Nodal pricing mechanism and method for power system considering N-1 accidents

Abstract

The present invention proposes a node pricing mechanism and method for a power system considering N‑1 accidents. The pricing method can decompose LMP into basic energy price, congestion price, and resilience improvement price, and considers the impact of node and transmission line flow changes under line accidents to obtain more accurate flow and node electricity prices. On the basis of the traditional LMP model, the line flow under the accident is calculated by LODF, and upper and lower limit constraints are constructed to ensure that the line does not exceed the limit under the accident. The accident information is injected and retained in the node LMP, so as to solve the electricity price component of the emergency event and obtain a more accurate node electricity price under the accident. Then, the effectiveness of the pricing model is analyzed by comparing the calculation results before and after the accident.

Description

Technical Field

[0001] This invention belongs to the field of power system node pricing mechanisms and methods, and particularly relates to a power system node pricing mechanism and method that takes into account N-1 accidents. Technical Background

[0002] With the increasing frequency of global climate change and severe weather events, more and more power systems are experiencing emergencies and power outages due to natural disasters. In cases of critical line faults and large-scale power flow shifts, cascading failures and outages may occur. Traditional location marginal price (LMP) models neglect unexpected power events. Therefore, traditional LMP models cannot reflect the safety requirements and reliability costs of preventing emergencies. To improve the resilience and flexibility of power systems, this invention proposes a pricing model and method that considers N-1 emergency events. Based on LMP, the marginal costs and prices of adding safety constraints under accidents are analyzed and evaluated. The proposed LMP is divided into energy, congestion, and safety components to obtain the safety price cost of the power system under emergencies.

[0003] Power system resilience analysis is an optimization method to improve the system's disaster prevention capabilities. In power system resilience analysis, extreme disasters generally cause N-1 or even Nk-level accidents, resulting in significant power flow shifts, leading to uneven power flow distribution on system lines and even cascading failures, ultimately developing into large-scale blackout accidents.

[0004] Researching power flow transfer algorithms under contingencies can improve the disaster prevention decision-making capabilities of power systems, further optimize unit allocation and economic dispatch, and enable the power grid to operate stably under conditions of N-1 or even Nk, reducing losses and avoiding large-scale power outages caused by imbalances in line power flow and load. The necessity of studying power flow transfer indices is self-evident, thus creating a demand for research on electricity market pricing models arising from power flow changes under contingencies.

[0005] Studying the characteristics of power system dispatching and power flow transmission under emergencies can improve the disaster prevention decision-making capabilities of power systems. Furthermore, under conditions of N-1 or even Nk, unit allocation and economic dispatch can be arranged more rationally and safely. Reasonable dispatching decisions can avoid large-scale power outages caused by uneven power flow across lines. Safe dispatching decisions under deregulated environments are receiving increasing attention.

[0006] Previous work aimed to improve the accuracy and expand the application of LMP (Local Power Management). Many scholars have established LMP pricing market models from different perspectives to optimize node pricing. During the research process, some methods were found to use virtual node demand (FND) to equivalently represent line losses, and then solve for the marginal pricing of locations considering both global and partial node loss compensation. Regarding the safety component of node pricing, some literature has proposed the concept of "marginal price of a safe location," constructing three stochastic market models to determine the meaning of pricing and compare settlements, while considering potential adjustments from day-ahead planning to real-time operation, providing compensation for market participants while controlling for N-1 reliability. Other methods consider line outages, adding corresponding constraints based on the line outage distribution coefficient, considering N-1 exceedance scenarios, implementing the concepts of checking, adding, and re-checking, and then evaluating subsequent disaster prevention or unit combination economic dispatch optimization problems.

[0007] As mentioned above, traditional LMP models cannot reflect the security requirements and reliability costs of preventative contingencies. Existing technologies also rarely rely on LODF indices to construct power flow matrices and describe power flow transfer without exceeding constraints. Furthermore, current technologies rarely consider the prices of LMP decomposition components. In fact, much line information and status can be reflected in LMP; for example, line congestion increases node electricity prices, which is the congestion cost in LMP. Correspondingly, emergency event security costs can also display the line status information under emergency conditions, enabling resilience prevention and protection.

[0008] In a power market environment, maintaining operational safety through reasonable electricity price signals remains a challenge. Electricity market pricing models that consider power flow changes under unforeseen events require further research. Taking into account the safety costs of unforeseen events, nodal pricing can more accurately calculate system electricity prices under different loads, balance electricity supply and demand, enhance the resilience of the power system, and ensure its safe and reliable operation. Simultaneously, it enables better system disaster prevention decisions, the development of electricity market plans, and increased efficiency. Summary of the Invention

[0009] This invention proposes a novel model to calculate the LMP security cost under N-1 contingent events. Upper and lower limits for power flow and voltage are constructed using LODF (Level of Flow Depth), and the dual variables of these equality or inequality constraints are expressed as the cost of satisfying the constraints. A security component of nodal electricity price under N-1 contingent events is established. The purpose of this invention is to improve the resilience of power systems. The concept of resilience has been introduced into power systems in recent years, becoming an indicator of the power system's adaptability and recovery capability in the face of major disasters. Against the backdrop of widespread grid expansion and frequent power outages under extreme weather disasters, grid resilience has received widespread attention from academic circles both domestically and internationally. To improve the system's ability to withstand and recover from extreme disasters, some resilience control measures have been proposed, mainly including pre-event preventive control, in-event corrective control, and post-event recovery control. Flexibility mainly focuses on the research of the ability to accommodate uncertainties in nodal power injection (uncertainty in renewable energy output, uncertainty in load demand, etc.). With the increasing penetration rate of renewable energy sources such as wind power and photovoltaics, research on flexibility indicators to cope with system volatility and ensure system economic security is crucial. Unlike grid resilience and flexibility, supply and demand elasticity reflects the sensitivity of power resource supply and demand to price changes. Load fluctuates elastically under the stimulus of price signals, providing greater controllability for power system operation optimization.

[0010] To achieve the above objectives, the technical solution adopted by this invention is: a power system node pricing mechanism and method considering N-1 accidents, the method comprising the following steps:

[0011] Step 1: Derive the LODF matrix formula for branch disconnection distribution factor based on the network power flow status, and use the correlation matrix to traverse the N-1 emergency incident set of the network topology to obtain the LODF matrix for each branch disconnection case.

[0012] Step 2: Establish an LMP model that considers emergency events. Based on the existing LMP nodal marginal electricity price model, calculate the line status through the LODF matrix, add security constraints that consider power flow changes under emergency scenarios, and expand the nodal electricity price information.

[0013] Step 3: Construct the Lagrangian function based on the model established in Step 2, and then calculate the marginal energy cost and safety margin cost of the node by adding load increments;

[0014] Step 4: Perform structural analysis on the results of Step 3, compare the constraint information corresponding to the dual factors in the results, assign corresponding physical meaning to each component in the results, and decompose the LMP composition under emergency event conditions.

[0015] Furthermore, the method for step one is as follows:

[0016] (1) Based on the line power flow transmission indices already studied in the industry, the power transfer distribution factor PTDF and the transfer factor SF, the power flow description equation is established and the relationship between PTDF and SF is obtained as follows:

[0017]

[0018] Among them, the mn line is the monitoring line, and the ij line is the accident line. In the event of an accident on the ij line, the mn line... use and The calculation is shown in the formula above; where, and Let i and j represent the power flow impact of the injections at nodes i and j before the line disconnection on line mn, respectively. Then PTDF represents the power flow change observed on the monitored line mn after line ij is disconnected. The superscript c indicates that the line is in a fault state at this time.

[0019] Based on the above theory, the power flow calculation index describing the outage under the sudden event of the line is derived, namely the branch disconnection distribution factor LODF. LODF is the increment under the influence of the power flow change of the specified line outage in the monitored line. It is caused by the outage of the fault line that was transmitting a unit of active power flow before the line was disconnected. The power flow increment in the monitored line mn caused by the disconnection of the fault line ij with any given power before the accident can be calculated by LODF.

[0020] By definition, the LODF in the DC model is represented as:

[0021]

[0022] in, This is due to the increased tidal flow caused by the shutdown of line ij due to the accident. The given power flow before the line ij fault is displayed. LODF is the ratio of the power flow change of the monitored line mn to the initial given power flow of the disconnected line ij, which represents the power flow change observed on the monitored line mn after the line ij is disconnected.

[0023] (2) Based on the above analysis of the LODF concept, by assuming a broken line, the LODF matrix under the N-1 emergency events of the line will be derived through the traversal and extraction of the incident set; an incident set traversal matrix will be constructed: node-broken line association matrix. Where i and j are nodes in the network, the value of the power flow injection node in the correlation matrix is ​​set to 1, and the value of the power flow out node is set to -1;

[0024] For a break in line 1-2, the proposed node-break correlation matrix is ​​denoted as follows: The tidal current changes observed along other routes can be written as... Where Ψ is the correlation matrix Ψ T If the transpose of line 2-3 is the observation line, then the change in power flow on line 2-3 is... Combining formulas (1) and (2), it can be seen that This forms the first row and second column of the LODF matrix. The first row and first column represent the observation of line 1-2 from line 1-2. Since this line is broken, it is a zero element. That is to say, all diagonal elements of the LODF are 0. And so on, establishing N L *N L A 3D LODF matrix for lines is represented as follows:

[0025]

[0026] Where, N L This represents the number of lines contained in the network.

[0027] Furthermore, the specific method for step two is as follows:

[0028] The LMP model for an N-1 emergency event, established using the branch interruption distribution factor (LODF) under the DC model, is as follows:

[0029] (1) Establish a cost-optimal objective function:

[0030] Min c T Pb T D (3)

[0031] Among them, c T This is the coefficient matrix of generator cost, b T It is a coefficient matrix of load generation cost, where P is the unit output and D is the load demand;

[0032] (2) Set the power flow constraints, security constraints, unit output and load constraints under the N-1 power system emergency as follows:

[0033] (2-1) The nodal power balance constraint established by Kirchhoff's first law is:

[0034] 1 T (K P ·PK D ·D)=0 (4)

[0035] Among them, K P It is the bus group association matrix, K D It is the bus load correlation matrix;

[0036] (2-2) Before a line fault, the upper and lower limits of power flow on the transmission line are constrained as follows:

[0037] SF(K P ·PK D ·D)≤PL max (5)

[0038] -SF(K P ·PK D ·D)≤PL max (6)

[0039] Where SF is the line transfer factor before the fault, and PL max The maximum transmission capacity limit of the line is defined by formula (5), which is the upper limit constraint and formula (6) is the lower limit constraint.

[0040] (2-3) Using the LODF matrix from step one to express the power flow calculation formula, the new constraints added to the basic LMP model are as follows: Under fault conditions, the line power on the power system transmission lines considering power flow changes and their upper and lower limit constraints are as follows:

[0041] PL C -LODF C ·SF C ·P inj -PL 0 =0 (7)

[0042] PL min ≤PL C ≤PL max (8)

[0043] P inj =K P ·PK D ·D (9)

[0044] Among them, PL C LODF represents the line power flow under fault conditions. C SF is the LODF matrix of the network under fault conditions. C P is the line transfer factor under fault conditions. inj It is the power injection of the line, PL 0 This represents the original initial power flow of the line before the fault.

[0045] Substituting equation (9) into equation (7), and proposing PL C By writing the inequality in equation (8), we can obtain the upper and lower limits of the line transmission power under fault conditions, which are easy to calculate, as shown in equations (10) and (11):

[0046] LODF C ·SF C ·(K G ·PKD ·D)+PL 0 ≤PL max (10)

[0047] PL min ≤LODF C ·SF C ·(K G ·PK D ·D)+PL 0 (11)

[0048] Among them, PL max and PL min These are the maximum and minimum transmission capacities of the line.

[0049] (2-4) The upper and lower limits of generator unit output are constrained as follows:

[0050] P min ≤P≤P max (12)

[0051] Among them, P min P is the minimum output of the generator. max This represents the maximum output power of the generator.

[0052] (2-5) The upper and lower limits of load demand are as follows:

[0053] D min ≤D≤D max (13)

[0054] Among them, D min D represents the minimum load. max This represents the maximum load value.

[0055] The above model takes into account the constraints that limit power flow on the line when unexpected events occur.

[0056] Furthermore, the specific method for step three is as follows:

[0057] The model constructed in the above steps uses a node decomposition expression. The price of each node can be composed of the sum of individual parts. Using the Lagrange multiplier method, the objective function and constraints listed in step two are combined into a Lagrange function. The dual variables of the above objective function and constraints are then expressed as the cost of satisfying the optimization objective and constraints, i.e., the node marginal electricity price. The price cost generated by the additional security constraints is defined as the security cost of LMP. The Lagrange function is constructed as follows:

[0058]

[0059] Formula (14) is a Lagrangian function established by the objective function, the model constraint expression of step two and its corresponding dual factor, where ΔL is the added load increment and is the derivative of the Lagrangian function F.

[0060] We introduce the Lagrange dual factor, which represents the optimality of the constraints in the linear programming problem. Here, it is introduced to represent the shadow price in economics, in order to calculate the nodal electricity price. The Roman symbol λ appears in the Lagrange function related to the constraints of the LMP model under N-1 emergency events. π T , κ T These are the dual factors of expressions (4), (5), (6), (10), and (11). These correspond to the upper and lower bound constraints of inequalities (12) and (13), respectively.

[0061] The power flow equation under emergency conditions is represented as PL C =PL 0 +LODF C ·PL, where PL represents line power flow, is replaced by an expression containing the load function SF. C The expression for D can be decomposed into nodes, with node load variables appearing in the constraint, while price information is retained in the Lagrange function. The method for calculating the complete expression for LMP under N-1 emergency events involves adding an increment to the load in the Lagrange function, then differentiating this load increment. The result, composed of the matrix coefficients of these dual factors and the corresponding constraints, thus corresponds to the constraints under N-1 emergency events and includes node price information.

[0062] Furthermore, the method for step four is as follows: Based on the principle of the LMP pricing model and the implementation plan in step three, the load increment in equation (14) is differentiated to obtain the following LMP expression:

[0063]

[0064] In the formula, the superscript T of SF denotes the transpose of the matrix;

[0065] By analyzing each component, it can be seen that LMP is the sum of three parts. The first term of the equation contains the dual factor of the objective function, which shows the energy cost of LMP:

[0066] LMP energy =1λ (16)

[0067] Furthermore, the second term of LMP includes the dual factor of line transmission flow capacity constraints (5) and (6), reflecting price changes under transmission capacity constraints, i.e., the congestion part of LMP:

[0068]

[0069] The congestion price derived from equation (15) is used to calculate the power system congestion cost caused by line transmission capacity limitation, as shown in constraints (5) and (6). The congestion price can be the cost of direct congestion management or the rent for scarce grid capacity, so the congestion cost is included in the nodal price.

[0070] The last term consists of the LODF matrix, SF matrix, and dual factor of the line flow capacity limit under the N-1 emergency event state. It shows information on keeping the flow within the limit and is the safety cost of the price.

[0071]

[0072] Expression (18) represents the security component of LMP, which contains information from constraints (10) and (11), and calculates the additional resilience enhancement price, i.e. security cost, for maintaining stable operation of the power system, considering power flow shifts and energy redistribution under N-1 emergency events.

[0073] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following significant advantages:

[0074] (1) Existing related technologies rarely utilize indicators that characterize power flow injection at network nodes and changes in line power flow. Since LODF is only related to system structure, calculating power flow and expressing power flow changes under N-1 faults based on the branch interruption distribution factor LODF matrix facilitates the description of power flow transfer on remaining lines under N-1 faults. Meanwhile, the LMP model proposed in this invention, considering emergency events, cleverly incorporates post-fault line power flow limit information into the model by adding safety constraints, then constructs it as a Lagrangian function. By differentiating the load increment, the marginal price of node locations in the power system is calculated. This new price includes information on power flow adjustments to withstand emergency events, thereby guiding the behavior of generators and users. Compared with existing technologies, this approach is simple and ingeniously designed.

[0075] (2) The node pricing model constructed in this invention is expressed by decomposable node balance equations, which means that the calculated LMP can be decomposed into different electricity price components, namely energy cost, congestion cost, and security cost. Each component is related to the dual factor of its corresponding constraint. Therefore, the contribution of each component to the electricity price and the impact of each line on the load node can be calculated by calling the expression of each component. This technology can be used to evaluate the ability of each line and each node to cope with emergency events and sudden disasters, and improve the resilience of the power system. Attached Figure Description

[0076] Figure 1 Consider the comparison of LMP components before and after the N-1 emergency event (node ​​3);

[0077] Figure 2 Consider the comparison of LMP components before and after the N-1 emergency event (node ​​5);

[0078] Figure 3 This is a flowchart of the method of the present invention. Detailed Implementation

[0079] This invention addresses the stability and resilience issues of power systems under natural disasters and emergencies using a novel nodal pricing mechanism and method. It incorporates security constraints into the conventional LMP model, describes power flow changes using LODF, and injects emergency event security costs, making nodal pricing decomposable and analyzable, thereby maintaining system stability and improving system resilience. This invention includes the following steps:

[0080] Step 1: Derive the branch disconnection distribution factor (LODF) matrix formula based on the network power flow status, and use the correlation matrix to traverse the N-1 emergency incident set of the network topology to obtain the LODF matrix under the condition of branch disconnection. The specific method is as follows: (1) Based on the line power flow transmission indicators that have been studied in the industry, such as the power transmission distribution factor (PTDF) and the transfer factor (SF), the power flow description equation is established, and the relationship between PTDF and SF can be obtained as follows:

[0081]

[0082] Where mn is the monitoring line, ij is the fault line, and the superscript 'c' indicates that the line is in a fault state. Therefore, in the event of an accident on ij, the mn line... use and The calculation is shown in the formula above. Where, and The numbers represent the power flow impact of the injection at nodes i and j on line mn before the line disconnection, respectively, with the superscript c indicating the fault state. Then, PTDF represents the power flow change observed on monitored line mn after line ij disconnection, with the superscript c indicating a fault state at this time.

[0083] Based on the above theory, a power flow calculation index describing the outage under a sudden event on a line is derived, namely the Branch Outage Distribution Factor (LODF). The LODF is the increment affected by the power flow change of a specified line in the monitored line that is out of service. This is caused by the outage of the faulted line that was transmitting one unit of active power before the line breakage. Therefore, the power flow increment in the monitored line mn caused by the breakage of a faulted line ij with any given power before the incident can be calculated from the LODF.

[0084] By definition, LODF in the DC model is represented as:

[0085]

[0086] in, This is due to the increased tidal flow caused by the shutdown of line ij due to the accident. The given power flow before the fault on line ij is displayed. LODF is the ratio of the power flow change on the monitored line mn to the initial given power flow on the disconnected line ij. It represents the power flow change observed on the monitored line mn after the line ij is disconnected. The superscript c indicates that the line is in a fault state at this time.

[0087] (2) Based on the above analysis of the LODF concept, the LODF matrix under the N-1 emergency events of the line will be derived by traversing and extracting the accident set by assuming the line is disconnected.

[0088] In this step, the present invention constructs an accident set traversal matrix: a node-disconnection association matrix. Where i and j are nodes in the network, the value of the power flow injection node in the correlation matrix is ​​set to 1, and the value of the power flow outflow node is set to -1.

[0089] Taking the line break at line 1-2 as an example, the node-break correlation matrix proposed in this scheme is denoted as follows: The tidal current changes observed along other routes can be written as... If line 2-3 is the observation line, then the change in power flow along line 2-3 is: Combining formulas (1) and (2), it can be seen that This forms the first row and second column of the LODF matrix (note that the first row and first column represent the observation of line 1-2 from line 1-2; since this line is broken, it is a zero element, meaning that all diagonal elements of the LODF are 0). And so on, establishing N... L*N L A 3D LODF matrix for lines is represented as follows:

[0090]

[0091] Where, N L This represents the number of lines contained in the network.

[0092] By using the established LODF matrix, the power flow under emergency events can be calculated, thus providing a basic solution for model building, extraction, and decomposition of shadow prices under emergency events in step two.

[0093] Step 2: Establish an LMP model that considers emergency events. Based on the existing LMP nodal marginal electricity price model, calculate the line status through the LODF matrix, add security constraints that consider power flow changes under emergency conditions, and expand nodal electricity price information.

[0094] The LMP model under N-1 emergency events, established using the branch interruption distribution factor (LODF) in the DC model, is as follows.

[0095] (1) Establish a cost-optimal objective function:

[0096] Min c T Pb T D (3)

[0097] Among them, c T This is the coefficient matrix of generator cost, b T It is a coefficient matrix of load generation cost, where P is the unit output and D is the load demand;

[0098] (2) Set the power flow constraints, security constraints, unit output and load constraints under the N-1 power system emergency as follows:

[0099] (2-1) The nodal power balance constraint established by Kirchhoff's first law is:

[0100] 1 T (K P ·PK D ·D)=0 (4)

[0101] Among them, K P It is the bus group association matrix, K D It is the bus load correlation matrix.

[0102] (2-2) Before a line fault, the upper and lower limits of power flow on the transmission line are constrained as follows:

[0103] SF(K P ·PK D ·D)≤PL max(5)

[0104] -SF(K P ·PK D ·D)≤PL max (6)

[0105] Where SF is the line transfer factor before the fault, and PL max The maximum transmission capacity limit of the line is defined by formula (5), which is the upper limit constraint and formula (6) is the lower limit constraint.

[0106] (2-3) This step adds new constraints to the basic LMP model by using the LODF matrix from step one to express the power flow calculation formula. Under fault conditions, the line power on the power system transmission lines considering power flow changes and their upper and lower limit constraints are as follows:

[0107] PL C -LODF C ·SF C ·P inj -PL 0 =0 (7)

[0108] PL min ≤PL C ≤PL max (8)

[0109] P inj =K G ·PK D ·D (9)

[0110] Among them, PL C LODF represents the line power flow under fault conditions. C SF is the LODF matrix of the network under fault conditions. C P is the line sensitivity transfer factor under fault conditions. inj It is the power injection of the line, PL 0 This represents the original initial power flow of the line before the fault.

[0111] Substituting equation (9) into equation (7), and proposing PL C By writing it in the form of the inequality shown in formula (8), we can obtain the upper and lower limits of the line transmission power under fault conditions, which are easy to calculate, as shown in formulas (10) and (11).

[0112] LODF C ·SF C ·(K G ·PK D ·D)+PL0≤PL max (10)

[0113] PLmin ≤LODF C ·SF C ·(K G ·PK D ·D)+PL 0 (11)

[0114] Among them, PL max and PL min These are the maximum and minimum values ​​of the line's transmission capacity;

[0115] (2-4) The upper and lower limits of generator unit output are constrained as follows:

[0116] P min ≤P≤P max (12)

[0117] Among them, P min P is the minimum output of the generator. max This represents the maximum output power of the generator.

[0118] (2-5) The upper and lower limits of load demand are as follows:

[0119] D min ≤D≤D max (13)

[0120] Among them, D min D represents the minimum load. max This represents the maximum load value.

[0121] The above model takes into account the constraints that limit power flow on the line when unexpected events occur.

[0122] Specifically, based on the basic LMP model, corresponding upper and lower bound conditions are added during accidents to limit line power flow exceeding limits, thereby ensuring system safety and reliability and guaranteeing the safe operation of lines. The following steps will explain in detail how the proposed LMP model can more accurately construct electricity prices.

[0123] Step 3: Construct the Lagrangian function based on the model established in Step 2, and then calculate the marginal energy cost and safety margin cost of the node by adding load increments.

[0124] The model constructed in the above steps uses a node decomposition expression, where the price of each node can be composed of the sum of individual parts. Therefore, in this step, the Lagrange multiplier method is used to construct a Lagrange function from the objective function and constraints listed in step two. The dual variables of the objective function and constraints are then expressed as the cost of satisfying the optimization objective and constraints, i.e., the node marginal electricity price. The price cost generated by the additional security constraints is defined as the security cost of LMP, and the Lagrange function is constructed as follows:

[0125]

[0126] Formula (14) is a Lagrangian function established by the objective function, the model constraint expression of step two and its corresponding dual factor, where ΔL is the added load increment and is the object of differentiation of the Lagrangian function F.

[0127] The Roman symbol λ appears in the Lagrangian function related to the constraints of the LMP model under the N-1 emergency event. π T , κ T , is the dual factor of expressions (4), (5), (6), (10), and (11). These correspond to the upper and lower bound constraints of inequalities (12) and (13), respectively.

[0128] The power flow equation under emergency conditions is represented as PL C =PL 0 +LODF*PL, where PL represents line power flow. This invention replaces PL with a functional expression for node load, SF*D. Therefore, the node load variable will appear in this constraint, meaning that price information can be retained in the Lagrange function derivation. The method of this invention for calculating the complete expression of LMP under N-1 emergency events is to add an increment to the load in the Lagrange function and then differentiate this load increment. The result is precisely composed of these dual factors and the matrix coefficients of the corresponding constraints, thus corresponding to the constraints under N-1 emergency events and including node price information.

[0129] Step 4: Perform structural analysis on the results of Step 3, compare the constraint information corresponding to the dual factors in the results, assign corresponding physical meaning to each component in the results, and decompose the LMP composition under emergency event conditions.

[0130] Based on the principles of the LMP pricing model and the implementation plan in step three, the load increment in equation (14) is differentiated to obtain the following LMP expression:

[0131]

[0132] In the formula, the superscript T of SF indicates the transpose of the matrix.

[0133] By analyzing each component, it can be seen that LMP is the sum of three parts. The first term of the equation contains the dual factor of the objective function, which shows the energy cost of LMP:

[0134] LMP energy=1λ (16)

[0135] Furthermore, the second term of LMP includes the dual factor of line transmission flow capacity constraints (5) and (6), reflecting price changes under transmission capacity constraints, i.e., the congestion part of LMP:

[0136]

[0137] The congestion price derived from equation (15) is used to calculate the power system congestion cost caused by line transmission capacity limitations, as shown in constraints (5) and (6). The congestion price can be the cost of direct congestion management or the rent for scarce grid capacity. Clearly, congestion costs are included in nodal tariffs, which increases the overall level of tariffs.

[0138] The last term consists of the LODF matrix, SF matrix, and dual factor of the line power flow capacity limit under the N-1 emergency event state. It shows the information on keeping the power flow within the limit and is the safety cost of the price.

[0139]

[0140] Expression (18) represents the security component of LMP, which includes information from constraints (10) and (11). Considering power flow shifts and energy redistribution under N-1 emergency events, the additional resilience enhancement price for maintaining stable operation of the power system, i.e., the security cost, is calculated.

[0141] The LMP (Local Power Management) component of this safety component can reflect the operating status of the power system and regulate the allocation of power resources. Specifically, the increase in safety costs leads to nodal tariffs, which reduces user load and generator output, thereby alleviating pressure on transmission lines and ensuring the stable and safe operation of the power system.

[0142] The following section verifies the effectiveness of pricing mechanisms and methods that take into account emergency situations.

[0143] The model proposed in this invention is primarily validated using the "IEEE-6" bus system. Based on the derivation and analysis in step four, the node LMP consists of an energy component, a congestion component, and a security component. This step decomposes the LMP and, relying on the Yalmip and Gurobi toolboxes, uses MATLAB to complete the effectiveness analysis of the invention.

[0144] In the file storing system data, the initial system values ​​are first set, and the generator output values, number of lines, line power flow, and load node limits are defined. Among them, nodes 3 and 5 are load nodes, meaning we mainly focus on the LMP composition of these two nodes.

[0145] First, under pre-emergency conditions, the LMP considers the line node balance equations and the non-overrun constraints of transmission line power flow. Next, the dual factor is calculated to obtain the LMP under normal conditions. The data for each component in the basic LMP model are then obtained, as shown in Table 1.

[0146] Table 1. Components of load node electricity prices under the basic LMP model.

[0147]

[0148] Then, constraints are added to ensure that the power flow under emergency N-1 does not exceed the line capacity limit. Based on the model in step three, the LMP calculation formula is modified to obtain the LMP node price under emergency N-1. The price and security cost (LMP increment) of each load node before and after the emergency event are shown in the table below.

[0149] Table 2 Comparison of LMP components before and after considering emergency events

[0150]

[0151] The data for the two nodes before and after the N-1 emergency event in the table above are plotted separately. Figure 1 and Figure 2 In the middle, it can be clearly seen that when considering the N-1 emergency event, the electricity price structure is more complex, the calculation is more accurate, and the information is more comprehensive.

[0152] from Figure 1 and Figure 2 The case study demonstrates that, by comparing data before and after an emergency event, LMP increases due to the cost of security components. Based on the N-1 emergency LMP model, this case study analyzes the effectiveness of nodes in reflecting security costs under emergency conditions in the N-1 scenario. It reflects the positive role of incorporating elasticity enhancement pricing into the elastic pricing mechanism, which can effectively ensure the safety of the power grid, has a certain disaster prevention capability, and has a positive impact on social benefits.

Claims

1. A power system node pricing mechanism and method considering N-1 accidents, characterized in that: The method comprises the following steps: Step 1: Derive the branch disconnection distribution factor LODF matrix formula according to the network flow state, use the association matrix to traverse the N-1 emergency accident set of the network topology, and obtain the LODF matrix when each branch is disconnected; Step 2: Establish an LMP model considering emergency accidents. Based on the existing LMP node marginal electricity price model, calculate the line status through the LODF matrix, add safety constraints considering the flow changes under accident situations, and expand the node electricity price information; Step 3: Construct the Lagrangian function based on the model established in step 2, and derive the energy marginal cost and safety marginal cost of the calculation node by adding load increments; Step 4: Perform structural analysis on the results of step 3, compare the constraint information corresponding to the dual factors in the results, assign corresponding physical meanings to each component in the results, and decompose the LMP composition under the emergency state; The specific method of step 2 is as follows: The LMP model under the N-1 emergency event established by using the branch disconnection distribution factor LODF under the DC model is as follows: (1) Establish a cost-optimal objective function: Min c T P-b T D (3) Among them, c T is the coefficient matrix of generator cost, b T is the coefficient matrix of load power generation cost, P is the unit output, and D is the load demand; (2) Set the power flow constraints, safety constraints, unit output and load constraints under the power system N-1 emergency event as follows: (2-1) The node power balance constraint established by Kirchhoff’s first law is: 1 T (K P ·P-K D ·D)=0 (4) Among them, K P is the bus unit association matrix, K D is the bus load association matrix; (2-2) Before the line fault, the upper and lower limits of the transmission line power flow are as follows: SF(K P ·P-K D ·D)≤PL max (5) -SF(K P ·P-K D ·D)≤PL max (6) Where SF is the line transfer factor before the fault, PL max is the maximum transmission capacity limit of the line, where formula (5) is the upper limit constraint and formula (6) is the lower limit constraint; (2-3) Using the LODF matrix in step 1 to express the power flow calculation formula, the new constraints added to the basic LMP model are as follows: PL C -LODF C ·SF C ·P inj -PL 0 =0 (7) PL min ≤PL C ≤PL max (8) P inj =K P ·P-K D ·D (9) Among them, PL C Indicates the line power flow under fault conditions, LODF C is the LODF matrix of the network under fault conditions, SF C is the line transfer factor under fault conditions, P inj is the power injected into the line, PL 0 is the original initial power flow of the line before the fault; Substitute equation (9) into equation (7), and propose PL C Written in the form of the inequality shown in formula (8), the upper and lower limits of the line transmission power under the fault state that are easy to calculate can be obtained, as shown in formulas (10) and (11): LODF C ·SF C ·(K G ·P-K D ·D)+PL 0 ≤PL max (10) PL min ≤LODF C ·SF C ·(K G ·P-K D ·D)+PL 0 (11) Among them, PL max and PL min are the maximum and minimum transmission capacity of the line; (2-4) The upper and lower limits of the generator set output are as follows: P min ≤P≤P max (12) Among them, P min is the minimum value of the generator output, P max is the maximum value of the generator output; (2-5) The upper and lower limits of load demand are as follows: D min ≤D≤D max (13) Among them, D min is the minimum value of the load, D max is the maximum value of the load; The above model takes into account the constraint information that the line power flow is restricted when an unexpected event occurs; The specific method of step three is as follows: the model constructed in the above steps uses a node decomposition expression. The price of each node can be composed of a single part. Using the Lagrange multiplier method, the objective function and constraints listed in step two are formed into a Lagrangian function. The dual variables of the above objective function and constraints are expressed as the cost that satisfies the optimization objectives and constraints, that is, the node marginal electricity price. The price fee generated by the additional safety constraint part is defined as the safety cost of LMP. The Lagrangian function is constructed as follows: Formula (14) is the Lagrangian function established by the objective function, the model constraint expression of step 2 and its corresponding dual factor, where ΔL is the added load increment and is the derivative object of the Lagrangian function F; The Lagrangian dual factor is introduced. The dual factor represents the optimality of the constraints of the linear programming problem. It is introduced here to represent the shadow price in economics in order to calculate the node electricity price; the Roman symbol that appears in the Lagrangian function related to the LMP model constraints under N-1 emergency events, namely λ, π T , κ T It is the dual factor of expressions (4), (5), (6), (10), (11). They correspond to the upper and lower constraints of inequalities (12) and (13), respectively; The power flow equation under emergency conditions is expressed as PL C =PL 0 +LODF C PL, where PL is the line flow, replace the overall expression of PL with the load function SF C ·D can be expressed in a node-by-node manner. The node load variables will appear in this constraint, keeping the price information in the Lagrangian function. The method to calculate the complete expression of the LMP under N-1 emergency events is to add an increment to the load in the Lagrangian function and then differentiate this load increment. The result consists of these dual factors and the matrix coefficients of the corresponding constraints. Therefore, it can correspond to the constraints under N-1 emergency events, which contain the price information of the nodes.

2. According to claim 1, a power system node pricing mechanism and method considering N-1 accidents is characterized in that: The method for step one is as follows: (1) Based on the line power flow transmission indicators: power transmission allocation factor PTDF and transfer factor SF, the power flow description equation is established to obtain the relationship between PTDF and SF as follows: Among them, the mn line is the monitoring line, and the ij line is the accident line. In the event of an accident on the ij line, the mn line use and Calculate as shown above; where, and They represent the influence of injection from node i and node j on the power flow of line mn before the line is disconnected, respectively. Then PTDF represents the power flow change observed on the monitoring line mn after line ij is disconnected. The superscript c represents the fault state at this time. Based on the above theory, the power flow calculation index describing the outage under the sudden incident of the line is derived, namely the branch disconnection distribution factor LODF. LODF is the increment under the influence of the power flow change of the specified line outage in the monitoring line. It is caused by the outage of the accident line that transmits one unit of active power flow before the line break. The power flow increment in the monitoring line mn caused by the line break of the fault line ij with any given power before the accident can be calculated by LODF. By definition, the LODF under the DC model is expressed as: in, is the increased power flow due to the outage of the accident line ij, It shows the given power flow before the fault of line ij. LODF is the ratio of the power flow change of monitored line mn to the initial given power flow of the broken line ij, which indicates the power flow change observed on the monitored line mn after the line ij is broken. (2) Based on the above LODF concept analysis, we will perform traversal extraction of the accident set by assuming a broken line, and derive the LODF matrix under the line N-1 emergency event; construct an accident set traversal matrix: node-broken line association matrix Among them, i and j are nodes in the network respectively. The value of the flow injection node in the association matrix is ​​assigned 1, and the value of the flow outflow node is assigned -1; For line 1-2 disconnection, the proposed node-disconnection association matrix is ​​recorded as The change in the power flow observed on other lines can be written as Where Ψ is the correlation matrix Ψ T If line 2-3 is the observation line, then the change of the power flow on line 2-3 is Combining formulas (1) and (2), we can see that This forms the first row and second column of the LODF matrix. The first row and first column represent observing line 1-2 on line 1-2. Since the line is disconnected, it is a zero element. In other words, the diagonal elements of LODF are all 0. Similarly, N is established. L *N L The line LODF matrix of dimension is expressed as follows: Among them, N L The number of lines contained in the network.

3. The power system node pricing mechanism and method considering N-1 accidents according to claim 1 is characterized in that: The method of step 4 is as follows: According to the principle of the LMP pricing model and the implementation plan in step 3, the load increment in equation (14) is derived to obtain the following LMP expression: In the formula, the superscript T of SF represents the transpose of the matrix; By analyzing the components, we can see that LMP is the sum of three parts. In the first term of the equation, there is the dual factor of the objective function, which shows the energy cost of LMP: LMP energy =1λ (16) In addition, the second term of LMP contains the dual factors of the line transmission flow capacity constraints (5) and (6), reflecting the price change under the transmission capacity constraint, that is, the blocking part of LMP: The congestion price obtained according to equation (15) is used to calculate the power system congestion cost caused by line transmission capacity limitation. As shown in constraints (5) and (6), the congestion price can be the cost of direct congestion management or the rent of scarce capacity of the power grid, so the congestion cost is included in the node electricity price; The last term consists of the LODF matrix, the SF matrix and the dual factor of the line power flow capacity limit under the N-1 emergency state, which shows the information to keep the power flow within the limit, which is the safety cost of the price: Expression (18) represents the security component of LMP, which contains the information of constraints (10) and (11), considers the power flow transfer and energy redistribution under N-1 emergency events, and calculates the additional resilience improvement price to maintain the stable operation of the power system, that is, the security cost.

Images