Load frequency control method applied to multi-region power system with hopping parameters

Abstract

The invention relates to the technical field of electric power control systems, in particular to a load frequency control method applied to a multi-region electric power system with hopping parameters, which takes a multi-region Markov hopping power system model as an asynchronous Markov process, introduces a Markov superposition technology into the system model, and improves the load frequency control accuracy. Operation state switching caused by factors such as different load requirements, element faults, environment changes and complex external disturbance in practical application is described. This Markov overlay process has been attempted for the first time in a multi-zone interconnected power system. Therefore, according to the method, a traditional power system model is popularized, the proposed power system model better conforms to an actual application scene, and any initial strategy pair can be selected to initialize the proposed algorithm. The algorithm makes up for insufficient experience of operators and avoids certain potential safety hazards of an actual device. The problem that an existing load frequency control method is low in practicability is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of power control systems, and in particular to a load frequency control method applied to a multi-region power system with jump parameters. Background Art

[0002] In power systems, load frequency control (LFC) plays a vital role in ensuring a balance between the total power generation of the system's generator sets and the total demand of the power loads and system losses. The power balance between the generator sets and the loads is achieved by maintaining the frequency and power exchange between the generator sets and the loads within a set range in the presence of load variations and external disturbances. Therefore, reducing the LFC problem to a zero-sum differential game problem or an H-infinity problem has yielded fruitful results. In multi-area power systems, power exchange through tie lines increases the complexity of frequency regulation. Compared to centralized load frequency control schemes, decentralized load frequency control schemes that rely only on local area status information to mitigate frequency deviations are a more practical solution. This is especially true in scenarios where information transmission involves wide geographical distances, making it well suited to address such challenges.

[0003] As an important part of robust control, H-infinity control has been rapidly developed in recent years, and it has efficient anti-disturbance control performance. However, when faced with the difficulty of identifying the dynamics of the actual power system, it becomes difficult to achieve a balance between load frequency and disturbance. In addition, in actual power systems, sudden changes in system structure due to component failures and environmental mutations often occur. Therefore, it is considered to use Markov jump systems to describe the mutations of the system, realize the switching between different load operating conditions of the power system, and combine adaptive dynamic programming (ADP) to overcome the difficulties of unknown system dynamics.

[0004] Due to the needs of various backgrounds, most modern power systems are required to operate in multiple modes, such as the need to interact between different regions or switch to different frequency modes. In recent years, the research on switching power systems has made breakthrough progress. Markov jump power system, as a typical switching system, has also received widespread attention. However, there are two challenges in dealing with multi-region Markov jump power systems: 1) Each region has its own Markov jump process, and they are asynchronous with each other, but when we want to consider the Markov jump coupling in the entire system, how to characterize it becomes a challenge; 2) Most of the existing literature designs and studies the above-mentioned LFC problem with jumps based on linear matrix inequality (LMI), which relies on strict system dynamics information.

[0005] With the rapid advancement of technology, data-driven algorithms have made rapid leaps. Its biggest advantage is that it uses online or offline data obtained from the system to design the controller. Especially in the field of optimal control, it has also attracted a lot of attention. In general optimal control, as the scale and nonlinearity of the system increase, it becomes more and more challenging to establish an accurate system model. In this case, model-based methods are not feasible, so ADP technology and reinforcement learning (RL) have gained popularity with the powerful advantages of data-driven. When solving linear optimal control problems, researchers often use policy iteration algorithms to achieve this, and the key technology to achieve this process is experience replay technology (ERT). ERT can reuse the collected data and avoid waste of resources, so that implicit expressions can be solved efficiently and cleverly by combining the collected data. When the system dynamics characteristics of the interconnected system are unknown, the present invention will take advantage of the ERT algorithm and propose an ADP algorithm based on ERT to effectively implement LFC with Markov jump parameters. The Nash equilibrium solution of the two-person zero-sum game problem depends on the game algebra Riccati equation and the Hamilton-Jacobin-Isaacs equation. Due to the existence of nonlinear terms, the solution of these two equations is relatively difficult. In recent years, many iterative solutions have emerged based on ADP. However, the disadvantage of the above algorithm is that it first needs to provide an initial stable control gain matrix and a perturbation gain matrix, which depends largely on the prior knowledge of the system dynamics. Summary of the invention

[0006] The purpose of the present invention is to provide a load frequency control method applied to a multi-area power system with jump parameters, aiming to solve the problem of low practicality of existing load frequency control methods.

[0007] To achieve the above object, the present invention provides a load frequency control method applied to a multi-region power system with jump parameters, comprising the following steps:

[0008] Establishing a mathematical model of an interconnected jump power system and using the mathematical model to perform modeling;

[0009] Define the performance index function, solve the optimal control gain pair according to the optimal control theory, and derive the game algebraic Riccati equation with jump parameters;

[0010] A new algorithm is designed to weaken the condition that the traditional policy iteration algorithm needs an initial stable control gain pair, and a rigorous proof is given using mathematical induction.

[0011] Analyze the stability and convergence of the new algorithm;

[0012] A two-region interconnected RDLFC with Markov jump parameters is simulated, and the effectiveness of the algorithm in solving the game algebraic Riccati equation is verified.

[0013] Among them, in "establishing a mathematical model of the interconnected jump power system and using the mathematical model for modeling", it includes: introducing a random jump process, using {r i (t), t≥0} to describe the sudden change of the actual power system i={1,2,…,N}.

[0014] Among them, in "defining the performance index function, solving the optimal control gain pair according to the optimal control theory, and deriving the game algebraic Riccati equation with jump parameters", it includes: defining the infinite time domain performance index as:

[0015]

[0016] in The following Hamiltonian function is defined:

[0017]

[0018] Among them, in "Designing a new algorithm to weaken the condition that the traditional policy iteration algorithm requires an initial stable control gain pair, and using mathematical induction to give a rigorous proof", it includes: giving a lemma to solve the condition that the initial stable control gain pair is required:

[0019] set up For any given symmetric positive definite matrix, For any pair of gain matrices (not necessarily Hurwitz stable), for all m∈M, k=0,1,...

[0020] (i) Update the symmetric positive definite matrix by solving

[0021]

[0022] in:

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] (ii) Update

[0030]

[0031] Then for k=0,1,2,...,κ,..., not only is Hurwitz stable, and is the only positive solution.

[0032] Among them, in "combining online data collection, and then using experience playback technology to implement the algorithm online, successfully solving the optimal control gain", including:

[0033] To obtain the appropriate constants online The RDLFC system can be rewritten as: in:

[0034]

[0035] Then consider By taking derivatives and integrating along the system and combining the ERT technology transformation, we can get: in:

[0036]

[0037]

[0038] t0<t1<...<t f Represents different sampling time instants.

[0039] Among them, in "stability and convergence analysis of the algorithm", it includes:

[0040] Convergence Theorem: For any initial strategy pair When k→∞, the sequence given by Algorithm 1 and Converge to and

[0041] Stability Theorem: Algorithm 1 gives The random stability of the system with disturbance level γ is guaranteed during the iteration process.

[0042] Among them, in "Simulating the two-region interconnected RDLFC with Markov jump parameters and verifying the effectiveness of the algorithm in solving the game algebraic Riccati equation", it includes: simulating the two-region interconnected RDLFC with Markov jump parameters and verifying the effectiveness of the algorithm in solving the game algebraic Riccati equation.

[0043] The load frequency control method applied to a multi-region power system with jump parameters of the present invention establishes a mathematical model of an interconnected jump power system and uses the mathematical model for modeling; defines a performance index function, and solves the optimal control gain pair according to the optimal control theory, and at the same time obtains the game algebraic Riccati equation with jump parameters; designs a new algorithm to weaken the condition that the traditional strategy iteration algorithm requires an initial stable control gain pair, and uses mathematical induction to give a rigorous proof; combines online data acquisition, and then uses the experience playback technology to implement the algorithm online, successfully solving the optimal control gain; performs stability and convergence analysis on the algorithm; simulates a two-region interconnected RDLFC with Markov jump parameters, and verifies the effectiveness of the algorithm in solving the game algebraic Riccati equation. The present invention regards the multi-region Markov jump power system model as an asynchronous Markov process, which is more general than the existing LFC system model; in particular, the Markov superposition technology is cleverly introduced into the system model, which depicts the operating state switching caused by different load demands, component failures, environmental changes, complex external disturbances and other factors in practical applications. This Markov superposition process was attempted for the first time in a multi-region interconnected power system. It can be seen that the present invention generalizes the traditional power system model, and the proposed power system model is more in line with actual application scenarios. A new algorithm for solving the zero-sum game Nash equilibrium solution is proposed. Unlike the traditional policy iteration-based algorithm that requires an initial stable policy pair, this initial condition is eliminated, and any initial policy pair (not necessarily stable) can be selected to initialize the proposed algorithm. In addition, the algorithm makes up for the lack of experience of the operator and avoids certain safety hazards of the actual device. The proposed algorithm is implemented online in combination with ADP technology. In order to further improve data utilization and save computing resources, ERT is applied to the efficiency of online solution of the optimal control strategy pair for Markov jump power systems. In particular, this advantage makes our algorithm more suitable for scenarios where the system dynamic information is unknown; thereby solving the problem of low practicality of existing load frequency control methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0045] Figure 1 is the schematic diagram of the power system in the ith region with Markov jump parameters.

[0046] Figure 2 yes Convergence effect diagram.

[0047] Figure 3 yes Convergence effect diagram.

[0048] Figure 4 yes Convergence effect diagram.

[0049] Figure 5 is u i (t) and w i (t)Effect diagram.

[0050] Figure 6 It is a diagram of the jump process of each area and the Markov superposition technology.

[0051] Figure 7 is the power system state response x i (t).

[0052] Figure 8 It is a flow chart of a load frequency control method applied to a multi-region power system with jump parameters provided by the present invention. DETAILED DESCRIPTION

[0053] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0054] See also Figures 1 to 8 The present invention provides a load frequency control method applied to a multi-region power system with jump parameters, comprising the following steps:

[0055] S1 establishes a mathematical model of the interconnected jump power system and uses the mathematical model to perform modeling;

[0056] Specifically, a mathematical model that can accurately describe the dynamic behavior of the multi-regional power system is constructed, taking into account the possible parameter jumps in the system; this step is the basis of the algorithm, ensuring that the model can reflect the complexity and uncertainty of the actual system. A random jump process is introduced, using {r i (t), t≥0} to describe the sudden change of the actual power system i={1,2,…,N}. Specifically, assuming r i (t) is a continuous-time discrete-state Markov process whose finite space set is M i ={1,2,…,M i}, the associated transition probability is defined as:

[0057]

[0058] Among them, h>0 and is the mode m from time t i Mode j at time t+h i The transition rate, and for m i ∈M i ,

[0059] The transition rate matrix of the process is defined as

[0060] Table 1 Physical meaning of system parameters in the ith region

[0061]

[0062] In order to simplify the RDLFC subsystem model into a linear time-invariant model, we define it as follows:

[0063] x i (t) = [Δf i (t),ΔP gi (t),ΔX gi (t),ΔE i (t),Δδ i (t)] T ,

[0064]

[0065] Taking into account the jump process, the equation is re-described as follows:

[0066]

[0067] in and They represent the power system state, control input and load disturbance of the ith power subsystem in the power grid. For simplicity, they are denoted as r i (t) = m i , then and Denoted as and

[0068] In actual power systems, the uncertainty and unidentifiability of dynamic information are inevitable and cannot be ignored. Therefore, we further assume that the matrix and It's all completely unknown.

[0069] Considering the frequency fluctuations of other interconnected systems as part of the interference, the mathematical model of the i-th region can be reconstructed as:

[0070]

[0071] in

[0072]

[0073] As we all know, each region has its own Markov jump process {r i (t), t≥0}, they are asynchronous with each other in the multi-region Markov power system, the multi-region jump coupling superposition is integrated, and the Markov superposition technique is applied to treat the asynchrony as artificial synchronization. Its advantage is that the multi-region Markov process is modeled in an overall Markov jump framework. The following theorem is crucial to solve the above problem.

[0074] In addition, as mentioned above, the processed space M = M1∪M2∪…∪M N The Markov superposition jump process on is represented by r(t), and the corresponding transition probability matrix is ​​expressed as in is the Kronecker sum operation.

[0075] Then, the system is expanded by integrating N regions equivalently, which can be modeled as:

[0076]

[0077] where x(t) = [x1(t), x2(t), …, x N (t)],u(t)=[u1(t),u2(t),…,u N (t)],

[0078]

[0079]

[0080] Then the decentralized control system model of the i-th region is:

[0081] S2 defines the performance index function and solves the optimal control gain pair according to the optimal control theory, and at the same time obtains the game algebraic Riccati equation with jump parameters;

[0082] Specifically, based on the optimal control theory, a performance index function is defined to evaluate the system control effect. By solving the performance index function, the optimal control gain pair is obtained, and then the game algebraic Riccati equation with jump parameters is derived; this step is the core of the algorithm, which determines the control target and optimization direction, and provides a theoretical basis for subsequent algorithm design; the infinite time domain performance index is defined as:

[0083]

[0084] in The following Hamiltonian function is defined:

[0085]

[0086] The optimal Nash equilibrium solution is:

[0087]

[0088] and will be the only positive definite solution to the following equation:

[0089]

[0090] S3 designs a new algorithm to weaken the condition that the traditional policy iteration algorithm requires an initial stable control gain pair, and gives a rigorous proof using mathematical induction;

[0091] Specifically, a new algorithm is developed to reduce the dependence on the initial stable control gain pair and improve the robustness of the algorithm. This step solves the problem of the traditional algorithm being sensitive to initial conditions through algorithm innovation and enhances the practicality of the algorithm. A lemma is given to solve the condition that the initial stable control gain pair is required:

[0092] set up For any given symmetric positive definite matrix, For any pair of gain matrices (not necessarily Hurwitz stable), for all m∈M, k=0,1,…

[0093] (i) Update the symmetric positive definite matrix by solving

[0094]

[0095] in:

[0096]

[0097] (ii) Update

[0098]

[0099] Then for k=0,1,2,…,κ,…, not only is Hurwitz stable, and is the only positive solution.

[0100] S4 combines online data collection and then uses experience playback technology to implement the algorithm online and successfully solve the optimal control gain;

[0101] Specifically, combined with online data collection, experience playback technology is used to simulate historical data to achieve online update and optimization of the algorithm; this step realizes real-time interaction between the algorithm and the actual system, improves the adaptability and real-time performance of the algorithm; in order to obtain appropriate constants online The RDLFC system can be rewritten as: in:

[0102]

[0103] Then consider By taking derivatives and integrating along the system and combining the ERT technology transformation, we can get: in:

[0104]

[0105]

[0106] t0<t1<…<t f Represents different sampling time instants.

[0107] Algorithm 1: Zero-sum differential game RDLFC improved ADP algorithm based on experience replay technology

[0108] Step 1: Create an experience replay buffer

[0109] Given any matrix pair application and To collect data and in and To explore noise.

[0110] Step 2: Get

[0111] (a) Initialize the positive definite matrix sequence and

[0112] (b) Calculate according to the formula

[0113] (c) If If it is a positive definite matrix, go to Step 3; otherwise, increase And repeat Step 2(b).

[0114] Step 3: Obtain the initial stable gain matrix pair

[0115] (a) Update using Step 2

[0116] (b) Update according to the formula and

[0117] (c) If Then go to Step 3(d); otherwise, let k←k+1 and repeat Step 3(b);

[0118] (d) Output the initial gain matrix pair

[0119] Step 4: Get the optimal gain pair

[0120] (a) Initialize k←0 and set

[0121] (b) Update and Then calculate and

[0122] (c) If If ε is a small positive number, go to Step 4(d); otherwise, let k←k+1 and repeat Step 4(b);

[0123] (d) Output optimal gain pair

[0124] Step 5: Obtain the optimal policy pair and calculate the optimal control input and

[0125] S5 analyzes the stability and convergence of the algorithm;

[0126] Specifically, the algorithm is rigorously analyzed mathematically to prove its stability and convergence, ensuring the reliability of the algorithm in the long term. This step is an important part of algorithm verification, ensuring that the algorithm is not only feasible in theory, but also works stably in practical applications. Convergence theorem: For any initial strategy pair When k→∞, the sequence given by Algorithm 1 and Converge to and

[0127] Stability Theorem: Algorithm 1 gives The random stability of the system with disturbance level γ is guaranteed during the iteration process.

[0128] S6 simulates a two-region interconnected RDLFC with Markov jump parameters and verifies the effectiveness of the algorithm in solving the game algebraic Riccati equation.

[0129] Specifically, simulation experiments are carried out in a two-area interconnected RDLFC system with Markov jump parameters to verify the effectiveness of the algorithm in solving zero-sum games; this step tests the performance of the algorithm under specific conditions through simulation experiments to verify the practical application value of the algorithm; we simulated the two-area interconnected RDLFC with Markov jump parameters and verified the effectiveness of the algorithm in solving zero-sum games. Further, assuming that the power system under consideration has two operating modes, use M i = {1,2} represents the normal operation and fault operation of each area respectively. The parameters are shown in Table 2. The interconnection gain K s12 (r i (t)) and K s21 (r i (t)) are all set to 0.5. Assuming that the power system randomly jumps between the two modes in each region, the corresponding transfer rate matrix of the two system modes is

[0130]

[0131] use The overall transfer rate matrix obtained by operation and Markov superposition technique is:

[0132]

[0133] Table 2 System parameter values ​​under different working conditions

[0134]

[0135] Therefore, the two-region interconnected power system can be modeled into four different modes as shown in Table 3.

[0136] Table 3 Four modes of the two-region interconnected power system

[0137] Modal Region 1 Area 2 r(t)＝1 <![CDATA[Normal (r1(t) = 1)]]> <![CDATA[Normal (r2(t) = 1)]]> r(t)＝2 <![CDATA[Fault (r1(t) = 2)]]> <![CDATA[Normal (r2(t) = 1)]]> r(t)＝3 <![CDATA[Normal (r1(t) = 1)]]> <![CDATA[Fault (r2(t) = 2)]]> r(t)＝4 <![CDATA[Fault (r1(t) = 2)]]> <![CDATA[Fault (r2(t) = 2)]]>

[0138] in addition, and The setting of reflects the system state weight and control input weight, which respectively determine the importance of state variables and control input. In , assuming that state variables and control inputs have the same importance, the weight matrices are defined as Choosing initial controller gains and external disturbance gain As shown below:

[0139]

[0140] and The corresponding eigenvalues ​​are shown in Table 4. It can be seen from the table that since the system is not Hurwitz, the system will become unstable.

[0141] Table 4 Corresponding eigenvalues ​​when taking the initial gain matrix pair

[0142]

[0143] Next, we verify the effectiveness of the designed algorithm.

[0144] and The convergence of Figure 2-Figure 4 As shown, Figure 5 The control input and external disturbance input are depicted respectively. It can be seen that based on the proposed algorithm 1, by applying the initial stable gain The power system eventually stabilized.

[0145] Finally, the optimal control strategy and optimal interference strategy obtained by Algorithm 1 are applied to the control of the power system to illustrate the effectiveness of the controller designed by the algorithm. For this purpose, two cases are considered. In particular, in the first two time intervals when the mode switching occurs, the given strategy pair is added to the system in both cases. However, from the moment when the third mode switching occurs to the end of the simulation, the strategy pair obtained by Algorithm 1 is applied in one case, while the original strategy pair is still executed in the second case. First, Figure 6 The jump mode evolution of each region and the Markov superposition jump process are shown in Figure 2. The trajectory of the system in these two cases is shown in Figure 2. Figure 7 As shown, in particular, Figure 7 (b) and Figure 7 (d) describes the state trajectory of the system under the originally selected control strategy and interference strategy. At this time, the system is unstable. However, Figure 7 (a) and Figure 7 (c) depicts the state trajectory of the system under the optimal strategy obtained by Algorithm 1, which shows that the proposed control algorithm is feasible and effective in controlling the system.

[0146] What is disclosed above is only a preferred embodiment of the load frequency control method of the present invention applied to a multi-regional power system with jump parameters. Of course, this cannot be used to limit the scope of rights of the present invention. Ordinary technicians in this field can understand that all or part of the processes of the above embodiments and equivalent changes made according to the claims of the present invention still fall within the scope of the invention.

Claims

1. A load frequency control method for a multi-region power system with jump parameters, characterized in that: The following steps are involved: Establishing a mathematical model of an interconnected jump power system and using the mathematical model to perform modeling; Define the performance index function, solve the optimal control gain pair according to the optimal control theory, and derive the game algebraic Riccati equation with jump parameters; A new algorithm is designed to weaken the condition that the traditional policy iteration algorithm needs an initial stable control gain pair, and a rigorous proof is given using mathematical induction. Combined with online data collection, the algorithm was then implemented online using experience playback technology to successfully solve the optimal control gain; Conduct stability and convergence analysis on the algorithm; A two-region interconnected RDLFC with Markov jump parameters is simulated, and the effectiveness of the algorithm in solving the game algebraic Riccati equation is verified.

2. The load frequency control method applied to a multi-region power system with jump parameters according to claim 1, characterized in that: In "Establishing a mathematical model of interconnected jump power system and using the mathematical model to perform modeling", it includes: introducing a random jump process, using {r i (t), t≥0} to describe the sudden change of the actual power system i={1,2,…,N}.

3. The load frequency control method applied to a multi-region power system with jump parameters as claimed in claim 2, characterized in that: In "Defining the performance index function, solving the optimal control gain pair according to the optimal control theory, and deriving the game algebraic Riccati equation with jump parameters", it includes: defining the infinite time domain performance index as: in The following Hamiltonian function is defined:

4. The load frequency control method applied to a multi-region power system with jump parameters as claimed in claim 3, characterized in that: In "Designing a new algorithm to weaken the condition that the traditional policy iteration algorithm requires an initial stable control gain pair, and using mathematical induction to give a rigorous proof", it includes: giving a lemma to solve the condition that the initial stable control gain pair is required: set up For any given symmetric positive definite matrix, For any pair of gain matrices (not necessarily Hurwitz stable), for all m∈M, k=0,1,... (i) Update the symmetric positive definite matrix by solving in: (ii) Update Then for k=0,1,2,...,κ,..., not only is Hurwitz stable, and is the only positive solution.

5. The load frequency control method applied to a multi-region power system with jump parameters as claimed in claim 4, characterized in that: In "Combining online data acquisition and then using experience playback technology to implement the algorithm online and successfully solve the optimal control gain", it includes: To obtain the appropriate constants online The RDLFC system can be rewritten as: in: Then consider By taking derivatives and integrating along the system and combining with ERT technology transformation, we can get: in: t0<t1<...<t f Represents different sampling time instants.

6. The load frequency control method applied to a multi-region power system with jump parameters as claimed in claim 5, characterized in that: In "Analyzing the Stability and Convergence of the Algorithm", include: Convergence Theorem: For any initial strategy pair When k→∞, the sequence given by Algorithm 1 and Converge to and Stability Theorem: Algorithm 1 gives The random stability of the system with disturbance level γ is guaranteed during the iteration process.

7. The load frequency control method applied to a multi-region power system with jump parameters according to claim 6, characterized in that: In "Simulation of two-region interconnected RDLFC with Markov jump parameters and verification of the effectiveness of the algorithm in solving the game algebraic Riccati equation", it includes: simulation of two-region interconnected RDLFC with Markov jump parameters and verification of the effectiveness of the algorithm in solving the game algebraic Riccati equation.

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