Distributed load flow calculation method and system for active power distribution network

Abstract

The invention provides a distributed power flow calculation method and system for an active power distribution network. The method comprises the following steps: constructing a steady-state branch power flow model and constraint conditions corresponding to the steady-state branch power flow model, constructing a transformer thermal aging model, and respectively constructing a first operation model and a second operation model about an electric vehicle and a distributed photovoltaic system; constructing an optimization problem model about a network side, an EV side and a PV side; defining a first decision variable related to the active power distribution network and a second decision variable related to the electric vehicle and photovoltaic, and generating an optimal power flow problem and a first optimization problem of the active power distribution network; introducing a reverse unequal function for the constraint condition, performing linear processing on the reverse unequal function, and introducing a penalty term to obtain a second optimization problem; and recursively solving the optimization problem models of the network side, the EV side and the PV side according to an improved solving algorithm. According to the method, direct interaction of sensitive data can be avoided, and individual privacy and independent calculation requirements of each participant are ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed power flow calculation, and particularly to a distributed power flow calculation method and system for an active distribution network. Background Art

[0002] To achieve the "dual carbon" goal and realize the clean and efficient energy system, the proportion of new energy mainly composed of photovoltaic (PV) and wind power in energy consumption has been continuously expanding, making the proportion of electric vehicles (EVs) in the distribution network load continue to increase. The uncertainty, volatility of new energy on the source side and the characteristics of a large number of EVs plugging and unplugging on the load side pose higher requirements for the safe operation of the distribution network. The active distribution network shows certain advantages in the coordinated regulation of the "source-load", and can effectively cope with the uncertainties on both sides of the "source-load". Therefore, the active distribution network has been vigorously developed. Among them, the system operator grasps the system state by solving the optimal power flow problem and obtains the best operation strategy, so as to ensure the safe and economic coordinated operation of various power generation resources and flexible loads in the active distribution network.

[0003] However, the limited information that can be interacted among multiple operation entities in the active distribution network increases the difficulty of unified analysis of the whole network power flow. Therefore, to ensure the privacy security and relative independence of individuals, there is an urgent need for a distributed calculation method for the optimal power flow of the active distribution network to achieve the individual solution of each entity and protect the interest demands of each entity. Summary of the Invention

[0004] The purpose of the present invention is to provide a distributed power flow calculation method and system for an active distribution network, aiming to solve the problem that the traditional centralized calculation method for the active distribution network is difficult to ensure the privacy security and relative independence of individuals.

[0005] In the first aspect, the present invention provides a distributed power flow calculation method for an active distribution network, and the method includes: Construct a steady-state branch power flow model of the active distribution network and its corresponding constraint conditions, construct a transformer thermal aging model, define electric vehicles and distributed photovoltaics as the types of energy access to the active distribution network, and respectively construct a first operation model for electric vehicles and a second operation model for distributed photovoltaics; Based on the steady-state branch power flow model, the transformer thermal aging model, the first operation model, and the second operation model, construct an optimization problem model for the network side, the EV side, and the PV side; Define a first decision variable related to the active distribution network and a second decision variable related to electric vehicles and photovoltaics, and generate an optimal power flow problem for the active distribution network and a first optimization problem related to the second decision variable according to the definition result; Introduce a reverse inequality function for the constraint condition, perform linear processing on the reverse inequality function, and introduce a penalty term to obtain a second optimization problem; Recursively solve the optimization problem models of the network side, EV side, and PV side according to the improved solution algorithm.

[0006] Further, the steps of constructing the steady-state branch power flow model of the active distribution network and its corresponding constraint conditions include: Construct a steady-state branch power flow model according to the following formula: ; Among them, Are the active and reactive powers of line At time t, , Are the resistance and reactance on line Respectively, Is the square of the current amplitude of line At time t, , Are the squares of the voltage amplitudes of nodes j and i at time t respectively, , Are the active and reactive powers of the load of node j at time t respectively, , Are the active and reactive powers of line At time t, k is the index of the downstream child node of node j, Is the set composed of the downstream child nodes of node j, s is the element index in the set, Is the set of electric vehicles connected to node j at time t, , Are the active and reactive power outputs of electric vehicles at node j respectively, Is the set of photovoltaics connected to node j at time t, , Are the active and reactive power outputs of photovoltaics at node j respectively, , Are the Lagrange multipliers corresponding to the equality constraints, T is the set of time periods, N is the set of nodes, Is the set of nodes except the root node, Is the only upstream parent node of node j; Construct constraint conditions according to the following formula: ; Among them, , Are the upper and lower limits of the square of the voltage amplitude respectively, is the upper limit of the square of the current amplitude, L is the set of lines, and T is the set composed of the indices of the optimization time periods.

[0007] Further, the steps of constructing the transformer thermal aging model, defining electric vehicles and distributed photovoltaics as the types of energy access to the active distribution network, and respectively constructing the first operation model and the second operation model for electric vehicles and distributed photovoltaics include: Construct the transformer thermal aging model according to the following formula: ; Where, is the aging acceleration factor of the transformer at time t, M represents the total number of segments, , are respectively the slope and intercept of the th segment, is the hottest spot temperature of the winding at time t, is the lower limit of the temperature range of the th segment, is the upper limit of the temperature range of the th segment, is the top oil temperature at time t, m is a constant, is the temperature rise of the hottest spot of the winding compared to the top oil temperature under rated load, is the square of the current amplitude at present, is the square of the rated current amplitude, is the Lagrange multiplier corresponding to the constraint, used to represent the impact of the load on the transformer life loss in the next working cycle when the transformer works for a cycle T, e is the index of the transformer in the working state, and E is the set of transformers in the working state; Construct the first operation model according to the following formula: ; Where, is the charging demand of the electric vehicle, is the maximum limit of the active power of the electric vehicle, is the maximum limit of the apparent power of the electric vehicle; Construct the second operation model according to the following formula: ; Where, is the maximum limit of the active power of the distributed photovoltaic, is the maximum limit of the apparent power of the distributed photovoltaic.

[0008] Further, the steps of constructing the optimization problem model for the network side, EV side, and PV side based on the steady-state branch power flow model, the transformer thermal aging model, the first operation model, and the second operation model include: For the network side, its final objective function is: ; Wherein, , , are respectively the active power price purchased from the root node, the reactive power unit cost, and the unit cost of transformer life loss. is the active power of line 01 at time t, is the reactive power of line 01 at time t; For the EV side, its initial objective function is: ; For the PV side, its initial objective function is: ; Wherein, is the node active power price at time t, is the node reactive power price at time t.

[0009] Furthermore, the steps of defining the first decision variables related to the active distribution network and the second decision variables related to electric vehicles and photovoltaic, and generating the optimal power flow problem of the active distribution network and the first optimization problem related to the second decision variables include: Define as the first decision variables related to the distribution network. The first decision variables include , , , , , , ; Define as the second decision variables related to electric vehicles and photovoltaic. The second decision variables include , , , ; Construct the first optimization problem according to the following formula: ; Wherein, represents the distribution network operation cost, is the feasible region of the first decision variables, is the feasible region of the second decision variables, is the node price matrix. A, B, and D are all coefficient matrices of the equality constraints related to the second decision variables in the steady-state branch power flow model, is the value of the known decision variables related to the second decision variables, To meet the relevant conditions; Given , solve the first optimization problem; Based on the first optimization problem, obtain the optimization problem regarding y, and solve the optimization problem regarding y to obtain : ; Among them, and are the values obtained from the k-th and (k + 1)-th iterative solutions respectively, is the variable value that minimizes the objective function, represents the operating cost related to electric vehicles and photovoltaics, is the transpose of the nodal electricity price matrix at the k-th iteration; Define and as the active and reactive power outputs of the photovoltaic at time t during the k-th iteration, and are the active and reactive power outputs of the electric vehicle at time t during the k-th iteration respectively. Then the final objective function on the EV side is: ; The final objective function on the PV side is: ; Among them, is the positive scalar parameter at the k-th iteration, is the nodal active electricity price at time t during the k-th iteration, is the nodal reactive electricity price at time t during the k-th iteration.

[0010] Furthermore, the steps of introducing a reverse inequality function for the constraint condition, linearly processing the reverse inequality function, and introducing a penalty term to obtain the second optimization problem include: The expression of the introduced reverse inequality function is as follows: ; Linearly process the reverse inequality function and introduce a penalty term to obtain: ; Among them, and are the active and reactive powers of line at time t obtained from the k-th iteration, is the square of the voltage amplitude of node i at time t obtained from the k-th iteration, is the square of the current amplitude of line at time t obtained from the k-th iteration, is the penalty term; A weight factor can be applied to the penalty term to obtain a second optimization problem: . .

[0011] Furthermore, the step of recursively solving the optimization problem models on the network side, EV side, and PV side according to the improved solution algorithm includes: Step 1: Starting from , given an initial scheduling strategy, including , , , , set the error tolerance and the iteration time limit ; Step 2: Solve the final objective function on the network side according to the given initial scheduling strategy, and determine whether the constraint conditions are binding; Step 2.1: If the constraint conditions are binding constraints, obtain the correct and , and proceed to Step 3; Step 2.2: If the constraint conditions are non-binding constraints, set the initial number of inner loop iterations ; Step 2.3: Solve the second optimization problem, and determine whether the error in the k-th iteration is greater than ; Step 2.4: If , let , and return to Step 2.3 to continue the solution; Step 2.5: If , solve the new network optimization problem model to obtain and , and proceed to Step 3. The new network optimization problem model includes the following expressions: ; Step 3: From the obtained and , solve the final objective functions on the EV side and PV side to obtain the scheduling strategy under the current iteration, and determine whether the scheduling strategy output in the current iteration meets the requirements or whether the current iteration reaches the iteration time; Step 4: If the requirements are met or the iteration time is reached, the iteration ends. If the requirements are not met and the iteration time is not reached, use the scheduling strategy output in the previous iteration as the new given scheduling strategy, and return to Step 2.

[0012] In a second aspect, the present invention provides an active distribution network distributed power flow calculation system, and the system includes: A power flow model construction module for constructing a steady-state branch power flow model of an active distribution network and its corresponding constraint conditions, constructing a transformer thermal aging model, defining electric vehicles and distributed photovoltaics as energy access types of the active distribution network, and respectively constructing a first operation model for electric vehicles and a second operation model for distributed photovoltaics; An optimization problem model construction module for constructing an optimization problem model regarding the network side, the EV side, and the PV side based on the steady-state branch power flow model, the transformer thermal aging model, the first operation model, and the second operation model; A decision variable definition module for defining a first decision variable related to the active distribution network and a second decision variable related to electric vehicles and photovoltaics, and generating an optimal power flow problem of the active distribution network and a first optimization problem related to the second decision variable according to the definition result; An optimization problem construction module for introducing a reverse inequality function into the constraint conditions, linearly processing the reverse inequality function, and introducing a penalty term to obtain a second optimization problem; A recursive solution module for recursively solving the optimization problem models of the network side, the EV side, and the PV side according to an improved solution algorithm.

[0013] In a third aspect, the present invention provides a storage medium storing one or more programs, which, when executed by a processor, implement the above-mentioned active distribution network distributed power flow calculation method.

[0014] In a fourth aspect, the present invention provides an electronic device, where the electronic device includes a memory and a processor, and: The memory is used for storing a computer program; The processor is used for implementing the above-mentioned active distribution network distributed power flow calculation method when executing the computer program stored on the memory.

[0015] Compared with the prior art, the present invention has the following advantages: 1. The present invention constructs a steady-state branch power flow model, a transformer thermal aging model, and operation models for electric vehicles and distributed photovoltaics in the active distribution network, and constructs an optimization problem model covering the network side, EV side, and PV side based on these models. At the same time, decision variables on different sides are defined and transformed into optimization problems, and then special function processing and linearization are performed on the constraint conditions and penalty terms are introduced to form the final optimization problem. Finally, an improved solution algorithm is used for recursive solution. This hierarchical modeling and optimization solution method naturally fits the distributed computing architecture, and different models and optimization problems can be processed in parallel by different computing nodes in the distributed computing environment, thus realizing distributed computing. And in the processing of each link, through reasonable data partitioning and model abstraction, only key parameters required for optimization solution are transmitted when necessary, avoiding direct interaction of sensitive data, and ensuring the needs of personal privacy and independent computing of each participating party.

[0016] 2. On the basis of considering the power purchase cost, the present invention also considers the transformer aging cost. And, for the error caused by second-order cone relaxation, the method establishes a reverse inequality, and through linearization processing and inner-loop iteration, it can be easily optimized while gradually reducing the relaxation error. At the same time, the method can ensure the executability of the temporary solutions obtained during the iteration process, and also enables dynamic adjustment of the target parameters and constraint conditions during each iteration process to cope with the real-time changing system state. When a violation is observed, the parameters of the optimization problem can be adjusted at any time. In actual engineering, dispatchers will follow a similar iterative update process while ensuring the feasibility of the solution. Check the dispatch plan, and if it is found that some unformulated constraint conditions are not met, incorporate these constraint conditions into the normalized optimization problem, or adjust the original parameters / constraint conditions to ensure feasibility. In day-ahead dispatch, this process will be repeated continuously until a feasible solution is found or the time is exhausted. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a flowchart of the distributed power flow calculation method for the active distribution network proposed in an embodiment of the present invention; Figure 2 is a schematic structural diagram of the distributed power flow calculation system for the active distribution network proposed in an embodiment of the present invention.

[0018] The following specific embodiments will further illustrate the present invention in conjunction with the above-mentioned drawings. SPECIFIC EMBODIMENTS

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention. Unless otherwise defined, the technical terms or scientific terms used herein shall have the ordinary meanings understood by those of ordinary skill in the art in the field to which the present invention pertains. The words such as "including" used herein mean that the elements or items appearing before this word cover the elements or items listed after this word and their equivalents, without excluding other elements or items.

[0020] As Figure 1 shown, an embodiment of the present invention proposes a distributed power flow calculation method for an active distribution network. The method includes steps S101 to S105, where: Step S101: Construct a steady-state branch power flow model of the active distribution network and its corresponding constraint conditions, construct a transformer thermal aging model, define electric vehicles and distributed photovoltaics as the types of energy access to the active distribution network, and respectively construct a first operation model for electric vehicles and a second operation model for distributed photovoltaics; It should be noted that in this step, first, a radial topology is adopted for the active distribution network, and let represent the node set, where 0 represents the root node. The root node 0 has no parent node, and the leaf nodes have no child nodes. represents the node set except the root node. The set is composed of the indices of the optimization periods. The set E of transformers in the working state is defined as a subset of the line set L.

[0021] In some embodiments, the steady-state branch power flow model of the active distribution network and its constraint conditions can be expressed as: ; where are the active and reactive powers of the line at time t, , are the resistance and reactance of the line respectively, is the square of the current amplitude of the line at time t, , are the squares of the voltage amplitudes of nodes j and i at time t respectively, , are the active and reactive powers of the load of node j at time t respectively, , are the active and reactive powers of the line during the t period, k is the index of the downstream child nodes of node j, is the set composed of the downstream child nodes of node j, s is the element index in the set, is the set of electric vehicles connected to node j during the t period, 、 are the active and reactive power outputs of the electric vehicles at node j respectively, is the set of photovoltaics connected to node j during the t period, 、 are the active and reactive power outputs of the photovoltaics at node j respectively, 、 are the Lagrange multipliers corresponding to the equality constraints, T is the set of time periods, N is the set of nodes, is the set of nodes except the root node, is the unique upstream parent node of node j, 、 are the upper and lower limits of the square of the voltage amplitude respectively, is the upper limit of the square of the current amplitude, L is the set of lines.

[0022] In addition, on the basis of considering the power flow, a transformer thermal aging model is introduced to consider the thermal aging cost of the transformer. The aging acceleration factor of the transformer is related to the hottest spot temperature of the winding and can be expressed by the following linearized approximate formula: ; The hottest spot temperature of the winding can be expressed as: ; The dynamic equation of the top oil temperature is: (9) where, where, is the aging acceleration factor of the transformer at time t, M represents the total number of segments, 、 are the slope and intercept of the th segment respectively, is the hottest spot temperature of the winding at time t, is the lower limit of the temperature range of the th segment, is the upper limit of the temperature range of the th segment, is the top oil temperature at time t, m is a constant, is the temperature rise of the hottest spot temperature of the winding compared with the top oil temperature under the rated load, is the square of the current amplitude at present, is the square of the rated current amplitude, is the Lagrange multiplier corresponding to the constraint, which is used to represent the impact of the load on the transformer life loss in the next working cycle at the end of one working cycle T of the transformer. e is the index of the transformer in the working state, and E is the set of transformers in the working state. is the temperature rise of the top oil temperature compared to the ambient temperature under the rated load. can be defined as the ratio of the square of the current amplitude to the square of the rated current amplitude, that is , where R is the ratio of the load loss to the no-load loss under the rated load. is the transformer oil time constant, and the commonly recommended value is 3h. and n are constants with recommended values of 1 and 0.8 respectively. Since the scheduling period in this paper is 1h, the difference processing can be performed on Equation (9) to obtain: ; where , The calculation formula of is as follows ; where m is a constant with a recommended value of 0.8. Therefore, can be expanded around the value 1 with as the variable to obtain an approximate linear equation. Similarly, can also be approximated in a similar way based on Taylor expansion to obtain: ; Substituting Equation (12) and Equation (13) into Equation (10) and Equation (11) respectively, we can get: ; Substituting Equation (15) into Equation (8), we can get ; According to Equation (14) and Equation (16), the hottest spot temperature of the winding can be calculated. Combining with the formula we can obtain the relationship between the aging acceleration factor and the square of the current amplitude. To ensure the cyclic solvability of the optimal power flow problem, additional constraints are needed, and its Lagrange multiplier represents the impact of the load on the transformer life loss in the next working cycle at the end of one working cycle T of the transformer: ; So far, the transformer thermal aging model is constructed.

[0023] In addition, in this embodiment, for the active distribution network, the access of two types of distributed energy sources, namely electric vehicles and distributed photovoltaics, is considered.

[0024] The first operation model of the electric vehicle can be expressed as follows: ; wherein, is the charging demand of the electric vehicle, is the maximum limit of the active power of the electric vehicle, is the maximum limit of the apparent power of the electric vehicle. Equations (19) and (20) respectively impose maximum limits on the active power and apparent power of the electric vehicle.

[0025] For distributed photovoltaic, its second operating model can be expressed as: ; wherein, is the maximum limit of the active power of the distributed photovoltaic, is the maximum limit of the apparent power of the distributed photovoltaic. Equations (21) and (22) respectively impose maximum limits on the active power and apparent power of the distributed photovoltaic.

[0026] Step S102: Construct an optimization problem model for the network side, EV side, and PV side based on the steady-state branch power flow model, the transformer thermal aging model, the first operating model, and the second operating model; It should be noted that for a given EV / PV scheduling strategy, namely , , , , the active / reactive power balance constraints of each node, namely Equations (1) and (2), are transformed into: ; For the network side, its final objective function is: ; wherein, , , are respectively the active power price, the reactive power unit cost, and the transformer life loss unit cost purchased from the root node, is the active power of line 01 at time t, is the reactive power of line 01 at time t.

[0027] Thus, the network optimization problem model for the network side includes: minimizing the objective function formula , and the constraint conditions include Equations (23)-(24), (3)-(7), (14), (16)-(17).

[0028] For EVs, each EV will adjust its output curve according to the node active / reactive power price ​Thus, the initial objective function of EV is to maximize its own profit. Therefore, the initial objective function of EV is: ; Thus, the EV optimization problem model can include minimizing the objective function , with the constraint condition being Equation - .

[0029] So far, the EV optimization problem model is obtained. In this model, when is negative, EV has the opportunity to sell active and reactive power to the power grid to obtain profit and charge during low electricity price periods to ensure normal use by users.

[0030] For PV, each PV will adjust its output curve according to the node active / reactive power price to maximize its own profit. Therefore, the initial objective function of PV is: ; Thus, the PV optimization problem model includes minimizing the objective function , with the constraint conditions being Equation - Equation .

[0031] So far, we have obtained the PV optimization problem model. In this model, when , let . When , PV can adjust the inverter power factor to provide reactive power to the power grid, thus ensuring .

[0032] So far, the network optimization problem model, the EV optimization problem model, and the PV optimization problem model are obtained.

[0033] Step S103: Define the first decision variables related to the active distribution network and the second decision variables related to electric vehicles and photovoltaics, and generate the optimal power flow problem of the active distribution network and the first optimization problem related to the second decision variables according to the definition results; It should be noted that in this step, define as the first decision variables related to the distribution network. The first decision variables include , , , , , , ; Define as the second decision variables related to electric vehicles and photovoltaics. The second decision variables include , , , . Based on this, the optimal power flow problem of the active distribution network can be written in the following compact form: ; where represents the operating cost of the distribution network, represents the operating cost related to EV / PV. Equation represents the relationship constraint between the decision variables related to the distribution network and the decision variables related to electric vehicles and photovoltaics. In Equation is the feasible region of the first decision variable. In Equation is the feasible region of the second decision variable. In addition, it should be noted that the motivation for the coordinated operation between the ADN operator and the distributed energy operator is to maximize its own profit while safely and stably meeting the load demand, or equivalently, to minimize the operating cost. Solving the traditional optimal power flow problem requires assuming the existence of a non-profit entity and using a centralized optimization algorithm to solve this complex non-convex optimization problem. The present invention will propose a distributed algorithm to solve the optimal power flow problem, without requiring the existence of such a high-level entity, nor requiring the ADN operator to have the ownership or control of the distributed energy. Instead, through the nodal price each distributed energy operator is incentivized to cooperate with the ADN operator. Each distributed energy operator optimizes its own profit based on the nodal price broadcast by the ADN operator and reports the adjusted output curve to the ADN operator. The ADN operator re-optimizes the distribution network power flow according to the latest output situation received, and thus faces the following first optimization problem: ; where represents the value of the decision variable known to be related to the second decision variable, is the nodal price matrix, , is the matrix that aggregates the nodal active power prices of all nodes in all time periods, is the matrix that aggregates the nodal reactive power prices of all nodes in all time periods. A, B, and D are the coefficient matrices of the equality constraints related to the second decision variable in the steady-state branch power flow model, satisfies the relevant conditions. Combining Equations (28)-(31) and the optimal values of the distribution network decision variables , then there is the following optimization problem for y: ; ​​It should be noted that when the dual decomposition algorithm and the alternating direction method of multipliers (ADMM) do not converge, the equality constraint cannot be satisfied. Therefore, the solution obtained is a solution that does not satisfy the security constraint and is not executable. Compared with the commonly used dual decomposition algorithm and ADMM algorithm, constructing the first optimization problem ensures that the equality constraint can be satisfied in each iteration process. This enables the suboptimal solution obtained by the algorithm to be used as a scheduling instruction even if it is interrupted before convergence.

[0034] Since the dual variables obtained by solving equations (32)-(34) correspond to the gradient value at . Therefore, equations (28)-(31) can be solved using an iterative method. This iterative method can update the variable y using the gradient obtained by solving equations (32)-(34). Here, the proximal algorithm is used to update the variable y. Let represent the value at the -th iteration. Given , solve the first optimization problem; then obtain the optimization problem regarding y based on the first optimization problem and solve the optimization problem regarding y to obtain : ; Let , and can be obtained by solving equations (32)-(34). is a positive scalar parameter.

[0035] Then, for the given , , the final objective function on the EV side is: ; For the given , , the final objective function on the PV side is: .

[0036] Step S104: Introduce a reverse inequality function for the constraint condition, linearly process the reverse inequality function, and introduce a penalty term to obtain a second optimization problem; It should be noted that in this embodiment, the constraint condition corresponds to equation (4), and equation (4) adopts the constraint representation of second-order cone relaxation. This non-exact relaxation may lead to providing incorrect price signals. Here, the error of the k-th iteration of the non-exact relaxation is defined is: ; Therefore, in order to ensure the equation holds, a reverse inequality function needs to be added: ; This equation is equivalent to: ; Since the inequality (43) is too complex, linearization can be considered for the function on the right side of the inequality sign, and a penalty term is introduced. Therefore, there is: ; Meanwhile, the penalty term can be imposed with the weight factor of the m-th inner loop. By continuously adjusting the weight factor and solving the following second optimization problem, the relaxation error can be continuously reduced : ; The constraint conditions of the second optimization problem include equations (23)-(24), equations (3)-(7), equation (14), equations (16)-(17), equations (44)-(45).

[0037] When the error is less than or equal to a pre-set error tolerance, the constraint equation (4) in the network optimization problem model needs to be replaced by an equation to obtain an operating point that follows the law of conservation of energy: ;

[0038] In summary, the second-order cone relaxation commonly introduced for the DistFlow model to achieve relaxation of the non-convex equality constraint of apparent power is an inexact relaxation, which has a certain error. Therefore, a reverse inequality is considered to be added, and linearization is designed for this reverse inequality and a penalty term is introduced. At the same time, an inner loop is designed to gradually reduce the relaxation error.

[0039] Step S105: Recursively solve the optimization problem models of the network side, EV side, and PV side according to the improved solution algorithm.

[0040] It should be noted that in some embodiments, the specific process of the improved solution algorithm is as follows: Step 1: Starting from , given an initial scheduling strategy, including , , , , set the error tolerance , the iteration time limit ; Step 2: Solve the network optimization problem model on the network side according to the given initial scheduling strategy. The network optimization problem model on the network side includes: solving the final objective function on the network side, that is, minimizing Equation , and the constraint conditions include Equations (23)-(24), (3)-(7), (14), (16)-(17); Step 2.1: If the constraint condition Equation (4) is an active constraint, obtain the correct and , and enter Step 3; Step 2.2: If the constraint condition is an inactive constraint, set the initial number of inner loop iterations ; Step 2.3: Solve the problem model with the second optimization problem, that is, Equation (46) as the objective function and Equations (23)-(24), (3)-(7), (14), (16)-(17), (44)-(45) as the constraint conditions, and judge the error in the k-th iteration is greater than ; Step 2.4: If , let , and return to Step 2.3 to continue solving; Step 2.5: If , solve the new network optimization problem model to obtain and , and enter Step 3. The new network optimization problem model is obtained by replacing Equation (4) in the network optimization problem model on the network side with Equation (47); Step 3: From the obtained and , separately solve the network optimization problem model on the EV side. The network optimization problem model on the EV side includes: minimizing the final objective function on the EV side, that is, minimizing Equation (39), and the constraint conditions include Equations (18)-(20); and separately solve the network optimization problem model on the PV side. The network optimization problem model on the PV side includes: minimizing the final objective function on the PV side, that is, minimizing Equation (40), and the constraint conditions include Equations (21)-(22), to obtain the scheduling strategy under the current iteration, and judge whether the scheduling strategy output in the current iteration meets the requirements or whether the current iteration reaches the iteration time; Step 4: If the requirements are met or the iteration time is reached, the iteration ends. If the requirements are not met and the iteration time is not reached, use the scheduling strategy output in the previous iteration as the new given scheduling strategy and return to Step 2. Meeting the requirements means that the obtained scheduling strategy is feasible.

[0041] Compared with the prior art, the present invention has the following advantages: 1. By constructing a steady-state branch power flow model, a transformer thermal aging model, and operation models for electric vehicles and distributed photovoltaics of the active distribution network, and based on these models, an optimization problem model covering the network side, EV side, and PV side is constructed. At the same time, decision variables on different sides are defined and transformed into optimization problems. Then, special function processing and linearization are performed on the constraint conditions and penalty terms are introduced to form the final optimization problem. Finally, an improved solution algorithm is used for recursive solution. This hierarchical modeling and optimization solution method naturally fits the distributed computing architecture, and different models and optimization problems can be processed in parallel by different computing nodes in the distributed computing environment, thus realizing distributed computing. And in the processing of each link, through reasonable data partitioning and model abstraction, only key parameters required for optimization solution are transmitted when necessary, avoiding direct interaction of sensitive data, and ensuring the needs of personal privacy and independent computing of each participating party.

[0042] 2. On the basis of considering the power purchase cost, the present invention also considers the transformer aging cost. And, for the error caused by second-order cone relaxation, a reverse inequality is established, and through linearization processing and inner-loop iteration, it is easy to optimize and can gradually reduce the relaxation error. At the same time, this method can ensure the executability of the temporary solutions obtained during the iteration process, and also enables dynamic adjustment of the target parameters and constraint conditions during each iteration process to cope with the real-time changing system state. When a violation is observed, the parameters of the optimization problem can be adjusted at any time. In actual engineering, dispatchers will follow a similar iterative update process while ensuring the feasibility of the solution. Check the dispatch plan. If it is found that some unformulated constraint conditions are not satisfied, these constraint conditions are incorporated into the standardized optimization problem, or the original parameters / constraint conditions are adjusted to ensure feasibility. In day-ahead dispatch, this process will be repeated continuously until a feasible solution is found or the time is exhausted.

[0043] As Figure 2 shown, the present invention also proposes an active distribution network distributed power flow calculation system, and the system includes: A power flow model construction module 10, configured to construct a steady-state branch power flow model of the active distribution network and its corresponding constraint conditions, construct a transformer thermal aging model, define electric vehicles and distributed photovoltaics as the energy access types of the active distribution network, and respectively construct a first operation model and a second operation model for electric vehicles and distributed photovoltaics; An optimization problem model construction module 20, configured to construct an optimization problem model for the network side, EV side, and PV side based on the steady-state branch power flow model, the transformer thermal aging model, the first operation model, and the second operation model; The decision variable definition module 30 is used to define the first decision variables related to the active distribution network and the second decision variables related to electric vehicles and photovoltaics, and generate the optimal power flow problem of the active distribution network and the first optimization problem related to the second decision variables according to the definition results; The optimization problem construction module 40 is used to introduce a reverse inequality function for the constraint conditions, linearly process the reverse inequality function, and introduce a penalty term to obtain the second optimization problem; The recursive solution module 50 is used to recursively solve the optimization problem models on the network side, EV side, and PV side according to the improved solution algorithm.

[0044] On the other hand, the present invention also proposes a storage medium, on which one or more programs are stored, and when the program is executed by a processor, the above-mentioned active distribution network distributed power flow calculation method is implemented.

[0045] On the other hand, the present invention also proposes an electronic device, including a memory and a processor, where the memory is used to store a computer program, and the processor is used to execute the computer program stored on the memory to implement the above-mentioned active distribution network distributed power flow calculation method.

[0046] Those skilled in the art can understand that the logic and / or steps represented in the flowchart or described in other ways herein, for example, can be considered as a defined sequence list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other systems that can fetch instructions from the instruction execution system, apparatus, or device and execute the instructions), or used in combination with these instruction execution systems, apparatus, or devices. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.

[0047] More specific examples (nonexhaustive list) of computer-readable media include the following: an electrical connection part with one or more wirings (electronic device), a portable computer disk cartridge (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other media, then editing, interpreting, or processing it in other suitable ways as necessary, and then storing it in a computer memory.

[0048] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, any one or a combination of the following techniques well known in the art can be used: discrete logic circuits having logic gate circuits for implementing logical functions on data signals, application specific integrated circuits having appropriate combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.

[0049] Although the embodiments of the present invention have been described in detail above, it will be apparent to those skilled in the art that various modifications and changes can be made to these embodiments. However, it should be understood that such modifications and changes are all within the scope and spirit of the present invention as described in the claims. Moreover, the present invention described herein can have other embodiments and can be implemented or realized in various ways.

Claims

1. A distributed power flow calculation method for an active distribution network, characterized in that The method includes: Constructing a steady-state branch power flow model of the active distribution network and its corresponding constraint conditions, constructing a transformer thermal aging model, defining electric vehicles and distributed photovoltaics as the types of energy access to the active distribution network, and respectively constructing a first operation model for electric vehicles and a second operation model for distributed photovoltaics; Based on the steady-state branch power flow model, the transformer thermal aging model, the first operation model, and the second operation model, constructing an optimization problem model for the network side, the EV side, and the PV side; Defining a first decision variable related to the active distribution network and a second decision variable related to electric vehicles and photovoltaics, and generating an optimal power flow problem for the active distribution network and a first optimization problem related to the second decision variable according to the definition results; Introducing a reverse inequality function for the constraint conditions, linearly processing the reverse inequality function, and introducing a penalty term to obtain a second optimization problem; Recursively solving the optimization problem models for the network side, the EV side, and the PV side according to an improved solution algorithm.

2. The active distribution network distributed power flow calculation method according to claim 1, characterized in that, The steps of constructing a steady-state branch power flow model of the active distribution network and its corresponding constraint conditions include: Constructing a steady-state branch power flow model according to the following formula: ； Among them, are the active and reactive powers of the line during the t period, and are the resistance and reactance of the line respectively, is the square of the current amplitude of the line during the t period, and are the squares of the voltage amplitudes of nodes j and i during the t period respectively, and are the active and reactive powers of the load of node j during the t period respectively, and are the active and reactive powers of the line during the t period. k is the index of the downstream child nodes of node j, is the set composed of the downstream child nodes of node j, s is the element index in the set, is the set of electric vehicles connected to node j during the t period, and are the active and reactive outputs of the electric vehicles at node j respectively, is the set of photovoltaics connected to node j during the t period, and are the active and reactive outputs of the photovoltaics at node j respectively, and are the Lagrange multipliers corresponding to the equality constraints. T is the set of time periods, N is the set of nodes, is the set of nodes except the root node, is the unique upstream parent node of node j; Constructing constraint conditions according to the following formula: ； Among them, and are the upper and lower limits of the square of the voltage amplitude respectively, is the upper limit of the square of the current amplitude, L is the set of lines, and T is the set composed of the indices of the optimization time periods.

3. The active distribution network distributed power flow calculation method according to claim 2, wherein, The steps of constructing a transformer thermal aging model, defining electric vehicles and distributed photovoltaics as the types of energy access to the active distribution network, and respectively constructing a first operation model for electric vehicles and a second operation model for distributed photovoltaics include: Constructing a transformer thermal aging model according to the following formula: ； Among them, is the aging acceleration factor of the transformer under the t time period, M represents the total number of segments, , are respectively the slope and intercept of the th segment, is the hottest spot temperature of the winding under the t time period, is the lower limit of the temperature range of the th segment, is the upper limit of the temperature range of the th segment, is the top oil temperature under the t time period, m is a constant, is the temperature rise of the hottest spot temperature of the winding compared to the top oil temperature under rated load, is the square of the current amplitude at present, is the square of the rated current amplitude, is the Lagrange multiplier corresponding to the constraint, used to represent the influence of the load on the life loss of the transformer in the next working cycle at the end of a working cycle T of the transformer. e is the index of the transformer in the working state, and E is the set of transformers in the working state; Constructing a first operation model according to the following formula: ； Among them, is the charging demand of the electric vehicle, is the maximum limit of the active power of the electric vehicle, is the maximum limit of the apparent power of the electric vehicle; Constructing a second operation model according to the following formula: ； Among them, is the maximum limit of the active power of distributed photovoltaics, is the maximum limit of the apparent power of distributed photovoltaics.

4. The active distribution network distributed power flow calculation method according to claim 3, characterized in that The steps of constructing an optimization problem model for the network side, the EV side, and the PV side based on the steady-state branch power flow model, the transformer thermal aging model, the first operation model, and the second operation model include: For the network side, its final objective function is: ； Among them, , , are the active power price, the reactive power unit cost, and the unit cost of transformer life loss purchased from the root node, respectively, is the active power of line 01 at time period t, is the reactive power of line 01 at time period t; For the EV side, its initial objective function is: ； For the PV side, its initial objective function is: ； Among them, is the active power price of the node at time t, is the reactive power price of the node at time t.

5. The active distribution network distributed power flow calculation method according to claim 4, characterized in that The steps of defining a first decision variable related to the active distribution network and a second decision variable related to electric vehicles and photovoltaics, and generating an optimal power flow problem for the active distribution network and a first optimization problem related to the second decision variable according to the definition results include: Definition is the first decision variable related to the distribution network, and the first decision variable includes , , , , , , ; Definition is the second decision variable related to electric vehicles and photovoltaics, and the second decision variable includes , , , ; Constructing a first optimization problem according to the following formula: ； Among them, represents the operating cost of the distribution network, is the feasible region of the first decision variable, is the feasible region of the second decision variable, is the nodal price matrix, and A, B, and D are all coefficient matrices of the equality constraints related to the second decision variable in the steady-state branch power flow model, is the value of the decision variable known to be related to the second decision variable, satisfies the relevant conditions; Given , solve the first optimization problem; An optimization problem regarding y is obtained based on the first optimization problem, and the optimization problem regarding y is solved to obtain : ； Among them, and are the values obtained by the k-th and (k + 1)-th iterative solutions respectively, is the variable value that minimizes the objective function, represents the operating cost related to electric vehicles and photovoltaics, is the transpose of the nodal electricity price matrix at the k-th iteration; Definition and are the active and reactive power outputs of the photovoltaic system at time period t during the k-th iteration. and are the active and reactive power outputs of the electric vehicle at time period t during the k-th iteration, respectively. Then, the final objective function on the EV side is as follows: ； The final objective function of the PV side is: ； wherein, is the positive scalar parameter at the k-th iteration, is the active power price of the node at the t-th period during the k-th iteration, is the reactive power price of the node at the t-th period during the k-th iteration.

6. The active distribution network distributed power flow calculation method according to claim 5, characterized in that The steps of introducing a reverse inequality function for the constraint conditions, linearly processing the reverse inequality function, and introducing a penalty term to obtain a second optimization problem include: The expression of the introduced reverse inequality function is as follows: ； Linearly processing the reverse inequality function and introducing a penalty term to obtain: ； Among them, , is the line obtained in the k-th iteration for the active and reactive powers during the t period, is the square of the voltage amplitude of node i obtained in the k-th iteration during the t period, is the line obtained in the k-th iteration for the square of the current amplitude during the t period, is the penalty term; The penalty term can be weighted by a weight factor to obtain a second optimization problem: .

7. The active distribution network distributed power flow calculation method according to claim 6, characterized in that The steps of recursively solving the optimization problem models for the network side, the EV side, and the PV side according to an improved solution algorithm include: Step 1, starting from , given an initial scheduling strategy, including , , , , set the error tolerance , and the iteration time limit ; Step 2: Solving the final objective function of the network side according to the given initial scheduling strategy, and determining whether the constraint conditions are binding; Step 2.1: If the constraint condition is an active constraint, obtain the correct and , and proceed to Step 3; Step 2.2, if the constraint condition is an inactive constraint, set the initial number of inner loop iterations ; Step 2.3, solve the second optimization problem and determine whether the error at the k-th iteration is greater than ; Step 2.4, if , let , return to Step 2.3 to continue the solution; Step 2.5, if , solve the new network optimization problem model to obtain and , enter Step 3. The new network optimization problem model includes the following expressions: ； Step 3: From the obtained and , solve the final objective functions on the EV side and PV side, obtain the scheduling strategy under the current iteration, and determine whether the scheduling strategy output in the current iteration meets the requirements or whether the current iteration reaches the iteration time; Step 4: If the requirements are met or the iteration time is reached, the iteration ends. If the requirements are not met and the iteration time is not reached, the scheduling strategy output in the previous iteration is used as the new given scheduling strategy, and Step 2 is returned.

8. A distributed power flow calculation system for an active distribution network, characterized in that, The system includes: A power flow model construction module, configured to construct a steady-state branch power flow model of the active distribution network and its corresponding constraint conditions, construct a transformer thermal aging model, define electric vehicles and distributed photovoltaics as the types of energy access to the active distribution network, and respectively construct a first operation model for electric vehicles and a second operation model for distributed photovoltaics; An optimization problem model construction module, configured to construct an optimization problem model for the network side, the EV side, and the PV side based on the steady-state branch power flow model, the transformer thermal aging model, the first operation model, and the second operation model; A decision variable definition module, configured to define a first decision variable related to the active distribution network and a second decision variable related to electric vehicles and photovoltaics, and generate an optimal power flow problem for the active distribution network and a first optimization problem related to the second decision variable according to the definition result; An optimization problem construction module, configured to introduce a reverse inequality function for the constraint conditions, perform linear processing on the reverse inequality function, and introduce a penalty term to obtain a second optimization problem; A recursive solution module, configured to recursively solve the optimization problem models for the network side, the EV side, and the PV side according to an improved solution algorithm.

9. A storage medium, characterized in that, The storage medium stores one or more programs, which when executed by a processor implement the active distribution network distributed power flow calculation method according to any one of claims 1-7.

10. An electronic device, characterized in that, The electronic device includes a memory and a processor, wherein: The memory is used for storing a computer program; The processor is configured to implement the active distribution network distributed power flow calculation method according to any one of claims 1-7 when executing the computer program stored on the memory.

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