A power distribution network voltage control and energy saving loss reduction coordination optimization method considering main distribution coordination

Abstract

The application provides a novel power distribution network voltage control and energy saving and loss reduction coordination optimization method considering main coordination, belongs to the technical field of power distribution network operation control, and comprises the following steps: S1, constructing an interactive boundary model between a main network and a power distribution network; S2, establishing a convex optimization model of the lower layer power distribution network; S3, constructing a two-stage robust optimization model considering multiple uncertainties; S4, constructing a multi-objective robust optimization model; and S5, jointly solving the multi-objective robust optimization model. Through the research on the coordination mechanism between the main network and the power distribution network, the voltage control is coordinately optimized, the power loss is reduced, the factors such as voltage level, reactive power compensation and load fluctuation are comprehensively considered, the problem of voltage fluctuation and energy consumption increase of the power distribution network after the access of new energy is solved, and thus the operation efficiency of the power distribution network is significantly improved, and the realization of voltage control and energy saving and loss reduction is promoted.

Description

Technical Field

[0001] This invention relates to the field of distribution network operation control technology, and in particular to a method for coordinated optimization of distribution network voltage control and energy saving and loss reduction that considers the coordination between main and distribution systems. Background Technology

[0002] With the increasing penetration of distributed wind power, photovoltaics and other new energy sources in the distribution network, and the large-scale access of flexible loads such as electric vehicles, the energy flow pattern of the distribution network is changing from the traditional one-way radial power supply to two-way interaction and multi-source mutual assistance. The problems of voltage exceeding limits and increased network losses are becoming increasingly prominent.

[0003] Existing research mainly falls into two categories: Regarding the optimization of primary and secondary coordination: Existing literature uses heterogeneous decomposition algorithms, two-stage robust optimization, and objective cascade methods to solve the optimal power flow problem of primary and secondary coordination, or introduces conditional risk value to quantify operational risk.

[0004] In terms of distribution network optimization, existing technologies include distributed photovoltaic local voltage control, integrated energy dispatch considering carbon emission constraints, and voltage reduction and energy saving control using reactive power regulation devices such as on-load tap-changing transformers and parallel capacitor banks.

[0005] Current research has yielded results in single or dual-objective areas such as "main-distribution coordination" architecture design, power quality management, and energy conservation and loss reduction. However, research on the systematic integration and coordinated optimization of these three aspects within the dynamic scenario of a high-penetration distribution network is still insufficient. The strong coupling and potential conflicts among these three aspects at the spatiotemporal scale have not been thoroughly revealed. In particular, when facing the multiple uncertainties brought about by the randomness of distributed power output, load diversity, and network structure complexity, a robust coordinated control strategy that can simultaneously ensure voltage safety and stability, improve power quality, and enhance operational economy is lacking. Summary of the Invention

[0006] This invention provides a coordinated optimization method for distribution network voltage control and energy saving / loss reduction considering main grid-distribution network collaboration. Taking power system construction as the background, it addresses the voltage control and energy saving / loss reduction problems in distribution networks under the "main grid-distribution network collaboration" scenario, proposing an optimized control strategy based on multiple uncertainties. By studying the collaboration mechanism between the main grid and the distribution network, it coordinates and optimizes voltage control, reduces power losses, and comprehensively considers factors such as voltage level, reactive power compensation, and load fluctuations. This solves the problems of voltage fluctuations and increased energy consumption in the distribution network after the integration of new energy sources, thereby significantly improving the operating efficiency of the distribution network and promoting energy saving / loss reduction.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for coordinated optimization of voltage control and energy saving / loss reduction in distribution networks, considering the coordination between main and distribution systems, includes: S1. Construct an interaction boundary model between the main grid and the distribution network, and determine the power-voltage feasible region of the interaction nodes between the main grid and the distribution network; the power-voltage feasible region consists of a reference voltage boundary, an active power boundary, and a reactive power boundary; S2. Establish a convex optimization model for the lower-level distribution network. Use the DistFlow branch power flow model to describe the power flow distribution of the distribution network, and use the second-order cone relaxation theory to transform the non-convex equality constraints in the power flow distribution into convex inequality constraints, thereby obtaining a convex distribution network operation constraint set. At the same time, establish energy storage system constraints and reactive power source constraints. Combine the convex distribution network operation constraint set, energy storage system constraints, and reactive power source constraints into a distribution network convex optimization constraint set. S3. Construct a two-stage robust optimization model that considers multiple uncertainties. Discrete control variables are used as decision variables in the first stage, and continuous control variables are used as decision variables in the second stage. Minimizing the active power loss of the distribution network is the single objective optimization function. The power-voltage feasible region of the interaction nodes between the main grid and the distribution network is used as the upper boundary constraint of the two-stage robust optimization model, and the convex optimization constraint set of the distribution network is used as the lower operating constraint of the two-stage robust optimization model. Solve the two-stage robust optimization model using a column constraint generation algorithm to obtain the optimal solution with the objective of minimizing the active power loss of the distribution network. The node voltage deviation value corresponding to the optimal solution is recorded as the first optimal value. S4. With the goal of minimizing node voltage deviation, solve for the optimal value of minimizing node voltage deviation, denoted as the second optimal value; determine the allowable upper limit threshold of voltage deviation based on the first and second optimal values. The value range of ; based on the two-stage robust optimization model, minimizing the node voltage deviation is added as the second optimization objective, forming a multi-objective robust optimization model; adopting The constraint method is used to solve the multi-objective robust optimization model, with minimizing the active power loss of the distribution network as the primary objective and minimizing the node voltage deviation as the auxiliary objective. The node voltage deviation objective is used as... Constraints, in the Within the range of values ​​of , a set of non-dominant Pareto solutions is obtained, and a compromise solution is selected from the Pareto solution set based on the center point strategy. S5. The power-voltage feasible domain of the interaction nodes between the main grid and the distribution network is substituted into the multi-objective robust optimization model as the upper-level constraint of the distribution network operation, and the model is solved jointly to output a distribution network optimization control strategy that satisfies the safety boundary of the main grid, adapts to multiple uncertainties, and takes into account voltage quality and energy saving and loss reduction.

[0008] In this specification, the method for determining the reference voltage boundary in S1 is as follows: obtain the net load forecast value of the distribution network, which is calculated based on the historical load data of the distribution network, the power output data of the new energy source of the distribution network, and the prediction model; perform power flow calculation based on the net load forecast value, set the voltage calculation result of the connection node between the main network and the distribution network as the basic feasible solution, and use the connection node voltage in the basic feasible solution as the reference voltage boundary.

[0009] In this specification, the method for determining the active power boundary in S1 is as follows: taking the net load prediction value as the center, and combining the pre-set net load fluctuation bandwidth and the transformer apparent power capacity, the upper and lower limits of active power are determined; the method for determining the reactive power boundary is as follows: taking the basic feasible solution as the starting point, by gradually increasing or decreasing the reactive load of the connection node, the boundary of power flow convergence is detected, thereby determining the upper and lower limits of reactive power; if the basic power flow solution fails, the safety boundary allowed by the transformer is taken as the reactive power boundary.

[0010] In this specification, the specific method for transforming non-convex equality constraints into convex inequality constraints using the second-order cone relaxation theory in S2 is as follows: the non-convex equality constraints between branch active power, branch reactive power, branch current, and node voltage in the DistFlow branch power flow model are relaxed into inequality constraints, and then the inequality constraints are constructed into second-order cone constraints, thereby obtaining the convex distribution network operation constraint set.

[0011] In this specification, the energy storage system constraints in S2 include: power balance constraints, upper and lower limits of remaining capacity constraints, mutual exclusion constraints of charging and discharging states, and charging and discharging power limit constraints; the reactive power constraints include the adjustment range constraints of continuous static var compensators and the number of switching groups of discrete grouped switching capacitor banks. The adjustment range constraints of static var compensators are the continuous adjustment range and upper and lower limits of their reactive power output. The number of switching groups of grouped switching capacitor banks are the product relationship between the number of switching groups and the compensation capacity of a single group, the upper limit constraint of the number of switching groups, and the limit on the number of operations within the scheduling cycle.

[0012] In this specification, in the two-stage robust optimization model of S3, the decision variables in the first stage are discrete variables, including the charging and discharging status flags of energy storage and the number of switching groups of capacitor banks; the decision variables in the second stage are continuous variables, including the charging and discharging power of energy storage and the reactive power compensation amount of the static var compensator.

[0013] In this specification, the specific steps of using the column constraint generation algorithm in S3 to solve the two-stage robust optimization model are as follows: decompose the original problem into a main problem and sub-problems and solve them iteratively; solve the optimal decision of the first-stage discrete variables in the current worst-case scenario and update the lower bound in the main problem; under the given decision of the main problem, find the uncertainty scenario that maximizes the network loss of the system, i.e., the worst-case scenario, and update the upper bound in the sub-problems; stop iterating when the difference between the upper bound and the lower bound is less than a preset threshold, otherwise generate new variables and constraints and add them to the main problem to continue solving.

[0014] In this specification, the subproblem has a maximization-minimization bilayer structure. Strong duality theory is used to transform this bilayer structure into a single-layer maximization problem. The Big M method is used to linearize the bilinear terms in the transformed objective function, thereby directly solving the worst-case scenario.

[0015] In this specification, S4 is based on The specific method for solving the Pareto solution set using the constraint method is as follows: The node voltage deviation target is taken as... The constraint, with the primary objective of minimizing active power losses in the distribution network, is as follows: Multiple values ​​are selected at equal intervals within the range of values ​​to solve the problem one by one, resulting in a set of non-dominant Pareto solutions. The method for selecting a compromise solution based on the center point strategy is as follows: the arithmetic mean of the voltage deviation values ​​of all solutions in the Pareto solution set is calculated as the reference value, and then the absolute distance between the voltage deviation value of each solution and the reference value is calculated. The solution with the smallest absolute distance is selected as the final compromise solution.

[0016] In this specification, the power distribution network optimization control strategy output in S5 includes: power charging and discharging command and charging and discharging status flag of the energy storage system, reactive power compensation command of the static var compensator, and command of the number of switching groups of the capacitor bank; the optimization control strategy simultaneously satisfies: power-voltage feasible domain boundary, distribution network convex optimization constraint set, and voltage deviation constraint value corresponding to the compromise solution.

[0017] In summary, the present invention has at least the following beneficial effects: It achieves safe and economical operation under the coordination of main grid and distribution network: By establishing the interaction boundary model of main grid and distribution network, the safety constraints of main grid are incorporated into the optimization of distribution network, ensuring that the power and voltage of main grid and distribution network interface are strictly limited within the safe and feasible domain, realizing mutual support and flexible backup between main grid and distribution network, and enhancing the flexibility and robustness of grid.

[0018] This method effectively addresses multiple uncertainties by employing a two-stage robust optimization model that can handle random fluctuations in distributed power output and load power. It identifies the worst-case operating scenario that leads to the greatest system network loss and provides a conservative optimization scheduling strategy within this scenario, effectively covering operational risks. Simulation results demonstrate that as prediction errors increase, this method can adjust the strategy to handle more extreme scenarios.

[0019] A coordinated optimization of voltage quality and energy saving and loss reduction has been achieved: Through a multi-objective optimization model, the Pareto optimal solution set for network loss and voltage deviation has been obtained. Decision-makers can choose solutions with different preferences based on actual needs (such as a preference for low voltage deviation or low network loss), and find a compromise solution that achieves the best balance between economy and power quality through the "center point" strategy or marginal trade-off analysis, thus avoiding the dilemma of pursuing ultimate quality at high cost.

[0020] Improved model solution efficiency and global optimality: By using second-order cone relaxation, the non-convex power flow model of the distribution network is transformed into a convex optimization model, enabling the original problem to obtain a globally optimal solution efficiently through mature commercial solvers, overcoming the disadvantages of non-convex models being difficult to solve and prone to getting trapped in local optima.

[0021] It provides a clear basis for decision-making: by analyzing the marginal trade-off curve between network loss and voltage deviation (which presents a "V-shaped" or "U-shaped" characteristic), it reveals the efficiency boundary in system operation and provides operators with a method to identify the critical point from the "high-efficiency improvement zone" to the "diminishing returns zone", which helps to achieve the most cost-effective collaborative optimization. Attached Figure Description

[0022] Figure 1 A schematic diagram of a coordinated optimization method for voltage control and energy saving and loss reduction in distribution networks that considers the coordination between main and distribution systems.

[0023] Figure 2 This is a schematic diagram of the two-stage robust optimization solution process involved in this invention.

[0024] Figure 3 This is a schematic diagram of the Pareto optimal solution set concept involved in this invention.

[0025] Figure 4 This is a schematic diagram of the reconstructed IEEE 33-node network involved in this invention.

[0026] Figure 5 This is a schematic diagram of the total wind power output and total active load curves involved in this invention.

[0027] Figure 6 This is a schematic diagram of the active load distribution of the system before optimization involved in this invention.

[0028] Figure 7This is a schematic diagram of the active load distribution of the optimized system involved in this invention.

[0029] Figure 8 This is a schematic diagram of the reactive load distribution of the system before optimization involved in this invention.

[0030] Figure 9 This is a schematic diagram of the reactive load distribution of the optimized system involved in this invention.

[0031] Figure 10 This is a schematic diagram of the worst-case scenario for wind power obtained by the robust optimization involved in this invention.

[0032] Figure 11 This is a schematic diagram of the total daily active power load curve with prediction error coefficient involved in this invention.

[0033] Figure 12 This is a schematic diagram of the voltage deviation before and after optimization involved in this invention.

[0034] Figure 13 This is a schematic diagram of the Pareto solution set involved in this invention.

[0035] Figure 14 This is a schematic diagram of the 24-hour network loss of the Pareto partial solution involved in this invention.

[0036] Figure 15 This is a schematic diagram of the maximum 24-hour voltage deviation of the Pareto partial solution involved in this invention.

[0037] Figure 16 This is a schematic diagram illustrating the effect of different reactive power output devices in the power distribution network when solving A, as involved in this invention.

[0038] Figure 17 This is a schematic diagram illustrating the effect of different reactive power output devices in the power distribution network when solving B, as involved in this invention.

[0039] Figure 18 This is a schematic diagram illustrating the marginal trade-off between network loss and voltage deviation involved in this invention.

[0040] Figure 19 This is a schematic diagram of the main network topology of case 30 node involving the distribution network involved in this invention.

[0041] Figure 20 This is a schematic diagram of the actual output power and boundary (active power) of the main distribution network interface involved in this invention.

[0042] Figure 21 This is a schematic diagram of the actual output power and boundary (reactive power) of the main distribution network interface involved in this invention.

[0043] Figure 22 This is a schematic diagram of the actual voltage and boundary of the main distribution network interface involved in this invention.

[0044] Figure 23 This is a schematic diagram of the total load of the distribution network, the total power of the generator sets, and the transmission power of the main distribution network involved in this invention. Detailed Implementation

[0045] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0046] like Figure 1 As shown, this embodiment provides a coordinated optimization method for voltage control and energy saving / loss reduction in distribution networks that considers main and distribution network coordination, including: S1. Construct an interaction boundary model between the main grid and the distribution network, and determine the power-voltage feasible region of the interaction nodes between the main grid and the distribution network; the power-voltage feasible region consists of a reference voltage boundary, an active power boundary, and a reactive power boundary; S2. Establish a convex optimization model for the lower-level distribution network. Use the DistFlow branch power flow model to describe the power flow distribution of the distribution network, and use the second-order cone relaxation theory to transform the non-convex equality constraints in the power flow distribution into convex inequality constraints, thereby obtaining a convex distribution network operation constraint set. At the same time, establish energy storage system constraints and reactive power source constraints. Combine the convex distribution network operation constraint set, energy storage system constraints, and reactive power source constraints into a distribution network convex optimization constraint set. S3. Construct a two-stage robust optimization model that considers multiple uncertainties. Discrete control variables are used as decision variables in the first stage, and continuous control variables are used as decision variables in the second stage. Minimizing the active power loss of the distribution network is the single objective optimization function. The power-voltage feasible region of the interaction nodes between the main grid and the distribution network is used as the upper boundary constraint of the two-stage robust optimization model, and the convex optimization constraint set of the distribution network is used as the lower operating constraint of the two-stage robust optimization model. Solve the two-stage robust optimization model using a column constraint generation algorithm to obtain the optimal solution with the objective of minimizing the active power loss of the distribution network. The node voltage deviation value corresponding to the optimal solution is recorded as the first optimal value. S4. With the goal of minimizing node voltage deviation, solve for the optimal value of minimizing node voltage deviation, denoted as the second optimal value; determine the allowable upper limit threshold of voltage deviation based on the first and second optimal values. The value range of ; based on the two-stage robust optimization model, minimizing the node voltage deviation is added as the second optimization objective, forming a multi-objective robust optimization model; adopting The constraint method is used to solve the multi-objective robust optimization model, with minimizing the active power loss of the distribution network as the primary objective and minimizing the node voltage deviation as the auxiliary objective. The node voltage deviation objective is used as... Constraints, in the Within the range of values ​​of , a set of non-dominant Pareto solutions is obtained, and a compromise solution is selected from the Pareto solution set based on the center point strategy. S5. The power-voltage feasible domain of the interaction nodes between the main grid and the distribution network is substituted into the multi-objective robust optimization model as the upper-level constraint of the distribution network operation, and the model is solved jointly to output a distribution network optimization control strategy that satisfies the safety boundary of the main grid, adapts to multiple uncertainties, and takes into account voltage quality and energy saving and loss reduction.

[0047] In some embodiments, the method for determining the reference voltage boundary in S1 is as follows: Obtain the net load forecast value of the distribution network, which is calculated based on historical load data of the distribution network, renewable energy output data of the distribution network, and a prediction model; perform power flow calculation based on the net load forecast value, set the voltage calculation results of the connection nodes between the main grid and the distribution network as the basic feasible solution, and use the connection node voltage in the basic feasible solution as the reference voltage boundary. Net load refers to the remaining load after deducting the output of distributed renewable energy sources (photovoltaics, wind power, etc.) within the region from the total power load of the system.

[0048] In some embodiments, the active power boundary in S1 is determined by: taking the net load prediction value as the center, and combining the pre-set net load fluctuation bandwidth and the transformer apparent power capacity to determine the upper and lower limits of active power; the reactive power boundary is determined by: taking the basic feasible solution as the starting point, and gradually increasing or decreasing the reactive load of the connection node to detect the boundary of power flow convergence, thereby determining the upper and lower limits of reactive power; if the basic power flow solution fails, the safety boundary allowed by the transformer is taken as the reactive power boundary.

[0049] In some embodiments, the specific method for transforming non-convex equality constraints into convex inequality constraints using the second-order cone relaxation theory in S2 is as follows: the non-convex equality constraints between branch active power, branch reactive power, branch current, and node voltage in the DistFlow branch power flow model are relaxed into inequality constraints, and then the inequality constraints are constructed into second-order cone constraints, thereby obtaining the convex distribution network operation constraint set.

[0050] In some embodiments, the energy storage system constraints in S2 include: power balance constraints, upper and lower limits of remaining capacity constraints, mutual exclusion constraints of charging and discharging states, and charging and discharging power limit constraints; the reactive power constraints include the adjustment range constraints of continuous static var compensators and the number of switching groups of discrete grouped capacitor banks, wherein the adjustment range constraints of static var compensators are the continuous adjustment range and upper and lower limits of their reactive power output, and the number of switching groups of grouped capacitor banks are the product relationship between the number of switching groups and the compensation capacity of a single group, the upper limit constraint of the number of switching groups, and the limit on the number of operations within the scheduling cycle.

[0051] In some embodiments, in the two-stage robust optimization model of S3, the decision variables in the first stage are discrete variables, including the charging and discharging status flags of energy storage and the number of switching groups of capacitor banks; the decision variables in the second stage are continuous variables, including the charging and discharging power of energy storage and the reactive power compensation amount of the static var compensator.

[0052] In some embodiments, the specific steps of using the column constraint generation algorithm to solve the two-stage robust optimization model in S3 are as follows: decompose the original problem into a main problem and sub-problems and solve them iteratively; solve the optimal decision of the first-stage discrete variables in the current worst-case scenario and update the lower bound in the main problem; under the given decision of the main problem, find the uncertainty scenario that maximizes the network loss of the system, i.e. the worst-case scenario, and update the upper bound in the sub-problems; stop iterating when the difference between the upper bound and the lower bound is less than a preset threshold, otherwise generate new variables and constraints and add them to the main problem to continue solving.

[0053] In some embodiments, the subproblem has a maximization-minimization bilayer structure. The strong duality theory is used to transform the bilayer structure into a single-layer maximization problem, and the Big M method is used to linearize the bilinear terms in the transformed objective function, thereby directly solving the worst-case scenario.

[0054] In some embodiments, the S4 is based on The specific method for solving the Pareto solution set using the constraint method is as follows: The node voltage deviation target is taken as... The constraint, with the primary objective of minimizing active power losses in the distribution network, is as follows: Multiple values ​​are selected at equal intervals within the range of values ​​to solve the problem one by one, resulting in a set of non-dominant Pareto solutions. The method for selecting a compromise solution based on the center point strategy is as follows: the arithmetic mean of the voltage deviation values ​​of all solutions in the Pareto solution set is calculated as the reference value, and then the absolute distance between the voltage deviation value of each solution and the reference value is calculated. The solution with the smallest absolute distance is selected as the final compromise solution.

[0055] In some embodiments, the distribution network optimization control strategy output in S5 includes: charging and discharging power commands and charging and discharging status flags of the energy storage system, reactive power compensation commands of the static var compensator, and commands for the number of switching capacitor banks in the group; the optimization control strategy simultaneously satisfies: the power-voltage feasible domain boundary, the distribution network convex optimization constraint set, and the voltage deviation constraint value corresponding to the compromise solution.

[0056] The technical concept of this invention is as follows: A method for coordinated optimization of voltage control and energy saving / loss reduction in distribution networks, considering the coordination between main and distribution systems, includes: Construct a main grid-distribution network interaction boundary model: determine the power-voltage feasible region that the distribution network can obtain from the main grid, including the reference voltage, active power boundary and reactive power boundary, to provide boundary conditions for internal optimization of the distribution network.

[0057] Establish a convex optimization model for the lower-level distribution network: For the high impedance ratio characteristics of the distribution network, the DistFlow branch power flow model is adopted, and the non-convex power flow constraints are transformed into convex constraints using the second-order cone relaxation theory; at the same time, constraints on energy storage system and reactive power sources (continuous SVC and discrete CB) are established.

[0058] A two-stage robust optimization model considering uncertainty is constructed: discrete variables (energy storage charging and discharging state, number of capacitor banks switched on and off) are used as decision variables in the first stage, and continuous variables (energy storage charging and discharging power, SVC reactive power compensation) are used as decision variables in the second stage, with the goal of minimizing the active power loss of the distribution network; a column constraint generation algorithm is used to solve the problem.

[0059] based on Constraint-based multi-objective collaborative optimization: simultaneously optimizing active power loss minimization and node voltage deviation minimization, employing... The constraint method is used to solve the Pareto solution set, and a compromise solution is selected based on the central point strategy.

[0060] Perform overall optimization and verification under the main and auxiliary coordination: Substitute the power-voltage feasible domain into the multi-objective robust optimization model for joint solution and output the optimized control strategy.

[0061] Specifically as follows: Step 1. Construct a main grid-distribution network interaction boundary model to determine the power-voltage feasible region that the distribution network can obtain from the main grid; Step 1 is used to establish the coordination boundary between the main grid and the distribution network, determine the power and voltage regulation range that the distribution network can obtain from the main grid under safe operation constraints, and provide boundary conditions for internal optimization of the distribution network; specifically, it includes the following sub-steps: Step 1.1: Construct the upper boundary model of the main grid. Using the voltage, active power, and reactive power of the nodes connecting the main grid and the distribution network as decision variables, solve the "power-voltage" feasible region that satisfies the internal safe operation constraints of the distribution network; the feasible region consists of a reference voltage boundary, an active power boundary, and a reactive power boundary.

[0062] The feasible "power-voltage" region that satisfies the internal safety operation constraints of the distribution network is as follows: (1-1) In the formula, , These represent the active and reactive power flowing from the main power grid to the distribution network, respectively. and They represent the two respectively.t Upper and lower limits of time; The voltage of the main and distribution network connection nodes; For connecting nodes t Reference voltage at any given time; The bandwidth that allows for voltage fluctuations.

[0063] Step 1.2: Calculate the reference voltage. Perform power flow calculations based on the predicted net load of the distribution network, set the voltage calculation results of the connection nodes as the basic feasible solution, and use them as the reference voltage.

[0064] Forecast values ​​of net load of the lower-level power grid Power flow calculations are performed on the loads acting as connection nodes, and the resulting solutions are considered basic feasible solutions. Reference voltage. Set to the voltage of the connected nodes in this solution. The predicted active power of the net load on the distribution network side is obtained by subtracting the predicted total active power output of distributed renewable energy from the predicted total active load of the distribution network. The predicted reactive power of the net load on the distribution network side is obtained by subtracting the predicted total reactive power output of distributed renewable energy from the predicted total reactive power load of the distribution network. j is the imaginary unit in power system phasor calculation.

[0065] Step 1.3: Calculate the active power boundary. Based on the net load forecast of the distribution network, and in conjunction with the allowable fluctuation bandwidth and the apparent power capacity of the transformer, determine the upper and lower limits of active power.

[0066] The active power boundary mainly considers two factors: first, it centers on the total net load forecast of the downstream power grid, allowing for a certain degree of fluctuation; second, under no circumstances should the absolute value of the exchange power exceed the apparent power capacity of the transformer. The specific formula is as follows: (1-2) (1-3) In the formula, To allow bandwidth to fluctuate around the predicted value; This represents the apparent power capacity of the transformer.

[0067] Step 1.4: Calculate the reactive power boundary. Based on the basic feasible solution, by gradually increasing or decreasing the reactive load of the connection nodes, the boundary of power flow convergence is detected, thereby determining the upper and lower limits of reactive power.

[0068] Based on the basic feasible solution, the reactive load at the connection point is gradually increased or decreased. (That is, changing the reactive power absorbed by the downstream power grid from the main power grid) ), to detect the boundary of the feasible region of reactive power.

[0069] Upper bound search: from the basic value Start with step size Gradually increase reactive power demand until the power flow cannot converge or the maximum number of steps in the search is reached. Let the total amount of reactive power successfully increased be . ,but: (1-4) Lower bound search: Similarly, from the basic value Initially, gradually reduce reactive power demand until the power flow cannot converge or the maximum number of steps in the search is reached. Let the total amount of reactive power successfully reduced be . ,but: (1-5) If the basic power flow solution fails, the reactive power boundary is set as the safety boundary allowed by the transformer, i.e., a geometrically conservative estimate based on the transformer's apparent power circle diagram: (1-6) Final output This forms a "power-voltage" envelope that describes the flexibility of the distribution network, providing a key input for the coordinated and optimized scheduling of the main grid and distribution network.

[0070] Step 2. Establish a convex optimization model for the lower-level distribution network and handle non-convex power flow constraints; Step 2, addressing the high impedance ratio characteristics of the distribution network, establishes an efficient solution model for the distribution network operation; specifically, it includes the following sub-steps: Step 2.1: Establish power flow constraints for the distribution network. Using the DistFlow branch power flow model suitable for radial distribution networks, establish node power balance constraints, branch voltage drop constraints, and constraints on the relationship between branch power and current / voltage. For the non-convex equality terms in these constraints, use second-order cone relaxation theory to transform them into convex inequality constraints, thereby transforming the original non-convex optimization problem into a convex optimization problem.

[0071] The main difference between distribution networks and transmission networks lies in the ratio of resistance to reactance. In distribution networks, the ratio is relatively close, while in transmission networks, the ratio of reactance to resistance is generally much greater than 1. Therefore, in traditional optimal power flow models for transmission networks, network losses and reactive power are often ignored to simplify calculations and reduce computational complexity, leading to a significant adoption of DC-based optimal power flow models for optimal scheduling. However, because the impedance ratio in distribution networks is close to 1, network losses are substantial. Therefore, directly using the widely used DC model in transmission networks may result in significant computational errors. Consequently, in the optimal scheduling of distribution networks, the actual topological characteristics of the distribution network must be considered, and more suitable optimal power flow models must be researched.

[0072] For radial power distribution systems, power flow distribution is usually described using the DistFlow branch power flow model, and the power flow constraints of the distribution network are shown below.

[0073] (2-1) (2-2) (2-3) (2-4) (2-5) (2-6) (2-7) In the formula, The active power transmitted at the head end of branch jl at time t; The reactive power transmitted at the head end of branch jl at time t; , They are respectively t time ij The active and reactive power of the branch circuit; , They are respectively t Time generator injection node j The active and reactive power; , They are respectively t Time Node j The active and reactive load power; , The lines are respectively ij Resistance and reactance; for t time ij The square of the current in the branch circuit; and They represent t Time Node j and nodes i The square of the voltage; , These are the lower limits of the active and reactive power of the generator set, respectively. , These are the upper limits of active and reactive power for the generator set, respectively. , They are respectively t Time Node i The active and reactive power generated by the generator set; , They are nodes i The maximum and minimum values ​​of the square of the voltage at the point; for ij The maximum value of the square of the branch current; , These are the lower limits of active and reactive power output from the main grid, respectively. , These are the upper limits of active and reactive power output from the main grid, respectively. , They are respectively t The main grid outputs active and reactive power at all times.

[0074] Equation (2-1) represents the power balance of the distribution network nodes; Equation (2-2) represents the voltage drop balance constraint of the branch; Equation (2-3) represents the relationship between the active and reactive power of the branch and the branch current and node voltage; Equation (2-4) represents the power constraint of the generator set; Equations (2-5) and (2-6) represent the safety constraints of the distribution network operation; Equation (2-7) represents the power constraint transmitted from the main grid to the distribution network.

[0075] As can be seen from the above model, except for equation (2-3), which is a nonlinear and non-convex equality constraint, all other functions are convex functions. Therefore, if the non-convex constraint can be transformed into a convex constraint, the non-convex distribution network optimization scheduling model established in this invention can be transformed into a convex optimization model. To this end, this invention utilizes the second-order cone (SOC) relaxation theory to relax the non-convex equality constraint in equation (2-3) into a convex inequality constraint, as shown in equation (2-8). This transforms the model from a non-convex optimization model into a convex optimization model. Compared to the original non-convex model, the solution difficulty of the distribution network optimization scheduling model after SOC convex relaxation is greatly reduced, and the global optimal solution can be obtained.

[0076] (2-8) Furthermore, let's rewrite the above formula in the form of SOC: (2-9) In summary, by relaxing non-convex equality constraints into inequality constraints, and then introducing SOC theory to construct SOC constraints, the model proposed in this invention is transformed into a SOC-based convex optimization model, which can directly obtain the global optimal solution by calling mature commercial solvers. Where... This represents the second-order cone norm.

[0077] Step 2.2: Establish constraints for the energy storage system. Construct a time-series model of the energy storage device, including: power balance constraints, upper and lower limits of remaining capacity constraints, mutual exclusion constraints of charge and discharge states, and limits of charge and discharge power.

[0078] The supporting role of energy storage in the distribution network typically includes: a) Peak shaving and valley filling improve load characteristics. Discharge during peak load and charge during valley load.

[0079] b) Improve voltage quality. Energy storage can mitigate the impact of irregular start-up and shutdown of distributed generation sources on the power supply quality of the distribution network.

[0080] c) Energy storage can disrupt the balance between supply and demand in the power system, effectively isolating the production and utilization of electricity over time.

[0081] Modeling energy storage devices involves temporal coupling and cannot be based on a single time segment. The specific constraint model is as follows: (2-10) (2-11) (2-12) (2-13) In the formula, for t Always connected to the node j The amount of electricity stored in the energy storage device on it; , , , They are respectively t Always connected to the node j The charging power, charging efficiency, discharging power, and discharging efficiency of the energy storage device on the device. The scheduling time interval; To continue j The maximum capacity of the energy storage device at the node; , The variables are 0 and 1, where 1 represents charging (discharging) and 0 represents not charging (discharging), ensuring that charging and discharging cannot occur simultaneously. , They are connected to j The maximum power of energy storage charging and discharging at the node.

[0082] Equation (2-10) is the power balance limit, which ensures that the power in the energy storage device at the previous moment is balanced with the power in the next moment and the charging and discharging power. Equation (2-11) is the remaining capacity limit of the energy storage device. Equation (2-12) is the energy storage state limit, which ensures that the energy storage can only be in one of the three states: charging, discharging, or neither charging nor discharging. Equation (2-13) is the maximum limit of charging and discharging power.

[0083] Step 2.3: Establish reactive power constraints. Model continuous and discrete reactive power sources respectively: For static var compensators, set the continuous adjustment range and upper and lower limits of their reactive power output; for grouped switching capacitor banks, their reactive power output is determined by the product of the number of switching groups and the compensation capacity of a single group, and set the upper limit of the number of switching groups and the limit of the number of operations within the scheduling cycle.

[0084] Reactive power sources are divided into discrete and continuous types. For continuous sources, the main consideration is the static var compensator (SVC), while for discrete sources, the main consideration is the capacitor bank (CB).

[0085] a) Static Var Compensator (SVC): Traditional SVCs install parallel reactors and capacitors, or combinations thereof, at the compensation nodes, and connect and disconnect them via mechanical switches. This compensation method results in discrete regulation and slow operation, failing to meet the dynamic requirements of power systems. With the development of electronic technology, SVCs incorporate power electronic devices, primarily consisting of thyristor-controlled reactors and thyristor-switched capacitors connected in parallel, enabling continuous and smooth regulation.

[0086] In distribution network optimization control, a simplified model is usually used, and the established constraint model is as follows: (2-14) In the formula, for t Always connected to the node j The reactive power of the SVC on the device; , To connect to the node j The upper and lower limits of reactive power output from the SVC on the device; T The scheduling period is [number].

[0087] b) Grouped Capacitor Bank Switching: Grouped capacitor bank switching is a traditional voltage regulation method, widely used due to its economy and simplicity. If the feeder is too heavy, capacitor banks can be switched on to increase the voltage, thereby reducing reactive power transmission and thus reducing network losses. The constraint model established for this project is as follows: (2-15) (2-16) (2-17) (2-18) In the formula, for t Always on j The switching reactive power of the CB at the node; To continue j A set of switching reactive power at the CB on the node; for t Always on j The number of CB (Chip Controller) groups on the node; for j The maximum number of CB throw groups on a node; The flag indicating whether the number of CB switching groups changes during the scheduling cycle is set to 1 if it changes and 0 if it doesn't. The maximum number of capacitor banks that can be switched at node j is an integer upper limit corresponding to the total number of capacitor banks installed.

[0088] Equation (2-15) shows the relationship between the number of switching groups and the compensation amount; Equation (2-16) shows the limit on the number of switching groups of CB; Equations (2-17) and (2-18) show the limit on the number of switching times within the scheduling cycle.

[0089] Step 3. Construct a two-stage robust optimization model that takes uncertainty into account; Step 3 is used to address the random fluctuations in distributed power output and load power; the decision variables are divided into discrete variables and continuous variables, which are optimized in the first and second stages respectively; specifically, it includes the following sub-steps: Step 3.1: Define decision variables and objective function. The decision variables in the first stage are discrete variables, including the charging and discharging status indicators of energy storage and the number of capacitor banks switched on and off; the decision variables in the second stage are continuous variables, including the charging and discharging power of energy storage and the reactive power compensation of static var compensators; the optimization objective is to minimize the active power loss of the distribution network.

[0090] Robust optimization is a method for solving uncertain problems. Unlike stochastic programming, which assumes that uncertainties follow a distribution with certain uncertain parameters, robust optimization avoids the over-reliance on prior knowledge and the assumption of following a probability distribution. The goal of robust optimization is to find a solution that satisfies all constraints and, for all possible scenarios, achieves the optimal objective function value in the worst-case scenario.

[0091] Two-stage robust optimization models transform uncertain linear programming problems into min-max-min problems. Solution methods include Column-and-Constraint Generation (C&CG) and Benders decomposition. C&CG outperforms Benders decomposition. The C&CG algorithm divides the problem into a main problem and subproblems. The main problem solves for a scheduling scheme under a pre-defined initial adverse scenario. Subproblems use the results of the main problem as initial conditions to further select adverse scenarios. The main and subproblems iteratively converge to find the optimal scheduling scheme for the uncertain problem under adverse scenarios.

[0092] The general model for two-stage robust optimization is as follows: (3-1) st (3-2) In the formula, The coefficient vector of the objective function. To constrain the right-hand side vector, The constraint coefficient matrix is ​​shown; the outer min problem is the first-stage problem. The first-stage decision variable vector corresponds to discrete control variables, including discrete scheduling variables that need to be determined in advance, such as energy storage charging and discharging status flags and the number of capacitor banks to be switched on and off in groups; the inner max-min layer represents the second-stage problem. u y is the vector of uncertain scenarios, corresponding to uncertain parameters such as power fluctuations in the distribution network load and power output fluctuations of distributed generation. obj is the objective function identifier of the optimization problem, representing the optimization objective of this two-stage robust optimization model; y is the vector of decision variables in the second stage, corresponding to continuous control variables, including continuous scheduling variables that can be adjusted in real time according to the operating scenario, such as energy storage charging and discharging power and reactive power compensation of static var compensators; F(x,u) is the set of feasible regions for the decision variables in the second stage, jointly determined by the decision results in the first stage and the uncertain scenarios; G is the constraint coefficient matrix corresponding to the decision variables in the second stage, representing the mapping relationship of the continuous variables' own operating constraints; h is the constant vector of the constraint right-hand side, corresponding to the benchmark parameters of various operating constraints such as distribution network voltage limits and equipment capacity limits; E is the constraint coefficient matrix corresponding to the decision variables in the first stage, representing the influence of discrete scheduling decisions on the feasible region of the system; M is the constraint coefficient matrix corresponding to the uncertain variables, representing the disturbance effect of load and new energy power output fluctuations on the system's operating constraints. The set of values ​​for the decision variables in the first stage is defined, restricting the range of values ​​and integer properties of the discrete scheduling variables; The set of values ​​for the decision variables in the second stage is used to limit the upper and lower limits and operating range of the continuous scheduling variables; The uncertainty set is defined as the set of uncertain variables, which limits the fluctuation range of distribution network load and new energy output, and serves as the uncertainty boundary for robust optimization.

[0093] The first stage begins by determining decision variables in the initial scenario, with the objective of minimizing network loss. The first stage is optimization; the second stage is to find the worst-case scenario that causes the highest running cost of the model, and then select the worst-case scenario. Feedback to Phase One.

[0094] Since frequent operation of devices containing discrete control variables reduces their lifespan and their startup cycle is relatively long, while devices with continuous variable control strategies can be controlled relatively quickly, discrete variables are used as the control variables in the first stage. x For example, the binary variable of the charge / discharge flag of energy storage, the number of switching groups of the CB, and using continuous variables as control variables in the second stage. y Examples include the charging and discharging power of energy storage and the compensation amount of SVC. The control strategy for discrete devices in the first stage needs to ensure that the distribution network operates under the worst-case scenario, while the control strategy in the second stage ensures that the distribution network operates safely, stably, and economically. x , y The specific expression is: (3-3) (3-4) The objective function of the two-stage robust optimization model is set as network loss, and the expression is as follows: (3-5) , : These are the energy storage charging status flag vector and the discharging status flag vector, respectively, which are composed of 0-1 discrete variables of each node at each time period; : Reactive power compensation capacity vector of grouped switching capacitor banks; : Vector of the number of switching capacitor banks in the group; : The group switching capacitor bank switching action flag vector is composed of 0-1 discrete action variables of each node at each time period; : Reactive power output vector of the static var compensator; , : These are the active power vector and reactive power vector of the primary and secondary interaction nodes, respectively; : Node voltage magnitude vector; : Vector of the square of the branch current; , : These are the active power vector and reactive power vector of the branch, respectively; The total number of time periods included in the scheduling cycle; The total number of branches in the power distribution network; The resistance value of branch ij; The square of the current in branch ij at time t; : The time interval for single-period scheduling.

[0095] Step 3.2: Construct a compact mathematical model. The power flow constraints, energy storage constraints, reactive power constraints, and the objective function described in Step 2 are uniformly expressed as a compact mixed-integer second-order cone programming form, and the first-stage variables, second-stage variables, and uncertainty variables are distinguished.

[0096] The two-stage robust optimization model active management device established in this invention includes energy storage, group switching CB, SVC, and DG. Specific constraints are described in detail in step 2, as shown in equations (2-1), (2-2), (2-4)~(2-7), and (2-9)~(2-18), where equation (2-1) is updated to the following: (3-6) For ease of expression, the constraints are represented using a compact expression as follows: (3-7) (3-8) (3-9) (3-10) (3-11) (3-12) in, u The expression is: (3-13) Equations (2-12) and (2-15) to (2-18) can be represented by equation (3-8); equations (2-2), (2-10), and (3-6) can be represented by equation (3-9); equations (2-6) and (2-13) can be represented by equation (3-10); equation (2-9) can be represented by equation (3-11); and equations (2-4) to (2-7), (2-11), and (2-14) can be represented by equation (3-12).

[0097] Step 3.3: Solve using a column constraint generation algorithm. The original problem is decomposed into a main problem and subproblems for iterative solution: the main problem solves the optimal decision of the discrete variables in the first stage under the worst-case scenario and updates the lower bound; the subproblems, under the given decision of the main problem, find the uncertainty scenario that maximizes the network loss of the system, i.e., the worst-case scenario, and update the upper bound; the iteration stops when the difference between the upper and lower bounds is less than a preset threshold, otherwise new variables and constraints are generated and added to the main problem for continued solution; among them, for the "max-min" two-level structure in the subproblems, strong duality theory is used to transform it into a single-level maximization problem, and the Big-M method is used for linearization.

[0098] The original problem is divided into a main problem and subproblems, and expressed using the following compact expression: Main Problem (MP): (3-14) In the formula, Number of scenes.

[0099] Subproblems (SP): (3-15) Since the subproblem involves a "max-min" problem, CPLEX cannot solve it directly. It can be transformed into a single-layer max model using KKT conditions or strong duality theory. This invention transforms the subproblem using strong duality theory. The dual variable to be introduced is expressed as follows: (3-16) Because in the objective function It is a bilinear quantity and is non-convex, therefore we linearize it because... u For uncertain variables, this invention considers the load and the output of distributed power sources, which fluctuate within a certain range and can be written in the following form: (3-17) Right now: (3-18) It varies between 0 and 1, so The value will be and The changes within the sub-problems are because the sub-problems themselves consider the worst-case scenario, therefore... The value can only be 0 or 1, which allows it to be separated effectively using the Big-M method.

[0100] (3-19) (3-20) M For a relatively large positive number, such as 10000, it can be seen from equation (3-20) that when hour, ;when hour, It is equivalent to equation (3-18).

[0101] When using the C&CG algorithm to solve the constructed two-stage robust optimization scheduling model, the problem is divided into MP and SP problems, and the solution process is as follows: Figure 2 As shown.

[0102] like Figure 2 As shown, the specific solution steps are as follows: Step 1. Randomly initialize the scene Set convergence criteria , cycle number upper and lower bounds of a cycle , .

[0103] Step 2. Solve for MP to obtain the optimal solution. and the first phase of decision Update the Nether .

[0104] Step 3. Substitute SP into the solution, solve for SP, and obtain the optimal solution. and harsh scenes Update the upper boundary .

[0105] Step 4. Set convergence conditions The loop iterates through the loop and determines whether the loop converges. If the loop fails to converge, it continues to the next step; if it converges, the loop stops and the result is output.

[0106] Step 5. Add variables ,make And add the following constraint (see equation (3-21)) to MP, (3-21) Return to Step 2.

[0107] Once the C&CG algorithm converges, the optimal scheduling scheme that minimizes the active power loss of the distribution network (including the charging and discharging power of each energy storage unit, the reactive power compensation of the SVC, and the number of CB switching groups) can be obtained. After the solution is completed, the obtained optimal scheduling scheme is substituted into the power flow equation of the DistFlow branch of the distribution network, and the voltage of each node is recalculated. The maximum absolute value of the voltage deviation among all nodes is taken as the node voltage deviation value corresponding to the optimal solution, which is recorded as the first optimal value.

[0108] Step 4. Based on The constraint method is used for multi-objective collaborative optimization. Based on step 3, the minimum node voltage deviation is taken as the single objective function, while keeping the power-voltage feasible region boundary constraints, the distribution network convex optimization constraint set, and the uncertainty set unchanged. The two-stage robust optimization model is reconstructed and solved. After the solution is completed, the obtained optimal scheduling scheme is substituted into the power flow equation of the distribution network DistFlow branch to calculate the voltage of each node. The maximum absolute value of the voltage deviation among all nodes is taken as the node voltage deviation value corresponding to the optimal solution, which is recorded as the second optimal value. Step 4, based on step 3, further coordinates the voltage quality and energy saving and loss reduction objectives; specifically, it includes the following sub-steps: Step 4.1: Establish a multi-objective optimization model. The optimization objectives include minimizing the active power loss of the distribution network and minimizing the node voltage deviation; the constraints are the same as in Steps 2 and 3.

[0109] Because decision-makers in actual power distribution network operation may need to optimize multiple objectives simultaneously, these objectives often include various types, such as minimizing network losses and minimizing voltage deviation, as considered in this section. Their dimensions are not uniform; therefore, it is necessary to introduce relevant theories and methods for multi-objective optimization.

[0110] Unlike single-objective optimization, which yields a unique global optimum, multi-objective optimization does not provide a single solution that simultaneously optimizes all objectives. Instead, multi-objective optimization often attempts to find a set of solutions that adequately satisfy all optimization objectives, where these solutions are mutually exclusive. This set of mutually exclusive solutions is often called the Pareto optimal set (also known as the Pareto front). Three important optimization concepts are Pareto improvement, Pareto dominance, and Pareto optimality. Pareto improvement, a concept from microeconomics, is primarily used to analyze the cost of improving one or more objectives without sacrificing any one; it represents the steps towards Pareto optimality. Pareto dominance occurs when any objective of a solution is superior to any other solution; in this case, the solution Pareto dominates the other. Pareto optimality means that no single optimization objective can be improved without worsening at least one objective or without any loss.

[0111] like Figure 3 As shown, when point C in the solution space becomes point A or B, both objectives in the multi-objective optimization decrease to some extent, thus it can be said that a Pareto improvement has been achieved. Correspondingly, since the objective functions of both solutions are better than solution C, solution A and Pareto dominate solution C. However, when we compare the objective functions corresponding to solutions A and B, although solution A has better objective functions than solution B, Pareto improves the overall performance of the solution. The time is less than solution B, but conversely, in the target Solution A is greater than solution B. Therefore, solutions A and B are not mutually exclusive in this case. Similarly, Figure 3 The blue point set shares the same characteristics, but it dominates the gray point set. Therefore, the solution set composed of the blue point set is the Pareto optimal surface that the multi-objective optimization needs to find.

[0112] In traditional multi-objective optimization methods, one classic approach is the weight-based method. This method assigns different weights to multiple objectives and then linearly weights them, ultimately merging them into a single objective function. This allows for the application of traditional single-objective optimization methods. Weight-based optimization methods are simple and easy to use. However, in practical applications, it is difficult to find the Pareto optimal solution simply by setting a set of weights. Furthermore, when multiple objectives have different dimensions, directly using weights for transformation is not feasible. Additionally, when some objective functions are non-convex, the weight method cannot guarantee a Pareto optimal solution.

[0113] Therefore, this invention adopts The constraint method is used to solve multi-objective optimization models. This method optimizes by retaining only one objective, and then sets other objectives... This method uses constraints to obtain Pareto optimal solutions. Compared to the weighted method, this method can obtain Pareto optimal solutions in both convex and non-convex function contexts, making it more suitable for engineering applications.

[0114] Step 4.2: Use The constraint method is used to solve the Pareto solution set. First, each individual objective optimization problem is solved separately to obtain the optimal value for each objective and determine the solution. The range of values; then the voltage deviation target is taken as Constraints, with the primary objective of minimizing network loss, in By selecting multiple values ​​at equal intervals within the range of values ​​and solving them one by one, a set of non-dominant Pareto solutions is obtained.

[0115] The mathematical model for multi-objective optimal scheduling of distribution networks in this invention can be simplified as follows:

[0116] st (4-1) In the formula, This represents a specific objective function to be optimized in a multi-objective optimization function. The other optimization objectives... Then limit. and These represent inequality constraints and equality constraints in the optimization model, respectively. The last line indicates the upper and lower bounds that the decision variables must satisfy.

[0117] based on The steps of the constraint method for solving multi-objective optimization problems are as follows: Step 1. Solve each objective function individually and store its optimal solution. For example, optimize... When the optimal solution is obtained, it is denoted as . ,and Then it is recorded as Accordingly, when only optimization When, the optimal solution obtained at this time is ,and Then it is recorded as .

[0118] Step 2. Construct a loop to achieve... The [obtained in the above steps] , Take the value from ] and put Add to optimization The solution is found in the optimization model. At this point... The number of possible values ​​for is the number of Pareto optimal solutions.

[0119] Step 4.3: Select a compromise solution based on the center point strategy. Calculate the average voltage deviation of all solutions in the Pareto solution set as the benchmark value. Calculate the absolute distance between the voltage deviation of each solution and the benchmark value, and select the solution with the smallest distance as the final compromise solution.

[0120] After obtaining the Pareto optimal solution for multi-objective optimal scheduling of the distribution network, the decision-maker still needs to select one of these non-dominated solutions for the final decision. Generally, the decision-maker can choose one based on expert recommendation or their own preference. This invention adopts a selection strategy based on a "center point," the core idea of ​​which is to find a solution in the objective space that is closest to the average level of all solutions. Taking network loss and voltage deviation as optimization objectives as an example, the specific solution steps are as follows: Step 1. Calculate the average value (baseline value) of the "voltage deviation" objective function value in the entire Pareto solution set. This average value represents a central position of the Pareto front in the voltage deviation dimension.

[0121] Step 2. Calculate the absolute distance between the voltage deviation value of each Pareto solution and this average value. This distance quantifies how far each solution deviates from the center point in the voltage deviation dimension.

[0122] Step 3. Among all Pareto solutions, select the one with the smallest absolute distance from the average value as the final solution (compromise solution). This means that this solution is closest to the overall average level of the Pareto solution set in terms of voltage deviation performance.

[0123] Step 5: Perform overall optimization and verification under master-slave collaboration; The power-voltage interaction boundary obtained in step 1 is used as the upper-level constraint for distribution network operation. It is substituted into the multi-objective robust optimization model established in step 4 for joint solution, and the output is a distribution network optimization control strategy that satisfies the main grid security boundary, adapts to multiple uncertainties, and takes into account voltage quality and energy saving and loss reduction.

[0124] In some embodiments, the simulation parameters and environment are as follows: Figure 4 As shown, this invention, based on the traditional Case 33 system, incorporates wind power, energy storage, SVC, and group switching CB for simulation calculations. The total wind power output and total active power load curves are shown below. Figure 5 As shown, wind power is connected to nodes 4, 18, and 22 respectively, and its output is equally distributed among the total wind power output. The specific load of each node is the original load amplified proportionally. The parameters of ESS, SVC, and group switching CB are shown in Tables 3-1, 3-2, and 3-3.

[0125] Table 3-1. Installation location and parameters of ESS ; Table 3-2. Installation location and parameters of SVC ; Table 3-3. Installation location and parameters of CB ; Two-stage robust optimization and comparative analysis were conducted: the optimization objective was set as minimizing network loss, and the load and wind power prediction deviation coefficients were set at 0.1. The C&CG algorithm was used to solve the two-stage robust optimization model. Figures 6 to 9 The active and reactive load distributions of the system before and after optimization are shown at 24 time points.

[0126] Figure 10 This paper presents the worst-case operating scenario identified by a robust optimization model aimed at minimizing system network losses. Theoretical analysis shows that the extreme operating condition with the greatest total network loss often occurs under the coexistence of high load and low wind power. This is because the line current is already very large under high load, and the low wind power penetration rate means that power must be transmitted over long distances from traditional power plants in distant locations. This results in concentrated power flow distribution, long transmission paths, and potentially lower voltage levels. The combination of these multiple factors leads to peak network losses.

[0127] like Figure 10As shown, in the worst-case scenario identified by robust optimization, the system load is at its highest level. However, the output of each wind power node is not uniformly at its minimum, indicating that the formation of the worst-case scenario is determined by the deterioration of the global power flow distribution induced by a specific output combination. This result reveals the core strategy of robust optimization in dealing with uncertainty: within a given set of uncertainties, it actively constructs an extreme scenario that maximizes the system network loss by coordinating the fluctuation combinations of wind power output, thereby achieving effective coverage of operational risks and a quantitative assessment of optimization conservatism.

[0128] To systematically evaluate the adaptability of robust optimization methods to prediction uncertainty, this invention analyzes the impact of different prediction error coefficients on system network loss. Figure 11 The study demonstrates the daily load curve fluctuation range under different prediction error coefficients. When the prediction error coefficient is 0.1, the load fluctuation is limited to within ±10% of the prediction baseline value; however, when the prediction error coefficient increases to 0.3, the load fluctuation range expands to ±30%. The results show that as the prediction error coefficient increases, the actual load fluctuation range significantly expands, and the uncertainty faced by the system increases accordingly.

[0129] Table 3-4 further lists the average network loss calculation results under different combinations of prediction errors. A horizontal comparison shows that when the wind power prediction error coefficient is fixed, the system network loss exhibits a monotonically increasing trend as the load prediction error coefficient increases. A vertical comparison shows that when the load prediction error coefficient remains constant, the network loss value increases with the increase of the wind power prediction error coefficient. The reason for this is that the expansion of the prediction error coefficient directly leads to an expansion of the set of uncertain scenarios, requiring the system to cope with more extreme uncertainties. This prompts the robust optimization model to adopt a more conservative scheduling strategy, ultimately resulting in an increase in network loss levels.

[0130] Table 3-4. Average network loss under different prediction error coefficients ; Perform multi-objective robust optimization solution: When considering voltage deviation... Robust optimization is performed based on constraints, with the goal of minimizing network loss. (Settings...) The value is 0.02, and the voltage deviation before and after optimization is as follows: Figure 12 As shown, the optimized hourly voltage deviation is strictly limited to between -0.02 and 0.02, indicating that the model established in this invention is correct.

[0131] Based on this, voltage deviations were analyzed to varying degrees. Constraints, parameters Eight experiments were conducted using eight equally spaced values ​​within the range of 0.02 to 0.04, yielding the following results: Figure 13The Pareto solution set is shown in the figure. The compromise solution is the one that is closest to the average voltage deviation of all Pareto solutions. Figure 14 and Figure 15 This represents the maximum 24-hour network loss and voltage deviation values ​​for the solutions with minimum network loss (Solution A), minimum voltage (Solution B), and compromise solution (Solution C). From... Figure 13 As can be seen, these eight solutions are non-dominant; that is, while one solution may be better for one objective, it will inevitably be worse for another. Taking solutions A and B as examples, solution A, with a voltage deviation of 0.02 pu, is better than solution B, which has a voltage deviation of 0.032 pu. However, correspondingly, in terms of network loss, solution A has a total daily network loss of 1.04402 MW, which is higher than the total daily network loss of 1.04387 MW corresponding to solution B. Therefore, the above Pareto solution set proves the effectiveness of the multi-objective model of this invention, reflecting the differences in solutions caused by different objective preferences.

[0132] like Figure 16 and Figure 17 As shown, this invention further compares the effects of different reactive power output devices in the distribution network under different Pareto solutions. Under solution A, decision-makers prefer lower voltage deviations. Figure 16 As can be seen, the output of each reactive power device is more uniform overall, maintaining a stable output for most of the time to provide basic reactive power support. Voltage fluctuations are precisely controlled through smooth reactive power adjustment, matching the optimization goal of low voltage deviation. In solution B, decision-makers prefer the lowest possible network loss, and the output adjustment of the reactive power devices is more targeted. The output fluctuation of SVC2, located at the end of the line, is more active. Precise reactive power compensation is used to maximize the reduction of network loss, meeting the optimization requirement of minimum network loss.

[0133] Figure 18 This study depicts the variation of the marginal trade-off between network loss and voltage deviation (defined as the ratio of change in network loss to change in voltage deviation) along the Pareto front. This indicator quantitatively characterizes the cost of sacrificing one objective to improve another when making decisions along the Pareto front. Analysis reveals that the marginal trade-off curve exhibits a "V-shaped" or "U-shaped" characteristic, first decreasing and then increasing. This nonlinear pattern profoundly reveals the efficiency boundary in system operation.

[0134] Depend on Figure 18 It can be seen that the right end of the curve (the high voltage deviation region, the segment where the tradeoff rate decreases) corresponds to a solution with poor power quality but good loss reduction. As the optimization process progresses, the system exhibits significant "scale benefits," meaning that a large improvement in voltage quality can be achieved with a small investment in network losses. The decreasing marginal tradeoff rate indicates that the efficiency of voltage quality improvement is continuously increasing at this stage.

[0135] At the left end of the curve (the low voltage deviation region, the rising tradeoff rate segment), the system is approaching the limit of voltage quality. The sharply rising marginal tradeoff rate signifies the emergence of the "diminishing returns" effect, meaning that in pursuit of ultimate voltage quality, every further reduction in voltage deviation requires an extremely high cost in network losses. The system operation has entered a range of extremely poor economic efficiency.

[0136] The lowest point on the curve (the minimum trade-off) represents the "optimal efficiency point" across the entire Pareto front. At this point, the additional network loss cost required to improve a unit voltage deviation is minimized. Therefore, the operating scheme corresponding to this point achieves the best balance between economy and power quality, representing a highly valuable compromise.

[0137] This "decrease first, then increase" trade-off is directly related to the nonlinear characteristics of the power flow equations in a power system. The trough (lowest point) of the curve clearly marks the critical point on the Pareto front from the "high-efficiency improvement zone" to the "diminishing returns zone." This conclusion provides operators with a crucial decision-making basis: from a pure efficiency perspective, choosing the Pareto solution corresponding to the lowest point of the curve can achieve synergistic optimization of economy and power quality with the highest cost-effectiveness, thereby avoiding the "uneconomical" dilemma of pursuing ultimate quality at high cost.

[0138] Robust optimization under master-distribution coordination: To verify the feasibility of the proposed distributed joint optimization scheduling method for the master-distribution network considering master-distribution coordination, such as... Figure 19 As shown, a distribution network using a main network with case 30 nodes is used (distribution network topology see...). Figure 4 Simulation verification was performed, in which the distribution network was connected to node 5 of the main network.

[0139] Considering the "power-voltage" boundary constraints of the main grid on the distribution network, we perform synergistic optimization to minimize the distribution network loss and the average voltage deviation. Figure 20 and Figure 21 The boundary between the actual output power of the main and distribution network interfaces and the output power obtained from the main network optimization. Figure 22 Comparing the actual voltage of the main distribution network interface with the voltage boundary obtained by the main network optimization, it can be seen that the power and voltage of the main distribution network interface are strictly limited to a certain range, indicating that the model established in this invention is correct.

[0140] like Figure 23As shown, in the joint distributed operation with the main grid, when the main grid transmits electrical energy to the distribution network (when the transmission power of the main and distribution networks is negative), the distribution network acts as a "power source," and the power of its generators will be greater than its own load; the main grid acts as a "load." Conversely, when the main grid transmits electrical energy to the distribution network (when the transmission power of the main and distribution networks is positive), the distribution network acts as a "load," and the power of its generators can be less than its own electrical load; the main grid acts as a "power source," which is equivalent to having an additional distributed power source for the distribution network. Therefore, through the joint distributed operation of the distribution network and microgrids, the two networks support and back each other, significantly enhancing the flexibility and robustness between the main and distribution grids.

Claims

1. A method for coordinated optimization of voltage control and energy saving / loss reduction in distribution networks considering main and distribution network coordination, characterized in that, include: S1. Construct an interaction boundary model between the main grid and the distribution network, and determine the power-voltage feasible region of the interaction nodes between the main grid and the distribution network; the power-voltage feasible region consists of a reference voltage boundary, an active power boundary, and a reactive power boundary; S2. Establish a convex optimization model for the lower-level distribution network. Use the DistFlow branch power flow model to describe the power flow distribution of the distribution network, and use the second-order cone relaxation theory to transform the non-convex equality constraints in the power flow distribution into convex inequality constraints, thereby obtaining a convex distribution network operation constraint set. At the same time, establish energy storage system constraints and reactive power source constraints. Combine the convex distribution network operation constraint set, energy storage system constraints, and reactive power source constraints into a distribution network convex optimization constraint set. S3. Construct a two-stage robust optimization model that considers multiple uncertainties. Discrete control variables are used as decision variables in the first stage, and continuous control variables are used as decision variables in the second stage. Minimizing the active power loss of the distribution network is the single objective optimization function. The power-voltage feasible region is used as the upper boundary constraint of the two-stage robust optimization model, and the convex optimization constraint set of the distribution network is used as the lower operating constraint of the two-stage robust optimization model. The two-stage robust optimization model is solved using a column constraint generation algorithm to obtain the optimal solution with the objective of minimizing the active power loss of the distribution network. The node voltage deviation value corresponding to the optimal solution is recorded as the first optimal value. S4. With the goal of minimizing node voltage deviation, solve for the optimal value of minimizing node voltage deviation, denoted as the second optimal value; determine the allowable upper limit threshold of voltage deviation based on the first and second optimal values. The range of values ​​for ; Based on the two-stage robust optimization model, minimizing node voltage deviation is added as a second optimization objective, forming a multi-objective robust optimization model; a method is adopted. The constraint method is used to solve the multi-objective robust optimization model, with minimizing the active power loss of the distribution network as the primary objective and minimizing the node voltage deviation as the auxiliary objective. The node voltage deviation objective is used as... Constraints, in the Within the range of values ​​of , a set of non-dominant Pareto solutions is obtained, and a compromise solution is selected from the Pareto solution set based on the center point strategy. S5. Substitute the power-voltage feasible region as the upper-level constraint for distribution network operation into the multi-objective robust optimization model, perform joint solution, and output a distribution network optimization control strategy that satisfies the main grid safety boundary, adapts to multiple uncertainties, and takes into account voltage quality and energy saving and loss reduction. The method for determining the reference voltage boundary in S1 is as follows: obtain the net load forecast value of the distribution network, which is calculated based on the historical load data of the distribution network, the power output data of the new energy source of the distribution network, and the prediction model; perform power flow calculation based on the net load forecast value, set the voltage calculation result of the connection node between the main network and the distribution network as the basic feasible solution, and use the connection node voltage in the basic feasible solution as the reference voltage boundary.

2. The method for coordinated optimization of distribution network voltage control and energy saving and loss reduction considering main and distribution network coordination as described in claim 1, characterized in that, The method for determining the active power boundary in S1 is as follows: taking the net load prediction value as the center, and combining the pre-set net load fluctuation bandwidth and the transformer apparent power capacity, the upper and lower limits of active power are determined; the method for determining the reactive power boundary is as follows: taking the basic feasible solution as the starting point, by gradually increasing or decreasing the reactive load of the connection node, the boundary of power flow convergence is detected, thereby determining the upper and lower limits of reactive power. If the basic power flow solution fails, the safety boundary allowed by the transformer will be used as the reactive power boundary.

3. The method for coordinated optimization of distribution network voltage control and energy saving and loss reduction considering main and distribution network coordination as described in claim 1, characterized in that, The specific method for transforming non-convex equality constraints into convex inequality constraints using the second-order cone relaxation theory in S2 is as follows: the non-convex equality constraints between branch active power, branch reactive power, branch current, and node voltage in the DistFlow branch power flow model are relaxed into inequality constraints, and then the inequality constraints are constructed into second-order cone constraints, thereby obtaining the convex distribution network operation constraint set.

4. The method for coordinated optimization of distribution network voltage control and energy saving and loss reduction considering main and distribution network coordination as described in claim 1, characterized in that, The energy storage system constraints in S2 include: power balance constraints, upper and lower limits of remaining capacity constraints, mutual exclusion constraints of charging and discharging states, and charging and discharging power limit constraints; the reactive power constraints include the adjustment range constraints of continuous static var compensators and the number of switching groups of discrete grouped capacitor banks. The adjustment range constraints of static var compensators are the continuous adjustment range and upper and lower limits of their reactive power output. The number of switching groups of grouped capacitor banks are the product relationship between the number of switching groups and the compensation capacity of a single group, the upper limit constraint of the number of switching groups, and the limit on the number of actions within the scheduling cycle.

5. The method for coordinated optimization of distribution network voltage control and energy saving and loss reduction considering main and distribution network coordination as described in claim 1, characterized in that, In the two-stage robust optimization model in S3, the decision variables in the first stage are discrete variables, including the charging and discharging status flags of energy storage and the number of switching groups of capacitor banks; the decision variables in the second stage are continuous variables, including the charging and discharging power of energy storage and the reactive power compensation amount of the static var compensator.

6. The method for coordinated optimization of distribution network voltage control and energy saving and loss reduction considering main and distribution network coordination as described in claim 1, characterized in that, The specific steps of using the column constraint generation algorithm in S3 to solve the two-stage robust optimization model are as follows: decompose the original problem into a main problem and sub-problems and solve them iteratively; solve the optimal decision of the first-stage discrete variables in the current worst-case scenario and update the lower bound in the main problem; under the given decision of the main problem, find the uncertainty scenario that maximizes the network loss of the system, i.e., the worst-case scenario, and update the upper bound in the sub-problems; stop iterating when the difference between the upper bound and the lower bound is less than a preset threshold, otherwise generate new variables and constraints and add them to the main problem to continue solving.

7. The method for coordinated optimization of distribution network voltage control and energy saving and loss reduction considering main and distribution network coordination as described in claim 6, characterized in that, The subproblem has a maximization-minimization bi-layer structure. Strong duality theory is used to transform this bi-layer structure into a single-layer maximization problem. The Big M method is used to linearize the bilinear terms in the transformed objective function, thereby directly solving the worst-case scenario.

8. The method for coordinated optimization of distribution network voltage control and energy saving and loss reduction considering main and distribution network coordination as described in claim 1, characterized in that, Based on the S4 The specific method for solving the Pareto solution set using the constraint method is as follows: The node voltage deviation target is taken as... The constraint, with the primary objective of minimizing active power losses in the distribution network, is as follows: Multiple values ​​are selected at equal intervals within the range of values ​​to solve the problem one by one, resulting in a set of non-dominant Pareto solutions. The method for selecting a compromise solution based on the center point strategy is as follows: calculate the arithmetic mean of the voltage deviation values ​​of all solutions in the Pareto solution set as the benchmark value, then calculate the absolute distance between the voltage deviation value of each solution and the benchmark value, and select the solution with the smallest absolute distance as the final compromise solution.

9. The method for coordinated optimization of distribution network voltage control and energy saving and loss reduction considering main and distribution network coordination as described in claim 1, characterized in that, The power distribution network optimization control strategy output in S5 includes: power charging and discharging command and charging and discharging status flag of the energy storage system, reactive power compensation command of the static var compensator, and command of the number of switching groups of the capacitor bank; the optimization control strategy simultaneously satisfies: power-voltage feasible domain boundary, power distribution network convex optimization constraint set, and voltage deviation constraint value corresponding to the compromise solution.

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