A Stochastic Dispatch Method for Power Systems Taking into Account the Uncertainty of Accident Occurrence

Abstract

This invention discloses a stochastic dispatching method for power systems that considers the uncertainty of accident occurrence, relating to the field of new energy. It obtains a power system dispatching strategy by constructing a stochastic dispatching model based on the uncertainty of accident occurrence and system operation safety criteria. Considering the uncertainty of accident occurrence, a fuzzy set of accident probability distribution based on a data-driven method is established. A stochastic dispatching model for the power system considering line fault accident constraints and system operation safety criteria is then constructed. Finally, a decoupled column and constraint generation algorithm is proposed to iteratively solve the problem, achieving stochastic optimal dispatching of the power system. Based on the stochastic dispatching method for power systems, this invention improves the reliability of the obtained dispatching strategy by introducing an accident constraint model for line faults. It can effectively characterize the operational constraints of the power system under line fault conditions while ensuring the efficiency of the optimization model solution, thereby improving both the reliability and efficiency of power grid operation.

Description

Technical Field

[0001] This invention relates to new energy sources, specifically a stochastic dispatching method for power systems that takes into account the uncertainty of accident occurrence. Background Technology

[0002] In recent years, the frequent occurrence of extreme weather events has led to an increase in the frequency of power system accidents, and the rapid development of new energy sources has further increased the instability of the power grid, significantly affecting the safe and reliable operation of the power system. The N-1 safety criterion, commonly used in industry, has been gradually extended to the Nk case, meaning that system safety must be guaranteed even when any k components fail. This criterion has been applied in many studies on power system operation, planning, and the electricity market. Therefore, it is necessary to study stochastic scheduling methods for power systems that consider the uncertainty of accident occurrence. Currently, stochastic scheduling methods that consider the uncertainty of accident occurrence mainly include stochastic optimization and robust optimization. However, existing methods often suffer from problems such as scenario dependence, low solution efficiency, and strong conservatism. Therefore, it is necessary to study stochastic scheduling methods for power systems that can accurately characterize the uncertainty of accident occurrence.

[0003] This invention addresses the problem that existing technologies fail to accurately characterize the uncertainty of line fault occurrence, proposing a stochastic dispatching method for power systems that takes into account this uncertainty. It establishes a fuzzy set of fault probability distributions based on a data-driven approach, constructs a stochastic dispatching model for the power system considering fault constraints and system operational safety criteria, and then proposes a decoupled column and constraint generation algorithm to iteratively solve the problem. This invention can effectively characterize the operational constraints of the power system under line fault conditions while ensuring the efficiency of the optimization model, thereby improving both the reliability and efficiency of power grid operation. Summary of the Invention

[0004] The purpose of this invention is to provide a random dispatching method for power systems that takes into account the uncertainty of accident occurrence, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A stochastic dispatching method for a power system that takes into account the uncertainty of accident occurrence includes the following steps:

[0007] (1) Constructing a stochastic dispatch model for the power system

[0008] A stochastic dispatch model for the power system considering the uncertainty of accident occurrence is constructed. The objective function of the model is to minimize costs, including unit start-up costs, shutdown costs, no-load costs, expected fuel costs under the worst-case distribution, and penalty costs for load shedding or over-generation. Constraints include minimum start-up time constraints and minimum shutdown time constraints for thermal power units, logical relationship constraints between thermal power unit start-up variables, shutdown variables and start-up states, power generation and consumption balance constraints, line capacity constraints based on approximate DC power flow, thermal power unit capacity constraints, and inter-time ramping capability constraints for thermal power units. The specific model is as follows:

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[0019] In the formula: t, g, k, n, l are the subscripts representing the time period, traditional generating unit, renewable energy, node, and line, respectively; N t N g N k N b N l These refer to the collections that include all time periods, traditional generating units, renewable energy sources, nodes, and lines; The scheduled output of unit g during time period t; The predicted power output of wind farm k in time period t; d nt Let n be the system load during time period t; Let Δ be the minimum and maximum output of unit g under operating conditions; d B is the scheduling time interval; l The susceptance of line l; A nl This is the relationship matrix between nodes and lines; f is the transmission capacity of transmission line l; lt For line l, the active power flow occurs during time period t; θnt x is the voltage phase angle of node n in time period t; gt The binary variable representing the on / off state of unit g during time period t is 1 for on and 0 for off; u gt A binary variable representing whether unit g is started in time period t, where 1 indicates start and 0 indicates no start; v gt The variable representing whether unit g is shut down during time period t is a binary variable, where 1 represents shutdown and 0 represents no shutdown. These are the no-load cost, start-up cost, and shutdown cost of unit g, respectively. These are the minimum start-up time and minimum shutdown time for unit g, respectively; These represent the unit's upward climbing ability per unit time in both the operating and start-up states, respectively. These represent the unit's downward ramping capability per unit time in both the operating and shutdown states, respectively.

[0020] In the model The minimum expected operating cost of the worst-case distribution under given unit switching states x, u, v, pre-scheduled unit output p^, and actual accident state z is equal to the objective function value of the following optimization problem; the model includes line power flow constraints based on DC power flow, node balance constraints, line capacity constraints, node phase angle constraints, and unit capacity constraints containing accident variables; among them, the line power flow constraints consider accident variables, and the expression is linearized using a sufficiently large constant M:

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[0030] In the formula: z g Let z be a binary random variable characterizing the accident state of unit g, where 1 represents normal and 0 represents fault; lThe binary random variable characterizing the fault state of line l is 1 for normal and 0 for fault. If a fault occurs on the line, the system topology will change, and the line power flow expression based on the distribution transfer factor will no longer be applicable.

[0031] (2) Constructing the fuzzy set of accident occurrence

[0032] Based on a data-driven approach and the Nk safety criterion, the following fuzzy set of accident occurrences containing probabilistic information is established:

[0033]

[0034] In the formula: For an empirical distribution with radius ∈ Ω is the set of all probability distributions centered at Ω, and Ω is the support region of the random variable.

[0035] (3) Abstract and formalize the constructed model

[0036] The constructed model can be written in the following abstract form:

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[0038] stx∈X,

[0039] Where Q(x,ξ) is the optimal value for the following optimization problem:

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[0041] stB+C C1 y C1 +C C2 y C2 ≥D(x)ξ,

[0042] y C1 ≥0.

[0043] In the formula: x represents the decision variable in the first stage (x g ,u g ,v g ); ξ represents a binary random variable (z) g ,z l ), y C1 =(p,q+,q-), y C2 =(f,θ), c,a C1 ,a C2 Coefficient vector, B, C C1 C C2 D is the constraint coefficient matrix;

[0044] (4) An iterative solution algorithm based on column and constraint generation is adopted for the proposed model.

[0045] The minimization problem Q(x,ξ) is transformed into a maximization problem using duality techniques, and the bilinear term τ between the dual variable and the random variable in the equation is linearized. i :=π T [D(x)] i ξ i For each sample s, the maximization problem is equivalent to the following mixed-integer linear programming problem:

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[0049] -Mξ≤τ≤Mξ

[0050] D(x) T π-M(e-ξ)≤τ≤D(x) T π+M(e-ξ),

[0051] e T ξ≥Im.

[0052] In the formula: π is the dual variable;

[0053] Iterative solution based on column and constraint generation algorithm: First, relax the main problem so that it contains only a few cut constraints. As the number of iterations increases, gradually increase the number of cut constraints until the stopping criterion is met.

[0054] As a further aspect of the present invention, the iterative solution steps of the solution algorithm based on column and constraint generation are specifically as follows:

[0055] (1) Parameter initialization: Set the initial cut constraint set to include only the scenario without component failure and not other failure cases. Set the initial lower bound LB:=-∞ and the upper bound UB:=∞. Set the optimal clearance tolerance ε and the maximum number of iterations N. Repeat the following steps for n=1,...,N until the stopping criterion is met.

[0056] (2) Solve the following main problem:

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[0058] stx∈X,λ≥0,y C1 ≥0,

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[0061] Record the optimal solution (x) n ,λ n ,φ n And the optimal objective function value, and set the new LB as the optimal objective function value;

[0062] (3) Solve the subproblem for all s∈S and record the optimal solution ξ for each s in this iteration. n and the optimal objective function value ψ n Set the new UB as:

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[0064] (4) If If (UB-LB) / LB≤ε, then stop the iteration and return the solution; otherwise, add a constraint with ξ to the cut constraint set. n Relevant cut constraints: The added cut constraint is Q. u (x,ξ n The original problem form is:

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[0068] At the same time, new relevant decision variables were added. Return to step two and solve the main problem again.

[0069] Compared with the prior art, the beneficial effects of the present invention are: the present invention is based on the random scheduling method of power system, and improves the reliability of the obtained scheduling strategy by introducing the accident constraint model of line fault. It can effectively characterize the operation constraints of power system under line fault conditions while ensuring the efficiency of optimization model solution, thereby improving the reliability of power grid operation and improving the efficiency of power grid operation. Attached Figure Description

[0070] Figure 1 A flowchart illustrating a random dispatching method for power systems that takes into account the uncertainty of accident occurrence.

[0071] Figure 2 This is a flowchart of an iterative solution algorithm based on columns and constraints. Detailed Implementation

[0072] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0073] Please see Figure 1 In this embodiment of the invention, a power system stochastic dispatch method that takes into account the uncertainty of accident occurrence includes the following steps:

[0074] (1) Constructing a stochastic dispatch model for the power system

[0075] A stochastic dispatch model for the power system considering the uncertainty of accident occurrence is constructed. The objective function of the model is to minimize costs, including unit start-up costs, shutdown costs, no-load costs, expected fuel costs under the worst-case distribution, and penalty costs for load shedding or over-generation. Constraints include minimum start-up time constraints and minimum shutdown time constraints for thermal power units, logical relationship constraints between thermal power unit start-up variables, shutdown variables and start-up states, power generation and consumption balance constraints, line capacity constraints based on approximate DC power flow, thermal power unit capacity constraints, and inter-time ramping capability constraints for thermal power units. The specific model is as follows:

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[0086] In the formula: t, g, k, n, l are the subscripts representing the time period, traditional generating unit, renewable energy, node, and line, respectively; N t N g N k N b Nl These refer to the collections that include all time periods, traditional generating units, renewable energy sources, nodes, and lines; The scheduled output of unit g during time period t; The predicted power output of wind farm k in time period t; d nt Let n be the system load during time period t; Let Δ be the minimum and maximum output of unit g under operating conditions; d B is the scheduling time interval; l The susceptance of line l; A nl This is the relationship matrix between nodes and lines; f is the transmission capacity of transmission line l; lt For line l, the active power flow occurs during time period t; θ nt x is the voltage phase angle of node n in time period t; gt The binary variable representing the on / off state of unit g during time period t is 1 for on and 0 for off; u gt A binary variable representing whether unit g is started in time period t, where 1 indicates start and 0 indicates no start; v gt The variable representing whether unit g is shut down during time period t is a binary variable, where 1 represents shutdown and 0 represents no shutdown. These are the no-load cost, start-up cost, and shutdown cost of unit g, respectively. These are the minimum start-up time and minimum shutdown time for unit g, respectively; These represent the unit's upward climbing ability per unit time in both the operating and start-up states, respectively. These represent the unit's downward ramping capability per unit time in both the operating and shutdown states, respectively.

[0087] In the model The minimum expected operating cost of the worst-case distribution under given unit switching states x, u, v, pre-scheduled unit output p^, and actual accident state z is equal to the objective function value of the following optimization problem; the model includes line power flow constraints based on DC power flow, node balance constraints, line capacity constraints, node phase angle constraints, and unit capacity constraints containing accident variables; among them, the line power flow constraints consider accident variables, and the expression is linearized using a sufficiently large constant M:

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[0097] In the formula: z g Let z be a binary random variable characterizing the accident state of unit g, where 1 represents normal and 0 represents fault; l The binary random variable characterizing the fault state of line l is 1 for normal and 0 for fault. If a fault occurs on the line, the system topology will change, and the line power flow expression based on the distribution transfer factor will no longer be applicable.

[0098] (2) Constructing the fuzzy set of accident occurrence

[0099] Based on a data-driven approach and the Nk safety criterion, the following fuzzy set of accident occurrences containing probabilistic information is established:

[0100]

[0101] In the formula: For an empirical distribution with radius ∈ Ω is the set of all probability distributions centered at Ω, and Ω is the support region of the random variable.

[0102] (3) Abstract and formalize the constructed model

[0103] The constructed model can be written in the following abstract form:

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[0105] stx∈X,

[0106] Where Q(x,ξ) is the optimal value for the following optimization problem:

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[0108] stB+C C1 y C1 +C C2 y C2 ≥D(x)ξ,

[0109] y C1 ≥0.

[0110] In the formula: x represents the decision variable in the first stage (x g ,u g ,v g ); ξ represents a binary random variable (z)g ,z l ), y C1 =(p,q+,q-), y C2 =(f,θ), c,a C1 ,a C2 Coefficient vector, B, C C1 C C2 D is the constraint coefficient matrix;

[0111] (4) An iterative solution algorithm based on column and constraint generation is adopted for the proposed model.

[0112] The minimization problem Q(x,ξ) is transformed into a maximization problem using duality techniques, and the bilinear term τ between the dual variable and the random variable in the equation is linearized. i :=π T [D(x)] i ξ i For each sample s, the maximization problem is equivalent to the following mixed-integer linear programming problem:

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[0114]

[0115]

[0116] -Mξ≤τ≤Mξ

[0117] D(x) T π-M(e-ξ)≤τ≤D(x) T π+M(e-ξ),

[0118] e T ξ≥Im.

[0119] In the formula: π is the dual variable;

[0120] Iterative solution based on column and constraint generation algorithm: First, relax the main problem so that it contains only a few cut constraints. As the number of iterations increases, gradually increase the number of cut constraints until the stopping criterion is met.

[0121] Preferably, the iterative solution steps of the solution algorithm based on column and constraint generation are as follows:

[0122] (1) Parameter initialization: Set the initial cut constraint set to include only the scenario without component failure and not other failure cases. Set the initial lower bound LB:=-∞ and the upper bound UB:=∞. Set the optimal clearance tolerance ε and the maximum number of iterations N. Repeat the following steps for n=1,...,N until the stopping criterion is met.

[0123] (2) Solve the following main problem:

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[0125] stx∈X,λ≥0,y C1 ≥0,

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[0128] Record the optimal solution (x) n ,λ n ,φ n And the optimal objective function value, and set the new LB as the optimal objective function value;

[0129] (3) Solve the subproblem for all s∈S and record the optimal solution ξ for each s in this iteration. n and the optimal objective function value ψ n Set the new UB as:

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[0131] (4) If If (UB-LB) / LB≤ε, then stop the iteration and return the solution; otherwise, add a constraint with ξ to the cut constraint set. n Relevant cut constraints: The added cut constraint is

[0132] Q u (x,ξ n The original problem form is:

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[0136] At the same time, new relevant decision variables were added. Return to step two and solve the main problem again.

[0137] As a preferred embodiment of the present invention, the analysis is as follows:

[0138] This section uses an IEEE 6-bus system for simulation analysis. The system comprises three thermal power units (G1, G2, and G3) and eight transmission lines. The system design considers the N-2 safety criterion, meaning that for each node with no more than two adjacent transmission lines, there is a sufficiently large thermal power unit to meet the load on that node. The base load of each node is set at 20MW, the optimization period is 24 hours, and the time interval is 1 hour. It is assumed that all three units are slow-start units; fast-start units are not considered in this example.

[0139] Considering a safety criterion of N-2, the proposed method was used to train on 200 samples, and the algorithm based on column and constraint generation was applied to solve the problem. The total number of iterations was 5, and the results of each iteration are shown in Tables 1 and 2. In the first iteration, unit G3 was powered on for all 24 hours, unit G2 was not powered on, and unit G1 was powered on for the first 21 hours. At this point, the worst-case scenario, determined by subproblems, was that units G1 and G3 would fail simultaneously. The upper and lower bounds of the objective function were also determined. It can be observed that due to the limited cut-set constraints considered in the early stages of the iteration, the upper bound obtained at this time was very large. In the second iteration, the powered-on units were G2 and G3, while unit G1 was not powered on. Therefore, the worst-case scenario at this time was that units G2 and G3 would fail simultaneously. In the third iteration, the powered-on units became G1 and G2, and the worst-case scenario... Therefore, the situation changed to simultaneous failure of units G1 and G2; in the fourth iteration, all three units were started up. This iteration greatly reduced the upper bound of the objective function value. At this time, different worst-case scenarios were generated for different training samples. In addition to the case of simultaneous failure of two units, it also included the case of failure of line 2-4, indicating that line 2-4 is a relatively weak link in the system network; finally, in the fifth iteration, the upper bound and lower bound of the objective function value were equal, and the optimal start-up arrangement and the optimal objective function value of the model were finally determined, proving the effectiveness of the proposed method and algorithm.

[0140] Table 1 Iteration process record

[0141] Table 1 Iteration process record

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[0143] Table 2 Startup Schedule for Each Iteration

[0144] Table 2 Unit commitment of each iretation

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[0146] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0147] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A stochastic dispatching method for power systems that takes into account the uncertainty of accident occurrence, characterized in that, Includes the following steps: (1) Constructing a stochastic dispatch model for the power system A stochastic dispatch model for the power system considering the uncertainty of accident occurrence is constructed. The objective function of the model is to minimize costs, including unit start-up costs, shutdown costs, no-load costs, expected fuel costs under the worst-case distribution, and penalty costs for load shedding or over-generation. Constraints include minimum start-up time constraints and minimum shutdown time constraints for thermal power units, logical relationship constraints between thermal power unit start-up variables, shutdown variables and start-up states, power generation and consumption balance constraints, line capacity constraints based on approximate DC power flow, thermal power unit capacity constraints, and inter-time ramping capability constraints for thermal power units. The specific model is as follows: In the formula: t, g, k, n, l are the subscripts representing the time period, traditional generating unit, renewable energy, node, and line, respectively; N t N g N k N b N l These refer to the collections that include all time periods, traditional generating units, renewable energy sources, nodes, and lines; The scheduled output of unit g during time period t; The predicted power output of wind farm k in time period t; d nt Let n be the system load during time period t; P g , Let Δ be the minimum and maximum output of unit g under operating conditions; d B is the scheduling time interval; l The susceptance of line l; A nl This is the relationship matrix between nodes and lines; Let l be the power transmission capacity of transmission line l; f lt This represents the active power flow of line l during time period t. θ nt x is the voltage phase angle of node n in time period t; gt The binary variable representing the on / off state of unit g during time period t is 1 for on and 0 for off; u gt A binary variable representing whether unit g is started in time period t, where 1 indicates start and 0 indicates no start; v gt The variable representing whether unit g is shut down during time period t is a binary variable, where 1 represents shutdown and 0 represents no shutdown. These are the no-load cost, start-up cost, and shutdown cost of unit g, respectively. These are the minimum start-up time and minimum shutdown time for unit g, respectively; These represent the unit's upward climbing ability per unit time in both the operating and start-up states, respectively. These represent the unit's downward ramping capability per unit time in both the operating and shutdown states, respectively. In the model, Q(x,u,v,p^,z,w) represents the minimum expected operating cost of the worst-case distribution under given unit switching states x,u,v, pre-scheduled unit output p^, and actual accident state z. It is equal to the objective function value of the following optimization problem. The model includes line power flow constraints based on DC power flow, node balance constraints, line capacity constraints, node phase angle constraints, and unit capacity constraints with accident variables. The line power flow constraints consider accident variables, and the expression is linearized using a sufficiently large constant M. In the formula: z g Let z be a binary random variable characterizing the accident state of unit g, where 1 represents normal and 0 represents fault; l The binary random variable characterizing the fault state of line l is 1 for normal and 0 for fault. If a fault occurs on the line, the system topology will change, and the line power flow expression based on the distribution transfer factor will no longer be applicable. (2) Constructing the fuzzy set of accident occurrence Based on a data-driven approach and the Nk safety criterion, the following fuzzy set of accident occurrences containing probabilistic information is established: In the formula: For an empirical distribution with radius ∈ Ω is the set of all probability distributions centered at Ω, and Ω is the support region of the random variable. (3) Abstract and formalize the constructed model The constructed model can be written in the following abstract form: stx∈X, Where Q(x,ξ) is the optimal value for the following optimization problem: s.t.B+C C1 y C1 +C C2 y C2 ≥D(x)ξ, y C1 ≥0. In the formula: x represents the decision variable in the first stage (x g ,u g ,v g ); ξ represents a binary random variable (z) g ,z l ), y C1 =(p,q+,q-), y C2 =(f,θ), c,a C1 ,a C2 Coefficient vector, B, C C1 C C2 D is the constraint coefficient matrix; (3) An iterative solution algorithm based on column and constraint generation is adopted for the proposed model. The minimization problem Q(x,ξ) is transformed into a maximization problem using duality techniques, and the bilinear terms between the dual variables and random variables in the equation are linearized. For each sample s, the maximization problem is equivalent to the following mixed-integer linear programming problem: -Mξ≤τ≤Mξ In the formula: π is the dual variable; Iterative solution based on column and constraint generation algorithm: First, relax the main problem so that it contains only a few cut constraints. As the number of iterations increases, gradually increase the number of cut constraints until the stopping criterion is met.

2. The power system stochastic dispatch method considering the uncertainty of accident occurrence according to claim 1, characterized in that, The iterative solution steps of the solution algorithm based on column and constraint generation are as follows: (1) Parameter initialization: Set the initial cut constraint set to include only the scenario without component failure and not other failure cases. Set the initial lower bound LB:=-∞ and the upper bound UB:=∞. Set the optimal clearance tolerance ε and the maximum number of iterations N. Repeat the following steps for n=1,...,N until the stopping criterion is met. (2) Solve the following main problem: s.t.x∈X,λ≥0,y C1 ≥0, Record the optimal solution (x) n ,λ n ,φ n And the optimal objective function value, and set the new LB as the optimal objective function value; (3) Solve the subproblem for all s∈S and record the optimal solution ξ for each s in this iteration. n and the optimal objective function value ψ n Set the new UB as: (4) If If (UB-LB) / LB≤ε, then stop the iteration and return the solution; otherwise, add a constraint with ξ to the cut constraint set. n Relevant cut constraints: The added cut constraint is Q. u (x,ξ n The original problem form is: At the same time, new relevant decision variables were added. Return to step two and solve the main problem again.

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