A power distribution network regulation and control boundary measurement method and system oriented to main coordination collaborative scheduling

Abstract

The application discloses a power distribution network regulation boundary measurement method and system facing main coordination scheduling, first, in the power distribution network topology, the high-dimensional state space promotion method based on the Kupmann theory is used to linearly represent the nonlinear relationship between the root node voltage amplitude, the PQ node active power, the PQ node reactive power and the PQ node voltage, and the state space mapping of the node power injection vector to the node voltage is obtained; the application realizes the function of obtaining the coefficient fixed boundary hyperplane expression under the given topology by constructing the static voltage safety domain by using the state space mapping method based on the Kupmann theory, and by explicitly introducing the static voltage safety domain into the construction process of the multi-microgrid power distribution network regulation feasible region, the internal node voltage safety constraint can be converted into the external boundary constraint, which not only reduces the dependence on the accurate network parameters and the repeated calculation of the point-by-point power flow, but also improves the representation accuracy of the regulation feasible region to the actual safe operation range, and is suitable for being widely promoted and used.

Description

Technical Field

[0001] This invention relates to the field of distribution network control boundary calculation technology, specifically to a method and system for calculating distribution network control boundaries for coordinated dispatching of main and distribution systems. Background Technology

[0002] With the high proportion of distributed energy resources (DERs) such as distributed photovoltaics and energy storage being integrated into the distribution network, the operation mode of the distribution network is gradually shifting from traditional one-way power supply to two-way interaction and multi-entity coordinated dispatch. Aggregated regulation of distributed resources through microgrids can significantly enhance the regulation capacity of the distribution network. However, the large number and heterogeneous types of DERs integrated into the distribution network make it difficult for the upper-level grid to directly obtain their detailed operational information and achieve individual coordinated control. Furthermore, the high proportion of DER integration also brings problems such as voltage exceeding limits and line overload. Therefore, it is necessary to accurately aggregate and characterize the regulation capacity of the massive controllable resources in the distribution network and construct a feasible domain for distribution network regulation to support multi-level coordinated regulation under the close coupling of the main grid, distribution network, and microgrids.

[0003] Currently, existing methods for calculating the control boundary of distribution networks generally focus on aggregating complex information within the system to provide a clear boundary representation for upper-level optimization. However, this approach does not deeply characterize the boundary characteristics dominated by voltage safety constraints in scenarios with a high proportion of DERs (Distribution and Reliable Grid Systems) access. This makes it difficult to fully characterize the adjustability of the distribution network while ensuring its safe operation. Furthermore, the large number and heterogeneous types of DERs accessed within the distribution network make it difficult for the upper-level power grid to directly obtain their detailed operational information and achieve individual coordinated control. At the same time, the high proportion of DERs access also leads to voltage overruns and line overloads. Therefore, it is necessary to design a method and system for calculating the control boundary of distribution networks oriented towards coordinated dispatching of primary and secondary distribution systems. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and to better and more effectively address the problem that existing methods for calculating the control boundary of distribution networks generally focus on aggregating complex information within the system to provide a clear boundary expression for upper-level optimization. However, this approach does not deeply characterize the boundary characteristics dominated by voltage safety constraints in scenarios with a high proportion of DERs (Distribution Controllers) access. This makes it difficult to fully characterize the adjustability of the distribution network while ensuring its safe operation. Furthermore, the large number and heterogeneous types of DERs accessed within the distribution network make it difficult for the upper-level power grid to directly obtain their detailed operating information and achieve individual coordinated control. At the same time, the high proportion of DER access also brings problems such as voltage exceeding limits and line overload. This invention provides a method and system for calculating the control boundary of distribution networks oriented towards coordinated scheduling of main and distribution networks. It realizes the function of constructing a static voltage safety domain using a state-space mapping method based on Koopman theory to obtain a fixed-coefficient boundary hyperplane expression under a given topology. Moreover, by explicitly introducing the static voltage safety domain into the construction process of the controllable feasible domain of the multi-microgrid distribution network, it can transform the internal node voltage safety constraints into external boundary constraints. This not only reduces the dependence on accurate network parameters and repeated calculations of point-by-point power flow, but also improves the accuracy of the controllable feasible domain in representing the actual safe operating range.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for calculating the control boundary of a distribution network oriented towards coordinated dispatching of primary and secondary systems includes the following steps: Step A: In the distribution network topology, the high-dimensional state-space lifting method based on Koopman theory is used to linearly characterize the nonlinear relationship between the root node voltage amplitude, PQ node active power, PQ node reactive power and PQ node voltage, and obtain the state-space mapping from the node power injection vector to the node voltage. Step B: Construct a static voltage security domain model for the distribution network based on the state-space mapping from node power injection vectors to node voltages; Step C: Based on the static voltage security domain model of the distribution network, construct an economic dispatch optimization model for the distribution network with the goal of minimizing the operating cost of distributed generators, the power cost of microgrid interaction, and the power exchange cost between the distribution network and the upper-level grid. This model includes constraints such as voltage security domain, distributed generator output, power balance, tie line transmission, power interaction between distribution and microgrids, and coupling constraints between the transmission and distribution network boundaries. Step D involves using the distribution network economic dispatch optimization model to calculate the feasible domain for the control of the multi-microgrid distribution network and obtain the distribution network control boundary.

[0006] The aforementioned method for calculating the control boundary of a distribution network oriented towards coordinated dispatching of primary and secondary nodes, in step A, employs a high-dimensional state-space lifting method based on Koopman theory in the distribution network topology to linearly characterize the nonlinear relationship between the root node voltage amplitude, active power of node PQ, reactive power of node PQ, and voltage of node PQ, and obtains the state-space mapping from the node power injection vector to the node voltage. The specific steps are as follows. Step A1: Let the set of nodes in the distribution network be N and the number of nodes be n+1, with node 0 being the root node. Then the operating point of the distribution network is shown in formula (1). (1) in, For the distribution network operation point, Let be the amount of active power injected into the nth PQ node. Let n be the reactive power injection amount at the nth PQ node. It is the transpose symbol; Step A2 involves using a high-dimensional state-space lifting method based on Koopman theory to linearly characterize the nonlinear relationship between the root node voltage magnitude, active power at node PQ, reactive power at node PQ, and voltage at node PQ. Specifically, this is achieved by establishing a dimension lifting function. Training state space mapping matrix As shown in formula (2), ; ; (2) in, The output matrix of the state-space mapping is the PQ node voltage matrix. This is the high-dimensional boosted matrix after dimensionality boosting. This is the original operating variable matrix of the distribution network. The root node voltage amplitude, For the active power of the PQ node, For PQ node reactive power, This refers to the voltage at the PQ node; Step A3: Use the least squares regression algorithm to map the state space matrix. The determination is made, as shown in formula (3). (3) in, This is a sample set of node voltage outputs composed of historical measurement data. It is the Moore-Penrose inverse function; Step A4, based on the state space mapping matrix The state-space mapping from the node power injection vector to the node voltage is constructed as shown in formula (4). (4) in, , , and Both are block matrices, and the block matrices are... , , and They are respectively and , , , The mapping relationship between them.

[0007] The aforementioned method for calculating the control boundary of a distribution network oriented towards coordinated dispatching of primary and secondary power sources, step B, involves constructing a static voltage security domain model of the distribution network based on the state-space mapping from node power injection vectors to node voltages. The specific steps are as follows: Step B1, the voltage at node i reaches the upper limit. and lower limit The boundary conditions are set, specifically by setting two sets of critical operating points, as shown in formula (5). ; (5) in, and These are the critical operating points corresponding to the upper and lower voltage limits of node i, respectively. and Let be the active power of the nth PQ node when node i reaches the upper and lower voltage limits, respectively. and These represent the reactive power of the nth PQ node when node i reaches the upper and lower voltage limits, respectively. Step B2 involves constructing the relationship between the node voltage change and the power injection change, as shown in formula (6). (6) in, This represents the PQ node voltage vector corresponding to the current operating point. and Let PQ be the voltage vectors of node i when it reaches the upper and lower voltage limits, respectively. This is the active power vector of the PQ node corresponding to the current operating point. and Let PQ be the active power vector of node i when it reaches the upper and lower voltage limits. This represents the reactive power vector of the PQ node corresponding to the current operating point. and Let PQ be the reactive power vectors of node i when it reaches the upper and lower voltage limits, respectively. and These are the dimensionality boosting function values ​​for the corresponding running points when node i reaches the upper and lower voltage limits, respectively; Step B3: Based on the relationship between node voltage changes and power injection changes, obtain the expression for the static voltage security domain boundary hyperplane of the distribution network, as shown in formula (7). ; ; ; ; (7) in, and These are the coefficient vectors of the active power variables in the upper and lower boundary hyperplanes of the static voltage security domain of the distribution network, respectively. and These are the coefficient vectors of reactive power variables in the upper and lower boundary hyperplanes of the static voltage security domain of the distribution network, respectively. This represents the static voltage security domain corresponding to node i in the distribution network. The operating point in the distribution network; Step B4: Construct the static voltage security domain model of the distribution network based on the hyperplane expression of the static voltage security domain boundary, as shown in formula (8). (8) in, For the global static voltage security domain of the distribution network, and These are the coefficients of the active power variable of the j-th PQ node in the upper and lower voltage boundary hyperplanes of node i, respectively. Inject a vector for the active power of the j-th PQ node. and These are the coefficients of the reactive power variable at the j-th PQ node in the upper and lower voltage boundary hyperplanes of node i, respectively. Inject the reactive power vector for the j-th PQ node. Number the PQ node.

[0008] The aforementioned method for calculating the control boundary of a distribution network oriented towards coordinated dispatching of primary and secondary power grids, in step C, involves constructing an economic dispatch optimization model for the distribution network based on the static voltage security domain model. This model aims to minimize the operating costs of distributed generators, the power exchange costs of microgrids, and the power exchange costs between the distribution network and the upper-level grid. The model includes constraints such as voltage security domain constraints, distributed generator output constraints, power balance constraints, tie-line transmission constraints, power exchange constraints between distribution and microgrids, and coupling constraints between the transmission and distribution network boundaries. The specific steps are as follows. Step C1: Construct the voltage security domain constraint for node i based on the static voltage security domain, as shown in formula (9). (9) in, Let be the injected active power of the j-th PQ node during time period t. Let be the injected reactive power of the j-th PQ node during time period t; Step C2: Construct the output constraints of the distributed generator, as shown in formula (10). (10) in, and Let be the lower limit and upper limit of the active power output of the distributed generator at node i. The output active power of the distributed generator. and Let be the lower limit and upper limit of the reactive power output of the distributed generator at node i. The output reactive power of the distributed generator. The set of nodes for controllable distributed generators connected to the distribution network; Step C3: Construct the power balance constraint for time period t, as shown in formula (11). (11) in, Let be the net active power injection at node i during time period t. The active power exchanged between the distribution network and the upstream power grid at the root node during time period t; Step C4: Construct the tie-line transmission constraints, as shown in formula (12). (12) in, and These are the lower and upper limits of the active power transmission capacity of the power transmission and distribution network interconnection lines, respectively. To transmit active power to the power transmission and distribution network interconnection lines, and These are the lower and upper limits of reactive power transmission capacity of power transmission and distribution network interconnections. To transmit reactive power to the power transmission and distribution network interconnection lines; Step C5: Construct the power constraints for the distribution microgrid interaction during time period t, as shown in formula (13). (13) in, The power exchange between the microgrid and the distribution network during time period t. Let t be the dispatchable domain of the microgrid during time period t; Step C6: Construct the boundary coupling constraints of the transmission and distribution network, as shown in formula (14). (14) in, Let t represent the active power transmitted through the transmission and distribution network interconnects on the transmission network side during time period t. Let be the active power exchange at the boundary node on the m side of the distribution network during time period t. Let t represent the reactive power transmitted by the transmission and distribution network interconnection line on the transmission network side during time period t. The reactive power exchange at the boundary node on the m side of the distribution network during time period t; Step C7: Based on voltage safety domain constraints, distributed generator output constraints, power balance constraints, tie-line transmission constraints, distribution microgrid interaction power constraints, and transmission and distribution network boundary coupling constraints, an economic dispatch optimization model for the distribution network is constructed with the goal of minimizing the operating cost of distributed generators within the distribution network, the interaction power cost of microgrids, and the power exchange cost between the distribution network and the upper-level grid. The specific model is shown in formula (15). (15) in, Let be the minimum objective function value of the m-th distribution network economic dispatch optimization model. The total number of time periods within the scheduling period. , and The operating cost coefficient of a controllable distributed generator. This refers to the set of nodes in a microgrid that are connected to the distribution network. For the set of transmission and distribution tie line nodes, The price at which the distribution network purchases electricity from the transmission network. Let t be the transmission power of the power transmission and distribution network tie lines during time period t. The microgrid purchase price for time period t; Step C8 involves rewriting the distribution network economic dispatch optimization model into a compact form, as shown in formula (16). ; ; (16) in, Let m be the decision variables for the distribution network optimization model during time period t. Let A be the planning parameter vector, and A be the decision variable. The corresponding constraint coefficient matrix, where D is the planning parameter vector. The corresponding constraint coefficient matrix, B is the constraint right-hand side constant matrix, Let be the coefficient vector of the objective function, which consists of the operating cost coefficient of the controllable distributed generator, the purchase price of electricity from the transmission and distribution tie line, and the purchase price of electricity from the microgrid.

[0009] The aforementioned method for calculating the control boundary of a distribution network oriented towards coordinated dispatching of primary and secondary distribution networks, in step D, involves using a distribution network economic dispatch optimization model to calculate the feasible region for control of the multi-microgrid distribution network and obtain the distribution network control boundary. The specific steps are as follows: Step D1, let Let be the optimal solution corresponding to the k-th constraint combination. Then, based on whether the constraints play a role in the optimization problem, all constraints in formula (16) are divided into a set of effective constraints and a set of ineffective constraints, as shown in formula (17). ; (17) in, , and All are valid constraints. , and All of these are invalid constraints. This is the optimal planning parameter vector corresponding to the kth constraint combination; Step D2, when the planning parameter w changes, the range defined by formula (17) is the feasible region. A critical region is identified, and new parameters are then explored. New constraint combinations can be obtained and new critical regions can be determined, thereby obtaining the critical regions of all combinations, and thus obtaining the control boundary of the distribution network, as shown in formula (18). (18) in, This represents the critical region corresponding to the k-th constraint combination.

[0010] A distribution network control boundary calculation system for primary and secondary coordinated dispatch includes a linear characterization module, a model building module, a model optimization module, and a control boundary calculation module. The linear characterization module uses a high-dimensional state-space lifting method based on Koopman theory to linearly characterize the nonlinear relationships between root node voltage amplitude, PQ node active power, PQ node reactive power, and PQ node voltage in the distribution network topology, obtaining a state-space mapping from node power injection vectors to node voltages. The model building module constructs a static voltage security domain model of the distribution network based on this state-space mapping. The model optimization module constructs an economic dispatch optimization model of the distribution network based on the static voltage security domain model, aiming to minimize the operating costs of distributed generators, microgrid interaction power costs, and power exchange costs between the distribution network and the upper-level grid. This model includes constraints such as voltage security domain constraints, distributed generator output constraints, power balance constraints, tie-line transmission constraints, distribution-microgrid interaction power constraints, and transmission-distribution network boundary coupling constraints. The control boundary calculation module uses the economic dispatch optimization model to calculate the feasible region for multi-microgrid distribution network control and obtain the distribution network control boundary.

[0011] The beneficial effects of this invention are as follows: This invention provides a method and system for calculating the control boundary of a distribution network oriented towards coordinated dispatching of primary and secondary power grids. First, in the distribution network topology, a high-dimensional state-space lifting method based on Koopman theory is used to linearly characterize the nonlinear relationship between the root node voltage amplitude, active power of nodes PQ, reactive power of nodes PQ, and voltage of nodes PQ, obtaining a state-space mapping from node power injection vectors to node voltages. Then, a static voltage security domain model of the distribution network is constructed based on this state-space mapping. Subsequently, based on the static voltage security domain model, an economic dispatch optimization model for the distribution network is constructed with the objectives of minimizing the operating costs of distributed generators, the power exchange costs of microgrids, and the power exchange costs between the distribution network and the upper-level grid. This model includes constraints on voltage security domains, distributed generator output, power balance, tie-line transmission, power exchange between distribution and microgrids, and the coupling constraints between the transmission and distribution network boundaries. Finally, an economic dispatch optimization model for the distribution network is adopted. The scheduling optimization model calculates the feasible region for the regulation of multi-microgrid distribution networks and obtains the distribution network regulation boundary. It effectively realizes the distribution network regulation boundary calculation method and system oriented towards main-distribution coordinated scheduling. It has the function of constructing a static voltage security domain using the state-space mapping method based on Koopman theory to obtain a fixed-coefficient boundary hyperplane expression under a given topology. Moreover, by explicitly introducing the static voltage security domain into the construction process of the feasible region for the regulation of multi-microgrid distribution networks, the internal node voltage security constraints can be transformed into external boundary constraints. This not only reduces the dependence on accurate network parameters and repeated calculations of point-by-point power flow, but also improves the accuracy of the regulation feasible region in representing the actual safe operating range. Furthermore, by using the multi-parameter programming method to divide the critical region of the multi-microgrid distribution network optimization problem, the feasible region for the regulation of the distribution network can be constructed, and the aggregation representation of multiple adjustable resources, network operation constraints, and boundary exchange capabilities within the distribution network can be realized. This facilitates the upper-level system to call its regulation capabilities without obtaining all internal detailed parameters. Attached Figure Description

[0012] Figure 1 This is an overall flowchart of a distribution network control boundary calculation method for primary and secondary coordinated scheduling according to the present invention. Figure 2 This is a schematic diagram of the feasible region projection for power distribution network regulation according to the present invention; Figure 3 This is a flowchart of the feasible region solution for the power distribution network according to the present invention; Figure 4 This is an embodiment of the IEEE 33-node distribution network topology diagram. Figure 5 This is a comparison chart of static voltage safety domains generated based on the fitting method and the method proposed in this invention in an embodiment of the present invention; Figure 6 This is a 24-hour feasible domain diagram of the IEEE 33-node system in an embodiment of the present invention. Detailed Implementation

[0013] The present invention will now be further described with reference to the accompanying drawings.

[0014] like Figure 1 As shown, the present invention provides a method for calculating the control boundary of a distribution network oriented towards coordinated dispatching of primary and secondary systems, comprising the following steps: Step A involves using a high-dimensional state-space lifting method based on Koopman theory in the distribution network topology to linearly characterize the nonlinear relationship between the root node voltage magnitude, active power at node PQ, reactive power at node PQ, and voltage at node PQ, and to obtain the state-space mapping from the node power injection vector to the node voltage. The specific steps are as follows. Step A1: Let the set of nodes in the distribution network be N and the number of nodes be n+1, with node 0 being the root node. Then the operating point of the distribution network is shown in formula (1). (1) in, For the distribution network operation point, Let be the amount of active power injected into the nth PQ node. Let n be the reactive power injection amount at the nth PQ node. It is the transpose symbol; Step A2 involves using a high-dimensional state-space lifting method based on Koopman theory to linearly characterize the nonlinear relationship between the root node voltage magnitude, active power at node PQ, reactive power at node PQ, and voltage at node PQ. Specifically, this is achieved by establishing a dimension lifting function. Training state space mapping matrix As shown in formula (2), ; ; (2) in, The output matrix of the state-space mapping is the PQ node voltage matrix. This is the high-dimensional boosted matrix after dimensionality boosting. This is the original operating variable matrix of the distribution network. The root node voltage amplitude, For the active power of the PQ node, For PQ node reactive power, This refers to the voltage at the PQ node; Step A3: Use the least squares regression algorithm to map the state space matrix. The determination is made, as shown in formula (3). (3) in, This is a sample set of node voltage outputs composed of historical measurement data. It is the Moore-Penrose inverse function; Step A4, based on the state space mapping matrix The state-space mapping from the node power injection vector to the node voltage is constructed as shown in formula (4). (4) in, , , and Both are block matrices, and the block matrices are... , , and They are respectively and , , , The mapping relationship between them.

[0015] like Figure 2 As shown, step B involves constructing a static voltage security domain model of the distribution network based on the state-space mapping from the node power injection vector to the node voltage. The specific steps are as follows: Step B1, the voltage at node i reaches the upper limit. and lower limit The boundary conditions are set, specifically by setting two sets of critical operating points, as shown in formula (5). ; (5) in, and These are the critical operating points corresponding to the upper and lower voltage limits of node i, respectively. and Let be the active power of the nth PQ node when node i reaches the upper and lower voltage limits, respectively. and These represent the reactive power of the nth PQ node when node i reaches the upper and lower voltage limits, respectively. Step B2 involves constructing the relationship between the node voltage change and the power injection change, as shown in formula (6). (6) in, This represents the PQ node voltage vector corresponding to the current operating point. and Let PQ be the voltage vectors of node i when it reaches the upper and lower voltage limits, respectively. This is the active power vector of the PQ node corresponding to the current operating point. and Let PQ be the active power vector of node i when it reaches the upper and lower voltage limits. This represents the reactive power vector of the PQ node corresponding to the current operating point. and Let PQ be the reactive power vectors of node i when it reaches the upper and lower voltage limits, respectively. and These are the dimensionality boosting function values ​​for the corresponding running points when node i reaches the upper and lower voltage limits, respectively; Step B3: Based on the relationship between node voltage changes and power injection changes, obtain the expression for the static voltage security domain boundary hyperplane of the distribution network, as shown in formula (7). ; ; ; ; (7) in, and These are the coefficient vectors of the active power variables in the upper and lower boundary hyperplanes of the static voltage security domain of the distribution network, respectively. and These are the coefficient vectors of reactive power variables in the upper and lower boundary hyperplanes of the static voltage security domain of the distribution network, respectively. This represents the static voltage security domain corresponding to node i in the distribution network. The operating point in the distribution network; Step B4: Construct the static voltage security domain model of the distribution network based on the hyperplane expression of the static voltage security domain boundary, as shown in formula (8). (8) in, For the global static voltage security domain of the distribution network, and These are the coefficients of the active power variable of the j-th PQ node in the upper and lower voltage boundary hyperplanes of node i, respectively. Inject a vector for the active power of the j-th PQ node. and These are the coefficients of the reactive power variable at the j-th PQ node in the upper and lower voltage boundary hyperplanes of node i, respectively. Inject the reactive power vector for the j-th PQ node. Number the PQ node.

[0016] Step C involves constructing an economic dispatch optimization model for the distribution network based on the static voltage security domain model. The model aims to minimize the operating costs of distributed generators within the distribution network, the power exchange costs of microgrids, and the power exchange costs between the distribution network and the upper-level grid. The model includes constraints on voltage security domain, distributed generator output, power balance, tie-line transmission, power exchange between distribution and microgrids, and the coupling between the transmission and distribution network boundaries. The specific steps are as follows. Step C1: Construct the voltage security domain constraint for node i based on the static voltage security domain, as shown in formula (9). (9) in, Let be the injected active power of the j-th PQ node during time period t. Let be the injected reactive power of the j-th PQ node during time period t; Step C2: Construct the output constraints of the distributed generator, as shown in formula (10). (10) in, and Let be the lower limit and upper limit of the active power output of the distributed generator at node i. The output active power of the distributed generator. and Let be the lower limit and upper limit of the reactive power output of the distributed generator at node i. The output reactive power of the distributed generator. The set of nodes for controllable distributed generators connected to the distribution network; Step C3: Construct the power balance constraint for time period t, as shown in formula (11). (11) in, Let be the net active power injection at node i during time period t. The active power exchanged between the distribution network and the upstream power grid at the root node during time period t; Step C4: Construct the tie-line transmission constraints, as shown in formula (12). (12) in, and These are the lower and upper limits of the active power transmission capacity of the power transmission and distribution network interconnection lines, respectively. To transmit active power to the power transmission and distribution network interconnection lines, and These are the lower and upper limits of reactive power transmission capacity of power transmission and distribution network interconnections. To transmit reactive power to the power transmission and distribution network interconnection lines; Step C5: Construct the power constraints for the distribution microgrid interaction during time period t, as shown in formula (13). (13) in, The power exchange between the microgrid and the distribution network during time period t. Let t be the dispatchable domain of the microgrid during time period t; Step C6: Construct the boundary coupling constraints of the transmission and distribution network, as shown in formula (14). (14) in, Let t represent the active power transmitted through the transmission and distribution network interconnects on the transmission network side during time period t. Let be the active power exchange at the boundary node on the m side of the distribution network during time period t. Let t represent the reactive power transmitted by the transmission and distribution network interconnection line on the transmission network side during time period t. The reactive power exchange at the boundary node on the m side of the distribution network during time period t; Step C7: Based on voltage safety domain constraints, distributed generator output constraints, power balance constraints, tie-line transmission constraints, distribution microgrid interaction power constraints, and transmission and distribution network boundary coupling constraints, an economic dispatch optimization model for the distribution network is constructed with the goal of minimizing the operating cost of distributed generators within the distribution network, the interaction power cost of microgrids, and the power exchange cost between the distribution network and the upper-level grid. The specific model is shown in formula (15). (15) in, Let be the minimum objective function value of the m-th distribution network economic dispatch optimization model. The total number of time periods within the scheduling period. , and The operating cost coefficient of a controllable distributed generator. This refers to the set of nodes in a microgrid that are connected to the distribution network. For the set of transmission and distribution tie line nodes, The price at which the distribution network purchases electricity from the transmission network. Let t be the transmission power of the power transmission and distribution network tie lines during time period t. The microgrid purchase price for time period t; Step C8 involves rewriting the distribution network economic dispatch optimization model into a compact form, as shown in formula (16). ; ; (16) in, Let m be the decision variables for the distribution network optimization model during time period t. Let A be the planning parameter vector, and A be the decision variable. The corresponding constraint coefficient matrix, where D is the planning parameter vector. The corresponding constraint coefficient matrix, B is the constraint right-hand side constant matrix, Let be the coefficient vector of the objective function, which consists of the operating cost coefficient of the controllable distributed generator, the purchase price of electricity from the transmission and distribution tie line, and the purchase price of electricity from the microgrid.

[0017] like Figure 3 As shown, step D involves using a distribution network economic dispatch optimization model to calculate the feasible region for multi-microgrid distribution network control and obtain the distribution network control boundary. The specific steps are as follows. Step D1, let Let be the optimal solution corresponding to the k-th constraint combination. Then, based on whether the constraints play a role in the optimization problem, all constraints in formula (16) are divided into a set of effective constraints and a set of ineffective constraints, as shown in formula (17). ; (17) in, , and All are valid constraints. , and All of these are invalid constraints. This is the optimal planning parameter vector corresponding to the kth constraint combination; Step D2, when the planning parameter w changes, the range defined by formula (17) is the feasible region. A critical region is identified, and new parameters are then explored. New constraint combinations can be obtained and new critical regions can be determined, thereby obtaining the critical regions of all combinations, and thus obtaining the control boundary of the distribution network, as shown in formula (18). (18) in, This represents the critical region corresponding to the k-th constraint combination.

[0018] A distribution network control boundary calculation system for primary and secondary coordinated dispatch includes a linear characterization module, a model building module, a model optimization module, and a control boundary calculation module. The linear characterization module uses a high-dimensional state-space lifting method based on Koopman theory to linearly characterize the nonlinear relationships between root node voltage amplitude, PQ node active power, PQ node reactive power, and PQ node voltage in the distribution network topology, obtaining a state-space mapping from node power injection vectors to node voltages. The model building module constructs a static voltage security domain model of the distribution network based on this state-space mapping. The model optimization module constructs an economic dispatch optimization model of the distribution network based on the static voltage security domain model, aiming to minimize the operating costs of distributed generators, microgrid interaction power costs, and power exchange costs between the distribution network and the upper-level grid. This model includes constraints such as voltage security domain constraints, distributed generator output constraints, power balance constraints, tie-line transmission constraints, distribution-microgrid interaction power constraints, and transmission-distribution network boundary coupling constraints. The control boundary calculation module uses the economic dispatch optimization model to calculate the feasible region for multi-microgrid distribution network control and obtain the distribution network control boundary.

[0019] To better illustrate the effects of the present invention, a specific embodiment of the method proposed in the present invention is described below.

[0020] This embodiment uses an IEEE 33-node distribution network including distributed photovoltaics and microgrids as a basis for a computational example analysis to verify the effectiveness of the proposed method. Its topology is as follows: Figure 4 As shown. All simulation models in this embodiment are implemented based on the MATLAB 2019a platform and the YALMIP language, with CPLEX 12.9.0 selected as the model solver. The example is based on a day-ahead time scale, with a total of 24 time periods set for analysis.

[0021] This embodiment uses Monte Carlo simulation to randomly generate active and reactive power data for photovoltaic (PV) power and load, with PV penetration covering [70%, 160%]. 1000 randomly generated training datasets are divided into two groups based on the net load power fluctuation range: Dataset 1: power fluctuation range [−100%, 0]; Dataset 2: power fluctuation range [0, 100%]. These two datasets aim to cover typical operating ranges from high penetration with light loads to low penetration with heavy loads, encompassing the vast majority of operating scenarios. This embodiment completes training on an IEEE 33-node distribution network based on these two sets of randomly generated data, calculating and statistically analyzing the differences between corresponding elements of L1 and L2 generated from the two datasets. The maximum average difference between matrix elements is 2.20 × 10⁻⁶. -4 The maximum standard deviation is 3.50 × 10⁻⁶. -4 This indicates that there are minimal differences between the matrix elements, and matrix L can be considered a constant.

[0022] The accuracy of the safety domain boundary calculated by the proposed method is verified using the static voltage safety domain boundary generated based on AC power flow model fitting as a benchmark. The maximum error of the static voltage safety domain boundary constructed by the proposed method is only 0.968%. Figure 5 As shown, it exhibits extremely high accuracy, meeting the requirements of practical engineering. Furthermore, the time required to generate the static voltage security domain boundary hyperplane based on the fitting method and the proposed method is shown in Table 1. From a computational efficiency perspective, the proposed method is far superior to the point-by-point method. Moreover, the proposed method can achieve rapid assessment of the node voltage security state without traditional power flow calculations, simplifying the operating constraints of the distribution network and thus significantly improving the problem-solving speed.

[0023] Table 1. Generation time of the hyperplane at the boundary of the static voltage security domain in the IEEE 33-bus system

[0024] like Figure 6 As shown, the feasible region of the IEEE 33-node system for 24 time periods is illustrated. The feasible region of the distribution network for each time period forms a closed polygon on the PQ plane, reflecting the power dispatchable range of the distribution network for each time period. The shape and size of the feasible region exhibit significant time-varying characteristics, primarily influenced by fluctuations in distributed photovoltaic (PV) output and changes in load demand. During the early morning period (e.g., 0:00-5:00), there is no PV output, and the load is at a relatively low level during the day, severely limiting the power adjustment space of the distribution network and shrinking the feasible region. During periods of high PV output (e.g., 6:00-17:00), the system possesses strong adjustment capabilities, and the feasible region expands. During the evening period (e.g., 18:00-20:00), PV output gradually weakens, and the load is at its evening peak, causing the feasible region to gradually shrink and shift towards the positive P-axis, reducing the system's adjustment flexibility. These changes in the feasible region characterize the dynamic boundary of the distribution network's adjustment capability at different time periods, providing an intuitive decision-making basis for formulating day-ahead coordinated dispatch plans for main and distribution systems, thereby improving the flexibility and reliability of system dispatch.

[0025] In summary, the present invention provides a method and system for calculating the control boundary of a distribution network oriented towards coordinated dispatching of primary and secondary power grids. First, in the distribution network topology, a high-dimensional state-space lifting method based on Koopman theory is used to linearly characterize the nonlinear relationship between the root node voltage amplitude, active power of nodes PQ, reactive power of nodes PQ, and voltage of nodes PQ, obtaining a state-space mapping from node power injection vectors to node voltages. Next, a static voltage security domain model of the distribution network is constructed based on this state-space mapping. Then, based on this static voltage security domain model, an economic dispatch optimization model of the distribution network is constructed with the objectives of minimizing the operating costs of distributed generators, the power exchange costs of microgrids, and the power exchange costs between the distribution network and the upper-level grid. This model includes constraints on voltage security domains, distributed generator output, power balance, tie-line transmission, power exchange between distribution and microgrids, and coupling constraints between the transmission and distribution network boundaries. Finally, economic dispatching of the distribution network is applied. The optimization model calculates the feasible region for the regulation of multi-microgrid distribution networks and obtains the distribution network regulation boundary. It effectively realizes the method and system for calculating the regulation boundary of distribution networks oriented towards main-distribution coordinated scheduling. It has the function of constructing a static voltage security domain using the state-space mapping method based on Koopman theory to obtain a fixed-coefficient boundary hyperplane expression under a given topology. Moreover, by explicitly introducing the static voltage security domain into the construction process of the feasible region for the regulation of multi-microgrid distribution networks, the internal node voltage security constraints can be transformed into external boundary constraints. This not only reduces the dependence on accurate network parameters and repeated calculations of point-by-point power flow, but also improves the accuracy of the regulation feasible region in representing the actual safe operating range. Furthermore, by using the multi-parameter programming method to divide the critical region of the multi-microgrid distribution network optimization problem, the feasible region for the regulation of distribution networks can be constructed, and the aggregation representation of multiple adjustable resources, network operation constraints, and boundary exchange capabilities within the distribution network can be realized. This facilitates the upper-level system to call its regulation capabilities without obtaining all internal detailed parameters.

[0026] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the control boundary of a distribution network oriented towards coordinated dispatching of primary and secondary systems, characterized in that: Includes the following steps, Step A: In the distribution network topology, the high-dimensional state-space lifting method based on Koopman theory is used to linearly characterize the nonlinear relationship between the root node voltage amplitude, PQ node active power, PQ node reactive power and PQ node voltage, and obtain the state-space mapping from the node power injection vector to the node voltage. Step B: Construct a static voltage security domain model for the distribution network based on the state-space mapping from node power injection vectors to node voltages; Step C: Based on the static voltage security domain model of the distribution network, construct an economic dispatch optimization model for the distribution network with the goal of minimizing the operating cost of distributed generators, the power cost of microgrid interaction, and the power exchange cost between the distribution network and the upper-level grid. This model includes constraints such as voltage security domain, distributed generator output, power balance, tie line transmission, power interaction between distribution and microgrids, and coupling constraints between the transmission and distribution network boundaries. Step D involves using the distribution network economic dispatch optimization model to calculate the feasible domain for the control of the multi-microgrid distribution network and obtain the distribution network control boundary.

2. The method for calculating the control boundary of a distribution network oriented towards coordinated dispatching of primary and secondary systems, as described in claim 1, is characterized in that: Step A involves using a high-dimensional state-space lifting method based on Koopman theory in the distribution network topology to linearly characterize the nonlinear relationship between the root node voltage magnitude, active power at node PQ, reactive power at node PQ, and voltage at node PQ, and to obtain the state-space mapping from the node power injection vector to the node voltage. The specific steps are as follows. Step A1: Let the set of nodes in the distribution network be N and the number of nodes be n+1, with node 0 being the root node. Then the operating point of the distribution network is shown in formula (1). （1） in, For the distribution network operation point, Let be the amount of active power injected into the nth PQ node. Let n be the reactive power injection amount at the nth PQ node. It is the transpose symbol; Step A2 involves using a high-dimensional state-space lifting method based on Koopman theory to linearly characterize the nonlinear relationship between the root node voltage magnitude, active power at node PQ, reactive power at node PQ, and voltage at node PQ. Specifically, this is achieved by establishing a dimension lifting function. Training state space mapping matrix As shown in formula (2), ； ； （2） in, The output matrix of the state-space mapping is the PQ node voltage matrix. This is the high-dimensional boosted matrix after dimensionality boosting. This is the original operating variable matrix of the distribution network. The root node voltage amplitude, For the active power of the PQ node, For PQ node reactive power, This refers to the voltage at the PQ node; Step A3: Use the least squares regression algorithm to map the state space matrix. The determination is made, as shown in formula (3). （3） in, This is a sample set of node voltage outputs composed of historical measurement data. It is the Moore-Penrose inverse function; Step A4, based on the state space mapping matrix The state-space mapping from the node power injection vector to the node voltage is constructed as shown in formula (4). （4） in, , , and Both are block matrices, and the block matrices are... , , and They are respectively and , , , The mapping relationship between them.

3. The method for calculating the control boundary of a distribution network oriented towards coordinated dispatching of primary and secondary systems, as described in claim 2, is characterized in that: Step B involves constructing a static voltage security domain model of the distribution network based on the state-space mapping from node power injection vectors to node voltages. The specific steps are as follows: Step B1, the voltage at node i reaches the upper limit. and lower limit The boundary conditions are set, specifically by setting two sets of critical operating points, as shown in formula (5). ； （5） in, and These are the critical operating points corresponding to the upper and lower voltage limits of node i, respectively. and Let be the active power of the nth PQ node when node i reaches the upper and lower voltage limits, respectively. and These represent the reactive power of the nth PQ node when node i reaches the upper and lower voltage limits, respectively. Step B2 involves constructing the relationship between the node voltage change and the power injection change, as shown in formula (6). （6） in, This represents the PQ node voltage vector corresponding to the current operating point. and Let PQ be the voltage vectors of node i when it reaches the upper and lower voltage limits, respectively. This is the active power vector of the PQ node corresponding to the current operating point. and Let PQ be the active power vector of node i when it reaches the upper and lower voltage limits. This represents the reactive power vector of the PQ node corresponding to the current operating point. and Let PQ be the reactive power vectors of node i when it reaches the upper and lower voltage limits, respectively. and These are the dimensionality boosting function values ​​for the corresponding running points when node i reaches the upper and lower voltage limits, respectively; Step B3: Based on the relationship between node voltage changes and power injection changes, obtain the expression for the static voltage security domain boundary hyperplane of the distribution network, as shown in formula (7). ； ； ； ； （7） in, and These are the coefficient vectors of the active power variables in the upper and lower boundary hyperplanes of the static voltage security domain of the distribution network, respectively. and These are the coefficient vectors of reactive power variables in the upper and lower boundary hyperplanes of the static voltage security domain of the distribution network, respectively. This represents the static voltage security domain corresponding to node i in the distribution network. The operating point in the distribution network; Step B4: Construct the static voltage security domain model of the distribution network based on the hyperplane expression of the static voltage security domain boundary, as shown in formula (8). （8） in, For the global static voltage security domain of the distribution network, and These are the coefficients of the active power variable of the j-th PQ node in the upper and lower voltage boundary hyperplanes of node i, respectively. Inject a vector for the active power of the j-th PQ node. and These are the coefficients of the reactive power variable at the j-th PQ node in the upper and lower voltage boundary hyperplanes of node i, respectively. Inject the reactive power vector for the j-th PQ node. Number the PQ node.

4. The method for calculating the control boundary of a distribution network oriented towards coordinated dispatching of primary and secondary systems, as described in claim 3, is characterized in that: Step C involves constructing an economic dispatch optimization model for the distribution network based on the static voltage security domain model. The model aims to minimize the operating costs of distributed generators within the distribution network, the power exchange costs of microgrids, and the power exchange costs between the distribution network and the upper-level grid. The model includes constraints on voltage security domain, distributed generator output, power balance, tie-line transmission, power exchange between distribution and microgrids, and the coupling between the transmission and distribution network boundaries. The specific steps are as follows. Step C1: Construct the voltage security domain constraint for node i based on the static voltage security domain, as shown in formula (9). （9） in, Let be the injected active power of the j-th PQ node during time period t. Let be the injected reactive power of the j-th PQ node during time period t; Step C2: Construct the output constraints of the distributed generator, as shown in formula (10). （10） in, and Let be the lower limit and upper limit of the active power output of the distributed generator at node i. The output active power of the distributed generator. and Let be the lower limit and upper limit of the reactive power output of the distributed generator at node i. The output reactive power of the distributed generator. The set of nodes for controllable distributed generators connected to the distribution network; Step C3: Construct the power balance constraint for time period t, as shown in formula (11). （11） in, Let be the net active power injection at node i during time period t. The active power exchanged between the distribution network and the upstream power grid at the root node during time period t; Step C4: Construct the tie-line transmission constraints, as shown in formula (12). （12） in, and These are the lower and upper limits of the active power transmission capacity of the power transmission and distribution network interconnection lines, respectively. To transmit active power to the power transmission and distribution network interconnection lines, and These are the lower and upper limits of reactive power transmission capacity of power transmission and distribution network interconnections. To transmit reactive power to the power transmission and distribution network interconnection lines; Step C5: Construct the power constraints for the distribution microgrid interaction during time period t, as shown in formula (13). （13） in, The power exchange between the microgrid and the distribution network during time period t. Let t be the dispatchable domain of the microgrid during time period t; Step C6: Construct the boundary coupling constraints of the transmission and distribution network, as shown in formula (14). （14） in, Let t represent the active power transmitted through the transmission and distribution network interconnects on the transmission network side during time period t. Let be the active power exchange at the boundary node on the m side of the distribution network during time period t. Let t represent the reactive power transmitted by the transmission and distribution network interconnection line on the transmission network side during time period t. The reactive power exchange at the boundary node on the m side of the distribution network during time period t; Step C7: Based on voltage safety domain constraints, distributed generator output constraints, power balance constraints, tie-line transmission constraints, distribution microgrid interaction power constraints, and transmission and distribution network boundary coupling constraints, an economic dispatch optimization model for the distribution network is constructed with the goal of minimizing the operating cost of distributed generators within the distribution network, the interaction power cost of microgrids, and the power exchange cost between the distribution network and the upper-level grid. The specific model is shown in formula (15). （15） in, Let be the minimum objective function value of the m-th distribution network economic dispatch optimization model. The total number of time periods within the scheduling period. , and The operating cost coefficient of a controllable distributed generator. This refers to the set of nodes in a microgrid that are connected to the distribution network. For the set of transmission and distribution tie line nodes, The price at which the distribution network purchases electricity from the transmission network. Let t be the transmission power of the power transmission and distribution network tie lines during time period t. The microgrid purchase price for time period t; Step C8 involves rewriting the distribution network economic dispatch optimization model into a compact form, as shown in formula (16). ； ； （16） in, Let m be the decision variables for the distribution network optimization model during time period t. Let A be the planning parameter vector, and A be the decision variable. The corresponding constraint coefficient matrix, where D is the planning parameter vector. The corresponding constraint coefficient matrix, B is the constraint right-hand side constant matrix, Let be the coefficient vector of the objective function, which consists of the operating cost coefficient of the controllable distributed generator, the power purchase price of the transmission and distribution tie line, and the power purchase price of the microgrid.

5. The method for calculating the control boundary of a distribution network oriented towards coordinated dispatching of primary and secondary systems, as described in claim 4, is characterized in that: Step D involves using a distribution network economic dispatch optimization model to calculate the feasible region for multi-microgrid distribution network control and obtain the distribution network control boundary. The specific steps are as follows. Step D1, let Let be the optimal solution corresponding to the k-th constraint combination. Then, based on whether the constraints play a role in the optimization problem, all constraints in formula (16) are divided into a set of effective constraints and a set of ineffective constraints, as shown in formula (17). ； （17） in, , and All are valid constraints. , and All of these are invalid constraints. This is the optimal planning parameter vector corresponding to the kth constraint combination; Step D2, when the planning parameter w changes, the range defined by formula (17) is the feasible region. A critical region is identified, and new parameters are then explored. New constraint combinations can be obtained and new critical regions can be determined, thereby obtaining the critical regions of all combinations, and thus obtaining the control boundary of the distribution network, as shown in formula (18). （18） in, This represents the critical region corresponding to the k-th constraint combination.

6. A distribution network control boundary calculation system for coordinated dispatching of primary and secondary distribution networks, wherein the specific calculation process of the distribution network control boundary calculation system is based on the distribution network control boundary calculation method according to any one of claims 1-5, characterized in that: It includes a linear characterization module, a model building module, a model optimization module, and a regulation boundary calculation module. The linear characterization module is used to linearly characterize the nonlinear relationship between the root node voltage amplitude, PQ node active power, PQ node reactive power, and PQ node voltage in the distribution network topology using a high-dimensional state space lifting method based on Koopman theory, and to obtain the state space mapping from the node power injection vector to the node voltage. The model building module is used to construct a static voltage security domain model of the distribution network based on the state-space mapping from node power injection vector to node voltage. The model optimization module is used to construct an economic dispatch optimization model for the distribution network based on the static voltage security domain model of the distribution network, with the goal of minimizing the operating cost of distributed generators, the power cost of microgrid interaction, and the power exchange cost between the distribution network and the upper-level grid. The model includes voltage security domain constraints, distributed generator output constraints, power balance constraints, tie line transmission constraints, distribution-microgrid interaction power constraints, and transmission-distribution network boundary coupling constraints. The control boundary calculation module is used to calculate the control feasible domain of the multi-microgrid distribution network using the distribution network economic dispatch optimization model and obtain the distribution network control boundary.

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