A method for critical state-based economic dispatch of power system with reliability constraints

Abstract

The application discloses a power system reliability constraint economic dispatch method based on critical state, and according to the LOLP index requirement of the power system, the system state is screened, the state in which the load will be lost is removed by using the chance constraint direct current optimal power flow model, then the worse state in the state set is screened according to the capacity of the fault element, finally, the worse state in the set is screened according to the tolerance of the output plan of the system state within the source load prediction error range, so that the critical state set is obtained. The application converts the reliability requirement into the constraint condition that the critical state does not occur load loss, effectively reduces the state quantity, reduces the calculation complexity of the power system reliability constraint economic dispatch, and significantly improves the efficiency and accuracy of the power system reliability constraint economic dispatch.

Description

Technical Field

[0001] This invention relates to the field of power system dispatching technology, and specifically to a power system reliability-constrained economic dispatching method based on critical state. Background Technology

[0002] Over the past few decades, the rapid growth in electricity demand and the large-scale grid connection of wind power have impacted the safe and reliable operation of the power system. There are two main factors affecting the reliability of power system operation: one is the intermittency and uncertainty of wind power and the random fluctuations in load; the other is mainly caused by random outages of components. Therefore, it is necessary to address economic dispatching for operations with operational risks or reliability issues to improve the reliability of the power system.

[0003] However, in studies considering component failures, reliability-constrained economic scheduling can be categorized into safety-constrained economic scheduling and risk-constrained scheduling, depending on whether the probability of event occurrence is considered. Safety-constrained economic scheduling requires the system to continue operating reliably after the anticipated system state occurs. Risk-constrained scheduling expresses reliability indicators as objective functions or constraints, controlling the risk of the anticipated system state rather than controlling individual random events. The complexity of both risk-constrained and safety-constrained economic scheduling increases with the number of anticipated system states. Since the number of system states grows exponentially, the computational complexity of economic scheduling models is extremely high. Therefore, reducing system states is an effective means of establishing reliability-constrained economic scheduling models, and the process of reducing anticipated system states determines the economy and reliability of scheduling decisions.

[0004] Several methods have been proposed in the prior art, such as umbrella-shaped contingency, universal generating functions, uniform design, and root events, to reduce computational burden by reducing system states. However, existing methods for reducing anticipated system states focus on screening high-risk system states to control expected power shortages (EENS) in reliability-constrained economic scheduling, and struggle to consider load loss probability (LOLP).

[0005] Therefore, how to propose a state selection method that significantly reduces the number of states used for reliability constraints while maintaining high accuracy of reliability indicators is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] To address the shortcomings of the existing technologies, this invention provides a power system reliability-constrained economic dispatch method based on critical states. This method transforms reliability requirements into constraints that prevent load losses in critical states, thereby reducing the computational complexity of power system reliability-constrained economic dispatch and improving the operational reliability of the power system.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] A power system reliability-constrained economic dispatch method based on critical state includes the following steps:

[0009] S1. Obtain the power system LOLP index requirements, and based on the obtained power system LOLP index requirements, obtain the cumulative probability requirements of the cutoff state;

[0010] S2. Based on the cumulative probability requirement of the truncation state, select the system state in descending order of probability to obtain the system state set H;

[0011] S3. Based on the obtained system state set, the opportunity-constrained DC optimal power flow model is used to obtain the corresponding load shedding amount in order to obtain the system state without load shedding, thereby obtaining the state set I.

[0012] S4. Using the upper and lower limits of the conventional units of each bus and the upper and lower limits of the transmission capacity between each bus pair as the criteria for the good and bad relationships between the system states in the state set I, update the state set I so that the system states in the state set I are in the worst state, thereby obtaining the state set A.

[0013] S5. Divide the system states in state set A into different subsets according to whether the faulty units are the same, and filter each subset in turn to select the worst system state, thereby obtaining the critical state set C.

[0014] S6. Based on the critical state set C, construct a reliability-constrained economic scheduling model with reliability constraints and solve it to obtain a scheduling scheme that meets the LOLP requirements.

[0015] Preferably, in step S1, the cumulative probability of the truncation state is calculated using the following formula:

[0016]

[0017] In the formula, This represents the cumulative probability requirement for the truncated state. ΔP represents the LOLP (Looseness-of-Placement) index requirement for the power system, and ΔP represents the slack variable that makes the screening state meet the LOLP index requirement for the power system.

[0018] Preferably, step S2 includes:

[0019] S21. Initialize the cumulative probability P = 0, the currently selected system state set H is an empty set, and the currently selected maximum state order k = 0;

[0020] S22. Calculate the probability of occurrence of each system state in the system state set, and sort the probability of occurrence of each system state in descending order. Where S i,m This represents the m-th system state selected in the i-th state. The probability of the m-th selected system state occurring in the i-th state;

[0021] S23. Based on the sorted system state list, select the system state that ranks first in the system state list and add it to the system state set H, and update the cumulative probability of the currently selected system state.

[0022] S24. If the cumulative probability of the currently selected system state is greater than the cumulative probability of the truncation state, then proceed to step S25; otherwise, proceed to step S26.

[0023] S25. System state selection stops, and the neighboring states of the selected system state are added to the system state set H. The final system state H is then output.

[0024] S26. Select the next state in the system state list as the currently selected system state and return to step S23.

[0025] Preferably, in step S22, the formula for calculating the probability of occurrence of each system state in the system state set is as follows:

[0026]

[0027] In the formula, P(s) represents the probability of a single system state s, and X represents the set of all components in the power system. d p represents the set of faulty components in the system state. i This represents the failure probability of component i.

[0028] Preferably, in step S3, the opportunity-constrained DC optimal power flow model is used to obtain the calculation formula for the corresponding load shedding:

[0029]

[0030] In the formula, p g , These represent the minimum, planned, and maximum output of a conventional unit, respectively, and p. w p w,f , These represent the planned output, predicted power generation, and actual power generation of the wind turbine, respectively; d b d b,f , These represent the planned, predicted, and actual load supply values ​​for bus b, respectively, and e. a This represents the total deviation of the injected power caused by the source load prediction error. These represent the power injection from conventional generating units, the power injection from renewable energy sources, and the power flow distribution factor, which translates load demand into line power flow. The wind curtailment volume (w) of the wind turbine generator, f l max ε represents the upper limit of the transmission capacity of line l. UR , ε DR , ε L , respectively, represent the confidence level of not violating the upper reserve / lower reserve / line power flow limits, G represents the set of all conventional units, W represents the set of all wind turbine units, and B represents the set of all buses.

[0031] Preferably, in step S4, the calculation formulas for the upper and lower limits of the conventional units of each bus in the system state set I are as follows:

[0032]

[0033] In the formula, This represents the upper limit of the output of the conventional units on bus b under system state s. This represents the lower limit of the output of the conventional units on bus b under system state s. This indicates the state g of a conventional unit under system state s;

[0034] The calculation formulas for the upper and lower limits of the transmission capacity between each bus pair are as follows:

[0035]

[0036] In the formula, This represents the upper limit of the transmission capacity between bus pairs (k, b) under system state s. This represents the lower limit of the transmission capacity between bus pairs (k, b) under system state s. Let (k,b) represent the state of line l under state s, and (k,b) represent a bus pair.

[0037] Preferably, step S5 includes:

[0038] S51. Initialize the critical state set C to be an empty set;

[0039] S52, Define different subsets N g Represents the number of types of faulty units, and the subsets The first state in Set it as the baseline state and initialize it to store the subsets. The set of states selected from the middle It is an empty set;

[0040] S53. Calculate the reference state. Under conditions of no load loss, the assembly Maximum optimal load shedding LS c and the corresponding state c;

[0041] S54, when LS c When LS equals 0, then execute step S55; when LS equals 0, then execute step S55. c If it is greater than 0, then update. for renew for Return to step S53;

[0042] S55, will Updated to As a new baseline state, up to the subset When each state in the equation is used as the baseline state, the critical state set C is updated as follows:

[0043] Preferably, in step S53, the calculation of the reference state... Under conditions of no load loss, the assembly Maximum optimal load shedding LS c The formula for calculating the corresponding state c is as follows:

[0044] maxLS c

[0045]

[0046] In the formula, p w,f These represent the actual and predicted values ​​of the power generation of the wind turbine, respectively. d b,f These represent the actual and predicted load values ​​for busbar b, respectively. f represents the planned output of conventional unit g and wind turbine w under state s, respectively. l s This represents the power flow of line l under state s. The state represents the phase angle of bus b under state s. This indicates the maximum predicted error for the power generation of the wind turbine unit w. This indicates the maximum predicted load error for busbar b.

[0047] Preferably, in step S6, the reliability constraint applies a no-loss constraint to each state in the critical state set C, and the specific steps are as follows:

[0048]

[0049] In the formula, This represents the output fluctuation of a conventional unit g caused by component failure under state s. This represents the total deviation of the injected power caused by the source load prediction error under state s. This represents the participation factor in the radiation control of a conventional unit g under state s. These represent the conventional unit's upper standby and lower standby configurations, respectively. These represent the power flow distribution factors that transform conventional unit injected power, renewable energy injected power, and load demand into line power flow under state s, respectively. p w These represent the actual and planned power generation of the wind turbine, respectively. p represents the actual load value of busbar b. g This indicates the planned output of the conventional unit g. f represents the amount of wind curtailed by the wind turbine in state s. l max This indicates the upper limit of the transmission capacity of line l. ε represents the state of unit g under state s. UR ε DR ε L G represents the confidence level of not violating the upper reserve / lower reserve / line power flow limits, respectively. s Let G represent the set of faulty units in state s. b Let G represent the set of conventional units on bus b, W represent the set of all conventional units, and B represent the set of all wind turbines.

[0050] Compared with the prior art, the present invention has the following technical effects:

[0051] (1) This invention reduces the number of states that need to be considered in the economic dispatch model by screening out the set of critical states in the power system, thereby reducing the computational complexity of the model. While reducing the number of states, it ensures the high accuracy of reliability indicators so that the reliability of the power system is not affected. The selected set of critical states is used to construct the system's reliability constraints. These constraints can ensure that no load loss occurs during the operation of the power system. Finally, the constructed reliability constraints are incorporated into the Reliability-Constrained Economic Dispatch (RECD) model, and the constraints of the model are modified or extended so that the dispatch scheme in the dispatch model can achieve economic dispatch while satisfying reliability.

[0052] (2) The power system reliability-constrained economic dispatch method based on critical states designed in this invention constructs reliability constraints based on a set of critical states, enabling accurate modeling of power system operational reliability, rapid and accurate assessment of power system operational reliability, and application to reliability-constrained economic dispatch to improve system operational reliability. It can effectively complement traditional power system economic dispatch and is of great significance for planning and dispatching that considers reliability. Attached Figure Description

[0053] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0054] Figure 1 This is a schematic diagram of the critical state in this invention;

[0055] Figure 2 This is a flowchart of a power system reliability-constrained economic dispatch method based on critical state disclosed in this invention;

[0056] Figure 3 This is a schematic diagram of the neighborhood state in an embodiment of the present invention. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but only to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0058] The present invention will now be described in further detail with reference to the accompanying drawings.

[0059] This invention addresses the problem of slow calculation speed in reliability-constrained economic dispatch in power systems by proposing a screening method based on critical states. This method transforms reliability requirements into constraints that prevent load loss in critical states, thereby reducing the complexity of reliability constraints, facilitating their inclusion in dispatch models, and providing more reliable support for the reliable and safe operation of new power systems.

[0060] To achieve the above objectives, it is necessary to establish the concept of a critical state of the power system. This means that the power system typically has specific requirements regarding the probability of load shedding (LOLP) during operation. For example, the requirement that "power outages should not exceed one day in ten years" can be converted into a LOLP requirement. Figure 1 The critical states shown are a specific set of states where load loss is prevented, ensuring that the cumulative probability of the set of states satisfying 1-LOLP will not result in load loss, thus guaranteeing the reliability of the power system. Using these states to establish reliability constraints significantly reduces the complexity of reliability constraints and facilitates the solution of reliability-constrained economic dispatch.

[0061] In specific implementation, the steps of this invention are as follows: Figure 2 As shown, it specifically includes:

[0062] S1. Obtain the power system LOLP index requirements, and based on the obtained power system LOLP index requirements, obtain the cumulative probability requirements of the cutoff state;

[0063] S2. Based on the cumulative probability requirement of the truncation state, select the system state in descending order of probability to obtain the system state set H;

[0064] S3. Based on the obtained system state set, the opportunity-constrained DC optimal power flow model is used to obtain the corresponding load shedding amount, so as to obtain the system state that will not lose load. When the cumulative probability of the system state that will not lose load meets the power system LOLP index requirement, the state set I is obtained.

[0065] S4. Using the upper and lower limits of the conventional units of each bus and the upper and lower limits of the transmission capacity between each bus pair as the criteria for the good and bad relationships between the system states in the state set I, update the state set I so that the system states in the state set I are in the worst state, thereby obtaining the state set A.

[0066] S5. Divide the system states in state set A into different subsets based on whether the faulty units are the same, and filter each subset in turn to select the worst system state, thereby obtaining the critical state set C.

[0067] S6. Based on the critical state set C, construct a reliability-constrained economic scheduling model with reliability constraints and solve it to obtain a scheduling scheme that meets the LOLP requirements.

[0068] In this embodiment, by selecting the set of critical states in the power system, the number of states that need to be considered in the economic dispatch model is reduced, thereby reducing the computational complexity of the model. While reducing the number of states, the high accuracy of reliability indicators is ensured, so that the reliability of the power system is not affected. The selected set of critical states is used to construct the system's reliability constraints. These constraints can ensure that no load loss occurs during the operation of the power system. Finally, the constructed reliability constraints are incorporated into the economic dispatch model, and the constraints of the model are modified or extended so that the dispatch scheme in the dispatch model can achieve economic dispatch while satisfying reliability.

[0069] In specific implementation, the cumulative probability of the truncation state in step S1 is required to be calculated using the following formula:

[0070]

[0071] In the formula, This represents the cumulative probability requirement for the truncated state. ΔP represents the LOLP (Looseness-of-Placement) index requirement for the power system, and ΔP represents the slack variable that makes the screening state meet the LOLP index requirement for the power system.

[0072] In specific application embodiments, components are rearranged in ascending order of availability and numbered 1, 2, ..., n. That is: p1 ≤ p2 ≤ ... ≤ p n In the formula, P1 represents the availability of component 1; the system status is represented by faulty components, such as S3(1,2,3) representing the faults of components 1, 2, and 3.

[0073] In specific implementation, step S2 includes:

[0074] S21. Initialize the cumulative probability P = 0, the currently selected system state set H is an empty set, and the currently selected maximum state order k = 0;

[0075] S22. Calculate the probability of occurrence of each system state in the system state set, and sort the probability of occurrence of each system state in descending order. Where S i,m This represents the m-th system state selected in the i-th state. The probability of the m-th selected system state occurring in the i-th state;

[0076] S23. Based on the sorted system state list, select the system state that ranks first in the system state list and add it to the system state set H, and update the cumulative probability of the currently selected system state.

[0077] S24. When it is determined that the cumulative probability of the currently selected system state is greater than the cumulative probability of the truncated state, step S25 is executed; otherwise, step S26 is executed.

[0078] S25. The selection of the system state stops, and the neighborhood states of the selected system state are added to the system state set H, and the final system state H is output.

[0079] S26. The next state in the system state list is used as the currently selected system state, and step S23 is returned.

[0080] Specifically, in step S22, the calculation formula for calculating the occurrence probability of each system state in the system state set is as follows:

[0081]

[0082] In the formula, P(s) represents the probability of a single system state s, X represents the set of all components in the power system, and X d represents the set of faulty components in this system state, and p i represents the failure probability of component i.

[0083] Among them, as Figure 3 shown, the generation of the neighborhood state follows the following rules: Assume that the serial number of the xth faulty component is "a", and the number of the x + 1th faulty component is "c". If there is a faulty component with the number b = a + 1 < c, then replace the component "a" with "b" to obtain a neighborhood state of the neighborhood state set.

[0084] Specifically, in step S3, an opportunity-constrained DC optimal power flow model is adopted, and the calculation formula for the corresponding load shedding amount is:

[0085]

[0086] In the formula, p g , respectively represent the minimum output, planned output, and maximum output of the conventional unit g, and p w , p w,f , respectively represent the planned output, predicted power generation, and actual power generation of the wind turbine w; d b , d b,f , respectively represent the planned supply value, predicted value, and actual value of the load of the bus b, and e a represents the total deviation of the injection power caused by the source-load prediction error, These represent the power injection from conventional generating units, the power injection from renewable energy sources, and the power flow distribution factor, which translates load demand into line power flow. The wind curtailment volume (w) of the wind turbine generator, f l max ε represents the upper limit of the transmission capacity of line l. UR , ε DR , ε L , respectively, represent the confidence level of not violating the upper reserve / lower reserve / line power flow limits, G represents the set of all conventional units, W represents the set of all wind turbine units, and B represents the set of all buses.

[0087] In specific implementation, in step S4, the calculation formulas for the upper and lower limits of the conventional units of each bus in the system state set I are as follows:

[0088]

[0089] In the formula, This represents the upper limit of the output of the conventional units on bus b under system state s. This represents the lower limit of the output of the conventional units on bus b under system state s. This indicates the state g of a conventional unit under system state s;

[0090] The calculation formulas for the upper and lower limits of the transmission capacity between each bus pair are as follows:

[0091]

[0092] In the formula, This represents the upper limit of the transmission capacity between bus pairs (k, b) under system state s. This represents the lower limit of the transmission capacity between bus pairs (k, b) under system state s. Let (k,b) represent the state of line l under state s, and (k,b) represent a bus pair.

[0093] In specific implementation, in step S5, within the source load prediction error range, under the same conventional unit output, the state more likely to lose load is considered a worse state. Based on the system state's tolerance to the output plan, the worse states in state set A are selected as the critical state set C. Ensuring that the states in C do not lose load guarantees that the states in state set I will not lose load. Step S5 includes:

[0094] S51. Initialize the critical state set C to be an empty set;

[0095] S52, Define different subsets N g Represents the number of types of faulty units, and the subsets The first state in Set it as the baseline state and initialize it to store the subsets. The set of states selected from the middle It is an empty set;

[0096] S53. Calculate the reference state. Under conditions of no load loss, the assembly Maximum optimal load shedding LS c and the corresponding state c;

[0097] S54, when LS c When LS equals 0, then execute step S55; when LS equals 0, then execute step S55. c If it is greater than 0, then update. for renew for Return to step S53;

[0098] S55, will Updated to As a new baseline state, up to the subset When each state in the equation is used as the baseline state, the critical state set C is updated as follows:

[0099] In specific implementation, in step S53, the calculation of the reference state... Under conditions of no load loss, the assembly Maximum optimal load shedding LS c The formula for calculating the corresponding state c is as follows:

[0100] maxLS c

[0101]

[0102] In the formula, p w,f These represent the actual and predicted values ​​of the power generation of the wind turbine, respectively. d b,f These represent the actual and predicted load values ​​for busbar b, respectively. f represents the planned output of conventional unit g and wind turbine w under state s, respectively. l s This represents the power flow of line l under state s. The state represents the phase angle of bus b under state s. This indicates the maximum predicted error for the power generation of the wind turbine unit w. This indicates the maximum predicted load error for busbar b.

[0103] The constraints that must be satisfied during economic dispatch in a power system include those related to the optimal DC power flow in state c and the baseline state; the load shedding in the baseline state is 0; the output of conventional units in state c is less than or equal to the output of conventional units in the baseline state; the actual values ​​of wind turbine power generation and load are within the prediction error range; and state c is a set. One of the states.

[0104] In specific implementation, in step S6, the reliability constraint is to apply a no-loss constraint to each state in the critical state set C, and the specific steps are as follows:

[0105]

[0106]

[0107] In the formula, This represents the output fluctuation of a conventional unit g caused by component failure under state s. This represents the total deviation of the injected power caused by the source load prediction error under state s. This represents the participation factor in the radiation control of a conventional unit g under state s. These represent the conventional unit's upper standby and lower standby configurations, respectively. These represent the power flow distribution factors that transform conventional unit injected power, renewable energy injected power, and load demand into line power flow under state s, respectively. p w These represent the actual and planned power generation of the wind turbine, respectively. p represents the actual load value of busbar b. g This indicates the planned output of the conventional unit g. f represents the amount of wind curtailed by the wind turbine in state s. l max This indicates the upper limit of the transmission capacity of line l. ε represents the state of unit g under state s. UR ε DR ε L G represents the confidence level of not violating the upper reserve / lower reserve / line power flow limits, respectively. s Let G represent the set of faulty units in state s. b Let G represent the set of conventional units on bus b, W represent the set of all conventional units, and B represent the set of all wind turbines.

[0108] Example:

[0109] To better understand the effects of this invention, the proposed method for screening anticipated system states is compared with the Nk criterion. By comparing the chance-constrained reliability-constrained economic scheduling model based on all anticipated system states, the Benders decomposition model based on all anticipated system states, and the stochastic optimization model based on the scenario method of all anticipated system states, the accuracy and computational efficiency of the critical state screening are demonstrated. The accuracy of the proposed RCED model is also demonstrated by comparing it with an adjustment constraint model that does not add substituted states.

[0110] The proposed critical state-based power system reliability-constrained economic dispatch method in this embodiment was tested on a modified IEEE RTS-79 system. The RTS-79 system consists of 32 generator units and 38 transmission lines, with an installed capacity of 3405 MW and a peak load of 2850 MW. Generators 1, 6, 7, 8, 10, 11, 12, 13, 21, 25, 26, 27, 28, and 30 were replaced by wind farms of equivalent capacity. The goal is to meet reliability requirements using both conventional and wind turbine generator units in a cost-optimal manner, while simultaneously (with a high probability) meeting all capacity and flow constraints. In other words, we aim to solve the problem. We consider a LOLP of 0.002, meaning the probability of system load shedding needs to exceed 0.998.

[0111] Table 1 shows the cost factor, minimum and maximum generating capacity, and maximum reserve capacity of conventional generators. The reactance and capacity of transmission lines are given in [reference needed]. PTDF matrix. Based on calculations, the objective of this embodiment is to ensure that the risk of insufficient system backup capacity and line overload does not exceed 5% under any anticipated system condition; therefore, α is set. UR ,α DR , and All values ​​are 0.05. The predicted power output of each wind turbine is 70% of its rated capacity, and the predicted load is 60% of the peak load. The random variable, the deviation between the prediction and actual generation, is assumed to follow a truncated normal distribution with a mean of zero and a cutoff interval of 15% of the predicted value. It is assumed that scheduling decisions are made approximately 15 minutes before the actual time demand is met. This demonstrates that the finite support assumption for the deviation between prediction and actual generation is reasonable. Note that, technically, wind turbine output can range from 0 MW to rated capacity, which is considered their physical limit. All case studies were conducted on a PC equipped with an AMD Ryzen 74800H 2.9GHz processor and 16GB of RAM. RCED was performed using the GUROBI YALMIP solver.

[0112] Table 1 Data for Conventional Power Generation Units

[0113]

[0114] At this point, the proposed method will be compared with three other methods for solving reliability-constrained economic scheduling problems. These methods are explained below:

[0115] Improvements in reliability and solvability of the scheduling model. First, compared with the Nk criterion, the anticipated system state screening method is analyzed for improvements in reliability and solvability of the scheduling model. In the Nk criterion, k = 1, 2, 3 is used.

[0116] The effectiveness of maximum probability state truncation was investigated. First, the speed and number of states involved in state truncation were studied. The reduction in the number of states by the maximum probability state truncation method was analyzed by comparing the commonly used Nk criterion with that of the Nk criterion. In the Nk criterion, k = 1, 2, 3 was used. The number of states and probabilities obtained by different state selection methods are given in Table 2. The Nk criterion does not consider the probability of system states and can quickly obtain the expected set of system states, with expected system state generation times of 0.1498s, 0.1629s, and 0.2604s, respectively. The proposed state truncation method selected a set of states that met the probability requirements in 12.0094s. However, the Nk criterion, by not selecting states based on probability, ignores high-probability states among higher-order states. The N-3 criterion considers a total of 29317 system states with a total state probability of 0.9892. The maximum probability state truncation method can consider states with a higher probability of occurrence, considering 18848 system states with a total state probability of 0.999. Under the same LOLP requirements, the maximum probability state truncation method considers fewer states, reducing the number of states used for reliability constraints and lowering model complexity. Furthermore, unlike the discontinuity in the expected system set probabilities generated by the Nk criterion, the maximum probability state truncation method can filter system states according to LOLP requirements. Therefore, using the maximum probability state truncation method can effectively reduce the number of system states used for reliability constraints.

[0117] Table 2 shows the number and probability of states obtained by different state selection methods.

[0118]

[0119] The necessity of removing load shedding states. The scheduling results obtained from different state screening methods are shown in Table 3. The N-1 criterion guarantees a system load shedding probability of 0.7648, a generator cost of 112.7945, and a reserve cost of 34.4406. However, it considers fewer states for reliability constraints and does not meet the LOLP requirements for system operation. The N-2 and N-3 criters and the cutoff state... The system contains states that will still lose load regardless of scheduling, therefore the scheduling model has no solution. Although the proposed pre-defined system state filtering method takes 132.8055s to remove the unloaded states, it ensures the solvability of the model after removing the unloaded states and can obtain scheduling results that meet the system LOLP requirements.

[0120] Table 3. Scheduling results obtained by different state filtering methods

[0121]

[0122] The effectiveness and efficiency of critical state screening. Table 2 shows that critical system state screening takes 268.4032 seconds, increasing the state preprocessing time, but reducing the number of states with reliability constraints from 19701 to 892. The solution time for Chance-and-Reliability-Constrained Economic Dispatch (CRCED) based on the critical system state set is 32.3042 seconds, with a total time of 300.7074 seconds from state screening to obtaining the scheduling result. The solution time for CRCED based on the anticipated system state is 728.5468 seconds, with a total time of 861.3523 seconds from state screening to obtaining the scheduling result.

[0123] When establishing reliability constraints, each system state requires corresponding decision variables to establish corresponding upper and lower reserves and line overload risk constraints. Therefore, the decision variables for reliability constraints in the unloaded state CRCED-AS are 20.72 times that of the critical system state CRCED-CS. Although corresponding adjustment constraints are added to CRCED-CS to ensure that the represented state has sufficient reserves to prevent unload, only the number of constraints is increased, not the number of decision variables, which greatly reduces the modeling and computational complexity.

[0124] Reliability and economy of critical system state screening. Table 3 shows that removing the off-load state CRCED-AS and the critical system state CRCED-CS results in a generation cost of 133.506 and a reserve cost of 199.5185, ensuring that the system state set is within the acceptable range under all states, with the risk of reserve requirements and line overload not exceeding 5%. No load loss. Under both methods, the unit output and standby have the same configuration, proving that the proposed state screening method reduces system states and speeds up the solution process without reducing the economy and reliability of the scheduling scheme.

[0125] The Necessity of Critical System State Screening. When the reliability level is further improved, such as when the system LOLP requirement is 0.001 (meaning the system's probability of not losing load is greater than 0.999), the comparison between the results of removing the loss-of-load state CRCED-AS and the critical system state CRCED-CS is shown in Table 4. Removing the loss-of-load state CRCED-AS increases the number of states used to establish reliability constraints to 36001, resulting in a model solution time of 2328.7654 s. In contrast, although the critical system state CRCED-CS takes an additional 230.6757 s for state screening, it reduces the number of states used to establish reliability constraints to 1178, and the model solution time is correspondingly reduced to 35.7859 s. Therefore, in large-scale systems, as the LOLP requirement increases, the number of states to be considered increases dramatically. Without further screening of the anticipated system states, the solution complexity of the CRCED model will increase dramatically, failing to meet the real-time requirements of system operation. Therefore, critical system state screening is essential for improving computational efficiency.

[0126] Table 4 Comparison of results between CRCED-AS and CRCED-CS

[0127]

[0128] In summary, this invention reduces the number of states that need to be considered in the economic dispatch model by screening out the set of critical states in the power system, thereby reducing the computational complexity of the model. While reducing the number of states, it ensures high accuracy of reliability indicators, so that the reliability of the power system is not affected. The screened set of critical states is used to construct the system's reliability constraints, which can ensure that no load loss occurs during the operation of the power system. Finally, the constructed reliability constraints are incorporated into the economic dispatch model, and the constraints of the model are modified or extended so that the dispatch scheme in the dispatch model can achieve economic dispatch while satisfying reliability.

[0129] This invention filters system states based on LOLP (Location-Based Power Flow) requirements, uses a chance-constrained DC optimal power flow model to remove states that will definitely lose load, then filters worse states from the state set based on the capacity of faulty components, and finally, within the source-load prediction error range, filters out even worse states from the set based on the system state's tolerance to the power output plan, thereby obtaining a critical state set. Through the above filtering method, the number of states is effectively reduced, and the efficiency and accuracy of power system reliability-constrained economic dispatch are significantly improved.

[0130] This invention presents a critical state-based economic dispatch method for power systems, which constructs reliability constraints based on a set of critical states. This method enables accurate modeling of power system operational reliability, rapid and accurate assessment of power system operational reliability, and can be applied to reliability-constrained economic dispatch to improve system operational reliability. It serves as a valuable supplement to traditional power system economic dispatch and is of great significance for planning and dispatching that considers reliability.

[0131] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described with reference to preferred embodiments, those skilled in the art should understand that various changes in form and detail can be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A power system reliability-constrained economic dispatch method based on critical state, characterized in that, Includes the following steps: S1. Obtain the power system LOLP index requirements, and based on the obtained power system LOLP index requirements, obtain the cumulative probability requirements of the cutoff state; S2. Based on the cumulative probability requirement of the truncation state, select the system state in descending order of probability to obtain the system state set H; S3. Based on the obtained system state set, the opportunity-constrained DC optimal power flow model is used to obtain the corresponding load shedding amount in order to obtain the system state without load shedding, thereby obtaining the state set I. S4. Using the upper and lower limits of the conventional units of each bus and the upper and lower limits of the transmission capacity between each bus pair as the criteria for the good and bad relationships between the system states in the state set I, update the state set I so that the system states in the state set I are in the worst state, thereby obtaining the state set A. S5. Divide the system states in state set A into different subsets according to whether the faulty units are the same, and filter each subset in turn to select the worst system state, thereby obtaining the critical state set C. S6. Based on the critical state set C, construct a reliability-constrained economic scheduling model with reliability constraints and solve it to obtain a scheduling scheme that meets the LOLP requirements.

2. The power system reliability-constrained economic dispatch method based on critical state as described in claim 1, characterized in that, In step S1, the cumulative probability requirement for the truncation state is calculated using the following formula: In the formula, This represents the cumulative probability requirement for the truncated state. ΔP represents the LOLP (Looseness-of-Placement) index requirement for the power system, and ΔP represents the slack variable that makes the screening state meet the LOLP index requirement for the power system.

3. The power system reliability-constrained economic dispatch method based on critical state as described in claim 1, characterized in that, Step S2 includes: S21. Initialize the cumulative probability P = 0, the currently selected system state set H is an empty set, and the currently selected maximum state order k = 0; S22. Calculate the probability of occurrence of each system state in the system state set, and sort the probability of occurrence of each system state in descending order. Where S i,m This represents the m-th system state selected in the i-th state. The probability of the m-th selected system state occurring in the i-th state; S23. Based on the sorted system state list, select the system state that ranks first in the system state list and add it to the system state set H, and update the cumulative probability of the currently selected system state. S24. If the cumulative probability of the currently selected system state is greater than the cumulative probability of the truncation state, then proceed to step S25; otherwise, proceed to step S26. S25. System state selection stops, and the neighboring states of the selected system state are added to the system state set H. The final system state H is then output. S26. Select the next state in the system state list as the currently selected system state and return to step S23.

4. The power system reliability-constrained economic dispatch method based on critical state as described in claim 3, characterized in that, In step S22, the formula for calculating the probability of occurrence of each system state in the system state set is as follows: In the formula, P(s) represents the probability of a single system state s, and X represents the set of all components in the power system. d p represents the set of faulty components in the system state. i This represents the failure probability of component i.

5. The power system reliability-constrained economic dispatch method based on critical state as described in claim 1, characterized in that, In step S3, the opportunity-constrained DC optimal power flow model is used to obtain the corresponding calculation formula for the unloaded amount: In the formula, p g , These represent the minimum, planned, and maximum output of a conventional unit, respectively, and p. w p w,f , These represent the planned output, predicted power generation, and actual power generation of the wind turbine unit, respectively. d b d b,f , These represent the planned, predicted, and actual load supply values ​​for bus b, respectively, and e. a This represents the total deviation of the injected power caused by the source load prediction error. These represent the power injection from conventional generating units, the power injection from renewable energy sources, and the power flow distribution factor, which translates load demand into line power flow. The wind curtailment volume (w) of the wind turbine generator, f l max ε represents the upper limit of the transmission capacity of line l. UR , ε DR , ε L , respectively, represent the confidence level of not violating the upper reserve / lower reserve / line power flow limits, G represents the set of all conventional units, W represents the set of all wind turbine units, and B represents the set of all buses.

6. The power system reliability-constrained economic dispatch method based on critical state as described in claim 1, characterized in that, In step S4, the calculation formulas for the upper and lower limits of the conventional units of each bus in the system state set I are as follows: In the formula, This represents the upper limit of the output of the conventional units on bus b under system state s. This represents the lower limit of the output of the conventional units on bus b under system state s. This indicates the state g of a conventional unit under system state s; The calculation formulas for the upper and lower limits of the transmission capacity between each bus pair are as follows: In the formula, This represents the upper limit of the transmission capacity between bus pairs (k, b) under system state s. This represents the lower limit of the transmission capacity between bus pairs (k, b) under system state s. Let (k,b) represent the state of line l under state s, and (k,b) represent a bus pair.

7. The power system reliability-constrained economic dispatch method based on critical state as described in claim 1, characterized in that, Step S5 includes: S51. Initialize the critical state set C to be an empty set; S52, Define different subsets N g Represents the number of types of faulty units, and the subsets The first state in Set it as the baseline state and initialize it to store the subsets. The set of states selected from the middle It is an empty set; S53. Calculate the reference state. Under conditions of no load loss, the assembly Maximum optimal load shedding LS c and the corresponding state c; S54, when LS c When LS equals 0, then execute step S55; when LS equals 0, then execute step S55. c If it is greater than 0, then update. for renew for Return to step S53; S55, will Updated to As a new baseline state, up to the subset When each state in the equation is used as the baseline state, the critical state set C is updated as follows:

8. The power system reliability-constrained economic dispatch method based on critical state as described in claim 7, characterized in that, In step S53, the baseline state is calculated. Under conditions of no load loss, the assembly Maximum optimal load shedding LS c The formula for calculating the corresponding state c is as follows: maxLS c In the formula, p w,f These represent the actual and predicted values ​​of the power generation of the wind turbine, respectively. d b,f These represent the actual and predicted load values ​​for busbar b, respectively. f represents the planned output of conventional unit g and wind turbine w under state s, respectively. l s This represents the power flow of line l under state s. The state represents the phase angle of bus b under state s. This indicates the maximum predicted error for the power generation of the wind turbine unit w. This indicates the maximum predicted load error for busbar b.

9. The power system reliability-constrained economic dispatch method based on critical state as described in claim 1, characterized in that, In step S6, the reliability constraint applies a no-loss constraint to each state in the critical state set C, and the specific steps are as follows: In the formula, This represents the output fluctuation of a conventional unit g caused by component failure under state s. This represents the total deviation of the injected power caused by the source load prediction error under state s. This represents the participation factor in the radiation control of a conventional unit g under state s. These represent the conventional unit's upper standby and lower standby configurations, respectively. These represent the power flow distribution factors, which represent the power injected by conventional generating units, the power injected by renewable energy, and the load demand converted into line power flow under state s, respectively. p w These represent the actual and planned power generation of the wind turbine, respectively. p represents the actual load value of busbar b. g This indicates the planned output of the conventional unit g. f represents the amount of wind curtailed by the wind turbine in state s. l max This indicates the upper limit of the transmission capacity of line l. ε represents the state of unit g under state s. UR ε DR ε L G represents the confidence level of not violating the upper reserve / lower reserve / line power flow limits, respectively. s Let G represent the set of faulty units in state s. b Let G represent the set of conventional units on bus b, W represent the set of all conventional units, and B represent the set of all wind turbines.

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