A frequency-robust optimal H2 / H microgrid with energy storage ∞ Controller Design Methodology

Abstract

This invention discloses a frequency-robust optimal H2 / H ratio for a microgrid with energy storage. ∞ This invention addresses the frequency oscillation problem in microgrids caused by power output fluctuations from renewable energy sources such as wind and solar power, as well as load variations. It constructs a microgrid system that utilizes energy storage and hydropower units for frequency regulation. The introduction of energy storage batteries effectively improves the transient stability of the microgrid. Furthermore, this invention proposes using the LMI tool to solve for the output feedback robustness H2 / H. ∞ The controller is designed and its parameters are optimized using the Seagull intelligent algorithm to achieve optimal control performance. The designed controller is introduced into the secondary frequency regulation loop of the hydro-solar-storage microgrid. By controlling the output of the hydro-generator and the energy storage battery, the transient and steady-state operating characteristics of the system are improved, keeping the frequency deviation of the microgrid within the allowable range. This invention is characterized by a frequency control method based on the state-space model of the hydro-solar-storage microgrid, which takes into account the robustness and robust stability of the system and has both theoretical research and engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of microgrid technology, specifically relating to a robust optimal H2 / H ratio based on intelligent algorithm-optimized output feedback. ∞ Design method of microgrid frequency controller. Background Technology

[0002] With the increasing demand for electricity in today's society, the power industry faces challenges such as constructing high-cost power plants and transmission and distribution networks. Utilizing distributed energy sources such as wind, solar, and hydropower to supply electricity to some local loads to form microgrids is an important solution to this problem. However, due to the volatility of power output from renewable energy sources like wind and solar, as well as the randomness of power consumption on the load side, microgrid frequency oscillations are easily caused, severely impacting the quality of regional power supply. Therefore, researching control methods to improve the frequency stability of microgrids is of great significance.

[0003] To maintain frequency stability in microgrids, traditional methods employ PID control. While PID controllers are simple in principle and easy to implement, their robustness and stability are not ideal. Some literature utilizes fuzzy control to design a frequency controller, which exhibits good robustness to system parameter perturbations; however, its control accuracy cannot be guaranteed. Sliding mode control and active disturbance rejection control, among other modern control theories, have achieved good robustness and dynamic performance in microgrid frequency stability control. However, their computational processes are complex, and proving the stability of the algorithms themselves is challenging. Nevertheless, this demonstrates the vast potential of intelligent algorithms for microgrid frequency stability.

[0004] Robust theoretical control strategies are considered one of the best solutions for achieving good microgrid operation under unstable power output and load disturbances, but many robust controller designs only focus on H ∞ The robustness performance index is represented by the norm, but the H2 norm, which characterizes the robustness and stability of the system, is not considered. H2 / H ∞ Robust controllers balance robustness and dynamic stability. Their overall performance is closely related to the selection of the evaluation function matrix and norm weights. Traditional methods use empirical or trial-and-error methods for selection, which is not only labor-intensive but also difficult to find the optimal solution. Using intelligent algorithms to optimize robust controller parameters has become an important optimization direction in recent years. Summary of the Invention

[0005] To address the frequency fluctuation problem caused by power disturbances in microgrids, this invention provides a microgrid frequency robust optimal H2 / H with energy storage. ∞ The controller design method compensates for fluctuations in photovoltaic power and load by controlling the output of hydropower units and energy storage batteries, thereby stabilizing the microgrid frequency.

[0006] The technical solution of this invention is as follows:

[0007] A frequency-robust optimal H2 / H microgrid with energy storage ∞ A controller design method for addressing frequency stability issues caused by photovoltaic output and load fluctuations in a hydro-solar-storage microgrid includes the following steps:

[0008] Step 1: Establish a linear model of load frequency regulation for the hydro-solar-storage microgrid to obtain the state-space equations of the hydro-solar-storage microgrid;

[0009] Step 2: Based on robust H ∞ Multi-objective control principle, design of output feedback robust H2 / H based on LMI tool solution ∞ Controller; Step 3: Apply the Seagull intelligent algorithm to the robust controller Z2 / Z ∞ Optimizing the performance evaluation matrix parameters and performance weight norms yields the robust optimal H2 / H. ∞ Frequency controller.

[0010] Preferably, step 1 establishes a linear model of load frequency regulation for the hydro-solar-storage microgrid, obtaining the state-space equations of the hydro-solar-storage microgrid. The specific steps are as follows:

[0011] Step 1-1: First, establish a frequency variation model for the hydro-solar-storage microgrid. Power changes in the microgrid will cause frequency changes. The dynamic model signal analysis of frequency variation is as follows:

[0012]

[0013] ΔP=ΔP s -ΔP L

[0014] ΔP s =ΔP PV +ΔP HY +ΔP Be

[0015] Where: G MG (s) is the characteristic function of the frequency variation of the hydro-solar-storage microgrid; s represents the Laplace operator, the same below; M is the system's inertia constant; D is the system's damping constant; Δf is the system's frequency variation; ΔP represents the system power; ΔP s ΔP represents the total power output of the hydro-solar-storage microgrid; L Indicates the load of the hydro-solar-storage microgrid; ΔP HY ΔP is the output power of the turbine unit. PV It is the output power of the photovoltaic panel; ΔP Be This refers to the output power of the energy storage battery.

[0016] Steps 1-2: Analyze the output models of each power source.

[0017] a. Dynamic model of the water turbine

[0018] The turbine model can be divided into two parts: the governor and the prime mover. The characteristic function G of the governor is... y The signal analysis is as follows:

[0019]

[0020]

[0021]

[0022] Where: ΔX g T is the output of the turbine governor actuator; y and k y These represent the time constant and gain of the turbine servo unit, respectively; R is the primary frequency regulation droop coefficient of the microgrid; Δu y (s) represents the control signal applied to the turbine governor; Δu L This is the control signal passed through the low-pass filter; t is the simulation time.

[0023] In the turbine prime mover stage, the IEEE linearized model of the turbine is used, and its characteristic function G w (s) is represented as follows:

[0024]

[0025] In the formula: T w Let ΔP be the inertial time constant of the water flow. HY This refers to the output power of the water turbine unit.

[0026] b. Dynamic model of photovoltaic panels

[0027] Dynamic model and characteristic function G of photovoltaic panel output PV The signal analysis is as follows:

[0028]

[0029]

[0030] In the formula: T PV and k PV The time constant and gain of the photovoltaic panel; ΔS PV This indicates the power of solar energy.

[0031] c. Dynamic model of energy storage battery

[0032] Dynamic model and characteristic function G of energy storage battery output Be (s) is represented as follows:

[0033]

[0034]

[0035] In the formula: T Be and k Be These represent the time constant and gain of the energy storage battery, respectively; Δu Be This indicates the control signal applied to the energy storage battery;

[0036] Based on the above model analysis, a linear model for frequency regulation of the hydro-solar-storage microgrid is established, and the characteristic function of the LPF is as follows:

[0037]

[0038] In the formula: T L is the time constant of LPF.

[0039] Steps 1-3: Establish state-space equations based on the linear model of frequency regulation in a hydro-solar-storage microgrid.

[0040] The state-space model is a dynamic time-domain model with time as the independent variable. The state-space equation of the linear model for frequency regulation of a hydro-solar-storage microgrid is expressed as:

[0041]

[0042] In the formula: x is the state variable; u is the control input variable; w represents the system disturbance variable; y represents the system output variable; A is the system state space matrix, determined by the system parameters; B1 is the system disturbance matrix; B2 is the system control matrix; C y D is the system output matrix. y1 and D y2 These are the disturbance and control matrices, respectively, representing the system output.

[0043] Based on the aforementioned model structure analysis, these matrices take the following values:

[0044] x=[ΔδΔfΔX g ΔP HY ΔP PV ΔP Be Δu L ] T

[0045] w=[ΔP L ΔS PV ] T

[0046]

[0047]

[0048]

[0049] C y =[1 0 0 0 0 0 0]

[0050] D y1 =[0 0]D y2 =[0].

[0051] Preferably, step 2 is based on robust H ∞ Multi-objective control principle, design of output feedback robust H2 / H based on LMI tool solution ∞ The controller, the specific steps are as follows:

[0052] Step 2-1: First, Z2 / Z needs to be added to the state-space equations of the microgrid. ∞ Two sets of performance evaluation functions are used to establish H2 / H ∞ The state-space equations of control:

[0053]

[0054] In the formula: Z2, Z ∞ For H2, H ∞ Robust performance output evaluation function, C1, D 11 D 12 C2, D 21 D 22 Z2 / Z ∞ The performance evaluation matrices are defined as follows:

[0055] C1=diag([x(1) x(2) x(3) 0 0 0 0]);

[0056] C2=diag([x(5) x(6) x(7) 0 0 0 0]);

[0057] D 11 =D 21 =0

[0058] x(1) to x(8) in the matrix are the parameters to be determined in the evaluation matrix. The parameters x(1), x(2), x(3), x(5), x(6), and x(7) are used to track load changes and suppress disturbances by setting performance targets for the controlled output. The parameters x(4) and x(8) are used to suppress overshoot by limiting the rate of change of the load setpoint signal of the regulator.

[0059] For mixed H2 / H ∞ By introducing an output feedback controller into the control system such that u = K(s)y, the corresponding closed-loop system state-space equations are obtained as follows:

[0060]

[0061] In the formula: A cl =A+B2KC y B cl =B1;x cl =x;C cl1 =C1+D 12 KC y ;D cl1 =D 11 C cl2 =C2+D 22 KC y ;D cl2 =D 21 ;K=K(s).

[0062] Step 2-2, based on H2 / H ∞ The core of designing a robust output feedback controller based on state-space equations lies in minimizing the distance from w to Z2 / Z in the control loop of the aforementioned closed-loop system. ∞ The closed-loop root mean square gain, H2 / H ∞ The mathematical approach to controller design is to find a suitable controller K(s) that allows the system to transition from disturbance w to performance evaluation Z. ∞ The closed-loop transfer function T of the output wz∞ H of (s) ∞ The norm does not exceed a given upper bound γ to ensure the closed-loop system is robust to uncertainties entering from w, while also ensuring that the closed-loop transfer function T from w to Z2 is... wz2 To ensure a good level of robust stability, the H2 norm of (s) should be minimized. This can be described using the linear matrix inequality (LMI):

[0063] a. Optimal H ∞ Control performance metrics: from w to Z ∞ The closed-loop root-mean-square gain does not exceed γ. This condition can be expressed using the linear matrix inequality LMI as follows: if and only if there exists a symmetric matrix X. ∞ Make:

[0064]

[0065] X ∞ >0

[0066] In the formula, I is the identity matrix, and the same applies below; without loss of generality, let γ = 1.

[0067] b. Performance index of optimal H2 control: The H2 norm of the closed-loop transfer function from w to Z2 does not exceed ν. Similarly, using LMI, it can be expressed as if and only if D cl2= 0 and there exist two symmetric matrices X2 and Q such that:

[0068]

[0069]

[0070] Trace(Q) < v 2

[0071] In the formula: Trace(Q) means to find the trace of matrix Q, while there are no restrictions on v.

[0072] To address the manipulability within the LMI framework described above, and to satisfy generality, a single Lyapunov matrix X is defined such that X... ∞ =X2=X, the pole placement uses the default extreme left region, and combined with the above LMI equation, the mixture H2 / H is obtained. ∞ The controller needs to meet the performance requirement that all closed-loop poles of the controlled object lie in the left half-open complex plane. The overall performance can be represented by the following function, which is expressed as:

[0073]

[0074] In the formula, α and β represent H2 / H ∞ The performance norm weights, by configuring different values ​​of α and β, can yield robust controllers with different performance characteristics.

[0075] The above LMI-based objective can be solved using the hinfmix solver in the LMI toolbox of MATLAB.

[0076] Preferably, step 3 applies the Seagull intelligent algorithm to Z2 / Z ∞ Optimizing the performance evaluation matrix parameters and performance weight norms yields the robust optimal H2 / H. ∞ The frequency controller, the specific steps are as follows:

[0077] Step 3-1: Define the fitness function for Seagull Algorithm optimization.

[0078] This invention uses the ISE metric, commonly used in engineering, as the fitness function for Seagull Algorithm parameter optimization to improve the efficiency of the algorithm. The fitness function formula is as follows:

[0079]

[0080] In the formula, Δf is the frequency deviation of the system output; t is the simulation time.

[0081] Step 3-2: Apply the Seagull Algorithm to robust controller parameter optimization.

[0082] From the above robust H2 / H∞ From the controller solution process, we can see that Z2 / Z ∞ The performance evaluation matrices C1, C2, and D in the middle 11 D 12 D 21 D 22 The values ​​of the two weighting coefficients, α and β, directly affect the control performance of the controller. The traditional method is to select them using empirical or trial-and-error methods, which is not only labor-intensive but also makes it difficult to find the optimal solution.

[0083] This invention applies the Seagull intelligent algorithm to the optimization selection of parameters in solving robust controller problems. The optimization process can be roughly represented as follows: the algorithm generates a flock of seagull individuals, each carrying a value of the parameter to be determined. The values ​​carried by these individuals are then sequentially assigned to the performance evaluation matrices C1, C2, and D that affect the controller solution. 11 D 12 D 21 D 22 The undetermined coefficients and the two weighting coefficients α and β are used, and the corresponding robust output feedback controller K(s) is calculated using the LMI toolbox in Matlab. An disturbance condition is then introduced into the closed-loop system formed by the currently calculated robust controller K(s) to obtain the corresponding performance evaluation index. This performance index is used as the fitness value of each seagull in the improved seagull algorithm. After ranking the fitness values ​​of the population, the optimal seagull is selected. Based on the optimal individual, the seagull algorithm continues to iterate in the direction of reducing the fitness value until the condition for algorithm exit is met.

[0084] Substituting the obtained optimal weight coefficients and coefficient matrix into the system's state-space equations, the robust H2 / H is obtained by solving the corresponding linear matrix inequality (LMI). ∞ Output feedback controller K(s).

[0085] The beneficial effects of this invention are:

[0086] (1) To address the frequency oscillation problem caused by power output fluctuations and load changes in new energy sources such as wind and solar power in microgrids, a hydro-solar-storage microgrid system utilizing energy storage and hydropower units for frequency regulation was constructed. This invention innovatively proposes a robust H2 / H solution based on the LMI method. ∞ Compared to traditional weight function solving methods, the LMI (Low Motion Matrix) approach for output feedback controllers is more convenient and efficient. Furthermore, the Seagull intelligent algorithm is introduced into the controller solution process to evaluate the parameters of the evaluation matrix affecting the controller's performance and the H2 / H2 ratio. ∞ The norm weighting coefficients are optimized to achieve the best controller performance, effectively improving the H2 / H ratio. ∞ Frequency stability performance of hybrid robust output feedback controller in hydro-solar-storage microgrid.

[0087] (2) The controller design method of the present invention fully considers the impact of the uncertainty of power output from new energy sources such as wind and solar and the uncertainty of load fluctuation on the frequency of microgrids. The microgrid system with the controller designed by the present invention is superior to the traditional control in terms of robustness and frequency dynamic stability. The method is applicable to microgrid scenarios with hydropower-photovoltaic-energy storage batteries and local loads. The load and photovoltaic power output changes are unpredictable and highly volatile. It can also be extended to other new energy microgrid fields with energy storage regulating power sources.

[0088] (3) The robust H2 / H proposed in this invention ∞ Output feedback control avoids the drawback of state feedback control, which requires real-time acquisition of system state variables. By establishing a simple mathematical model of the controlled object, it overcomes the requirement of precise modeling of the controlled object in modern control theory, making controller design more effective and practical. Attached Figure Description

[0089] Figure 1 This is a design flowchart of the present invention.

[0090] Figure 2 A linear model for frequency regulation in microgrids;

[0091] Figure 3 For standard robust mixing of H2 / H ∞ Control principle diagram;

[0092] Figure 4 A flowchart for optimizing robust controller parameters for the algorithm;

[0093] Figure 5 Diagram showing interference between solar energy and load power;

[0094] Figure 6 This is a diagram showing the controller frequency control deviation response under power interference conditions. Detailed Implementation

[0095] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0096] Example 1

[0097] A frequency-robust optimal H2 / H microgrid with energy storage ∞ Controller design methodology, combined with Figure 1 It includes the following steps:

[0098] Step 1: Establish a linear model of load frequency regulation for the hydro-solar-storage microgrid to obtain the state-space equations of the hydro-solar-storage microgrid;

[0099] Step 1-1: Establish a frequency variation model for the hydro-solar-storage microgrid.

[0100] Power changes in a microgrid lead to frequency changes, and the dynamic model of frequency changes is represented by the following signal analysis:

[0101]

[0102] ΔP=ΔP s -ΔP L

[0103] ΔP s =ΔP PV +ΔP HY +ΔP Be

[0104] Where: G MG (s) is the characteristic function of the frequency variation of the hydro-solar-storage microgrid; s represents the Laplace operator; M is the system's inertia constant; D is the system's damping constant; Δf is the system's frequency variation; ΔP represents the system power; ΔP s ΔP represents the total power output of the hydro-solar-storage microgrid; L Indicates the load of the hydro-solar-storage microgrid; ΔP HY ΔP is the output power of the turbine unit. PV It is the output power of the photovoltaic panel; ΔP Be This refers to the output power of the energy storage battery.

[0105] Steps 1-2: Analyze the output models of each power source.

[0106] a. Dynamic model of the water turbine

[0107] The turbine model consists of two parts: a governor and a prime mover. The characteristic function G of the governor is... y The signal analysis is as follows:

[0108]

[0109]

[0110]

[0111] Where: ΔX g T is the output of the turbine governor actuator; y and k y These represent the time constant and gain of the turbine servo unit, respectively; R is the primary frequency regulation droop coefficient of the microgrid; Δu y (s) represents the control signal applied to the turbine governor; Δu L This is the control signal passed through the low-pass filter; t is the simulation time.

[0112] In the turbine prime mover stage, the IEEE linearized model of the turbine is used, and its characteristic function G w (s) is represented as follows:

[0113]

[0114] In the formula: T w Let ΔP be the inertial time constant of the water flow. HY This refers to the output power of the turbine unit;

[0115] b. Dynamic model of photovoltaic panels

[0116] Dynamic model and characteristic function G of photovoltaic panel output PV The signal analysis is as follows:

[0117]

[0118]

[0119] In the formula: T PV and k PV The time constant and gain of the photovoltaic panel; ΔS PV Indicates solar power output;

[0120] c. Dynamic model of energy storage battery

[0121] Dynamic model and characteristic function G of energy storage battery output Be (s) is represented as follows:

[0122]

[0123]

[0124] In the formula: T Be and k Be These represent the time constant and gain of the energy storage battery, respectively; Δu Be This indicates the control signal applied to the energy storage battery;

[0125] Based on the above model analysis, a linear model for frequency regulation of the hydro-solar-storage microgrid is established as follows: Figure 2 In the figure, LPF is a low-pass filter; Δu represents the second frequency modulation control signal; Δδ is the integral of the frequency deviation; the characteristic function of LPF is as follows:

[0126]

[0127] In the formula: T L The time constant of LPF;

[0128] Steps 1-3: Establish state-space equations based on the linear model of frequency regulation in a hydro-solar-storage microgrid.

[0129] according to Figure 2 A linear model of load frequency regulation for a hydro-solar-storage microgrid was developed. Seven state variables were selected, and the state-space equations of the system were derived based on the relationships between system parameters as follows:

[0130]

[0131] In the formula: x is the state variable; u is the control input variable; w represents the system disturbance variable; y represents the system output variable; A is the state space matrix, determined by the system parameters; B1 is the system disturbance matrix; B2 is the system control matrix; C y D is the system output matrix. y1 and D y2 These are the disturbance and control matrices, respectively, representing the system output.

[0132] Based on the aforementioned model structure analysis, these matrices take the following values:

[0133] x=[ΔδΔfΔX g ΔP HY ΔP PV ΔP Be Δu L ] T

[0134] w=[ΔP L ΔS PV ] T

[0135]

[0136]

[0137]

[0138] C y =[1 0 0 0 0 0 0]

[0139] D y1 =[0 0]D y2 =[0].

[0140] Step 2, Robust H2 / H based on LMI solution ∞ Controller Design

[0141] Step 2-1: First, Z2 / Z needs to be added to the state-space equations of the hydro-solar-storage microgrid. ∞ Two sets of performance evaluation functions are used to establish H2 / H ∞ The state-space equations of control:

[0142]

[0143] In the formula: Z2, Z ∞ For H2, H ∞ Robust performance output evaluation function, C1, D 11 D 12 C2, D 21 D 22 Z2 / Z ∞ The performance evaluation matrix for Z2 / Z ∞ Performance evaluation function matrices C1, C2, D 11 D 12 D 21 D 22 Defined as:

[0144] C1=diag([x(1) x(2) x(3) 0 0 0 0]);

[0145] C2=diag([x(5) x(6) x(7) 0 0 0 0]);

[0146] D 11 =D 21 =0

[0147] In the formula, x(1)…x(8) are undetermined matrix parameters and also weighting coefficients for system performance evaluation. Artificial intelligence optimization algorithms are used to change the weighting coefficients to select the optimal performance combination for system stability and frequency regulation accuracy. For the above formula H2 / H… ∞ By introducing an output feedback controller K(s) such that u = K(s)y, the corresponding closed-loop system state-space equations are obtained as follows:

[0148]

[0149] In the formula: A cl =A+B2KC y B cl =B1;x cl =x;C cl1 =C1+D 12 KC y ;D cl1 =D 11 C cl2 =C2+D 22 KC y ;D cl2 =D 21 K = K(s);

[0150] Step 2-2, Figure 3 For standard robust mixing of H2 / H ∞ Control principle diagram, based on H2 / H ∞ The core of designing a robust output feedback controller based on state-space equations lies in minimizing the distance from w to Z2 / Z in the control loop of the aforementioned closed-loop system. ∞ The closed-loop root-mean-square gain. H2 / H ∞ The mathematical approach to controller design is to find a suitable controller K(s) that allows the system to transition from disturbance w to performance evaluation Z. ∞ The closed-loop transfer function T of the output wz∞ H of (s) ∞ The norm does not exceed a given upper bound γ to ensure the closed-loop system is robust to uncertainties entering from w. Simultaneously, the closed-loop transfer function T from w to Z2 is such that... wz2 The H2 norm of (s) should be as small as possible to ensure that the robust stability of the system is at a good level. This can be described using the linear matrix inequality (LMI):

[0151] a. Optimal H ∞ Control performance metrics: from w to Z ∞ The closed-loop root-mean-square gain does not exceed γ. This condition can be expressed using the linear matrix inequality (LMI) as follows: if and only if there exists a symmetric matrix X. ∞ Make:

[0152]

[0153] X ∞ >0

[0154] In the formula, I is the identity matrix, and the same applies below; without loss of generality, let γ = 1;

[0155] b. Performance index of optimal H2 control: The H2 norm of the closed-loop transfer function from w to Z2 does not exceed ν. Similarly, using LMI, it can be expressed as if and only if D cl2 = 0 and there exist two symmetric matrices X2 and Q such that:

[0156]

[0157]

[0158] Trace(Q) < v 2

[0159] In the formula: Trace(Q) means to find the trace of matrix Q, while there are no restrictions on v.

[0160] To address the manipulability within the LMI framework described above, and to satisfy generality, a single Lyapunov matrix X is defined such that X... ∞=X2=X, the pole placement uses the default extreme left region, and combined with the above LMI equation, the mixture H2 / H is obtained. ∞ The controller needs to meet the performance requirement that all closed-loop poles of the controlled object lie in the left half-open complex plane. The overall performance can be represented by the following function, which is expressed as:

[0161]

[0162] In the formula, α and β represent H2 / H ∞ The performance norm weights, by configuring different values ​​of α and β, can yield robust controllers with different performance characteristics;

[0163] The above LMI-based objective can be solved using the hinfmix solver in the LMI toolbox of MATLAB.

[0164] Step 3: Apply the Seagull intelligent algorithm to optimize the parameters of the robust controller, thereby achieving optimal controller performance.

[0165] Step 3-1: This invention uses the ISE index, commonly used in engineering, as the fitness function for Seagull Algorithm parameter optimization to improve the efficiency of the algorithm optimization. The fitness function formula is as follows:

[0166]

[0167] In the formula, Δf is the frequency deviation of the system output; t is the simulation time.

[0168] Step 3-2: Apply the Seagull Algorithm to robust controller parameter optimization.

[0169] From the above robust H2 / H ∞ From the controller solution process, we can see that Z2 / Z ∞ The performance evaluation matrices C1, C2, and D in the middle 11 D 12 D 21 D 22 The values ​​of the two weighting coefficients, α and β, directly affect the control performance of the controller. Traditional methods use empirical or trial-and-error approaches to select these coefficients, which is not only labor-intensive but also makes it difficult to find the optimal solution. This invention applies the Seagull intelligent algorithm to optimize the selection of parameters in solving robust controller problems.

[0170] The optimization process is as follows Figure 4 As shown, it can be roughly represented as follows: The algorithm generates a flock of seagulls, each carrying 10 parameter values ​​to be determined. The values ​​carried by the individuals in this flock are then assigned sequentially to matrices C1, C2, and D. 11 D 12 D 21 D 22The undetermined coefficients and the two weight coefficients α and β are used to calculate the corresponding robust output feedback controller K(s) using the LMI toolbox in Matlab. Various disturbance conditions are introduced into the closed-loop system formed by the currently calculated robust controller K(s) to obtain the corresponding performance evaluation index. This performance index is used as the fitness value of each seagull in the improved seagull algorithm. After sorting the fitness values ​​of the population, the optimal seagull is selected. Based on the optimal individual, the seagull algorithm continues to iterate in the direction of reducing the fitness value until the condition for algorithm exit is met.

[0171] Perform simulation:

[0172] The simulated system parameters are: T y =0.08; k y =1;T w =0.5; T PV =1.8; k PV =1;T Be =0.1; k Be =1;T L =0.3; M=0.2; D=0.012;

[0173] The optimal coefficient matrix obtained after algorithm iteration is:

[0174] C1=diag([0.6718 0.189 0.097 0 0 0 0])

[0175]

[0176] C2=diag([0.9916 0.2007 0.2542 0 0 0 0])

[0177]

[0178] The two robust H2 / H values ​​obtained ∞ The optimal weighting coefficient is:

[0179] α = 0.5141 β = 0.1236

[0180] Substituting the obtained coefficient matrix into the system's state-space equations, the robust H2 / H can be obtained by solving the corresponding linear matrix inequality (LMI). ∞ The output feedback controller K(s) is:

[0181]

[0182] In the formula: n1=-28.23; n2=-1.513e06; n3=-4.745e07; n4=-4.631e08; n5=-1.656e09; n6=-2.94e09; n7=-3.815e09; n8=-1 .662e09; d1=1; d2=198.7; d3=1.037e05; d4=3.887e06; d5=-1.24e07; d6=-1.515e08; d7=3.734e09; d8=2.115e09.

[0183] Based on the above parameter settings, the SOA-H2 / H designed using the method of this invention will be... ∞ Controller and robust H2 / H using conventional self-tuning parameters ∞ The controller and a PID controller optimized using the same method were simulated and compared to obtain the controlled system's performance. Figure 5 The frequency deviation response under the power interference condition shown is as follows: Figure 6 As shown, simulation results demonstrate that the SOA-H2 / H obtained using the design method proposed in this invention... ∞ The robust controller exhibits strong robustness against external power disturbances; its damping characteristics, such as maximum overshoot, maximum steady-state error, and maximum settling time, are superior to those of the traditional H2 / H controller. ∞ Controllers and PID controllers.

[0184] This embodiment relies on the Seagull intelligent algorithm to optimize the controller operation. The key to solving the controller problem lies in the H2 / H... ∞ The controller achieves the target LMI criterion transformation and calls the LMI toolbox in MATLAB. The examples demonstrate the optimal H2 / H2 ratio proposed in this invention based on intelligent algorithm optimization. ∞ The output feedback robust controller has superior control performance in frequency control of hydro-solar-storage microgrids.

[0185] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent transformations or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A frequency-robust optimal H2 / H∞ controller design method for microgrid with energy storage, characterized in that, ∞ a controller design method characterized in that, Step 1: Establish a linear model for load frequency regulation of the hydro-solar-storage microgrid to obtain the state-space equations of the hydro-solar-storage microgrid. The specific steps are as follows: Step 1-1: Establish a frequency variation model for the hydro-solar-storage microgrid. Power changes in a microgrid lead to frequency changes, and the dynamic model of frequency changes is represented by the following signal analysis: In the formula: G MG (s) is the characteristic function of the frequency variation of the hydro-solar-storage microgrid; s represents the Laplace operator, the same below; M is the system's inertia constant; D is the system's damping constant; Δf is the system's frequency variation; ΔP represents the system power; ΔP s ΔP represents the total power output of the hydro-solar-storage microgrid; L Indicates the load of the hydro-solar-storage microgrid; ΔP HY ΔP is the output power of the turbine unit. PV It is the output power of the photovoltaic panel; ΔP Be This refers to the output power of the energy storage battery. Steps 1-2: Analyze the output models of each power source. a. Dynamic model of the water turbine The turbine model consists of two parts: a governor and a prime mover. The characteristic function G of the governor is... y The signal analysis is as follows: Where: ΔX g T is the output of the turbine governor actuator; y and k y These represent the time constant and gain of the turbine servo unit, respectively; R is the primary frequency regulation droop coefficient of the microgrid; Δu y (s) represents the control signal applied to the turbine governor; Δu L It is the control signal passed through the low-pass filter; t is time. In the turbine prime mover stage, the IEEE linearized model of the turbine is used, and its characteristic function G w (s) is represented as follows: In the formula: T w Let ΔP be the inertial time constant of the water flow. HY This refers to the output power of the turbine unit; b. Dynamic model of photovoltaic panels Dynamic model and characteristic function G of photovoltaic panel output PV The signal analysis is as follows: In the formula: T PV and k PV The time constant and gain of the photovoltaic panel; ΔS PV Indicates solar power output; c. Dynamic model of energy storage battery Dynamic model and characteristic function G of energy storage battery output Be (s) is represented as follows: In the formula: T Be and k Be These represent the time constant and gain of the energy storage battery, respectively; Δu Be This indicates the control signal applied to the energy storage battery; Based on the above model analysis, a linear model for frequency regulation of the hydro-solar-storage microgrid is established, with LPF as a low-pass filter. The characteristic function of LPF is as follows: In the formula: T L The time constant of LPF; Steps 1-3: Establish state-space equations based on the linear model of frequency regulation in a hydro-solar-storage microgrid. The state-space equation of the linear model for frequency regulation of a hydro-solar-storage microgrid is expressed as: In the formula: x is the state variable; u is the control input variable; w represents the system disturbance variable; y represents the system output variable; A is the system state space matrix; B1 is the system disturbance matrix; B2 is the system control matrix; C y D is the system output matrix. y1 and D y2 These are the disturbance and control matrices, respectively, representing the system output. Based on the aforementioned model structure analysis, these matrices take the following values: x=[ΔδΔfΔX g ΔP HY ΔP PV ΔP Be Δu L ] T w=[ΔP L ΔS PV ] T ； Step 2: Based on robust H ∞ Multi-objective control principle, design of output feedback robust H2 / H based on LMI tool solution ∞ The controller, the specific steps are as follows: Step 2-1: Add Z2 / Z to the state-space equations of the hydro-solar-storage microgrid. ∞ Two sets of performance evaluation functions are used to establish H2 / H ∞ The state-space equations of control: In the formula: Z2, Z ∞ For H2, H ∞ Robust performance output evaluation function, C1, D 11 D 12 C2, D 21 D 22 Z2 / Z ∞ The performance evaluation matrix is ​​defined as follows: ； ； D 11 =D 21 =0 x(1)~x(8) in the matrix are the parameters to be determined in the evaluation matrix; parameters x(1), x(2), x(3), x(5), x(6), and x(7) are used to track load changes and suppress disturbances by setting performance targets for the controlled output; parameters x(4) and x(8) are used to suppress overshoot by limiting the rate of change of the load setpoint signal of the regulator. For mixed H2 / H ∞ The control system introduces an output feedback controller K(s) such that u = K(s)y, resulting in the following closed-loop system state-space equations: In the formula: A cl =A+B2KC y B cl = B1; x cl = x;C cl1 = C1 +D 12 KC y ;D cl1 =D 11 C cl2 = C2 + D 22 KC y ;D cl2 = D 21 K = K(s); Step 2-2, based on H2 / H ∞ The core of designing a robust output feedback controller based on state-space equations lies in minimizing the distance from w to Z2 / Z in the control loop of the aforementioned closed-loop system. ∞ The closed-loop root mean square gain, H2 / H ∞ The mathematical approach to controller design is to find a suitable controller K(s) that allows the system to transition from disturbance w to performance evaluation Z. ∞ The closed-loop transfer function T of the output wz∞ H of (s) ∞ The norm does not exceed a given upper bound γ to ensure the closed-loop system is robust to uncertainties entering from w, while also ensuring that the closed-loop transfer function T from w to Z2 is... wz2 The H2 norm of (s) should be as small as possible to ensure that the robust stability of the system is at a good level. It is described by the linear matrix inequality (LMI): a. Optimal H ∞ Control performance metrics: from w to Z ∞ The closed-loop root-mean-square gain does not exceed γ. This condition is expressed by the linear matrix inequality (LMI) as follows: if and only if there exists a symmetric matrix X. ∞ Make: In the formula, I is the identity matrix, and the same applies below; without loss of generality, let γ=1; b. Performance index of optimal H2 control: The H2 norm of the closed-loop transfer function from w to Z2 does not exceed ν, and similarly expressed using LMI, it is given by the condition that D cl2 = 0 and there exist two symmetric matrices X2 and Q such that: In the formula: Trace(Q) means to find the trace of matrix Q, while there are no restrictions on v; Define a single Lyapunov matrix X such that X ∞ = X2 = X, the pole placement uses the default extreme left region, and combined with the above LMI equation, the mixture H2 / H is obtained. ∞ The controller needs to meet the performance requirement that all closed-loop poles of the controlled object lie in the left half-open complex plane. The overall performance can be represented by the following function, which is expressed as: In the formula, α and β represent H2 / H ∞ The performance norm weights, by configuring different values ​​of α and β, yield robust controllers with different performance characteristics; Step 3: Apply the Seagull intelligent algorithm to the robust controller Z2 / Z ∞ Optimizing the performance evaluation matrix parameters and performance weight norms yields the robust optimal H2 / H. ∞ The specific steps of the frequency controller are as follows: Step 3-1: Define the fitness function for Seagull Algorithm optimization. The ISE metric, commonly used in engineering, is adopted as the fitness function for parameter optimization in the Seagull Algorithm. The fitness function formula is as follows: In the formula, Δf is the frequency deviation of the system output; t is time; Step 3-2: Apply the Seagull Algorithm to robust controller parameter optimization. The specific process is as follows: A flock of seagulls is generated, each carrying a value of a parameter to be determined. The values ​​carried by the individuals in this flock are then sequentially assigned to the performance evaluation matrices C1, C2, and D that affect the controller solution. 11 D 12 D 21 D 22 The undetermined parameters and the two weight coefficients α and β are used to calculate the corresponding robust output feedback controller K(s) using the LMI toolbox in Matlab. Then, disturbance conditions are introduced into the closed-loop system formed by the currently calculated K(s) to obtain the corresponding performance evaluation index. This performance index is used as the fitness value of each individual seagull in the improved seagull algorithm. After sorting the fitness values ​​of the population, the optimal seagull individual is selected. Based on the optimal individual, the seagull algorithm continues to iterate in the direction of reducing the fitness value until the condition for algorithm exit is reached. Substituting the obtained optimal weight coefficients and coefficient matrix into the system's state-space equations, the robust H2 / H is obtained by solving the corresponding linear matrix inequality (LMI). ∞ Output feedback controller K(s).

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