A differentiated node price calculation method considering line congestion

Abstract

This invention discloses a method for calculating differentiated nodal prices considering line congestion. The method includes: Step 1: Establishing an AC optimal power flow model based on the target power grid to be detected; the AC optimal power flow model includes an objective function, equality constraints, and inequality constraints; Step 2: Initializing the AC optimal power flow model and constructing initial points; inputting the initial points into the model, and iteratively solving the model using a modified primal-dual interior-point method until convergence conditions are met, thereby obtaining differentiated nodal prices considering line congestion; Step 3: Based on the differentiated nodal prices, outputting power grid interaction evaluation quantities; and calculating the final apparent power utilization rate of the lines to determine the location and degree of congestion, and adjusting the prices in real time to resolve nodal and line congestion. Through this invention, differentiated nodal prices are obtained, and prices are adjusted in real time, effectively solving line congestion.

Description

Technical Field

[0001] This invention belongs to the field of power system operation optimization and grid control technology, specifically relating to a method for calculating differentiated nodal electricity prices that takes into account line congestion. Background Technology

[0002] With the continuous expansion of the power system and the large-scale integration of electric vehicles, distributed power sources, and adjustable loads, power grid operation exhibits stronger spatiotemporal coupling and uncertainty characteristics. The concentrated integration of user-side loads, the synchronization of charging behavior, and rapid regional load fluctuations can easily trigger power flow offsets at specific voltage level nodes in the upstream power grid and their associated transmission corridors, leading to local congestion. This results in problems such as line over-limit risks, increased dispatch costs, and abnormal fluctuations in node marginal quantities (such as node marginal electricity prices / shadow prices). To ensure the safe and economical operation of the power grid, it is urgent to quantitatively assess the interaction mechanism between node-level load changes and power flow congestion, and to provide an interpretable decision-making basis for demand-side guidance and incentive strategies.

[0003] In existing research and engineering practice, the impact assessment of electric vehicle charging loads or adjustable loads often employs methods such as superimposing typical daily load curves, empirical regional summarization, or simulation analysis on the distribution side / local area. Meanwhile, in terms of congestion identification, most methods focus on static power flow results or line load rate judgment under a single operating condition, using individual line overruns as a congestion symptom. While these methods are simple to implement, they generally suffer from unclear node mapping relationships, inconsistent load aggregation granularity, and difficulty in covering disturbances across multiple time periods and scenarios. This makes it difficult to establish a stable and transferable correspondence between user-side load changes and the congestion risk of key nodes in the upstream power grid. Especially at the 220kV node level, the selection of congestion-prone nodes often relies on experience or a limited number of indicators, failing to systematically reflect the complete chain of "load disturbance—power flow allocation—congestion triggering—marginal quantity change," thus affecting the interpretability and generalizability of the assessment conclusions.

[0004] Furthermore, existing modeling and algorithm systems still face significant bottlenecks in engineering implementation: On the one hand, power grid interaction assessment typically requires simultaneous satisfaction of multiple constraints such as power balance, line capacity, and voltage. If the modeling is too coarse, it is difficult to accurately depict the congestion formation mechanism; if the modeling is too fine, the complexity of parameter acquisition and computation increases significantly, making it difficult to form a reusable parameterized framework. On the other hand, congestion-oriented incentive and control strategies are often decoupled from the power grid constraint model, often employing uniform rates or empirical segmentation rules, lacking quantitative evidence that reflects the differences in congestion sensitivity at different nodes and time periods. Meanwhile, in terms of optimization solutions and iterative algorithms with multiple types of equality / inequality constraints, existing methods still have shortcomings in convergence stability, parameter tuning, and computational efficiency in large-scale scenarios, making it difficult to achieve rapid assessment and strategy closed-loop verification for multiple scenarios. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for calculating differentiated node electricity prices that takes into account line congestion.

[0006] The objective of this invention is achieved through the following technical solution: a method for calculating differentiated nodal pricing that takes line congestion into account, the method comprising the following sub-steps: Step 1: Based on the target power grid to be detected, establish an AC optimal power flow model; the AC optimal power flow model includes an objective function, equality constraints, and inequality constraints; Step 2: Initialize the AC optimal power flow model and construct initial points; input the initial points into the model, and use the improved original dual interior point method to iteratively solve the model until the convergence condition is met, thereby obtaining the differentiated node electricity price considering line congestion. Step 3: Based on differentiated node electricity prices, output grid interaction assessment quantities; and calculate the final line apparent power utilization rate to determine the location and degree of congestion, and adjust the electricity price in real time to resolve node and line congestion.

[0007] Furthermore, step one includes the following sub-steps: (1.1) Collect and summarize user-side load data in the target power grid according to 220KV nodes, and then perform standardization processing to obtain input data; (1.2) Construct an equivalent model of the target power grid, input the input data into the model, and map it onto each bus and line of the model to form the load parameters of each bus and the capacity parameters of the line; then obtain the node admittance matrix based on the model to construct a seven-node AC-OPF constraint system, which includes equality constraints and inequality constraints. (1.3) Construct the objective function, wherein the objective function is: ;in, , For unit cost coefficient, This represents the active power output of each generating unit.

[0008] Furthermore, obtaining the nodal admittance matrix in step (1.2) specifically includes the following sub-steps: (1.2.1) Based on the equivalent model of the target power grid, construct a seven-node equivalent topology diagram of the target power grid that includes power source access; this topology diagram is an AC power grid and includes a set of buses. , Three of them are generator busbars and four are load busbars; (1.2.2) Four parameters are configured for each line in the topology diagram, including resistance, reactance, susceptance and capacity; (1.2.3) Adopt The model assembles the four parameters to obtain the node admittance matrix. , where G represents the real part of the node admittance matrix, B represents the imaginary part of the node admittance matrix, and j represents the imaginary unit.

[0009] Furthermore, in step (1.2), the equivalence constraints include the active / reactive power balance of nodes; the inequality constraints include line capacity, generator active / reactive power output boundaries, voltage boundaries, and phase angle boundaries.

[0010] Furthermore, step two specifically includes the following sub-steps: (2.1) Transform the inequality constraints into equality constraints to complete the initialization process; construct an initial point that simultaneously satisfies the controllable residuals and strict interior point requirements of the equality constraints; initialize the Lagrange multipliers in the original equality constraints to Initialize the Lagrange multipliers in the inequality constraints to ,in, The dual variable representing the equality constraint. Represents the dual variable in the inequality constraint; (2.2) Calculate the current apparent power utilization rate of the line, and determine the blocked line based on the utilization rate threshold; determine the blocked line based on the dual variable in the inequality constraint or the dual variable of the previous iteration, combined with the dual variable threshold; merge the two blocked lines to form a blocked line set; and construct a blockage perception weight matrix to quantify the cost sharing relationship of each node to the blocked line. (2.3) Construct the Lagrangian function, and based on this, construct the KKT conditions and form the residual vector; (2.4) Linearize the residual vector to obtain a system of linear equations; solve the system of equations by elimination and simplification to obtain the Newton direction. ;in, The direction of correction for slack variables. The direction of the correction of the Lagrange multiplier corresponding to the inequality constraint. The direction of correction representing the original decision variables, The direction of correction of the Lagrange multiplier corresponding to the equality constraint; (2.5) Based on the Newton direction, a prediction-correction strategy is adopted to obtain a more accurate Newton direction; then the step size is determined to obtain the updated point; and the updated point is made feasible and stable through the fraction to boundary rule, the line search evaluation function and the numerical lower bound protection. (2.6) Perform convergence determination, repeat steps (2.2.1)-(2.2.4) until convergence is satisfied, and output the differentiated node electricity price.

[0011] Further, step (2.1) includes the following sub-steps: (2.1.1) Unify all inequality constraints into standard form ,and Introducing slack variables in this standard form ,and This transforms inequality constraints into equality constraints, thus enabling... Where x represents the original variable vector, including voltage, phase angle, and active / reactive power output of the generator set; (2.1.2) Constructing the initial point This point satisfies the equality constraint, the residual is controllable, and the strict interior point requirement is met. This leads to the slack variables. This ensures that the initial point satisfies the strict interior point condition of the transformed system, i.e. .

[0012] Furthermore, the formula for calculating the apparent power utilization rate of the current line in step (2.2) is as follows: in, Representing the power flow at both ends of the line, Representing the apparent power at both ends of the line, Representing a larger apparent power, Represents the maximum capacity of the line; Utilization threshold is The value range is 0.70 to 0.90; the threshold for the dual variable is... The value ranges from 0.05 to 0.20; The blocking sensing weight matrix is: ; in, , The weakening weights for non-candidate constraints.

[0013] Furthermore, the Lagrange function in step (2.3) is: ; in, Representative node active / reactive power balance equation constraint, Represents the objective function; The residual vector includes stationary residuals. ,in, Represents the objective function with respect to the original variables. gradient, Representing equality constraints For the original variables Jacobian matrix, Inequality constraints For the original variables Jacobian matrix; equality-constrained residuals, Inequality constraints are transformed into equality constraint residuals. Complementary condition residuals ,in, For the barrier parameter, This represents element-wise multiplication. This represents an m×1 column vector with μ as its element.

[0014] Furthermore, the elimination and simplification in step (2.4) specifically involves: ... , Related equations are eliminated or combined, thus simplifying the original system of linear equations into a system mainly concerning... Substituting back into the core linear equations, we obtain... This reduces the condition number of linear systems and improves numerical stability.

[0015] Furthermore, the prediction-correction strategy in step (2.5) is as follows: first, the affine scaling direction is calculated to estimate the decreasing trend of the complementary gap; then, based on the estimation results, a centering parameter is constructed and a correction direction is calculated to improve the degree of satisfaction of the complementary condition and accelerate overall convergence; the step size is selected using a fraction-to-boundary rule to ensure that the updated points still satisfy the strict interior point condition, i.e. and When necessary, a penalty function with a barrier term is introduced as the evaluation function for the line search to ensure that the residuals and target values ​​decrease steadily during the iteration process, avoiding oscillations or numerical divergence caused by excessively large step sizes; and A numerical lower bound is applied to prevent the complementary system from exhibiting near-machine-accuracy degradation, thereby improving the accessibility of dual residual reduction.

[0016] The beneficial effects of this invention are as follows: While existing sensitivity methods can quickly determine "which node is more sensitive to adjustment," they are essentially local heuristic analyses, typically only reflecting the marginal impact of node load changes on the power flow or congestion rate of a certain line. They struggle to simultaneously answer questions such as "how prices are formed," "how congestion costs are shared," "whether the total system cost after adjustment is optimal," and "whether the physical operating boundaries of the entire network are still satisfied under multi-constraint coupling conditions." In contrast, this invention achieves node-level aggregation injection of user-side loads (especially electric vehicle charging loads) through 220kV node mapping, and solves it uniformly in a seven-node AC-OPF evaluation model that explicitly incorporates power access lines, voltage boundaries, unit boundaries, and line capacity constraints. This allows for the simultaneous output of optimal operating state, node marginal price, congestion shadow price, and congestion location and degree information, while satisfying power flow balance and operating boundaries. Furthermore, through "improved original-dual interior-point method +..." and By adopting the technical approach of "coupling differentiated pricing", this invention not only realizes congestion identification, but also realizes the interpretable price expression and executable allocation of congestion costs, thereby providing a unified, quantitative and engineering-applicable technical foundation for power grid congestion management, node differentiated incentives and subsequent market-based settlement. Attached Figure Description

[0017] Figure 1 This is a topological diagram of the research object in this invention; Figure 2 This is a flowchart of the present invention; Figure 3 This is a schematic diagram of the parameters in this invention; Figure 4 This is a schematic diagram of the AC optimal power flow model in this invention; Figure 5 This is a flowchart of the improved original dual interior point method in this invention; Figure 6 This is a schematic diagram of the apparent power utilization rate of the bus line in a specific embodiment of the present invention; Figure 7 This is a schematic diagram of the electricity price results according to a specific embodiment of the present invention; Figure 8 This is a schematic diagram illustrating the optimized convergence of a specific embodiment of the present invention; Figure 9 This is the optimal voltage distribution diagram for each node in this invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention.

[0019] This invention provides a method for calculating differentiated nodal pricing that takes line congestion into account, including the following steps: Figure 2 As shown: Step 1: Based on the target power grid to be detected, establish an AC optimal power flow model; the AC optimal power flow model includes an objective function, equality constraints, and inequality constraints.

[0020] Specifically, such as Figure 4 The diagram shown is a schematic of the optimal power flow model.

[0021] Step one includes the following sub-steps: (1.1) Collect and summarize user-side load data in the target power grid according to 220KV nodes, and then perform standardization processing to obtain input data; Specifically, the standardization process involves converting the collected data into a field structure consistent with the OPF data table.

[0022] (1.2) Construct an equivalent model of the target power grid, input the input data into the model, and map it onto each bus and line of the model to form the load parameters of each bus and the capacity parameters of the line; then obtain the node admittance matrix based on the model to construct a seven-node AC-OPF constraint system, which includes equality constraints and inequality constraints. Specifically, the load parameters of the busbar include active load. and reactive load Additionally, when considering electric vehicle charging scenarios, the electric vehicle charging load is collected in the same way. This electric vehicle charging load is then superimposed on the base load as an external injection to obtain the active power load of the bus. ,in, Represents the basic active power load. Represents the active load of the electric vehicle; the reactive load of the bus is obtained. , Represents basic reactive load. This represents the reactive load of electric vehicles. When considering electric vehicle charging scenarios, the load parameters are only used as input parameters and do not change the constraint form.

[0023] The step (1.2) of obtaining the nodal admittance matrix specifically includes the following sub-steps: (1.2.1) Based on the equivalent model of the target power grid, construct a seven-node equivalent topology diagram of the target power grid, including power source access; this topology diagram is an AC power grid and includes a bus set N. Three of them are generator busbars and four are load busbars; Specifically, such as Figure 1 The diagram shown is an equivalent topology of a seven-node target power grid, which includes a set of buses. The seven bus nodes correspond to Thermal Power Plant 1, Qiaosi, Youquan, Nuclear Power Plant, Genshan, Yongchao, and Thermal Power Plant 2, respectively. Thermal Power Plant 1, Nuclear Power Plant, and Thermal Power Plant 2 correspond to generator access buses, forming a generator bus set; Qiaosi, Youquan, Genshan, and Yongchao correspond to load access buses, forming a load bus set. The Qiaosi bus also serves as the system reference bus, used to set the voltage phase angle reference and participate in system power balance.

[0024] Specifically, the equivalent topology diagram of the seven-node target power grid also needs to set generator sets, load buses, and line connection relationships, wherein the generator set is... Each unit in this set is ,and Each unit Connected to the designated generator bus, the bus number is represented as follows: ,and This mapping relationship determines the injection position of each unit in the node power balance equation. The four load buses act as load injection nodes (ESCOs), and their active / reactive power demands are given by external parameters.

[0025] (1.2.2) Four parameters are configured for each line in the topology diagram, including resistance, reactance, susceptance and capacity; In addition, such as Figure 3 As shown, a. Regarding generator parameters: the upper and lower limits of generator active power output are... The upper and lower limits of generator reactive power output are: You also need to enter the cost coefficient. and , Used to describe the unit's output. Used to describe operating costs.

[0026] b. Regarding load parameters: Input active load for each bus. and reactive load .

[0027] c. Regarding route parameters: The daily route number is... , ;in, This indicates the two bus terminals connected by this line; input start and end buses, resistance. Reactance susceptance and capacity And calculate the series admittance. .

[0028] d. Regarding busbar operating boundary parameters: Set upper and lower limits for voltage amplitude for each busbar. Set upper and lower limits for phase angle boundaries. Select reference busbar and fix This is done to eliminate phase angle degrees of freedom and ensure the uniqueness of the solution to the power flow equations.

[0029] (1.2.3) Adopt The model assembles the four parameters to obtain the node admittance matrix. , where G represents the real part of the node admittance matrix, B represents the imaginary part of the node admittance matrix, and j represents the imaginary unit.

[0030] In step (1.2), the equivalence constraints include the active / reactive power balance of nodes; the inequality constraints include line capacity, generator active / reactive power output boundaries, voltage boundaries, and phase angle boundaries.

[0031] Specifically, the active / reactive power balance at the node is as follows: in, Represents the imaginary part of the admittance matrix element, The real part of the admittance matrix element is represented; the above equation constraint ensures the consistency of active and reactive power injection and network voltage state for each bus.

[0032] The specific line capacity constraints are as follows: , in, and Represents the power flow at both ends of the line; Represents node voltage.

[0033] Engineering implementations are typically written in quadratic form: , The active / reactive power output boundaries of the generator set are as follows: The voltage boundary is specifically: The phase angle boundary is specifically as follows: .

[0034] (1.3) Construct the objective function, wherein the objective function is: ;in, , For unit cost coefficient, This represents the active power output of each generating unit.

[0035] Specifically, the objective function is in quadratic form, used to solve for the minimum power generation cost of the unit. The objective function is: ;in, , This is the unit cost coefficient; specifically... Used to describe the unit's output. Used to describe operating costs, This represents the active power output of each generating unit. The objective function is used to characterize the marginal cost differences of different generating units at different output levels, and reflects the impact of network architecture (congestion, voltage constraints, reactive power support demand, etc.) on economic dispatch results through constraint coupling.

[0036] In addition, when multi-period evaluation and scenario comparison are required, static load parameters (active / reactive load parameters) can be extended to time-series inputs.

[0037] Step 2: Initialize the AC optimal power flow model and construct initial points; input the initial points into the model, and use the improved original dual interior point method to iteratively solve the model until the convergence condition is met, thereby obtaining the differentiated node electricity price considering line congestion. like Figure 5 As shown, step two specifically includes the following sub-steps: (2.1) Transform the inequality constraints into equality constraints to complete the initialization process; construct an initial point that simultaneously satisfies the controllable residuals and strict interior point requirements of the equality constraints; initialize the Lagrange multipliers in the original equality constraints to Initialize the Lagrange multipliers in the inequality constraints to ,in, The dual variable representing the equality constraint. Represents the dual variable in the inequality constraint; Step (2.1) includes the following sub-steps: (2.1.1) Unify all inequality constraints into standard form ,and Introducing slack variables in this standard form ,and This transforms inequality constraints into equality constraints, thus enabling... Where x represents the original variable vector, including voltage, phase angle, and active / reactive power output of the generator set; (2.1.2) Constructing the initial point This point satisfies the equality constraint, the residual is controllable, and the strict interior point requirement is met. This leads to the slack variables. This ensures that the initial point satisfies the strict interior point condition of the transformed system, i.e. .

[0038] (2.2) Calculate the current apparent power utilization rate of the line, and determine the blocked line based on the utilization rate threshold; determine the blocked line based on the dual variable in the inequality constraint or the dual variable of the previous iteration, combined with the dual variable threshold; merge the two blocked lines to form a blocked line set; and construct a blockage perception weight matrix to quantify the cost sharing relationship of each node to the blocked line. The formula for calculating the apparent power utilization rate of the line in step (2.2) is as follows: in, Representing the complex power flow at both ends of the line, Representing the apparent power at both ends of the line, Representing a larger apparent power, Represents the maximum capacity of the line; Utilization threshold is The value range is 0.70 to 0.90; the threshold for the dual variable is... The value ranges from 0.05 to 0.20 (the specific value depends on the simulation). The reason for taking a small positive number is to determine possible congested lines. Even when there is a slight positive trend, the utilization rate will not be small. The blocking sensing weight matrix is: ; in, , The weakening weights for non-candidate constraints.

[0039] Specifically, based on the current line apparent power utilization rate and the dual variables in inequality constraints or the dual variables of the previous iteration. Select the one that satisfies or The blocked lines are formed by the combination of the two sets of blocked lines. In the first iteration, the dual variables in the inequality constraints, combined with the threshold values ​​of the dual variables, are used to determine the blocked lines. Subsequent iterations use the dual variables from the previous iteration. Congested lines are identified by combining the threshold values ​​of dual variables; subsequently, a congestion-aware weight matrix is ​​introduced into the line capacity constraint residuals. This approach allows the iterative process to prioritize line capacity constraints that have the greatest impact on congestion price formation without compromising overall feasibility constraints, thereby improving the stability and effectiveness of congestion shadow price extraction.

[0040] (2.3) Construct the Lagrangian function, and based on this, construct the KKT conditions and form the residual vector; The Lagrange function in step (2.3) is: ; in, Representative node active / reactive power balance equation constraint, Represents the objective function; The residual vector includes stationary residuals. ,in, Represents the objective function with respect to the original variables. gradient, Representing equality constraints For the original variables Jacobian matrix, Inequality constraints For the original variables Jacobian matrix; equality-constrained residuals, Inequality constraints are transformed into equality constraint residuals. Complementary condition residuals ,in, For the barrier parameter, This represents element-wise multiplication. This represents an m×1 column vector with μ as its element.

[0041] Specifically, to facilitate subsequent calculations of differentiated incentive strategies and interpretation of congestion economics, this embodiment explicitly retains the Lagrange multipliers of equality constraints in the model construction. In particular, the multipliers of the nodal active power balance constraints are denoted as... In the absence of significant or only slight congestion, it can be used to form a node marginal price indicator (commonly defined as...). ), used to measure at the node Increase the rate of change of the optimal target value when the active power demand is small; when the line capacity constraint is active, the line constraint multiplier can reflect the congestion shadow price component, thus providing a direct pricing basis and sensitivity quantification input for the "congestion-oriented differentiated incentive strategy model".

[0042] (2.4) Linearize the residual vector to obtain a system of linear equations; solve the system of equations by elimination and simplification to obtain the Newton direction. ,in, The direction of correction for slack variables. The direction of the correction of the Lagrange multiplier corresponding to the inequality constraint. The direction of the correction representing the original decision variables, The direction of correction of the Lagrange multiplier corresponding to the equality constraint; The elimination and simplification in step (2.4) specifically involves: ... , Related equations are eliminated or combined, thus simplifying the original system of linear equations into a system mainly concerning... Substituting back into the core linear equations, we obtain... This reduces the condition number of linear systems and improves numerical stability.

[0043] (2.5) Based on the Newton direction, a prediction-correction strategy is adopted to obtain a more accurate Newton direction; then the step size is determined to obtain the updated point; and the updated point is made feasible and stable through the fraction to boundary rule, the line search evaluation function and the numerical lower bound protection. The prediction-correction strategy in step (2.5) is as follows: first, the affine scaling direction is calculated to estimate the decreasing trend of the complementary gap; then, based on the estimation results, a centering parameter is constructed and a correction direction is calculated to improve the degree of satisfaction of the complementary condition and accelerate overall convergence; the step size is selected using a fraction-to-boundary rule to ensure that the updated points still satisfy the strict interior point condition, i.e. and When necessary, a penalty function with a barrier term is introduced as the evaluation function for the line search to ensure that the residuals and target values ​​decrease steadily during the iteration process, avoiding oscillations or numerical divergence caused by excessively large step sizes; and A numerical lower bound is applied to prevent the complementary system from exhibiting near-machine-accuracy degradation, thereby improving the accessibility of dual residual reduction.

[0044] Furthermore, for strongly nonlinear constrained problems such as AC-OPF, this embodiment can use central difference or analytical methods to calculate the Jacobian matrix. This is to ensure the validity and stability of the Newtonian direction.

[0045] Specifically, after determining the step size, the variables are updated as follows: in, The decision variable representing the k-th iteration, The decision variable representing the (k+1)th iteration, This represents the learning rate (step size).

[0046] And update the barrier parameters simultaneously. (For example, adaptively reducing the current complementary gap) to gradually approach the optimal KKT point through iteration. Iteration stops when a preset termination criterion is met. The termination condition can be a combination of equality-constrained residuals, stationary point residuals, inequality-equalized residuals, and a complementary gap threshold. For example, it may require... , , ,as well as ,in For a given precision threshold, The number of inequality constraints.

[0047] (2.6) Perform convergence determination, repeat steps (2.2.1)-(2.2.4) until convergence is satisfied, and output the differentiated node electricity price.

[0048] Specifically, convergence is judged based on a threshold.

[0049] Specifically, through the improved primal-dual interior point iteration described above, this embodiment not only obtains the optimal primal solution (unit output and bus voltage state) that satisfies power flow balance and operating boundary conditions, but also obtains the dual variables constrained by the nodal power balance equation. Dual variables with line capacity constraints Among them, the active power balance multiplier at the node Used to characterize nodes The fundamental marginal power supply value, and the dual variables of line capacity constraints. Used to characterize the circuit The cost of blocking shadows. Furthermore, this embodiment not only... Instead of using it as a blockage identification indicator, it distributes the weight among nodes. The electricity price is allocated to relevant nodes and coupled with the marginal electricity price of the base nodes to generate a differentiated node electricity price, the expression of which is: in, For the set of blocked lines, For nodes For blocked lines The congestion cost sharing weight is determined. This allows the cost of line capacity scarcity to be endogenized into nodal electricity prices, enabling the generated nodal electricity prices to simultaneously reflect both the marginal cost of energy supply and the additional cost of congestion, thus providing a direct basis for subsequent congestion mitigation based on price signals.

[0050] Specifically, after completing the AC-OPF modeling of the 7-node equivalent network and solving it using the primal-dual interior-point method, to ensure the reliability of the inputs for subsequent evaluation stages such as "line apparent power utilization / congestion location identification" and "nodal price (LMP) and congestion shadow price extraction," this embodiment performs convergence and physical rationality checks on the solution process and the final solution. For example... Figure 8 As shown, firstly, the KKT residual indices (power balance equation residuals and complementary gaps) are recorded synchronously during the iteration process, and the algorithm convergence curve is plotted on logarithmic coordinates. The results show that the complementary gap is approximately... The magnitude experienced two distinct declines and eventually dropped to approximately The order of magnitude, the power balance residual is approximately The magnitude gradually decreases and converges to approximately [value missing] at the end of the iteration. The algorithm exhibits typical "prediction-correction + fractional to boundary step" interior point iteration characteristics. In the early stages, it prioritizes maintaining strictly feasible interior points, resulting in a slow decrease in residuals. In the mid-to-late stages, as the barrier parameters advance, the complementary gap shrinks rapidly, driving a synchronous decrease in the original residuals. This convergence pattern indicates that the algorithm can stably advance and obtain KKT approximate solutions with engineering-usable accuracy. Secondly, the final voltage amplitude and phase angle solutions are checked for operational boundary and power flow morphology rationality: such as... Figure 9 As shown in the "Optimal Voltage Distribution Diagram for Each Node", the voltage amplitude of each node is approximately distributed as follows: Within the pu range, the voltage at the Qiaosi station (balance node) is approximately 1.0018 pu, with a fixed phase angle of 0°. The phase angles of the other nodes are all slightly offset (approximately...). The overall voltage level is close to 1.0 pu and does not reach the upper or lower voltage limits, indicating that the voltage constraint in this example is not a tight constraint. Meanwhile, the voltage at the node where Power Plant 2 is located, at approximately 0.987 pu, is slightly lower than the other nodes but still meets the operating boundary, reflecting the typical electrical characteristic of relatively weak voltage support when this node is located at the end of the network (via the "Qiaosi-Yongchao-Power Plant 2" branch). Based on the above convergence curves and the physical verification results of the voltage / phase angle solutions, it can be considered that the original solution obtained from this AC-OPF solution meets the input requirements for subsequent evaluation calculations in terms of both numerical stability and engineering interpretability.

[0051] Specifically, during the iterative solution process, all line capacity constraints are not treated with equal weight. Instead, key line capacity constraints are dynamically activated and dual-updated based on the apparent power utilization rate of the lines and the set of congested lines. Simultaneously, the rate of change control of the node marginal price and congestion shadow price is introduced into the barrier parameter update and termination criterion. This ensures that the output dual variable not only meets the numerical convergence requirement but also possesses the stability required for subsequent differentiated price generation. Unlike existing interior-point methods that solve all line capacity constraints simultaneously, this embodiment first constructs a set of congested lines based on the apparent power utilization rate of the lines, historical power flow distribution, and the previous round's dual value. Only the line capacity constraints in the candidate set are preferentially activated and their dual-updated. During the iteration process, the constraint set is dynamically expanded or contracted based on changes in the apparent power utilization rate of the lines and the congestion shadow price, thus forming an improved primitive-dual interior-point method for congestion identification, price extraction, and differentiated node price generation.

[0052] Step 3: Based on differentiated node electricity prices, output grid interaction assessment quantities; and calculate the final line apparent power utilization rate to determine the location and degree of congestion, and adjust the electricity price in real time to resolve node and line congestion.

[0053] Specifically, the final line apparent power utilization rate is calculated using the same formula as the current line apparent power utilization rate, which is the aforementioned line apparent power utilization rate calculation formula.

[0054] Specifically, after obtaining the optimal original solution of AC-OPF, this embodiment further organizes the line power flow and dual information to form a structured output oriented towards "blockage assessment and differentiated excitation". First, the complex power flow at both ends of each line is calculated based on the π-type line model. and with Define the apparent power utilization rate of the lines, and then sort the entire network lines from high to low utilization rate to identify potential congestion bottlenecks. For example... Figure 6As shown, the results indicate that under the current load and line capacity settings, the apparent power utilization rate of line L25 (Qiaosi-Genshan) reaches 99.90%, significantly higher than the other lines, indicating it has entered near-full-load operation and is the most critical bottleneck line under the current conditions. Following L26 (Qiaosi-Yongchao, approximately 70.52%) and L42 (Nuclear Power-Qiaosi, approximately 60.98%), although experiencing some transmission pressure, have not yet formed a substantial tight constraint. The utilization rates of other lines such as L23, L34, L67, and L12 are approximately 35.76%, 26.98%, 15.38%, and 8.46%, respectively, all within the non-stressful operating range. Further examination of the inequality dual multipliers corresponding to the line capacity constraints reveals that only the congestion shadow price of L25 is significantly positive, reaching 350.00 yuan / MVA, while the shadow prices of the other lines are all 0. This indicates that the current price differentiation is not caused by widespread network-wide tension, but rather by the activation of L25 line capacity constraints. L25 has transformed from a "high-utilization channel" into a "critical congested line with marginal scarcity value." For example... Figure 7 As shown, in terms of nodal electricity price output, the overall LMP (Local Price Per Quantity) for each node is distributed in the range of approximately 354–381 yuan / MWh. The Gengshan station node has the highest price, while the nuclear power plant-side node price is relatively lower, with the remaining nodes falling between the two, exhibiting a spatial distribution characteristic of decreasing prices from the constrained side to the power supply side. This result is consistent with the aforementioned congestion identification conclusion: when the Qiaosi-Gengshan corridor approaches its capacity limit, new loads on the constrained side will significantly increase the local marginal cost of power supply, while the price level of nodes in areas with weaker constraint influence is relatively low. Therefore, the LMP obtained in this embodiment is no longer simply an energy price, but a comprehensive price signal reflecting the node supply and demand status, network congestion level, and constraint scarcity. Simultaneously, the shadow price of line capacity constraints can serve as a quantitative indicator of "congestion tension," forming, together with the LMP, the input basis for subsequent differentiated nodal pricing.

[0055] Specifically, after identifying the price differentiation of key congested lines and nodes, this embodiment further constructs a differentiated node pricing strategy of "basic marginal price + congestion additional cost" to explicitly transmit the congestion cost to user-side load decisions. Here, the dual multiplier λ of the node power balance constraint serves as the basic marginal price, reflecting the marginal power supply value at the node level; the dual multiplier μ of the line capacity constraint serves as the congestion additional cost, reflecting the cost of scarce occupancy of key channel resources, and is mainly added to the L25-related nodes through weighted allocation, especially the restricted-side Genshan station, thus forming a differentiated price signal for congestion mitigation. It should be noted that this pricing strategy differs from simply relying on sensitivity for node reduction: the former addresses the question of "how prices are formed and how congestion costs enter the node price," while the latter addresses the question of "which node is more effective to adjust." Based on the node load-congestion sensitivity analysis results in this scenario, the absolute sensitivity κ of Genshan station to L25 reaches 1.0794, corresponding to a congestion rate sensitivity η of 0.8635% / MW, far higher than other nodes, while the sensitivity of other nodes is almost zero. This means that, under current operating conditions, if the differentiated nodal pricing strategy prioritizes the charging load at the Genshan substation, then for every 1 MW reduction in load, the apparent power utilization rate of line L25 can decrease by approximately 0.8635 percentage points. Based on the current utilization rate of 99.90%, only a small-scale load transfer at Genshan substation is needed to pull the critical line from near-congestion to a safer range. Implementing the same level of adjustment at other nodes would have a very limited effect on alleviating L25's congestion. Therefore, the constructed nodal pricing strategy can couple congestion shadow costs with marginal nodal prices, guiding price signals to prioritize high-value adjustment nodes, thereby releasing critical channel margins with minimal load adjustment costs and achieving a closed-loop effect of "price signal—load response—congestion mitigation." This result further illustrates that, compared to a uniform price or load reduction based solely on experience, the differentiated nodal pricing strategy proposed in this embodiment better reflects physical feasibility, economic optimality, and market transmission, and can directly support the design of subsequent orderly electric vehicle charging guidance, grid congestion mitigation, and commercial settlement mechanisms.

[0056] This invention further proposes a differentiated node electricity price generation mechanism that differs from existing simple LMP extraction or sensitivity reduction strategies. The dual variable corresponding to the node active power balance equation constraint is... Used to characterize the basic marginal power supply value at the node level, the dual variables of the inequality corresponding to the line capacity constraint The shadow cost and scarce channel occupancy cost are used to characterize congested lines; based on this, the present invention does not... Instead of serving as an auxiliary indicator for congestion identification, it allocates the load-sharing weight to both ends of the congested line or affected nodes through preset node-sharing weights, and couples it with the marginal price of the basic node to form a differentiated node price that includes "marginal energy cost + congestion surcharge". Thus, the generated node price not only reflects the node's supply and demand status and the marginal cost of generation, but also explicitly endogenizes the local network congestion cost into the price signal, thereby directly guiding the load transfer of high-value nodes through the price mechanism to alleviate congestion.

[0057] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and various changes and modifications can be made without departing from the spirit and scope of the invention, all of which fall within the scope of protection claimed by the present invention. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for calculating differentiated nodal pricing considering line congestion, characterized in that, The method includes the following sub-steps: Step 1: Based on the target power grid to be detected, establish an AC optimal power flow model; the AC optimal power flow model includes an objective function, equality constraints, and inequality constraints; Step 2: Initialize the AC optimal power flow model and construct initial points; input the initial points into the model, and use the improved original dual interior point method to iteratively solve the model until the convergence condition is met, thereby obtaining the differentiated node electricity price considering line congestion. Step 3: Based on differentiated node electricity prices, output grid interaction assessment quantities; and calculate the final line apparent power utilization rate to determine the location and degree of congestion, and adjust the electricity price in real time to resolve node and line congestion.

2. The method for calculating differentiated nodal pricing considering line congestion according to claim 1, characterized in that, Step one includes the following sub-steps: (1.1) Collect and summarize user-side load data in the target power grid according to 220KV nodes, and then perform standardization processing to obtain input data; (1.2) Construct an equivalent model of the target power grid, input the input data into the model, and map it onto each bus and line of the model to form the load parameters of each bus and the capacity parameters of the line; then obtain the node admittance matrix based on the model to construct a seven-node AC-OPF constraint system, which includes equality constraints and inequality constraints. (1.3) Construct the objective function, wherein the objective function is: ;in, , For unit cost coefficient, This represents the active power output of each generating unit.

3. The method for calculating differentiated nodal pricing considering line congestion according to claim 2, characterized in that, The step (1.2) of obtaining the nodal admittance matrix specifically includes the following sub-steps: (1.2.1) Based on the equivalent model of the target power grid, construct a seven-node equivalent topology diagram of the target power grid that includes power source access; this topology diagram is an AC power grid and includes a set of buses. , Three of them are generator busbars and four are load busbars; (1.2.2) Four parameters are configured for each line in the topology diagram, including resistance, reactance, susceptance and capacity; (1.2.3) Adopt The model assembles the four parameters to obtain the node admittance matrix. , where G represents the real part of the node admittance matrix, B represents the imaginary part of the node admittance matrix, and j represents the imaginary unit.

4. The method for calculating differentiated nodal pricing considering line congestion according to claim 2, characterized in that, In step (1.2), the equivalence constraints include the active / reactive power balance of nodes; the inequality constraints include line capacity, generator active / reactive power output boundaries, voltage boundaries, and phase angle boundaries.

5. The method for calculating differentiated nodal pricing considering line congestion according to claim 1, characterized in that, Step two specifically includes the following sub-steps: (2.1) Transform the inequality constraints into equality constraints to complete the initialization process; construct an initial point that simultaneously satisfies the controllable residuals and strict interior point requirements of the equality constraints; initialize the Lagrange multipliers in the original equality constraints to Initialize the Lagrange multipliers in the inequality constraints to ,in, The dual variable representing the equality constraint. Represents the dual variable in the inequality constraint; (2.2) Calculate the current apparent power utilization rate of the line, and determine the blocked line based on the utilization rate threshold; determine the blocked line based on the dual variable in the inequality constraint or the dual variable of the previous iteration, combined with the dual variable threshold; merge the two blocked lines to form a blocked line set; and construct a blockage perception weight matrix to quantify the cost sharing relationship of each node to the blocked line. (2.3) Construct the Lagrangian function, and based on this, construct the KKT conditions and form the residual vector; (2.4) Linearize the residual vector to obtain a system of linear equations; solve the system of equations by elimination and simplification to obtain the Newton direction. ;in, The direction of correction for slack variables. The direction of the correction of the Lagrange multiplier corresponding to the inequality constraint. The direction of correction representing the original decision variables, The direction of correction of the Lagrange multiplier corresponding to the equality constraint; (2.5) Based on the Newton direction, a prediction-correction strategy is adopted to obtain a more accurate Newton direction; then the step size is determined to obtain the updated point; and the updated point is made feasible and stable through the fraction to boundary rule, the line search evaluation function and the numerical lower bound protection. (2.6) Perform convergence determination, repeat steps (2.2.1)-(2.2.4) until convergence is satisfied, and output the differentiated node electricity price.

6. The method for calculating differentiated nodal pricing considering line congestion according to claim 5, characterized in that, Step (2.1) includes the following sub-steps: (2.1.1) Unify all inequality constraints into standard form ,and Introducing slack variables in this standard form ,and This transforms inequality constraints into equality constraints, thus enabling... Where x represents the original variable vector, including voltage, phase angle, and active / reactive power output of the generator set; (2.1.2) Constructing the initial point This point satisfies the equality constraint, the residual is controllable, and the strict interior point requirement is met. This leads to the slack variables. This ensures that the initial point satisfies the strict interior point condition of the transformed system, i.e. .

7. The method for calculating differentiated nodal pricing considering line congestion according to claim 5, characterized in that, The formula for calculating the apparent power utilization rate of the current line in step (2.2) is as follows: in, Representing the power flow at both ends of the line, Representing the apparent power at both ends of the line, Representing a larger apparent power, Represents the maximum capacity of the line; Utilization threshold is The value range is 0.70 to 0.90; the threshold for the dual variable is... The value ranges from 0.05 to 0.20; The blocking sensing weight matrix is: ; in, , The weakening weights for non-candidate constraints.

8. The method for calculating differentiated nodal pricing considering line congestion according to claim 5, characterized in that, The Lagrange function in step (2.3) is: ； in, Representative node active / reactive power balance equation constraint, Represents the objective function; The residual vector includes stationary residuals. ,in, Represents the objective function with respect to the original variables. gradient, Representing equality constraints For the original variables Jacobian matrix, Inequality constraints For the original variables Jacobian matrix; equality-constrained residuals, Inequality constraints are transformed into equality constraint residuals. Complementary condition residuals ,in, For the barrier parameter, This represents element-wise multiplication. This represents an m×1 column vector with μ as its element.

9. The method for calculating differentiated nodal pricing considering line congestion according to claim 5, characterized in that, The elimination and simplification in step (2.4) specifically involves: ... , Related equations are eliminated or combined, thus simplifying the original system of linear equations into a system mainly concerning... Substituting back into the core linear equations, we obtain... This reduces the condition number of linear systems and improves numerical stability.

10. The method for calculating differentiated nodal pricing considering line congestion according to claim 5, characterized in that, The prediction-correction strategy in step (2.5) is as follows: first, the affine scaling direction is calculated to estimate the decreasing trend of the complementary gap; then, based on the estimation results, a centering parameter is constructed and a correction direction is calculated to improve the degree of satisfaction of the complementary condition and accelerate overall convergence; the step size is selected using a fraction-to-boundary rule to ensure that the updated points still satisfy the strict interior point condition, i.e. and When necessary, a penalty function with a barrier term is introduced as the evaluation function for the line search to ensure that the residuals and target values ​​decrease steadily during the iteration process, avoiding oscillations or numerical divergence caused by excessively large step sizes; and A numerical lower bound is applied to prevent the complementary system from exhibiting near-machine-accuracy degradation, thereby improving the accessibility of dual residual reduction.

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