake numerical model. Linearization is performed using the first-order form of Taylor expansion, and discretization is completed by combining the backward Euler method. This discretization is then used as the prediction model for the controller. Step 4: Design a wind farm power optimization strategy, set cost functions and constraints based on model predictive control, and achieve wind farm power scheduling through multi-machine collaboration.
2. The wind turbine field-level power collaborative optimization control strategy considering wake effect according to claim 1, characterized in that, Step 1 is described in detail as follows: 1.1) Transmission system modeling The shaft system of the wind turbine is modeled as follows: It is the rotor's equivalent moment of inertia. It is the equivalent rotational inertia of the generator. It is the mechanical torque generated by the wind acting on the fan rotor. It is low-speed shaft torque. It is the generator torque. It is the angular velocity of the wind turbine rotor. It is the generator's angular velocity. It is the gear ratio of the fan gearbox; Considering the flexible deformation of the low-speed shaft in the wind turbine drive train, the following mathematical model is established: in, It is the torsional stiffness coefficient. It is the torsional damping coefficient. It is the relative angular displacement between the two ends of the low-speed shaft; 1.2) Modeling of the pitch angle actuator It is the inertial time constant of the pitch actuator. It is the reference pitch angle output by the controller. It is the actual pitch angle output by the pitch actuator; 1.3) Aeroelastic Dynamics Modeling in, It is aerodynamic thrust. It is air density. It is the radius of the wind turbine blade. It is the power capture factor. It is the thrust coefficient. For the tip speed ratio, It is the rotor angular velocity. It is the wind speed acting on the plane of the wind turbine; 1.4) Modeling of asynchronous generators It is the generator's inertial time constant. It is the reference generator torque output by the controller. It refers to power generation capacity. It refers to generator efficiency.
3. The wind turbine field-level power collaborative optimization control strategy considering wake effect according to claim 1, characterized in that, Step 2 is described in detail below: 2.1) Establish a numerical model of the wake. Using a single wake model, the cross-sectional radius of the wake generated by the upstream wind turbine is related to the longitudinal distance between the upstream and downstream wind turbines as follows: It is the radius of the wake section acting on the downstream wind turbine within the wake range of the upstream wind turbine. This indicates the radius of the wind turbine rotor. It is the longitudinal distance between the upstream and downstream wind turbines. The wake expansion rate, and These are the wheel hub height and the ground surface roughness, respectively. The effective wind speed acting on downstream wind turbine j is: Let be the thrust coefficient of wind turbine i; 2.2) Establish a corrected model that considers yaw angle. Since wind turbines involve controlling the yaw angle, which adjusts the direction of the wake generated by upstream wind turbines and accelerates the recovery of the inflow wind speed in front of the downstream wind turbine rotor, and since the yaw angle affects the power capture capability of wind turbines, the aeroelastic dynamics expression is updated: Where 'a' is the axial induction factor of the wind turbine. It is the yaw angle; The revised expression is: It is the power factor loss correction factor. It is the yaw angle correction factor.
4. The wind turbine field-level power collaborative optimization control strategy considering wake effect according to claim 1, characterized in that, Step 3 is as follows: 3.1) Model linearization: set up ,for Its Taylor expansion is expressed as follows: Refers to the system The value at the operation point. This refers to the increment of a state variable relative to an operation point; similarly, the output of the system can be linearized. Based on the linearization described above, the state variables of the system are defined as follows: The output is The details are as follows: The state-space equations that can be constructed are as follows: in These are system control variables and disturbance variables, respectively. 3.2) Model Discretization: Discretize the above equations using the Euler method: These represent the values of the state variables, control variables, and disturbance variables in the system's discrete equations at time k; These are the values of the system control quantity and the output quantity at time k+1, respectively.
5. The wind turbine field-level power collaborative optimization control strategy considering wake effect according to claim 1, characterized in that, Step 4 is described in detail below: 4.1) Cost Function In order to meet the power dispatch command Y assigned by the wind turbine dispatch center dem (k), while considering the minimization of fatigue load on wind turbine units, is the objective cost function for wind farm design. : N is the control range of the controller, i represents the control step size of the controller, M represents the total number of wind turbines in the wind farm, and l represents the serial number of the wind turbine. This indicates the actual output power of the wind turbine. This indicates the output power command issued by the dispatch center to the wind turbine. This indicates the rate of change of the control variables for the wind turbine generator. , These represent the weight adjustment matrices for the quadratic forms of the output and control quantities, respectively. 4.2) Constraints Constraints include output constraints and control variable change rate constraints; Due to practical physical limitations, pitch control and generator speed are typically subject to amplitude or rate constraints. Furthermore, to prevent overly aggressive control inputs and outputs, the controller constraints are set as follows: Here, and These represent the minimum and maximum output limits of the wind turbine, specifically including generator speed, low-speed shaft torque, tower bending moment, and generator power. and These represent the minimum and maximum limits of the rate of change of the control quantity, respectively; By ensuring the cost function under constraints The minimum required is sufficient to ensure that all M wind turbine generators in the wind farm can fulfill their assigned power commands. Tracking enables coordinated power scheduling at the field level under the influence of wake effects.