Application of time-delay uncertain singular system based on alpha-pessimistic value criterion in electric power

Abstract

The invention relates to the technical field of electric power system operation and control, in particular to application of a time-delay uncertain singular system based on an alpha-pessimistic value criterion in electric power. The method comprises the following steps: establishing a time-delay uncertain singular system model of a power system; based on an alpha-pessimistic value criterion, constructing an index function for evaluating the operation performance of the power system; constructing a zero-sum game framework; and equivalently converting the time-delay uncertain singular system model into a standard uncertain system model through model transformation to obtain an optimal source side control sequence and an optimal load side control sequence. According to the application of the time-delay uncertain singular system based on the alpha-pessimistic value criterion in power, time delay, uncertainty and system singularity are considered in power system optimization, and the alpha-pessimistic value criterion is introduced, so that a decision maker can flexibly express the risk preference of the decision maker by adjusting the confidence level alpha; extreme risks caused by uncertainty are avoided according to the alpha value, and the toughness of the power system in an uncertain environment is enhanced.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power system operation and control technology, and particularly relates to application of time-delay uncertain singular system based on alpha-pessimistic value criterion in power. BACKGROUND

[0002] Modern power systems are developing towards high proportion of renewable energy access, which brings great uncertainty to the safe and stable operation of the system. At the same time, the widespread application of power electronic devices makes the inherent time delay characteristics of the system dynamic process more and more significant. In addition, under fault analysis or specific operating mode, the system model may exhibit singular (or differential-algebraic) characteristics, that is, there are both dynamic processes described by differential equations and constraint relationships (such as power balance constraints) described by algebraic equations in the system.

[0003] Traditional power system optimization control methods, such as stochastic optimization or robust optimization based on expected value, have limitations in dealing with such complex problems. The expected value criterion may not effectively avoid extreme risks, while robust optimization may be too conservative and result in poor economic performance. The zero-sum game theory provides a framework for describing the conflict and cooperation between multiple interest subjects (such as dispatch centers and power users) in the power system, but under the complex model of time-delay uncertain singular system, how to solve its equilibrium strategy is a great challenge. The existing technology lacks a unified modeling and solving framework that can handle time delay, uncertainty, and system singularity, and can flexibly adjust the risk preference of decision makers.

[0004] Therefore, the application of time-delay uncertain singular system based on alpha-pessimistic value criterion in power is designed to provide another technical solution to the above technical problems. SUMMARY

[0005] Therefore, it is necessary to provide the application of time-delay uncertain singular system based on alpha-pessimistic value criterion in power to solve the technical problems proposed in the background art.

[0006] To solve the above technical problems, the present application adopts the following technical solutions: The application of time-delay uncertain singular system based on alpha-pessimistic value criterion in power has the following steps: S1: Establish a time-delay uncertain singular system model of the power system, the state variables of the model include the operating state variables of the power system, the control variables include the source-side control strategy and the load-side control strategy, the model parameters include a singular matrix to describe the algebraic constraints of the power system, and an uncertain vector is introduced to represent the uncertainty of the renewable energy output and / or load in the power system; S2: Based on the α-pessimistic value criterion, construct an index function to evaluate the operating performance of the power system, where α is the confidence level, used to characterize the risk preference of decision-makers; S3: Construct a zero-sum game framework with the source-side control strategy as the first player strategy and the load-side control strategy as the second player strategy; transform the time-delay uncertain singular system model into a standard uncertain system model through model transformation, and solve the equilibrium strategy of the zero-sum game of the standard uncertain system to obtain the optimal source-side control sequence and load-side control sequence. S4: Apply the optimal source-side control sequence and load-side control sequence to the actual power system to coordinate the scheduling of source-side resources and load-side resources.

[0007] As a preferred embodiment of the application of the time-delay uncertain singular system based on the α-pessimistic value criterion provided by the present invention in the power industry, in step S1, the source-side control strategy is the charging and discharging power command of the energy storage system, and the load-side control strategy is the adjustable load increase / decrease command of the power user.

[0008] As a preferred embodiment of the application of the time-delay uncertain singular system based on the α-pessimistic value criterion provided by the present invention in the power industry, in step S1, the expression of the time-delay uncertain singular system model is: ; in, Let be the system state vector. For source-side control variables, For load-side control variables, It is a singular matrix. These are mutually independent uncertain vectors.

[0009] As a preferred embodiment of the application of the time-delay uncertain singular system based on the α-pessimistic value criterion provided by the present invention in the power industry, in step S2, the performance index function expression is: ; in, This represents the α-pessimistic value criterion. For stage cost function, This is the terminal cost function.

[0010] As a preferred embodiment of the application of the time-delay uncertain singular system based on the α-pessimistic value criterion provided by the present invention in power, in step S3, the model transformation includes state augmentation to eliminate time delay, and decoupling the singular system and equivalently transforming it into a standard uncertain system using matrix decomposition and linear transformation.

[0011] As a preferred embodiment of the application of the time-delay uncertain singular system based on the α-pessimistic value criterion provided by the present invention in the power industry, when the performance index function is a linear quadratic form, the optimal source-side control sequence and load-side control sequence have explicit analytical solution forms.

[0012] As a preferred embodiment of the application of the time-delay uncertain singular system based on the α-pessimistic value criterion provided by the present invention in the power industry, in step S3, the process of solving the equilibrium strategy includes establishing and solving the equilibrium equation of the game of the transformed standard uncertain system, and the equilibrium equation has a dynamic programming form.

[0013] As a preferred embodiment of the application of the time-delay uncertain singular system based on the α-pessimistic value criterion provided by the present invention in the power industry, the uncertainty vector follows a linear uncertainty distribution or a normal uncertainty distribution.

[0014] It is clear without a doubt that the technical solution described above in this application can solve the technical problem that this application aims to address.

[0015] Meanwhile, through the above technical solutions, the present invention has at least the following beneficial effects: 1. The application of the time-delay uncertain singular system based on the α-pessimistic value criterion provided by this invention in the power industry simultaneously considers time delay, uncertainty and system singularity in power system optimization. By introducing the α-pessimistic value criterion, decision-makers can flexibly express their risk preferences by adjusting the confidence level α. The higher the α value, the more conservative the optimization strategy, and the better it can avoid the extreme risks brought about by uncertainty, thus enhancing the resilience of the power system in uncertain environments.

[0016] 2. This invention uses a zero-sum game framework to explicitly model the conflict of interest between the dispatch center (source side, such as energy storage) and the power user (load side, such as adjustable load), and obtains the optimal equilibrium strategy for both parties under a given risk preference, thus realizing true risk collaborative management.

[0017] 3. This invention avoids the difficulty of directly solving complex original systems through model transformation. For linear systems, it can obtain explicit analytical solutions with high computational efficiency; for specific nonlinear systems, it can also be solved through effective numerical methods, showing good prospects for engineering applications. Attached Figure Description

[0018] Fig. 1 This is a schematic diagram of the balance control trajectory of the present invention; Fig. 2 This is a schematic diagram of the equilibrium values ​​at different confidence levels of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0020] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0021] It should be noted that, unless otherwise specified, the embodiments and features and technical solutions in the present invention can be combined with each other.

[0022] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0023] Example 1 Reference Figs. 1-2 Application of time-delay uncertain singular systems based on the α-pessimistic value criterion in power.

[0024] Symbol explanation: and They represent Void space and The set of real number matrices. f T represents a vector f The transpose of . Representing vectors f The 1-norm of the matrix. A The determinant of a matrix is ​​denoted as det( A Its rank is determined by rank ( A (Given). · ]inf(α) represents the α-pessimistic value. I m represents m x m The identity matrix, where 0 represents the zero matrix of the corresponding dimension.

[0025] 1. Preliminary The uncertainty measure M is defined based on the following three axioms. (i) M{Γ}=1, where Γ is the universal set; (ii) For any event B, M{B} + M{Bc} = 1; (iii) For any countable set of events Bi, i = 1, 2, ..., ; The triple (Γ, L, M) constitutes an uncertainty space, where Γ represents a non-empty set, L represents a σ-algebra, and M represents an uncertainty measure. An uncertain variable is a measurable function from this space to the set of real numbers. If for any Borel sets B1,..., B m satisfies , then the uncertain variables ζ1,..., ζ m are said to be independent. The uncertainty distribution of the uncertain variable ζ is defined as . Given a confidence level α ∈ (0, 1], its α-pessimistic value is defined as (1) For a linear uncertain variable ζ that follows distribution, its α-pessimistic value can be simplified to . In particular, when α = 0.5, the 0.5-pessimistic value is exactly the same as the expected value, and at this time, the α-pessimistic value criterion degenerates into an expectation-based evaluation framework. In addition, if two uncertain variables ζ and η are independent, then their pessimistic values satisfy additivity: (2) 2. Zero-sum game constructed by α-pessimistic value Study an uncertain singular system with time delay: (3) where h and N are positive integers. The vector represents the system state at the j-th stage. and represent the control variables of player 1 and player 2 respectively. The matrices are both deterministic matrices and satisfy the rank condition rank(E) = q < m. The uncertain vectors , are assumed to be independent. In addition, the following rank condition holds: (4) For a given confidence level α (0, 1), the performance index based on the α-pessimistic value is defined as: (5) where, . Here, f and g are scalar-valued functions. According to this criterion, the corresponding time-delay uncertain zero-sum game is: (6) In this game, the goal of player 1 is to maximize the performance index while player 2 attempts to minimize it. The equilibrium value of this game is denoted as: ; Therefore, we have: (7) (8) in, and , respectively represent and The control domain.

[0026] To determine the equilibrium control variable u in game theory formula (6) and v Apply the following transformation: , ,

[0027] (9) Therefore, the time-delayed game (6) can be equivalently rewritten as a zero-sum game without time delay: (10) in, (11) in, satisfy The transformed matrix satisfies: (12) Singular Matrix The existence of [variable] complicates the search for equilibrium solutions in the zero-sum game (10). To address this, we transform the uncertain singular zero-sum game (10) into a zero-sum game of a standard uncertain system. The detailed preparation process will be described later. For the second equation in game (10), according to matrix factorization theory, there exists a non-singular matrix [variable]. , so that: , ,

[0028] ; in, Furthermore, all submatrices are dimensionally compatible. This transformation generates an equivalent zero-sum game with decoupled subsystems: (13) and (14) in It is a dimension of The identity matrix.

[0029] For the zero-sum game (10), we use matrix factorization to transform it into a game involving two subsystems (13). However, when examining these subsystems, we find that the states in the two subsystems... and The coupling relationships between the subsystems complicate the solution process. To address this challenge, it is necessary to analyze the coupling relationships between the subsystems in depth and construct an invertible transformation to simplify the system, converting it into a system involving only the coupling relationships between the subsystems. The standard uncertain system.

[0030] From equation (12), we can obtain

[0031]

[0032] (15) This means the matrix It has full row rank, that is This constitutes the prerequisite guarantee for constructing non-singular matrices.

[0033] To construct an invertible transformation, we introduce a matrix. This makes matrix B given in the following form: (16) This is a non-singular matrix, and its inverse is denoted as: (17) pass Establish original variables With new variables Linear transformation relationship between them: (18) Substituting this into the second equation (13) in the game theory, we get: (19) For the third equation in game (13), by utilizing and its inverse matrix Based on the structure and properties of , we derive the following relationship: (20) As can be seen from equation (20), by applying the transformation in equation (18) and... Substitution The expression yields (twenty one) By using equations (9) and (20) and substituting them into (14), we obtain: (twenty two) In this stage, we transform the coupled subsystem into a standard uncertain system (21), thus obtaining the corresponding equivalent game (22). However, as shown in equation (9), the control quantity... It depends not only on the original control quantities u(j) and v(j), but also on the uncertainty vector. The influence of this increases system complexity and management difficulty. To simplify the control process, we will use the inverse transformation method to restore the control variables to their original forms, namely u(j) and v(j).

[0034] By integrating equations (16), (18), and (20), we obtain: (twenty three) (twenty four) when Solve We can obtain: (25) Substituting equation (25) into (24), we get: (26) when At that time, we obtained:

[0035]

[0036]

[0037]

[0038] (27) By substituting equation (27) into (25), we obtain

[0039]

[0040]

[0041] (28) Substitute (27) and (28) into (22) and denote it as (29) Therefore, under the α-pessimistic criterion, the zero-sum game of a standard uncertain system is the following problem: (30) in: ; ; ; ; Define the equilibrium value function from stage k to N as follows:

[0042] ; Status is With a confidence level of α, we then establish the following equilibrium equations.

[0043] Theorem 2.1. For game (30), the equilibrium equation is: (31) (32) for ,in .

[0044] Proof. Assume u and v If the equilibrium control pair constitutes the game (30), then u Solve the following given v Uncertain optimal control problem: (33) Similarly, v Solved the problem in fixed u The optimal control problem under the following conditions: (34) To solve problems (33) and (34), dynamic programming can be used. In the k-th stage, the value function satisfies: (35) (36) From equation (35), we can obtain: (37) Similarly, it can be derived from equation (36): (38) Define a function: (39) Then for any The following inequalities hold: (40) This leads to the conclusion: (41) Combining inequalities (37), (38), and (41), we obtain equations (31) and (32). At the terminal stage k=N, the value function satisfies the boundary conditions. This is consistent with the definition of the equilibrium value function, thus completing the proof.

[0045] 3. Linear time-delay uncertain singular zero-sum game Given confidence level We consider the following zero-sum game in a linear time-delay uncertain singular system: (42) The performance index is defined as follows: (43) in, A deterministic vector on.

[0046] Applying transformation (9) to game theory (42) yields an equivalent rewrite as: (44) get: (45) in, Indicates a A row vector that begins with zero. Under the condition... ,as well as The game (44) is transformed into: (46) get: ; and ; ; ; ; ; Applying Theorem 3.1, we can derive the equilibrium solution of the zero-sum game (46) as follows.

[0047] Theorem 4.1. Equilibrium control quantity u in game (46) (j) and v (j) is given by the following formula: ; ; for ,in and Represent the first and second digits of the corresponding vectors, respectively. and Components. The corresponding balance value is: ; prove, ; According to Theorem 3.1, we obtained ,in ,for Applying the equilibrium equation (31), we obtain:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] ; Therefore, the equilibrium control variables for stage N-1 are: ; ; The corresponding equilibrium value is given by the following formula: ; get, ; for A similar derivation is given:

[0054]

[0055] ; The relevant balance control is as follows: ; ; The corresponding equilibrium value becomes:

[0056] ; in, The theorem is proved by induction.

[0057] 4. Extension Zero-sum games involving linear time-delay uncertain singular systems were discussed. The scope of the discussion is then extended to zero-sum games involving nonlinear time-delay uncertain singular systems: (47) in: (48) and The meanings of the other symbols are the same as in game theory (6). Furthermore, the matrices E and A, and the vectors... satisfy: (49) set up ,and The game theory (47) can be restated as: (50) Note that, apart from the control in game (6) being high-dimensional and the control in game (50) being one-dimensional, the two games are similar in form. Therefore, applying the proposed transformation method, when det and Then, the game (50) can be transformed into a zero-sum game of a standard uncertain system: (51) in and They represent and The control domain. A, C, D, and F have the same meaning as in (30), and: (52) Using a similar proof process to Theorem 3.1, the equilibrium equation of game (51) can be expressed as follows: (53) (54) for Therefore, the linear framework can be extended to nonlinear time-delay uncertain singular systems by utilizing the equilibrium equations (53) and (54) to determine the equilibrium solution. Next, we analyze the equilibrium solution of the zero-sum game (47) of the nonlinear time-delay uncertain singular system in the case of p=q=2.

[0058] Given confidence level We consider the following zero-sum game in a nonlinear time-delay uncertain singular system: (55) The performance index is defined as follows:

[0059] (56) in For deterministic real numbers. Other symbols have the same meanings as in game theory (42). In addition, matrices E and A, and vectors satisfy: (57) set up Then game (55) can be rewritten as: (58) get: (59) In the game (55), applying transformation (9) can be equivalently rewritten as: (60) get: (61) in Indicates a A row vector that begins with zero and ends with zero. Under the condition... and The game (60) then transforms into: (62) get: (63) and

[0060]

[0061]

[0062] ; ; ; ; ; Given the applicability of equations (53) and (54), the equilibrium solution of game (62) is given below.

[0063] Theorem 5.1. Equilibrium control u of game (62) (j) and v (j) is given by the following: ; ; in, ,for The corresponding equilibrium value is: ; in, ; Proof. First, we have ,in .for Applying formula (32), we can obtain:

[0064] =

[0065]

[0066]

[0067] ; Among them, the maximum value The sum is shown below: and : ; minimum point The value is The summary is as follows: ; The corresponding balance values ​​are given below: ; in .

[0068] The same analytical method can be applied to By using inductive reasoning from N-1 to 0, the balance control u is achieved. (j) and v (j), and the corresponding equilibrium value. For all All of them follow the stated form, thus completing the proof.

[0069] According to Theorems 4.1 and 5.1, it is clear that the equilibrium value is closely related to the α-pessimistic value of the uncertainty vector. Specifically, once the uncertainty vector is defined... The equilibrium outcome can then be easily determined. Therefore, considering the α-pessimistic value of the uncertain vector is crucial, especially in certain special cases.

[0070] Example 5.1. Let Let represent an uncertain vector, where These are independent uncertain variables that follow a linear uncertainty distribution: ; therefore, The α-pessimistic value is: ; Example 5.2. Let Let represent an uncertain vector, where These are independent uncertain variables that follow a normal uncertainty distribution: ; therefore, The α-pessimistic value is: ; It is worth noting that when When the α-pessimistic value is consistent with the expected value, both linear and normally uncertain variables exhibit the same α-pessimistic value. This finding suggests that the α-pessimistic value can be viewed as a generalized form of the expected value, providing a unified and flexible framework for studying zero-sum games in uncertain environments.

[0071] 6 Numerical Examples We illustrate the proposed method using a zero-sum game approach with linear time-delay uncertain singular systems, as shown below: (64) in, ; get: , , , , , ; , ; Singular Matrix The choice satisfies the definition of a singular system because rank( =1 < 2. Combining matrices A, A1, C, and D, this choice satisfies the following rank condition: ; This satisfies the rank condition (4), ensuring that the system can be transformed into its standard form. Control quantity , Restricted to the range This is a commonly used constraint form in linear systems. For Uncertain vector From independent unknown variables and Both components are independent linear unknown variables that follow an uncertainty distribution. This distribution is widely used in uncertainty theory and is often applied to uncertain systems. By applying transformation (9), the game (64) is transformed into: ; in, (65) The transformed matrix and the extended state vector are as follows: , , , ; , ; There exists a non-singular matrix: ; Make: , , , , ; definition: , , , ; lead to: , ; Further extract the following block components: ; , , ; Known and Then the game problem (65) can be rewritten as follows: (67) in: ; and ; ; According to Theorem 4.1, the equilibrium control variable u of the game (67) can be obtained. (j) and v (j), and the corresponding equilibrium value. The results are summarized in Table 1.

[0072] Table 1: Comparison of equilibrium outcomes of game (67) when α = 0.1, 0.3, 0.5, 0.7, 0.9

[0073] As can be seen from Theorem 4.1, balance control and This is independent of the confidence level α. This means that the balance control remains unchanged regardless of the choice of α. The results of these balance controls are listed in the second and third columns of Table 1, and are as follows: Fig. 1 As shown. However, the equilibrium value Influenced by the pessimistic value of α. For example... Fig. 2 As shown, the equilibrium value increases with the increase of the confidence level α, which is consistent with the definition of the pessimistic value of α.

[0074] Fig. 1 In the middle, (a) regarding the control quantity The balance control trajectory, (b) regarding v The equilibrium value trajectory of (j) ; Fig. 2 Let be the equilibrium value of the game (67) at different confidence levels α=0.1, 0.3, 0.5, 0.7, 0.9.

[0075] To verify the robustness and effectiveness of the proposed method, two parameter adjustment scenarios were designed to analyze the variation patterns of the equilibrium results.

[0076] Case 1: Distribution of the original uncertain variables Adjusted to (This narrowed the uncertainty range), while other parameters remained unchanged. The equilibrium results are shown in Table 2.

[0077] Table 2: Comparison of equilibrium outcomes of game (67) when α = 0.1, 0.3, 0.5, 0.7, 0.9

[0078] Balanced control variables and The values ​​are the same as in Table 1, indicating that these balance control variables are stable even if the magnitude of uncertainty fluctuates. Furthermore, the balance values... The value has increased compared to the value in Table 1, which aligns with the intuitive concept that reduced uncertainty leads to lower system risk costs, thus confirming the correctness of the results.

[0079] Case 2: Original control constraints Adjusted to (Tighten control limits), while keeping other parameters unchanged. The balancing results are shown in Table 3.

[0080] Table 3: Comparison of equilibrium outcomes of game (67) when a = 0.1, 0.3, 0.5, 0.7, 0.9

[0081] The direction of balance control (e.g., The negative / positive values ​​are consistent with those in Table 1, except that their magnitudes are determined by stricter constraints (from...). Adjusted to The controls were adjusted accordingly, which indicates that these controls are well consistent.

[0082] To further verify the generality of the proposed method, we compare the α-pessimistic value criterion introduced in this paper with the traditional expected value criterion. The following is a zero-sum game based on the expected value criterion: (68) get: ; These symbols have the same meaning as those in game (64). By applying the transformation method, we can convert game (68) into a zero-sum game of the following standard uncertain system: (69) get: ; Since the uncertainty vector in game (69) consists of linear uncertain variables, we can derive the equilibrium results of the game, as shown in Table 4. These results are based on Example 5.1, and equations (31) and (32).

[0083] Table 4: Comparison of Equilibrium Outcomes of Game (69)

[0084] Balance controllers in Table 4 and Same as in Table 1. Furthermore, the equilibrium value under the expected value criterion... It perfectly matches the α-pessimistic value in Table 1. This equivalence is no coincidence: for linear uncertain variables, a pessimistic value of 0.5 equals the expected value, as shown in Example 5.1. This confirms that the proposed method generalizes the expected value criterion. It not only reduces to the traditional standard at α=0.5, but also adapts to risk-averse or risk-seeking decision preferences by adjusting α.

[0085] 6 Applications To demonstrate the practical applicability and effectiveness of our theoretical framework, we present a numerical analysis-based example of a nonlinear time-delay uncertain singular dynamical system: ; in, Indicates the system status. The net active power of the corresponding regional power grid, This represents the critical bus voltage. Matrix E captures the instantaneous voltage drop caused by power network faults. Control This represents the charging and discharging scheduling strategy of the energy storage system, where Indicates complete discharge. This indicates a full charge. Similarly, This indicates the power adjustment strategy for user-adjustable loads, where Maximize load reduction, Maximize load increase. Uncertainty vector. External fluctuation loads of the model.

[0086] The performance index of this system is defined as follows: ; This performance metric integrates the conflicting goals of the scheduling center and the users, as well as their respective risk protections. Therefore, we can express the zero-sum game of a nonlinear time-delay uncertain singular system as follows: ; We set: , , , , , , , ; ; Uncertain variables It follows an uncertain distribution Independent normally distributed random variables. Furthermore, satisfy: ; set up The game theory (70) can be restated as: (71) in: ; By applying transformation (9), the game (71) is transformed into: (72) in: ; The transformed matrix and the extended state vector are as follows: , , , ; , ; There exists a non-singular matrix: ; Make: , , , , ; definition: , , ; lead to: , ; Further extract the following block components: , ; , , , , ; Given, det and The game can then be restated as follows: (73) in: ; and: , , , ;

[0087] ; According to Theorem 5.1, the equilibrium control variable of game (73) and and the corresponding equilibrium value The results were obtained and summarized in Table 5.

[0088] Table 5: Comparison of equilibrium outcomes of game (73) when α = 0.1, 0.3, 0.5, 0.7, 0.9

[0089] The second and third columns of Table 5 show the balance control for phases 0 to 5. During the early morning hours (phases 0 to 2), renewable energy output is low due to the lack of sunlight, while user base load remains high. In this situation, the dispatch center instructs the energy storage system to charge at full power. This is in preparation for the upcoming peak demand. At the same time, users are increasing their adjustable loads. This is to take advantage of off-peak electricity prices. In the middle of the morning (Phase 3), renewable energy generation, such as photovoltaic output, gradually increases, but a moderate power shortage still exists. The dispatch center partially releases energy storage systems. To supplement the power supply, while users reduce their adjustable load. To alleviate grid pressure. During the evening peak (Phase 5), user demand surges while renewable energy output declines as photovoltaic power generation decreases after sunset. To meet peak demand, the dispatch center increases the discharge power of energy storage systems. Meanwhile, users continue to reduce adjustable load. To prevent voltage drop.

[0090] Table 5 shows the different confidence levels ( The equilibrium value emphasizes the crucial role of the pessimistic value in systemic risk management. As increases, the equilibrium value... The corresponding increase indicates that a higher 'a' reflects a more conservative and risk-averse attitude from the dispatch center in maintaining power supply reliability. From the user's perspective, a larger 'a'... This implies stronger protection against cost fluctuations, which in turn contributes to an improvement in the overall equilibrium performance index. Furthermore, since the uncertain vector elements in this game are modeled as ordinary random variables, the analysis of the relationship between the expected value and the a-pessimistic value of the ordinary random variables in Example 5.2 shows that when... At this point, the α-pessimistic value simplifies to the expected value. In this case, the equilibrium value... This represents a risk-neutral compromise between the dispatch center and the user. The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. Application of time-delay uncertain singular systems based on a-pessimistic value criterion in power, characterized in that, The steps are as follows: S1: a time-delay uncertain singular system model of a power system is established, state variables of the model include operating state variables of the power system, control variables include source-side control strategies and load-side control strategies, model parameters include a singular matrix to describe algebraic constraints of the power system, and an uncertain vector is introduced to represent uncertainty of renewable energy output and / or load in the power system; S2: based on an α-pessimistic value criterion, an index function for evaluating operation performance of the power system is constructed, where α is a confidence level for representing risk preference of a decision maker; S3: a zero-sum game framework is constructed with the source-side control strategies as first player strategies and the load-side control strategies as second player strategies, the time-delay uncertain singular system model is equivalently converted into a standard uncertain system model through model transformation, and an equilibrium strategy of the standard uncertain system zero-sum game is solved to obtain optimal source-side control sequences and load-side control sequences; S4: the optimal source-side control sequences and load-side control sequences are applied to an actual power system to cooperatively schedule source-side resources and load-side resources.

2. The application of a time-delay uncertain singular system based on a- pessimistic value criterion in power according to claim 1, characterized in that, In step S1, the source-side control strategies are charge-discharge power instructions of an energy storage system, and the load-side control strategies are adjustable load increase-decrease instructions of power users.

3. The time-delay uncertain singular system based on a-priori pessimistic value criterion for application in power according to any of claims 1 or 2, characterized in that, In step S1, the time-delay uncertain singular system model has the following expression: ； where is the system state vector, is the source-side control variable, is the load-side control variable, is a singular matrix, are mutually independent uncertain vectors.

4. The application of a time-delay uncertain singular system based on a- pessimistic value criterion in power according to claim 1, characterized in that, In step S2, the performance index function has the following expression: ； wherein, denotes the a-pessimistic value criterion, is the stage cost function, is the terminal cost function.

5. The application of a time-delay uncertain singular system based on a- pessimistic value criterion in power according to claim 1, characterized in that, In step S3, the model transformation includes state augmentation to eliminate time delay, and matrix decomposition and linear transformation are used to decouple and equivalently convert the singular system into a standard uncertain system.

6. The application of a time-delay uncertain singular system based on a- pessimistic value criterion according to claim 5, characterized in that, When the performance index function is a linear quadratic form, the optimal source-side control sequences and load-side control sequences have an explicit analytical solution.

7. The application of a time-delay uncertain singular system based on a- pessimistic value criterion in power according to claim 6, characterized in that, In step S3, the process of solving the equilibrium strategy includes establishing and solving an equilibrium equation of the converted standard uncertain system game, and the equilibrium equation has a dynamic programming form.

8. The application of a time-delay uncertain singular system based on a- pessimistic value criterion in power according to claim 1, characterized in that, The uncertain vector is subject to a linear uncertainty distribution or a normal uncertainty distribution.

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