A two-stage optimization scheduling method for power supply area source network load storage

Abstract

The application provides a kind of two-stage optimization scheduling method of source network load storage of transformer area, belong to the field of transformer area source network load storage collaborative optimization operation field, provide including as follows steps: collect transformer area three-phase topology data and operation data, form input data set;Based on input data, establish three-phase network model, and couple photovoltaic, energy storage, adjustable load and time sequence injection model of emergency reduction, establish three-phase source network load storage model;Network security constraint and VUF explicit constraint of three-phase source network load storage model are constructed;Second-order convex relaxation is implemented, and the relaxed three-phase source network load storage model is obtained;Budget type uncertain set is constructed;Day-ahead and day-ahead two-stage robust optimization model is constructed;The worst disturbance scenario is searched iteratively, and the worst disturbance scenario is added to the disturbance scenario set of two-stage robust optimization model main problem, and iteration is updated until the upper and lower bounds converge, to obtain transformer area autonomous scheduling strategy.The application improves the safety margin, resource utilization and strategy implementability of transformer area grid-connected operation.

Description

Technical Field

[0001] This invention belongs to the field of coordinated optimization operation of power generation, grid, load and storage in power distribution areas, and relates to a two-stage optimization scheduling method for power generation, grid, load and storage in power distribution areas during the day and day. Background Technology

[0002] Low-voltage distribution areas are typical power supply units at the end of the distribution network, directly bearing the electricity demand of residential and small industrial and commercial users. With the large-scale integration of distributed photovoltaic (PV) and user-side small-scale energy storage, the net load curve of distribution areas has gradually evolved from the traditional single-peak type to a multi-peak and rapid-climbing type. Furthermore, differences in the integration of different phases result in a significant imbalance in the three-phase power distribution. This three-phase imbalance can cause phase voltage shifts, an increase in negative sequence components, an increase in neutral current, an increase in line losses, and local overloads. It is more likely to trigger phase voltage exceedances and branch overcurrent risks when PV output changes rapidly or load changes abruptly. Due to the significant inter-phase coupling characteristics of the distribution area's line impedance, the changes in three-phase power flow are not independent. Single-phase or equivalent simplified models cannot accurately characterize the impact of inter-phase coupling on voltage and current, leading to deviations in the actual implementation of dispatch strategies.

[0003] On the other hand, there are significant uncertainties in the operation of distribution transformer areas. Available photovoltaic output is affected by cloud cover and irradiance fluctuations, while load power is influenced by weather and user behavior; both day-ahead and intraday forecasts have deviations. Deterministic dispatch methods typically optimize based on forecast values. When actual output deviates from the forecast, strategies that originally met constraints may result in voltage, current, or transformer capacity exceeding limits, necessitating rapid compensation through energy storage or triggering emergency cutoffs to maintain safe operation. This passive compensation not only causes frequent switching and lifespan reduction of energy storage charging and discharging but also leads to excessive disturbance to adjustable loads on the user side and a decrease in comfort, ultimately reducing the stability and economy of autonomous operation of the distribution transformer area.

[0004] Existing research often employs empirical indicators or post-hoc verification methods to control three-phase imbalance, making it difficult to incorporate negative-sequence levels as explicit optimizable constraints into the scheduling model. Uncertainty handling typically relies on fixed margins or conservative boundaries, lacking feasibility guarantees under worst-case disturbances and easily leading to infeasibility or significant reductions in extreme scenarios. Furthermore, directly using non-convex three-phase power flow models to construct the optimization problem can result in convergence difficulties and uncontrollable time consumption for the solver, failing to meet the requirements of stable solutions and timely data delivery from transformer edge terminals. Therefore, there is an urgent need for a self-governing optimization scheduling method for transformer areas that can simultaneously characterize three-phase inter-phase coupling, imbalance risk, and prediction error disturbances, while possessing solvability and engineering deployability. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, such as insufficient expression of three-phase imbalance constraints, lack of feasibility guarantees under prediction error disturbances, and instability in solving three-phase non-convex power flow, this invention proposes a two-stage optimization scheduling method for power distribution area (PDA) based on source-grid-load-storage (PGS) scheduling. This method is grounded in three-phase power flow up-dimensional modeling, explicitly incorporating VUF (Variable Uncertainty Factor) into security constraints using matrix trace inequalities, employing budgetary uncertainty sets to describe photovoltaic and load prediction errors, and forming a DDA autonomous strategy within a two-stage robust framework.

[0006] This application adopts a two-stage optimization scheduling method for source-grid-load-storage in a distribution area, including the following steps: 1) Collect three-phase topology data and operational data of the transformer area, and unify the collected data to the same time granularity to form an input dataset; 2) Based on the input data, construct the three-phase voltage square matrix, branch current square matrix and branch complex power matrix as three-phase up-dimensional variables. Based on the three-phase Branch Flow model containing the inter-phase coupling impedance matrix, establish a three-phase network model and couple the time-series injection models of photovoltaic, energy storage, adjustable load and emergency load shedding to establish a three-phase source-grid-load-storage model. 3) Constructing network security constraints and explicit VUF constraints for a three-phase source-grid-load-storage model; 4) Implement second-order conical-convex relaxation on the non-convex coupling constraint of the three-phase power flow in the three-phase source-grid-load-storage model, and transform the established three-phase source-grid-load-storage model into a solvable conical programming form to obtain the relaxed three-phase source-grid-load-storage model. 5) Construct a budgetary uncertainty set based on the input dataset; 6) Based on the budget-type uncertain set and the relaxed three-phase source-grid-load-storage model, a two-stage robust optimization model is constructed for day-ahead and intraday periods; 7) The worst-case disturbance scenario is searched iteratively using a row and column generation algorithm. The worst-case disturbance scenario is added to the disturbance scenario set of the main problem of the two-stage robust optimization model. The algorithm is iteratively updated until the upper and lower bounds converge to obtain the autonomous scheduling strategy of the transformer area.

[0007] The time-series power injection model is the resource-side model in the three-phase power generation, grid, load, and storage model, used to describe the time-series power injection of photovoltaic, energy storage, adjustable loads, and emergency load shedding. The three-phase power generation, grid, load, and storage model also includes a three-phase network model and corresponding security constraints. Three-phase asymmetric power flow modeling, three-phase imbalance index constraints, robust optimization solutions for prediction error disturbances, and day-ahead and day-intraday two-stage optimization scheduling for autonomous deployment enable robust coordination of power generation, grid, load, and storage under three-phase imbalance constraints in the distribution area, and edge-side executable deployment, improving the safety margin, resource utilization, and strategy feasibility of grid-connected operation in the distribution area.

[0008] Furthermore, taking the three-phase asymmetrical distribution network of the transformer substation as the object, the topology data includes the node phase connection relationship, the branch phase coupling impedance matrix, the transformer capacity threshold and the branch current threshold, and the operation data includes the photovoltaic available output prediction sequence, the load power prediction sequence, the initial energy and power boundary of energy storage, the adjustable load adjustment boundary and the emergency reduction boundary.

[0009] Furthermore, the network security constraints include: establishing branch voltage drop equations and node power balance equations based on a three-phase Branch Flow model containing interphase coupling impedance matrices, and establishing time-series injection models and boundary constraints for photovoltaic, energy storage, adjustable loads, and emergency load shedding on the node injection side.

[0010] Furthermore, the explicit VUF constraint includes: constructing positive-order and negative-order voltage transformation vectors and their energy projection matrices based on symmetric component transformation, transforming the voltage imbalance factor (VUF) threshold constraint into a trace inequality of an upgraded matrix, and ensuring model feasibility under extreme perturbations and suppressing negative-order risk by setting non-negative relaxation variables and penalty terms.

[0011] Furthermore, the second-order cone-convex relaxation process includes: relaxing the non-convex equality relationship between the square of the branch complex power amplitude and the product of the square of the node voltage and the square of the branch current in the three-phase power flow into an inequality relationship, and transforming it into a second-order cone constraint. At the same time, the rank-one constraint of the up-dimensional variable is omitted, resulting in a second-order cone-convex relaxation model.

[0012] Furthermore, the process of constructing a budget-type uncertain set includes: using interval perturbation for the prediction errors of available photovoltaic power output and load active power; using a phase power factor preservation method to determine the corresponding load reactive power based on the perturbed load active power; applying joint budget constraints to load perturbations of different phases at the same node to limit the cumulative intensity of three-phase load perturbations at the same node in the dispatch time domain; and setting time-domain budget parameters for available photovoltaic power output perturbations to limit their cumulative intensity in the dispatch time domain, thus forming a budget-type uncertain set.

[0013] Furthermore, the process of constructing the two-stage robust optimization objective function includes: Under network security and VUF constraints, a day-ahead stage cost function is constructed based on photovoltaic curtailment, energy storage charging and discharging, adjustable load adjustment, active power loss of distribution lines, slack variables and their weights. For disturbances within the budgetary uncertainty set, an intraday remedial strategy is formed based on the day-ahead baseline strategy. Based on the remedial costs corresponding to energy storage readjustment, adjustable load readjustment, photovoltaic curtailment correction, emergency reduction and slack variables, a remedial stage cost function is constructed. A two-stage robust optimization objective function is constructed with the goal of minimizing the sum of the day-ahead stage cost and the minimum remedial cost under the worst-case perturbation within the budgetary uncertainty set.

[0014] In the day-ahead phase, a baseline trajectory covering the entire time domain is formed. The baseline trajectory includes the energy storage charging and discharging power trajectory and energy trajectory, the adjustable load adjustment trajectory, the photovoltaic curtailment and reactive power support baseline, and the emergency reduction reserve baseline.

[0015] Furthermore, the row and column generation algorithm includes iterative processes of the main problem and the separation subproblems, specifically including: The main problem is to jointly solve the pre-dawn baseline variables and the remedial variables for each scenario on the current scenario set to obtain the target lower bound. Given the current day-ahead baseline variables, the separation subproblem searches for the perturbation scenario that maximizes the optimal remedy cost within the uncertainty set. Based on the day-ahead stage cost and the optimal remedy cost, the target upper bound is obtained, and the worst perturbation scenario is determined. If the difference between the upper bound and the lower bound of the target is greater than the threshold, the worst-case scenario is added to the scenario set and the main problem is solved repeatedly until convergence. After the solution is completed, the output includes the photovoltaic active power limitation and reactive power support settings, energy storage charging and discharging power settings and energy trajectory, adjustable load adjustment settings and emergency reduction settings for each node and phase, as well as the node voltage square, branch current square and VUF constraint margin.

[0016] The inventive principle of this invention is as follows: This invention provides a two-stage day-ahead and intraday optimization scheduling method for grid-connected autonomous operation of distribution networks (source-grid-load-storage). Taking the three-phase asymmetrical distribution network of a distribution area as the object, this method establishes a three-phase power flow up-dimensional model including inter-phase coupling impedance to accurately characterize the coupling and transmission mechanism of three-phase voltage, current, and power. Addressing the difficulty in explicitly controlling the risk of three-phase imbalance in distribution areas, based on symmetrical component energy projection, the voltage imbalance factor (VUF) threshold constraint is transformed into a matrix trace inequality, and non-negative relaxation and penalty order relations are introduced, transforming the negative order risk from ex-post verification to ex-ante controllability and optimizability. A budget-type uncertainty set is used to describe the disturbance interval and limit the cumulative intensity of the disturbance. A two-stage robust optimization structure of day-ahead baseline strategy and intraday remedial strategy is constructed, enabling constraint closure under any uncertain disturbance. To meet the requirements of stable solution and controllable time consumption for edge autonomous deployment, a second-order conical relaxation is implemented for the three-phase non-convex power flow coupling, transforming the problem into conical programming. A row and column generation algorithm is then used to iteratively search for the worst-case disturbance scenario until convergence. This achieves improved safety margin, resource utilization, and policy feasibility for robust source-grid-load-storage coordination and grid-connected autonomous operation under three-phase imbalance constraints.

[0017] The beneficial effects of this invention are as follows: 1) Significantly enhance the controllability and over-limit management capability of three-phase imbalance risk in the transformer area: By using three-phase power flow up-dimensional modeling, the phase coupling impedance, three-phase voltage current and power coupling relationship are incorporated into a unified variable system, and the voltage imbalance factor VUF is transformed into matrix trace constraint explicit entry into optimization, so that negative sequence risk is transformed from ex-post verification to ex-ante controllability and optimizability. Under the conditions of rapid photovoltaic ramp-up and phase load imbalance, the risk of phase voltage deviation and branch overcurrent is suppressed, and the safety margin of grid-connected operation of the transformer area is improved.

[0018] 2) Maintain robust feasibility and improve resource utilization under worst-case forecast error perturbation: Characterize the forecast error of available photovoltaic output and load power through budget-type uncertainty set and establish an integrated two-stage robust model of day-ahead baseline and intraday remediation. Use row and column generation algorithm to iteratively search for worst-case perturbation scenarios and drive the baseline strategy and remediation strategy to converge in tandem, avoiding excessive conservatism caused by fixed margin. At the same time, keep the voltage, current, transformer capacity and VUF constraints satisfied or satisfied under minimum relaxation under worst-case perturbation, reducing the probability of unnecessary power curtailment and emergency reduction triggering.

[0019] 3) Improve online solution stability and edge-side deployability: By using second-order conical relaxation, the three-phase non-convex power flow coupling constraint is transformed into a solvable conical program, and relaxation and penalty mechanisms are introduced to enhance feasibility fallback, enabling both the main problem and the separation subproblems to be solved stably with controllable time consumption. The output strategy is directly mapped to active power limiting and reactive power support commands for photovoltaic inverters, charging and discharging power and energy trajectory commands for energy storage converters, adjustable load adjustment commands, and emergency reserve reduction commands, facilitating local closed-loop monitoring and rapid execution at the edge of the distribution area. Attached Figure Description

[0020] Figure 1 A flowchart of the two-stage optimized scheduling method for power generation, grid, load, and storage in the day-ahead period of the power grid in the power distribution area; Figure 2 A comparison chart of the lowest node voltages under different disturbance scenarios; Figure 3 A comparison chart of the maximum voltage imbalance factor under different disturbance scenarios; Figure 4 This is a diagram showing the day-ahead reserve range and intraday output of energy storage under typical disturbance scenarios. Detailed Implementation

[0021] The technical solution of the present invention will be further described below with reference to the embodiments. These embodiments are used to explain the implementation process of the present invention and are not intended to limit the scope of protection of the present invention.

[0022] To ensure the operability of edge autonomous deployment, this implementation method is broken down into eight stages: data access and timing synchronization, three-phase up-dimensional power flow modeling and resource injection assembly, construction of security constraints and explicit VUF constraints, construction of uncertain sets, two-stage robust optimization modeling, second-order cone convex relaxation processing, row and column generation and solution, and strategy output and instruction mapping. Each stage is given with directly implementable variable definitions and constraint expressions, facilitating model assembly and solution invocation at the transformer terminal.

[0023] The baseline strategy generated during the daytime phase is used to cover normal operation across the entire time domain. During the intraday phase, a remedial strategy is used to readjust and close any disturbance within the budgetary uncertainty set. The model does not introduce the interaction decision variables between power purchase and sale and boundary power. The power exchange between the distribution area and the outside world is naturally formed by the three-phase power flow. The decision only applies to the photovoltaic inverters, energy storage converters, adjustable loads, and emergency load shedding within the distribution area.

[0024] To address the hard infeasibility risk under extreme disturbances, non-negative relaxation variables are introduced into the voltage, current, transformer capacity, and VUF constraints, and a penalty order relationship is set in the objective function to ensure the executability of the output strategy and that risk exposure can be directly quantified through the relaxation level. The row and column generation algorithm provides upper and lower bounds and the worst-case scenario in each iteration, facilitating convergence diagnosis and computation time limit control during engineering operation.

[0025] A two-stage optimization scheduling method for power grid-source-load-storage distribution in a transformer substation, such as... Figure 1 As shown, it includes the following steps: 1) Collect three-phase topology data and operational data of the transformer substation, and unify the collected data to the same time granularity to form an input dataset; collect network topology and equipment parameters of the transformer substation to form a node set. N Set with branch roads E Branch parameters include the three-phase interphase coupling impedance matrix. Z ij Along with current thresholds, transformer parameters include capacity thresholds and low-voltage side rated voltage. Operational data is collected to form photovoltaic available output prediction sequences and load power prediction sequences, and initial energy of energy storage is also collected. E 1. The upper bound of charging and discharging power and the energy boundary, as well as the adjustable load regulation boundary and the upper bound of emergency reduction. Unify all time-series data to the same scheduling step size Δ. t And complete the timestamp alignment.

[0026] 2) Based on the input data, construct the three-phase voltage square matrix, branch current square matrix and branch complex power matrix as three-phase up-dimensional variables. Based on the three-phase Branch Flow model containing the inter-phase coupling impedance matrix, establish a three-phase network model and couple the time-series injection models of photovoltaic, energy storage, adjustable load and emergency load shedding to establish a three-phase source-grid-load-storage model. The three-phase dimensionality-upgrading variables are established as follows:

[0027] In the formula: For nodes i At any moment t The three-phase voltage vector; branch road ij At any moment t The three-phase current vector; For nodes i At any moment t The voltage square matrix; branch road ij At any moment t The square matrix of currents; branch road ij At any moment t The complex power matrix; H This indicates the conjugate transpose.

[0028] The branch voltage drop equation is:

[0029] In the formula: For nodes j At any moment t The voltage square matrix, branch road ij The three-phase interphase coupling impedance matrix; E For branch set; i and j These are the beginning and end nodes of the branch road, respectively.

[0030] The node power balance equation is:

[0031] In the formula: branch road ij At any moment t The complex power matrix, For nodes j At any moment t The three-phase complex power injection vector; N is a set of nodes; 0 represents a network node; diag indicates that the vector elements are constructed into a diagonal matrix.

[0032] Source-load storage time-series injection model: for any node i Parting Φ time t The net injection of the node is established as follows:

[0033] In the formula: Net active power is injected into the node; Contributed to the actual generation of photovoltaic power; Net output for energy storage; The active power of the load after the disturbance; This is the adjustable load adjustment amount; The amount was reduced as an emergency measure.

[0034]

[0035] In the formula: Net reactive power injection into the node; For photovoltaic reactive power; For energy storage reactive power; The reactive power of the load after the disturbance.

[0036] 3) Constructing network security constraints and explicit VUF constraints for a three-phase source-grid-load-storage model; The available photovoltaic output and inverter capacity constraints are as follows:

[0037] In the formula: This represents the upper limit of the usable photovoltaic output after the disturbance. This is the upper bound of the inverter's apparent power capacity, used to constrain the combined output of active and reactive power.

[0038] Energy storage power and energy dynamic constraints are as follows:

[0039] In the formula: This refers to the discharge power. This refers to the charging power. Net output for energy storage; This represents the upper limit of charging power. This represents the upper limit of the discharge power. The energy storage and aggregation status of the transformer area; For charging efficiency; For discharge efficiency; and These are the lower and upper bounds of the energy storage capacity, respectively. This is the scheduling step size.

[0040] Adjustable load and emergency load shedding constraints are:

[0041] In the formula: and These are the lower and upper limits of the adjustable load adjustment amount, respectively. This is the upper limit for emergency load reduction for adjustable loads.

[0042] Safety constraints and relaxation of voltage, current, and transformer capacity: The voltage square threshold constraint is:

[0043] In the formula: and These are the lower and upper voltage limits, respectively. and These are, respectively, voltage-limited relaxation and voltage-limited relaxation. These are the diagonal elements of the squared nodal voltage matrix.

[0044] The branch current square threshold constraint is:

[0045] In the formula: branch road ij Parting Φ The upper limit of current; For current exceeding the limit relaxation; These are the diagonal elements of the branch current square matrix.

[0046]

[0047] In the formula: all the above slack variables are non-negative variables, used as a fallback for feasibility under extreme perturbations.

[0048] The transformer capacity constraint is:

[0049] In the formula: r As the downstream first node of grid-connected node 0, branch 0 r Characterizes the low-voltage side outlet of the distribution transformer; and These represent the combined active and reactive power of the three phases of the transformer at time t; Im indicates taking the imaginary part. It is a three-phase all-one vector; The apparent capacity limit of the distribution transformer; It is a capacity relaxation variable for the distribution transformer, used as a feasibility fallback under extreme perturbations, and is given a high penalty coefficient in the objective function.

[0050] VUF explicit constraints: The positive-order and negative-order energy projection matrices are constructed as follows:

[0051] In the formula: a For complex number operators, a = e j 2π / 3 ; t 1 and t2 are the positive and negative order transformation vectors, respectively.

[0052]

[0053] In the formula: A 1 and A 2 are the positive and negative order energy projection matrices, respectively.

[0054]

[0055] In the formula: Tr represents the trace of the matrix; VUF threshold; These are VUF slack variables, and are non-negative.

[0056] 4) Implement second-order conical-convex relaxation on the non-convex coupling constraint of the three-phase power flow in the three-phase source-grid-load-storage model, and transform the established three-phase source-grid-load-storage model into a solvable conical programming form to obtain the relaxed three-phase source-grid-load-storage model.

[0057] Applying a second-order cone constraint to the three-phase power flow coupling:

[0058] In the formula: These are the elements of the branch complex power matrix.

[0059] To further enhance the tightness of convex relaxation, positive semidefinite constraints can be applied to the increased-dimensional variables while omitting the rank-one constraints:

[0060] In the formula: symbol 0 indicates a positive semidefinite constraint; this constraint, together with the second-order cone inequality, characterizes the convex feasible region between power voltage and current, and both the main problem and the remedial problem can be transformed into a cone programming stable solution.

[0061] The precise form of dimensionality-upgrading modeling typically includes The rank-one constraint is used to ensure equivalence with the original three-phase power flow equation. The rank-one constraint is discarded in the convex relaxation and is checked for consistency by voltage, current and VUF margin.

[0062] 5) Construct a budgetary uncertainty set based on the input dataset; Interval disturbance constraints, load active and reactive power coupling constraints, and budget constraints together constitute a budget-type uncertainty set.

[0063] Available photovoltaic power output and active power disturbance of load satisfy:

[0064] In the formula: For nodes i Parting Φ existt The available power output of photovoltaic forecasts at any given time; For nodes i Parting Φ exist t The amount of photovoltaic disturbance at any given moment; This represents the upper limit of the photovoltaic disturbance amplitude. Active power for load forecasting; For nodes i Parting Φ exist t The load disturbance at any given time; This represents the upper limit of the load disturbance amplitude.

[0065] To maintain load reactive power consistency under three-phase imbalance conditions, based on the load active power after the aforementioned disturbance, a load reactive power disturbance is constructed using a phase power factor preservation method:

[0066] In the formula: For nodes i Parting Φ The power factor parameter; and They are nodes i Parting Φ exist t The formula, which combines the predicted load reactive power after a disturbance at a given time, is used to maintain the coupling relationship between active and reactive power under uncertain disturbances. This formula determines the corresponding load reactive power based on the load active power after the aforementioned disturbance; no independent disturbance variable is set for the load reactive power.

[0067] To reflect the correlation of three-phase disturbances at the same node, a joint budget constraint is applied to load disturbances of different phases at the same node, namely:

[0068] In the formula: For nodes i The load joint budget parameters are used to limit the cumulative normalized deviation intensity of the three-phase load disturbance at the same node in the time domain, so as to avoid excessive conservatism caused by different phases reaching the maximum disturbance at the same time throughout the entire period.

[0069] A time-domain budget constraint is set for the available photovoltaic output disturbance, namely:

[0070] In the formula: This is the photovoltaic perturbation budget parameter, used to limit the cumulative perturbation intensity of photovoltaic prediction errors in the scheduling time domain. In summary, this is the budgetary uncertainty set. UIt is composed of interval constraints on photovoltaic and load forecasting errors, active and reactive power coupling constraints on loads, joint budget constraints on three-phase loads at the same node, and time-domain budget constraints on photovoltaics.

[0071] The original load phase-by-phase time-domain budget and the joint budget of the three-phase load at the nodes have overlapping constraint functions. To avoid duplication, the joint budget of the three-phase load at the nodes and the photovoltaic time-domain budget are retained, while the load phase-by-phase time-domain budget is deleted, and the role of the constraints of the two types of budgets is clearly defined.

[0072] 6) Based on the budget-type uncertain set and the relaxed three-phase source-grid-load-storage model, a two-stage robust optimization model is constructed for day-ahead and day-intraday.

[0073] The two-stage robust structure is as follows:

[0074] In the formula: y This is the full policy vector; For the current baseline policy variables; For remedial strategy variables; These are uncertain parameters; U It is an uncertain set.

[0075]

[0076] In the formula: F The cost function for the current stage; G For the remedial phase cost function; both include penalties for slack variables with emergency reduction as the highest penalty term.

[0077] To ensure the feasibility of the objective function and the relationship between the penalty order, the current stage cost function... F It can be constructed as follows:

[0078] In the formula: , , , , These are the cost weights for photovoltaic power generation curtailment, energy storage charging and discharging, adjustable load regulation, line loss, and slack variables, respectively. Limited photovoltaic power generation; and These are the positive and negative decomposition variables of the adjustable load adjustment amount; It contributes to the loss of power lines in the transformer area; It represents the set of relaxed variables such as voltage, current, transformer capacity, and VUF, and assigns a high penalty coefficient to the target; T The scheduling period is [number].

[0079] The positive and negative decomposition of photovoltaic power curtailment and adjustable load satisfies:

[0080] In the formula: For nodes i Parting Φ At any moment t The limited amount of photovoltaic power generation.

[0081]

[0082] In the formula: This is the adjustable load adjustment amount; and Used to characterize the up-adjustment and down-adjustment of regulation and in the objective function + Include the cost of the action.

[0083] Line losses and active power can be calculated from the square matrix of branch currents and the resistance matrix:

[0084] In the formula: branch road ij The three-phase resistance matrix is ​​taken as The real part of ; Tr represents the trace of the matrix.

[0085] Cost function of the remedial phase G The readjustment cost and emergency fallback cost, used to characterize the worst-case perturbation, can be constructed as follows:

[0086] In the formula: , , These are the cost weights for energy storage readjustment, adjustable load readjustment, and photovoltaic curtailment correction, respectively. and For the positive and negative decomposition variables of energy storage readjustment; , These are the positive and negative decomposition variables of the adjustable load readjustment; , These are the positive and negative decomposition variables of the photovoltaic power curtailment correction amount; The emergency reduction cost weight is set as the highest penalty item to ensure that it is only triggered when necessary; For the voltage, current, transformer capacity, and VUF relaxation variables during the remedial phase; This represents the corresponding relaxation penalty weight.

[0087]

[0088] In the formula: This represents the net energy storage output at the day-ahead baseline. The amount of readjustment relative to the baseline during the remedial phase; The adjustable load readjustment amount relative to the day-ahead baseline during the remedial phase; This is a correction to the photovoltaic power generation curtailment relative to the current baseline during the remedial phase.

[0089] To enhance feasibility, energy storage operation smoothing constraints can be introduced:

[0090] In the formula: Net output of energy storage in the power distribution area; This represents the upper limit of the climbing slope.

[0091] 7) The worst-case disturbance scenario is searched iteratively using a row and column generation algorithm. The worst-case disturbance scenario is added to the disturbance scenario set of the main problem of the two-stage robust optimization model. The algorithm is iteratively updated until the upper and lower bounds converge to obtain the autonomous scheduling strategy of the transformer area.

[0092] The row and column generation algorithm consists of a main problem and a separation subproblem. The main problem is in the current scene set. K By jointly solving the pre-dated baseline variables and the remedial variables for each scenario, the lower bound of the target is obtained. LB The subproblem of separating subproblems in uncertain sets U The internal search maximizes the perturbation scenario with the highest optimal remedy cost, thus obtaining the upper bound of the target. UB worst-case scenario .like UB and LB The difference is greater than the threshold ε If the worst-case scenario is added to the scenario set, the main problem is solved repeatedly until convergence.

[0093] For ease of implementation, the row and column generation algorithm is numbered according to iteration number. n Organization. (Number) n The scene set for the next iteration is denoted as follows: K n ,initialization K 1 Includes both nominal disturbance and zero disturbance scenarios.

[0094] The main problem can introduce auxiliary variables. η The main problem, representing the upper bound of the worst-case remediation cost on the current scenario set, takes the form:

[0095] In the formula: η The upper bound variable for the main problem with respect to the worst-case remediation cost; for each added scenario. k Corresponding to a set of remedial variables It also satisfies the three-phase network constraint, VUF constraint, and resource constraint. Solving the main problem yields the current lower bound. LBn equal The optimal value.

[0096] Baseline strategy for separating subproblems under a given date Below, in the budgetary uncertain set U Internal search is the most costly perturbation to remedy. Its form is:

[0097] In the formula: the worst perturbation output by the separator problem. And the corresponding minimum cost of remediation, thus obtaining the current upper bound. UB n equal F Add the value of the remedy cost.

[0098] The criteria for updating and terminating upper and lower bounds can be expressed as follows:

[0099] In the formula: and For the first n Solution to the main problem in the next iteration; This represents the minimum cost of remediation for the segregator problem under the worst-case perturbation.

[0100]

[0101] In the formula: This is the convergence threshold. When the threshold is met, iteration stops and a robust policy is output. Otherwise, [the policy is terminated]. Add to scene set K n+1 And continue to iterate.

[0102] The main problem is expressed as:

[0103] In the formula: For the scene k The following are the remedial variables; For the scene k The corresponding uncertain parameter values; K This is the set of scenarios that have already been introduced.

[0104] After the solution is completed, the system outputs the photovoltaic active power curtailment and reactive power support settings, energy storage charging and discharging power settings and energy trajectory, adjustable load regulation settings, and emergency reserve reduction settings for each node and phase. It also outputs the node voltage square, branch current square, and VUF constraint margin. The distribution terminal generates equipment-side control commands based on the output strategy and issues them in sequence for execution. Through measurement feedback, it forms a closed-loop monitoring system for voltage, current, VUF, and resource status, used for further optimization or switching to a conservative strategy during abnormal periods.

[0105] Case Analysis To verify the effectiveness of the day-ahead and day-intraday robust optimization scheduling method proposed in this invention, a case study was conducted on a 41-node three-phase unbalanced low-voltage distribution area. The case study considered resources such as fixed loads, distributed photovoltaics, energy storage, and adjustable loads, and set up nominal operating scenarios as well as disturbance scenarios such as photovoltaic output deviation, load power deviation, and phase imbalance, forming a total of 12 operating scenarios.

[0106] Figure 2 The minimum node voltages under different disturbance scenarios are presented. In unoptimized operation, low voltage exceeding limits occurs in scenarios with increased partial load and phase imbalance, with the worst-case scenario having a minimum node voltage of 0.9260 pu. After adopting this method, the minimum node voltages for all disturbance scenarios remain above 0.95 pu, and the minimum node voltage for the worst-case scenario increases to 0.9515 pu. This indicates that the proposed method can reduce the risk of low voltage caused by uncertain disturbances through day-ahead regulation capacity reservation and intraday remedial regulation.

[0107] Figure 3 The maximum voltage imbalance factor (VUF) under different disturbance scenarios is presented. In the unoptimized operation, the maximum VUF in the worst-case scenario reaches 2.02%, exceeding the set upper limit. After adopting robust scheduling, the maximum VUF is reduced to 1.92%, and all operating scenarios remain within the 2% constraint range. This demonstrates that explicitly incorporating VUF into the three-phase network security constraints can suppress the risk of negative sequence voltage under disturbances such as load phase imbalance.

[0108] Figure 4 The paper presents the day-ahead reserve range and intraday output results for energy storage under typical disturbance scenarios. During the day-ahead phase, energy storage up- and down-adjustment capabilities are reserved based on the baseline operating status, forming a reserve range available for each time period. When the actual source-load state deviates during the day, the corresponding energy storage output is activated according to the disturbance situation. During periods of high photovoltaic output, energy storage absorbs excess power through charging and performs corresponding discharge adjustments in subsequent periods, thereby coordinating day-ahead regulation capacity preparation with intraday remedial control.

[0109] Furthermore, the highest node voltage in each scenario under unoptimized operation reached 1.0543 pu, which was controlled to 1.0480 pu after adopting this method. Three-phase power flow verification showed that all disturbance scenarios after robust scheduling met the constraints of node voltage, branch current, transformer capacity, and VUF. These results demonstrate that this invention can improve the safety and regulation capability of grid-connected operation of power generation, grid, load, and energy storage in a distribution area under conditions of photovoltaic and load forecast deviations and three-phase imbalance, through the synergistic effect of day-ahead baseline optimization and intraday remedial regulation.

Claims

1. A two-stage optimized scheduling method for power generation, grid, load, and storage in a transformer substation, characterized in that, Includes the following steps: 1) Collect three-phase topology data and operational data of the transformer area, and unify the collected data to the same time granularity to form an input dataset; 2) Based on the input data, construct the three-phase voltage square matrix, branch current square matrix and branch complex power matrix as three-phase up-dimensional variables. Based on the three-phase Branch Flow model containing the inter-phase coupling impedance matrix, establish a three-phase network model and couple the time-series injection models of photovoltaic, energy storage, adjustable load and emergency load shedding to establish a three-phase source-grid-load-storage model. 3) Constructing network security constraints and explicit VUF constraints for a three-phase source-grid-load-storage model; 4) Implement second-order conical-convex relaxation on the non-convex coupling constraint of the three-phase power flow in the three-phase source-grid-load-storage model, and transform the established three-phase source-grid-load-storage model into a solvable conical programming form to obtain the relaxed three-phase source-grid-load-storage model. 5) Construct a budgetary uncertainty set based on the input dataset; 6) Based on the budget-type uncertain set and the relaxed three-phase source-grid-load-storage model, a two-stage robust optimization model is constructed for day-ahead and intraday periods; 7) The worst-case disturbance scenario is searched iteratively using a row and column generation algorithm. The worst-case disturbance scenario is added to the disturbance scenario set of the main problem of the two-stage robust optimization model. The algorithm is iteratively updated until the upper and lower bounds converge to obtain the autonomous scheduling strategy of the transformer area.

2. The two-stage optimized scheduling method for source-grid-load-storage in the transformer substation area according to claim 1, characterized in that, Taking the three-phase asymmetrical distribution network of the transformer substation as the object, the topology data includes the node phase connection relationship, the branch phase coupling impedance matrix, the transformer capacity threshold and the branch current threshold, and the operation data includes the photovoltaic available output prediction sequence, the load power prediction sequence, the initial energy and power boundary of energy storage, the adjustable load adjustment boundary and the emergency reduction boundary.

3. The two-stage optimized scheduling method for source-grid-load-storage in the transformer substation area according to claim 1, characterized in that, The network security constraints include: establishing branch voltage drop equations and node power balance equations based on a three-phase Branch Flow model containing interphase coupling impedance matrices, and establishing time-series injection models and boundary constraints for photovoltaic, energy storage, adjustable loads and emergency load shedding on the node injection side.

4. The two-stage optimized scheduling method for source-grid-load-storage in the transformer substation area according to claim 1, characterized in that, The explicit VUF constraints include: constructing positive and negative order voltage transformation vectors and their energy projection matrices based on symmetric component transformation; transforming the voltage imbalance factor (VUF) threshold constraint into a trace inequality of an up-dimensional matrix; and setting non-negative relaxation variables and penalty terms to ensure model feasibility under extreme perturbations and suppress negative order risks.

5. The two-stage optimized scheduling method for source-grid-load-storage in the transformer substation area according to claim 1, characterized in that, The second-order cone-convex relaxation process includes: relaxing the non-convex equality relationship between the square of the branch complex power amplitude and the product of the square of the node voltage and the square of the branch current in the three-phase power flow into an inequality relationship, and transforming it into a second-order cone constraint. At the same time, the rank-one constraint of the up-dimensional variable is omitted, resulting in a second-order cone-convex relaxation model.

6. The two-stage optimized scheduling method for source-grid-load-storage in the transformer substation area according to claim 1, characterized in that, The process of constructing a budget-type uncertain set includes: using interval perturbation for the prediction errors of available photovoltaic power output and active power of load; using a phase power factor preservation method to determine the corresponding reactive power of load based on the perturbed active power of load; using joint budget constraints for load perturbations of different phases at the same node to limit the cumulative intensity of three-phase load perturbations at the same node in the dispatch time domain; and setting time-domain budget parameters for perturbations of available photovoltaic power output to limit their cumulative intensity in the dispatch time domain, thus forming a budget-type uncertain set.

7. The two-stage optimized scheduling method for source-grid-load-storage in the transformer substation area during the day-ahead and intraday as described in claim 1, is characterized in that, The process of constructing a two-stage robust optimization objective function includes: Under network security and VUF constraints, a day-ahead stage cost function is constructed based on photovoltaic curtailment, energy storage charging and discharging, adjustable load adjustment, active power loss of distribution lines, slack variables and their weights. For disturbances within the budgetary uncertainty set, an intraday remedial strategy is formed based on the day-ahead baseline strategy. Based on the remedial costs corresponding to energy storage readjustment, adjustable load readjustment, photovoltaic curtailment correction, emergency reduction and slack variables, a remedial stage cost function is constructed. A two-stage robust optimization objective function is constructed with the goal of minimizing the sum of the day-ahead stage cost and the minimum remedial cost under the worst-case perturbation within the budgetary uncertainty set.

8. The two-stage optimized scheduling method for source-grid-load-storage in the transformer substation area during the day-ahead and intraday as described in claim 1, is characterized in that, The row and column generation algorithm includes iterative processes of the main problem and the separation of subproblems, specifically: The main problem is to jointly solve the pre-dawn baseline variables and the remedial variables for each scenario on the current scenario set to obtain the target lower bound. Given the current day-ahead baseline variables, the separation subproblem searches for the perturbation scenario that maximizes the optimal remedy cost within the uncertainty set. Based on the day-ahead stage cost and the optimal remedy cost, the target upper bound is obtained, and the worst perturbation scenario is determined. If the difference between the upper bound and the lower bound of the target is greater than the threshold, the worst-case scenario is added to the scenario set and the main problem is solved repeatedly until convergence. After the solution is completed, the output includes the photovoltaic active power limitation and reactive power support settings, energy storage charging and discharging power settings and energy trajectory, adjustable load adjustment settings and emergency reduction settings for each node and phase, as well as the node voltage square, branch current square and VUF constraint margin.

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