A fuzzy chance-constrained optimal power flow calculation method based on credibility theory

Abstract

The application discloses a fuzzy chance-constrained optimal power flow calculation method based on credibility theory and belongs to the technical field of renewable energy consumption of distribution networks.The method comprises the following steps: constructing a credibility distribution function of net load prediction error; establishing a fuzzy chance-constrained optimization model considering the net load prediction uncertainty; deriving the certainty equivalence of voltage, active power and reactive power fuzzy chance-constrained based on the credibility theory; further deriving the linear expression of the certainty equivalence by introducing auxiliary variables; establishing a distribution network certainty optimization model considering the prediction uncertainty; and obtaining optimal controllable generator dispatching schemes meeting different safety margins by selecting different confidence levels to solve the distribution network optimization model.The application constructs an optimal power flow model based on the credibility theory, can effectively reduce the voltage violation risk under the influence of uncertainty and solves the safe and economic operation problem of the renewable energy-containing distribution network.

Description

Technical Field

[0001] A fuzzy chance-constrained optimal power flow calculation method based on credibility theory belongs to the technical field of renewable energy consumption in distribution networks. Background Technology

[0002] Several core tasks in power system operation, such as unit commitment, reserve procurement, market clearing, and security assessment, rely on solutions based on incidental proportional feedback (OPF) technology. In recent years, with the accelerated development of the global economy, energy shortages and environmental pollution have become serious problems, driving the research and development of renewable energy generation. However, inaccurate forecasting of renewable energy (RESs) introduces uncertainty into the OPF problem. Furthermore, as the share of RESs generation in the distribution system increases, forecast uncertainty increases by several orders of magnitude. This leads to significant forecast errors when using OPF decisions based on RESs predictions, potentially causing frequent violations of system constraints during real-time operation, such as network voltage exceeding limits. Since voltage amplitude directly affects users' normal electricity consumption, addressing the uncertainty in RESs generation forecasting within OPF becomes a crucial issue.

[0003] Currently, the main methods for handling uncertain RESs in OPF (Optical Problem Function) include: robust optimization methods, whose solutions satisfy the worst-case uncertainty realization, thus the derived solutions are often overly conservative; stochastic optimization methods, which give operators more freedom to balance cost and safety, but require repeated sampling, which may affect the efficiency of the solution; and chance-constrained optimization methods, another commonly used approach for solving uncertain optimization problems, only require restricting system variables to meet a predetermined confidence level. Therefore, compared to robust optimization, the obtained solutions are less conservative, but in most cases, they can still guarantee system safety.

[0004] Most existing opportunity-constrained methods assume that prediction errors follow a Gaussian distribution with mean and variance, or require precise information on the first and second moments of the prediction error distribution. However, empirical measurements for solar and wind power generation are often asymmetric. Therefore, the Gaussian assumption of RESs uncertainty, as a symmetry assumption, may misjudge the impact of prediction errors from nodes with significant asymmetry, leading to ineffective and inefficient operational decisions. Furthermore, in addition to stochasticity, uncertainty also includes fuzziness. Existing opportunity-constrained OPF models primarily focus on the stochastic properties of RESs, while research utilizing credibility theory to address RESs uncertainty considering fuzziness is relatively limited. Summary of the Invention

[0005] The technical problem to be solved by this invention is to overcome the shortcomings of the prior art and provide a fuzzy chance-constrained optimal power flow calculation method based on credibility theory that can effectively reduce the risk of voltage violations under the influence of uncertainty and solve the problem of safe and economical operation of distribution networks containing renewable energy.

[0006] The technical solution adopted by this invention to solve its technical problem is: a fuzzy chance-constrained optimal power flow calculation method based on credibility theory, characterized by the following steps:

[0007] Construct a reliability distribution function for net load forecasting error;

[0008] Establish a fuzzy chance-constrained optimization model that takes into account the uncertainty of net load forecasting;

[0009] Based on the credibility theory, the deterministic equivalence of fuzzy chance constraints on voltage, active power, and reactive power is derived.

[0010] By introducing auxiliary variables, we can further derive deterministically equivalent linear expressions;

[0011] Establish a deterministic optimization model for the distribution network that takes into account forecasting uncertainties;

[0012] By selecting different confidence levels to solve the distribution network optimization model, the optimal controllable generator scheduling schemes that satisfy different safety margins are obtained.

[0013] Preferably, the confidence distribution of the net load forecast error is as follows:

[0014] ;

[0015] in, For nodes The net load output prediction error, It is a node Fuzzy parameters of prediction error.

[0016] Preferably, the node Net load output prediction error for:

[0017] ;

[0018] in, It is represented as a set of all nodes.

[0019] Preferably, the method further includes real-time net active load affected by prediction errors. for:

[0020] ;

[0021] in, It is the net load vector. It is the prediction error fuzzy vector;

[0022] The real-time active and reactive power of each controllable generator are:

[0023] ;

[0024] ;

[0025] in, It is the total active power mismatch. , , It is a controllable generator dispatching decision based on net load forecasting, vector Index is .

[0026] Preferably, the method further includes the following: the expected operating cost is:

[0027] ;

[0028] ;

[0029] in, , , They represent the first The fuel cost coefficient of a generator.

[0030] Preferably, the method further includes, considering the uncertainty of renewable energy power forecasting, the fuzzy chance-constrained optimization model is as follows:

[0031] ;

[0032] in, and It is the fuzzy confidence level of the opportunity constraint, parameter .

[0033] Preferably, the method further includes the real-time output of the controllable generator being:

[0034] ;

[0035] ;

[0036] ;

[0037] in, and These represent the sum of the prediction errors for active and reactive power, respectively. .

[0038] Preferably, the method further includes defining , , Then the deterministic constraint is:

[0039] ;

[0040] Define matrix :

[0041] ;

[0042] .

[0043] Preferably, the deterministic constraint is:

[0044] ;

[0045] ;

[0046] in, , , , , For continuous variables, , It is a binary variable. It is a positive integer.

[0047] Preferably, the establishment of the deterministic optimization model for the distribution network that considers prediction uncertainties is as follows:

[0048]

[0049]

[0050]

[0051]

[0052] .

[0053] Compared with the prior art, the beneficial effects of this invention are:

[0054] This invention employs a fuzzy chance-constrained optimal power flow calculation method based on credibility theory. By selecting different confidence levels to solve the distribution network optimization model, it obtains optimal controllable generator dispatch schemes that satisfy different safety margins. This invention constructs an optimal power flow model based on credibility theory, which can effectively avoid the uncertainties of renewable energy generation with asymmetric characteristics, thus solving the problem of safe and economical operation of distribution networks containing renewable energy. This invention presents optimal dispatch schemes under different confidence levels. By reasonably selecting the confidence level, the Distributed Power Streaming (DSO) can achieve the expected goals, providing new tools and ideas for addressing the uncertainty risks of distribution systems. Attached Figure Description

[0055] Figure 1 This is a flowchart of a fuzzy chance-constrained optimal power flow calculation method based on credibility theory. Detailed Implementation

[0056] The present invention will be further described below with reference to specific embodiments. However, those skilled in the art should understand that the detailed description given here with reference to the accompanying drawings is for better explanation. The structure of the present invention necessarily exceeds the limited embodiments described herein. Some equivalent alternatives or common means will not be described in detail here, but still fall within the protection scope of this application.

[0057] Figure 1 This is the preferred embodiment of the present invention, which is described below in conjunction with the accompanying drawings. Figure 1 The present invention will be further described below.

[0058] like Figure 1 As shown: A fuzzy chance-constrained optimal power flow calculation method based on credibility theory includes the following steps:

[0059] Construct a reliability distribution function for net load forecasting error;

[0060] Establish a fuzzy chance-constrained optimization model that takes into account the uncertainty of net load forecasting;

[0061] Based on the credibility theory, the deterministic equivalence of fuzzy chance constraints on voltage, active power, and reactive power is derived.

[0062] By introducing auxiliary variables, we can further derive deterministically equivalent linear expressions;

[0063] Establish a deterministic optimization model for the distribution network that takes into account forecasting uncertainties;

[0064] By selecting different confidence levels to solve the distribution network optimization model, the optimal controllable generator scheduling schemes that satisfy different safety margins are obtained.

[0065] This invention constructs a fuzzy chance-constrained optimal power flow model, which can effectively handle uncertainties in the power distribution system and avoid possible voltage violations, making it suitable for solving the problem of safe and economical operation of power distribution networks containing renewable energy.

[0066] As one possible implementation of this embodiment, the process of constructing the reliability distribution function of the net load forecast error is as follows:

[0067] Considering that renewable energy is installed on the user side, a behind-the-meter technique is used to represent net load as the difference between node load and renewable energy output. Because renewable energy generation cannot be accurately predicted, prediction errors in net load are unavoidable. This invention assumes that the node... Net load output prediction error It follows a trapezoidal fuzzy distribution, that is:

[0068] ;

[0069] in, It is a node The fuzzy parameters of the prediction error can usually be determined from historical data. This is represented as the set of all nodes. Therefore, the membership function associated with each prediction error... for:

[0070] ;

[0071] Then, based on the credibility measure:

[0072] ;

[0073] in, It is a symbol for measuring credibility. It is the membership function of the fuzzy variable. This is the symbol representing the supremum. The confidence distribution of the prediction error is as follows:

[0074] ;

[0075] The value of the credibility distribution function refers to the fuzzy variable Less than or equal to Credibility.

[0076] As one possible implementation of this embodiment, the process of establishing a fuzzy chance-constrained optimization model that considers the uncertainty of net load forecasting is as follows:

[0077] Real-time net active load affected by prediction errors for:

[0078] ;

[0079] in, It is the net load vector. This is the prediction error fuzzy vector; the reactive power component of each prediction error is represented as: ,in, .

[0080] To avoid real-time power imbalances caused by prediction errors, distribution system operators (DSOs) must adjust the output of controllable generators to maintain a balance between active and reactive power. An affine strategy is employed to allow vectors... Index is , This represents the participation factor for each generator. The total power mismatch caused by prediction errors will be distributed among the generators according to the participation factor. Therefore, the real-time active and reactive power of each controllable generator can be modeled as follows:

[0081] ;

[0082] in, It is the total active power mismatch. , , It is a controllable generator scheduling decision based on net load forecasting.

[0083] Subsequently, other state variables of the distribution system, line power flow and node voltage, will respond to these changes according to system control and its physical relationships. Therefore, they will also change with the prediction error, as expressed as... , , .

[0084] The production cost of each generator can be approximated by a quadratic function:

[0085] ;

[0086] in, , , They represent the first The fuel cost coefficient of a generator.

[0087] Considering the impact of prediction errors, according to reliability theory, the reliability mean and reliability variance of fuzzy variables have the same properties as those of random variables. Therefore, the fuzzy mean of power generation cost is:

[0088] ;

[0089] in, This represents the average value of the total active power mismatch. Let represent the variance. When using the assumption of symmetry in the prediction error, the expected operating cost can be simplified to:

[0090] ;

[0091] Considering the uncertainty in RESs power prediction, the FCC AC-OPF model is as follows:

[0092] ;

[0093] Among them, the target To minimize the expected operating costs under conditions of uncertainty. Constraints It is the LinDistFlow linear expression for the AC power flow formula when uncertainties exist, ensuring that node power balance is applicable to any uncertainty. Constraints It is a fuzzy opportunity constraint on controllable resources to ensure that violations of controllable generator power generation and the square of voltage amplitude under the influence of uncertainty will not exceed a given confidence level. and It is the fuzzy confidence level of the opportunity constraint, parameter Equation This refers to line capacity constraints. Note: Since power distribution systems are typically limited by voltage in actual operation, the reliability constraints of line power flow are ignored.

[0094] As one possible implementation of this embodiment, the process of establishing the deterministic equivalence of voltage, active power, and reactive power fuzzy chance constraints based on credibility theory is as follows:

[0095] This invention assumes that all nodes except the root node have uncontrollable renewable energy generators. That is, for nodes with… The radial system of nodes, used to represent the fuzzy vector of prediction error. yes Via. and It is defined as the sum of active and reactive power prediction errors because the fuzzy variables of the prediction errors are independent of each other. and for:

[0096] ;

[0097] ;

[0098] In order to obtain a definite equivalence class of constraints The real-time output of the controllable generator is written in the following form:

[0099] ;

[0100] in, ,definition , , , Therefore, according to credibility theory, opportunity constraint It can be represented in the following form:

[0101] ;

[0102] Similarly, we can obtain The deterministic equivalent formula.

[0103] constraint Active and reactive power at all nodes are limited to achieve real-time power balance under uncertainty. Due to the use of affine control and the setting of participation factors, when the total participation coefficient and the limit are... At that time, the generator output based on the affine strategy, coupled with the uncertain output, always matches the total demand precisely. Therefore It can be modified to:

[0104] ;

[0105] and similar, This can now be represented as a deterministic equality constraint.

[0106] To obtain a deterministic equivalent formula for the square of the voltage magnitude, this invention reconstructs the equation for the square of the voltage magnitude under uncertainty, making this equation represent the node prediction error. The linear representation of is

[0107] ;

[0108] in, This represents the set of nodes excluding the root node. The node voltage of the root node is the reference voltage on the secondary side of the substation. . It is a unit vector. It is an identity matrix. . It is a diagonal matrix, and the main diagonal elements are the resistance and reactance of each line. It is the correlation matrix between lines and nodes. Represents the set of all lines. The elements in are:

[0109] ;

[0110] This invention defines a matrix :

[0111] ;

[0112] Therefore, the square of the node voltage magnitude affected by uncertain power injection is converted to:

[0113] ;

[0114] Based on the credibility theory, this invention defines the definition. , , .therefore, The opportunity constraint in the equation can be reformulated as the following deterministic constraint:

[0115] ;

[0116] As one possible implementation of this embodiment, the process of further deriving the deterministically equivalent linear expression by introducing auxiliary variables is as follows:

[0117] constraint It is by and The piecewise constraints introduced by this problem prevent the model from being solved directly using a solver. This invention considers linearizing the piecewise constraints by setting auxiliary variables. Setting continuous variables , , , , binary variables , and a positive integer And make them satisfy the constraints given below:

[0118] ;

[0119] Therefore, constraints It is restated to the following linear form:

[0120] (20)

[0121] and Similarly, opportunity constraints It can be reformulated as a linear deterministic constraint:

[0122] ;

[0123] As one possible implementation of this embodiment, the process of establishing a deterministic optimization model for the distribution network that considers prediction uncertainties is as follows:

[0124] ;

[0125] Among them, the equation It is a constraint Deterministic equivalence. Constraints These are fuzzy chance constraints derived from credibility theory. The linear deterministic equivalence class.

[0126] As one possible implementation of this embodiment, the optimal controllable generator scheduling scheme with different safety margins is obtained by using the SCIP optimization solver to solve the distribution network optimization model at different confidence levels. This invention provides the optimal scheduling scheme under different confidence levels. By reasonably selecting the confidence level, the DSO can achieve the expected goal, providing a new tool and approach for addressing the uncertainty risks of distribution systems.

[0127] The following example illustrates the fuzzy chance-constrained optimal power flow calculation method based on credibility theory of this invention. In this example, an improved 15-bus system is used as the simulation object, where controllable distributed generators are connected at nodes 6 and 11. The cost parameters of the DERs at nodes 6 and 11 are set as follows: , The power generation cost of the substation is as follows: , The parameters are set to encourage the priority use of controlled DERs to hedge against uncertainties in node injection power.

[0128] The prediction error of the net load in this invention is set to follow an asymmetric distribution to verify that this invention can escape the limit of the symmetric distribution, and its four fuzzy parameters are used. Set as ,in . It indicates the degree of deviation between the predicted value and the actual value. A higher value means that a larger prediction error may occur.

[0129] In the DET-OPF method, the constraints are deterministic, i.e. , As for the GCC-OPF method, it does not consider the impact of uncertainties on voltage, and constrains... It is deterministic. As expected, in this invention, the voltage amplitude is constrained by chance. This drive ensures that voltage violations occur less frequently during real-time operation. The set value. With As the value decreases, the voltage amplitude at node 2-11 also decreases. This indicates that overvoltage may occur at node 2-11 even with a large positive prediction error, because... The value represents the concept of risk. By analogy, because... The higher the value, the smaller the voltage amplitude at node 1. Node 1 faces the risk of undervoltage in the presence of negative prediction errors.

[0130] Furthermore, compared to FCC-OPF, we observed significantly higher voltage amplitudes at nodes 2-11 in the DET-OPF and GCC-OPF cases because both employ deterministic voltage constraints, neglecting the impact of uncertainties on voltage. Therefore, DET-OPF and GCC-OPF may lead to frequent violations of voltage constraints in the distribution system during real-time operation. This highlights the need for the present invention to avoid frequent violations of real-time operating limits.

[0131] Table 1. GCC-OPF and FCC-OPF in different... Participation factors

[0132]

[0133] Table 1 shows the participation factors of GCC-OPF and FCC-OPF at different confidence levels. The role of the participation factor is to distribute the total power mismatch caused by prediction errors among generators to maintain real-time power balance. As can be seen from Table 1, the substation participation factor of FCC-OPF is significantly higher than that of GCC-OPF at different confidence levels because the participation coefficient is subject to the chance constraint in FCC-OPF. This indicates that when prediction errors exist in the system, substations need to provide more power to balance the system and maintain voltage safety margin. Furthermore, although the participation factor values ​​for FCC-OPF and GCC-OPF are not the same, their trends are similar. With... As the value increases, the participation factor of the substation decreases, while the participation factor of the controllable generator gradually increases. This phenomenon reflects that when the model-allowed risk increases, in order to achieve maximum economic benefits, the system will reduce the active power output of the substation and utilize more controllable generators to eliminate uncertainties in the power distribution system.

[0134] Using the Monte Carlo sampling method, 1000 sets of prediction error samples were obtained, under different... and The expected generation costs of DET-OPF, GCC-OPF, and FCC-OPF solutions. The expected cost is expressed as an equation. The value of the objective function shown reflects the expected dispatch cost before the occurrence of uncertainties. As expected, the expected generation cost increases with the introduction of additional opportunity constraints, thus ensuring a larger safety margin. The value represents the difference between the predicted net load and the actual net load. A higher value indicates a potentially larger prediction error, leading to higher costs for balancing the system in real-time operations. Furthermore, The value represents the concept of risk in the scheduling model. A lower value indicates a lower risk level. This indicates a lower tolerance for constraint violations, thus requiring more conservative and costly scheduling decisions. Generally, risk and cost are a trade-off. Slightly relaxing constraints may increase the total cost of the system. However, if constraints are relaxed too much, voltage limits may lead to violations. Therefore, in optimal power flow and renewable energy integration, choosing a reasonable confidence level to balance risk and cost requirements is essential.

[0135] For this invention, firstly, the DSO requires a given confidence level such that the frequency of system constraint violations does not exceed an acceptable level of violation. Models with high violation rates can lead to unsafe operations and may become infeasible. Secondly, DSO hopes... This reflects the trade-off between cost and security. The empirical violation rate of this invention is below an acceptable confidence level, and... As the value decreases, the voltage violation frequency also decreases. Furthermore, the empirical violation frequency of this invention varies with different... This aligns with expectations. This proves the feasibility of the present invention.

[0136] By reducing parameters Tightening the opportunity constraint by adjusting the value of the constraint can reduce the frequency of violations, and may even completely eliminate violations by some nodes, further confirming this. This symbolizes the magnitude of the risk. (Within the set value) At that time, there is a 24.8% chance that the voltage limit of node 6 will be violated; if the setting is set to 5%, no violation will occur on node 6.

[0137] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A fuzzy chance-constrained optimal power flow calculation method based on credibility theory, characterized in that: Includes the following steps: Construct a reliability distribution function for net load forecasting error; Establish a fuzzy chance-constrained optimization model that takes into account the uncertainty of net load forecasting; Based on the credibility theory, the deterministic equivalence of fuzzy chance constraints on voltage, active power, and reactive power is derived. By introducing auxiliary variables, we can further derive deterministically equivalent linear expressions; Establish a deterministic optimization model for the distribution network that takes into account forecasting uncertainties; By selecting different confidence levels to solve the distribution network optimization model, the optimal controllable generator scheduling schemes that satisfy different safety margins are obtained. The process of establishing a deterministic optimization model for a distribution network that takes into account forecasting uncertainty is as follows: ； in, For expected operating costs, It is the prediction error fuzzy vector. , Indicates the error parameter, parameter , , The first is affected by the prediction error. The active power and real-time net active load of the node. This represents the set of nodes excluding the root node. , It is a continuous variable.

2. The fuzzy chance-constrained optimal power flow calculation method based on credibility theory according to claim 1, characterized in that: The confidence distribution of the net load forecast error is as follows: ； in, For nodes The net load output prediction error, It is a node Fuzzy parameters of prediction error It is a symbol for measuring credibility. It is a fuzzy variable.

3. The fuzzy chance-constrained optimal power flow calculation method based on credibility theory according to claim 2, characterized in that: The node Net load output prediction error for: ； in, It is represented as a set of all nodes.

4. The fuzzy chance-constrained optimal power flow calculation method based on credibility theory according to claim 1, characterized in that: The method also includes real-time net active load affected by prediction errors. for: ； in, It is the net load vector. It is the prediction error fuzzy vector; The real-time active and reactive power of each controllable generator are: ； ； in, It is the total active power mismatch. , The reactive power component for each prediction error, , It is a controllable generator dispatching decision based on net load forecasting, vector Index is .

5. The fuzzy chance-constrained optimal power flow calculation method based on credibility theory according to claim 4, characterized in that: The method also includes the following: The expected operating costs are: ； ； in, , , They represent the first Fuel cost coefficient of generator; Indicates variance.

6. The fuzzy chance-constrained optimal power flow calculation method based on credibility theory according to claim 5, characterized in that: The method further includes, considering the uncertainty of renewable energy power forecasting, a fuzzy chance-constrained optimization model as follows: ； in, and It is the fuzzy confidence level of the opportunity constraint, parameter .

7. The fuzzy chance-constrained optimal power flow calculation method based on credibility theory according to claim 1, characterized in that: The method further includes the following: the real-time output of the controllable generator is: ； ； ； in, , The fuzzy parameters representing the active power of a controllable generator. and These represent the sum of the prediction errors for active and reactive power, respectively. .

8. The fuzzy chance-constrained optimal power flow calculation method based on credibility theory according to claim 1, characterized in that: The method also includes defining , , Then the deterministic constraint is: ； Define matrix : ； ； in, It is an incidence matrix; It is a unit vector. It is an identity matrix.

9. The fuzzy chance-constrained optimal power flow calculation method based on credibility theory according to claim 8, characterized in that: The deterministic constraints are: ； ； in, , , , , For continuous variables, , It is a binary variable. It is a positive integer.

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