A power distribution network hierarchical distributed optimization method considering spatial and temporal distribution of charging load

Abstract

This invention discloses a hierarchical distributed optimization method for distribution networks that considers the spatiotemporal distribution of charging loads. Belonging to the field of distribution network operation optimization technology, it solves the problems of existing distribution networks' incomplete consideration of the characteristics of hierarchical operation based on voltage levels and lack of consideration for the coupled operation of transportation networks and distribution networks. The invention includes the following steps: S1: Establishing a multi-layered collaborative operation architecture for transportation-medium-low voltage distribution networks; S2: Simulating charging loads; S3: Establishing a dynamic economic dispatch model for medium-low voltage distribution networks; S4: Solving using a distributed algorithm. This invention improves the traditional centralized serial computing mode to a distributed multi-machine parallel computing mode, effectively improving the system's computational efficiency. Simulation tests demonstrate the effectiveness and superiority of the proposed strategy.

Description

Technical Field

[0001] This invention relates to the field of distribution network operation optimization technology, and specifically to a hierarchical distributed optimization method for distribution networks that takes into account the spatiotemporal distribution of charging load. Background Technology

[0002] In recent years, against the backdrop of countries worldwide vigorously promoting the low-carbon transformation of energy systems, a large number of distributed power sources have been connected to distribution networks. Simultaneously, electric vehicles, as an important mode of transportation for reducing carbon emissions, have experienced rapid development, while also strengthening the coupling between transportation networks and distribution networks. Therefore, with the large-scale integration of source-side distributed generation (DG) and load-side electric vehicles (EVs), the distributed characteristics of distribution networks are becoming increasingly apparent, making traditional centralized control methods insufficient for flexible and effective control of distribution networks containing various distributed resources. Therefore, conducting research on hierarchical distributed optimization operation of distribution networks that considers the spatiotemporal distribution of electric vehicle charging loads is of great significance.

[0003] Currently, most existing research on EV charging load modeling focuses on both temporal and spatial dimensions. Some studies use statistical methods to obtain the probability distribution functions of EV initiation charging time and daily mileage, and then use Monte Carlo simulations to generate EV charging scenarios. However, these studies only analyze EV charging behavior from a temporal perspective, neglecting the spatial distribution characteristics of EV charging load. Other studies employ artificial intelligence algorithms such as deep learning to solve the EV charging load prediction problem, but fail to consider the impact of actual traffic networks and road flow on vehicle traffic. Still others establish dynamic vehicle transfer models to describe the impact of real-time traffic changes on vehicle traffic, but these studies lack sufficient analysis of user travel characteristics.

[0004] On the other hand, considering the distributed nature of distribution networks, scholars worldwide have conducted a series of studies on distributed optimization of distribution networks. Some studies have used distributed optimization algorithms to achieve voltage control in distribution networks and effectively improve voltage quality. Other studies have used distributed algorithms to solve distributed energy management problems in distribution networks. Still others have improved the solution speed of distribution network optimization problems by modifying distributed algorithms. However, these studies do not comprehensively consider the characteristics of distribution networks operating hierarchically according to voltage levels, and also lack consideration for the coupled operation of transportation networks and distribution networks. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a hierarchical distributed optimization method for distribution networks that takes into account the spatiotemporal distribution of charging load. Its purpose is to realize hierarchical decoupled calculation of medium and low voltage distribution networks, improve the traditional centralized serial calculation mode to a distributed multi-machine parallel calculation mode, effectively improve the system's calculation efficiency, and demonstrate the effectiveness and superiority of the proposed strategy through simulation tests.

[0006] The technical solution adopted in this invention is as follows:

[0007] A hierarchical distributed optimization method for distribution networks that takes into account the spatiotemporal distribution of charging load includes the following steps:

[0008] S1: Establish a multi-level collaborative operation architecture for transportation-medium and low voltage distribution networks. Based on the current operating characteristics of urban transportation networks and distribution networks, the scenario of coupled operation of transportation networks and distribution networks, and the characteristics of distribution networks operating in layers according to voltage levels, establish a multi-level collaborative operation architecture for transportation-medium and low voltage distribution networks.

[0009] S2: Simulate charging load. Based on the multi-layer collaborative operation architecture of transportation-medium and low voltage power distribution network, firstly, a travel probability model of EV residents is established; secondly, considering road congestion, a real-time vehicle dynamic transfer model is established; then, based on actual road network data, an abstract urban traffic network model is established; the three models are run together to simulate the charging load generated by EVs during a day's travel.

[0010] S3: Establish a dynamic economic dispatch model for medium and low voltage distribution networks. Based on the charging load and operation of medium and low voltage distribution networks in S2, and according to the power flow distribution characteristics of the distribution network, an improved power flow model is proposed. Considering the operating characteristics of new energy units, energy storage systems, distributed power sources and EV charging stations, a dynamic economic dispatch model for medium and low voltage distribution networks is established.

[0011] S4: A distributed algorithm is used to solve the problem. Based on the dynamic economic dispatch model of the medium and low voltage distribution network obtained in S3, a hierarchical distributed optimization solution strategy for the medium and low voltage distribution network is proposed.

[0012] Preferably, the establishment of a multi-level collaborative operation architecture for the transportation-distribution network in S1 specifically involves:

[0013] Considering the respective operating characteristics of urban transportation networks and distribution networks, as well as the characteristics of the coupled operation of urban transportation networks and distribution networks, a multi-level collaborative operation architecture of transportation-medium and low-voltage distribution networks is established. First, EVs drive in urban transportation networks and generate charging loads. Subsequently, the charging loads are connected to the low-voltage distribution network, which integrates local distributed resources and absorbs new energy sources when the load is met. Then, when the power supply capacity of the low-voltage distribution network is insufficient or excessive, it is connected to the medium-voltage distribution network for power transmission.

[0014] Preferably, the specific steps for establishing the travel probability model for EV residents in S2 are as follows:

[0015] To describe the probability distribution characteristics of EV travel times, based on the NHTS2017 dataset, the first departure time of EVs under all travel demands was statistically analyzed, and the generalized extreme value distribution was used to describe the probability distribution of EV travel times; the obtained probability density function is shown in the following equation:

[0016]

[0017] In the formula, μ, σ, and ξ represent the mean, standard deviation, and shape parameter of GEV, respectively, z is an intermediate variable, and t is time.

[0018] Preferably, the establishment of the real-time vehicle dynamic transfer model in S2 specifically involves:

[0019] To describe the traffic network in which EVs actually travel, a graph theory method is used to abstractly model the actual traffic network, resulting in a simplified directed graph of the road network, as shown in the following equation:

[0020]

[0021]

[0022] Wherein, the adjacency matrix D represents the connection relationship between two traffic network nodes, d ij This represents the distance between two nodes, l ij Indicates the length of the road directly connecting node i and node j, while inf indicates that there is no road directly connecting node i and node j.

[0023] Preferably, the establishment of the city's traffic network model in S2 specifically involves:

[0024] The Dijstra algorithm is adopted, with the shortest passage time of EVs as the guiding objective. Its expression is as follows:

[0025] minW R,a→b =∑s ij (t)

[0026] Where a and b correspond to the departure node and destination node, respectively; W R,a→b Let R represent the travel time required from node a to node b, and let R represent the set of all possible roads from node a to node b.

[0027] Meanwhile, based on research by the U.S. Highway Bureau, the relationship between vehicle travel time and traffic volume is shown in the following formula.

[0028]

[0029] Among them, t ij and t ij,0c represents the time required for an EV to travel on a road under current traffic flow and zero traffic flow conditions. ij x ij 、 and v ij These represent the road's maximum capacity, current traffic flow, and average road speed, respectively.

[0030] Preferably, the specific process of S3 is as follows:

[0031] The traditional DistFlow power flow model is simplified by two simplification assumptions:

[0032] 1) The power transmitted through the lines in the distribution network is much greater than the power lost along the lines;

[0033] 2) The voltage at a single node in the distribution network is much greater than the voltage difference between two nodes;

[0034] The improved power flow model is shown in the following equation:

[0035]

[0036] in U i =V 2i V1 is the balancing node voltage, P ij and Q ij Let r represent the active and reactive power transmitted in branch ij, respectively. k:j→k represents the set of terminal nodes for all lines with node j as the starting point. ij and x ij p represents the resistance and reactance on line ij, respectively. j,l and q j,l It represents the active and reactive power of the load demand at node j, p j,g and q j,g ε represents the active and reactive power generated by the generator at node j, and ε represents the allowable voltage deviation of the distribution network, which is generally set to 0.05pu.

[0037] Secondly, the objective function for the optimal scheduling of the medium-voltage distribution network is to minimize the sum of the generation cost of distributed power sources, the network loss cost of the medium-voltage distribution network, and the interaction cost with the low-voltage distribution network. The objective function is as follows:

[0038] minF M =F G,M -F sell +F loss,M

[0039] Where F M It is the total operating cost of the medium-voltage distribution network, F G,M It is the generation cost of distributed power sources in medium-voltage distribution networks, F sellThis refers to the revenue generated from the sale of electricity from the medium-voltage distribution network to the low-voltage distribution network, F. loss,M This refers to the network loss cost of the medium-voltage distribution network;

[0040]

[0041]

[0042]

[0043] Where T is the scheduling period, P G,i (t) represents the output power of the i-th distributed power source during time period t, and n represents the number of distributed power sources in the medium-voltage distribution network. j,L λ(t) represents the power sold by the medium-voltage distribution network to the j-th low-voltage distribution network during time period t. When its value is positive, it indicates that the medium-voltage distribution network sells electricity to the low-voltage distribution network. When its value is negative, it indicates that the medium-voltage distribution network purchases electricity from the low-voltage distribution network. λ(t) is the base electricity price during time period t, and m represents the number of low-voltage distribution networks.

[0044] The objective function for optimizing the scheduling of low-voltage distribution networks is similar to that of medium-voltage distribution networks, and its expression is shown in the following formula.

[0045] minF S =F G,s +F buy +F loss,s

[0046] Meanwhile, the optimized operation of medium and low voltage distribution networks also needs to meet the following constraints:

[0047] (1) Power balance constraints of the system:

[0048]

[0049] (2) Upper and lower limits of distributed power source output power constraints:

[0050] P G,i,min ≤P G,i (t)≤P G,i,max

[0051] (3) Ramp-up constraints on the output power of distributed power sources:

[0052] -R≤P G,i (t)-P G,i (t-1)≤R

[0053] (4) Operational constraints of energy storage systems:

[0054]

[0055] Among them, P G,i (t), P PV(t), P WT (t), P dis,ess (t), P Load (t), P ch,ess (t) and P ch,ev (t) represents the output power of the i-th distributed power source, photovoltaic, wind turbine, discharge and charge power of energy storage, and charge power of EV, respectively. G,i,max ,P G,i,min These represent the maximum and minimum output power of the distributed power source, respectively. R represents the maximum output power increment of the distributed power source. E(t) represents the real-time capacity of the energy storage. max and E min U represents the upper and lower limits of energy storage capacity. ch (t) and U dis (t) represents the state of charge / discharge quantity, which takes the value of 0 or 1.

[0056] Preferably, the specific process of S4 is as follows:

[0057] Considering the characteristics of the ADMM distributed algorithm and the hierarchical operation of medium and low voltage distribution networks according to voltage levels, a hierarchical decoupling optimization architecture for medium and low voltage distribution networks is established.

[0058] The virtual boundary variable between low-voltage distribution network i and medium-voltage distribution network j is X. ij '={P ij ',Q ij ',V ij The virtual boundary variable between medium-voltage distribution network j and low-voltage distribution network i is X. i’j ={P i’j Q i’j V i’j The reference value for the virtual boundary variable in the current iteration is the average value of the virtual boundary variable in the previous iteration, and its expression is as follows:

[0059]

[0060] Where m is the number of iterations, X i’j,m+1,ref and X ij’,m+1,ref X is the virtual boundary variable reference value for medium-voltage distribution network j and low-voltage distribution network i in the (m+1)th iteration. i’j,m and X ij’,m It is the virtual boundary variable for medium-voltage distribution network j and low-voltage distribution network i in the m-th iteration;

[0061] The virtual boundary variables of medium-voltage distribution network j and low-voltage distribution network i are updated respectively. The update rule is to find the variable values ​​that minimize the augmented Lagrangian function of the medium- and low-voltage distribution network optimization scheduling model. The expression is as follows:

[0062] X ij′,m+1 =argminLij′ (X ij′,m ,X ij′,m,ref ,λ ij′,m )

[0063] X i′j,m+1 =argmin L i′j (X i′j,m ,X i′j,m,ref ,λ i′j,m )

[0064]

[0065]

[0066] The updated Lagrange multipliers are expressed as follows:

[0067] λ ij′,m+1 =λ ij′,m +(X ij′,m -X ij′,m,ref )

[0068] λ i′j,m+1 =λ i′j,m +(X i′j,m -X i′j,m,ref )

[0069] The convergence criterion for the ADMM algorithm is that the residuals of the virtual boundary variables in medium and low pressure converge to 0, as shown below:

[0070]

[0071] Among them, L i’j (X i’j,m ,X i’j,m,ref ,λ i’j,m ) and L ij’ (X ij’,m ,X ij’,m,ref ,λ ij’,m ) represent the augmented Lagrangian functions corresponding to the optimal scheduling models of medium-voltage distribution network j and low-voltage distribution network i, respectively, ρ is the penalty coefficient of the ADMM algorithm, and λ i’j,m and λ ij’,m These represent the Lagrange multipliers of medium- and low-voltage distribution networks, which are mainly composed of active power, reactive power, and voltage on the interconnecting lines of the medium- and low-voltage distribution networks; λ ij’,m ={λ P,ij',m ,λ Q,ij',m ,λ V,ij',m}, λ i’j,m ={λ P,i'j,m ,λ Q,i'j,m ,λ V,i'j,m}

[0072] In summary, the present invention has the following beneficial effects:

[0073] (1) This invention establishes a hierarchical distributed optimization method for medium and low voltage distribution networks, taking into account the time distribution characteristics of EV charging load, the impact of actual traffic network and road traffic on vehicle passage, and user travel characteristics.

[0074] (2) Based on the ADMM hierarchical distributed optimization algorithm, this invention realizes hierarchical decoupling calculation of medium and low voltage distribution networks, improves the traditional centralized serial calculation mode into a distributed multi-machine parallel calculation mode, and effectively improves the system's calculation efficiency.

[0075] (3) The effectiveness and superiority of the proposed strategy are demonstrated by simulation tests. Attached Figure Description

[0076] The present invention will be described by way of example and with reference to the accompanying drawings, wherein:

[0077] Figure 1 This is a schematic diagram of the strategy process of the present invention;

[0078] Figure 2 This is a schematic diagram of the multi-level collaborative operation architecture of transportation and power grid according to the present invention;

[0079] Figure 3 This is a schematic diagram of the simulation model architecture of the present invention;

[0080] Figure 4 This is a schematic diagram of the spatiotemporal distribution of EV charging load according to the present invention;

[0081] Figure 5 This is a schematic diagram of the active and reactive power convergence results of the medium and low voltage distribution network according to the present invention.

[0082] Figure 6 This is a schematic diagram of the optimized scheduling results of the medium and low voltage power distribution network according to the present invention;

[0083] Figure 7 This is a schematic diagram of the voltage distribution at medium and low voltage distribution network nodes according to the present invention;

[0084] Figure 8 This is a schematic diagram comparing the voltage at distribution network nodes and network losses before and after optimization according to the present invention. Detailed Implementation

[0085] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0086] In the description of the embodiments of this application, it should be noted that the terms "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application. In addition, the terms "first," "second," and "third," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0087] The following is combined Figures 1-8 The present invention will be described in detail below.

[0088] 1. Spatiotemporal distribution prediction of EV charging load.

[0089] First, to describe the probability distribution characteristics of EV travel times, this invention uses the NHTS2017 dataset and the BPR function to statistically analyze the first departure time of EVs under all travel demands, and then uses the generalized extreme value distribution (GEV) to describe the probability distribution of EV travel times. The fitting results are as follows: Figure 3 As shown, the obtained probability density function is as follows:

[0090]

[0091] In the formula, μ, σ and ξ represent the mean, standard deviation and shape parameter of GEV, respectively, z is an intermediate variable and t is time, and the best fit is achieved when μ = 805.9612, σ = 241.0934 and ξ = 0.0265.

[0092] As can be seen from the figure, compared with the normal distribution, the generalized extreme value distribution can be used to better fit the morning peak travel characteristics of EVs. The R-value obtained by comparing the goodness of fit between GEVs and the normal distribution is shown in the figure. 2The values ​​are 0.9425 and 0.8763 respectively, indicating that the GEV distribution has a better fit.

[0093] Secondly, to describe the destination distribution characteristics of EV trips, this invention uses an EV trip chain model to describe a single EV trip. Furthermore, statistical analysis of NHTS2017 data reveals that a large number of EV trip chains begin and end in residential areas. Therefore, this invention sets a complete EV trip chain as starting from a residential area and ending when that residential area becomes the next sampling destination.

[0094] Then, to describe the traffic network in which the EV actually travels, this invention uses graph theory to abstractly model the actual traffic network, obtaining its simplified directed graph. Here, the adjacency matrix D represents the connection relationship between two traffic network nodes, and d... ij This represents the distance between two nodes, l ij Indicates the length of the road directly connecting node i and node j, while inf indicates that there is no road directly connecting node i and node j.

[0095]

[0096]

[0097] Subsequently, for path planning of EVs, this invention adopts Dijstra's algorithm and uses the shortest travel time of EVs as the guiding objective, the expression of which is as follows:

[0098] minW R,a→b =∑s ij (t)

[0099] Where a and b correspond to the departure node and destination node, respectively. W R,a→b Let R represent the travel time required from node a to node b, and let R represent the set of all possible roads from node a to node b.

[0100] Meanwhile, since the degree of road congestion affects the travel speed and travel time of EVs, in order to quantitatively characterize the impact of this congestion effect on transportation, this invention is based on the research of the U.S. Bureau of Public Roads (BPR) and the relationship between vehicle travel time and traffic flow, as shown in the following formula.

[0101]

[0102] Among them, t ij and t ij,0 c represents the time required for an EV to travel on a road under current traffic flow and zero traffic flow conditions. ij xij 、 and v ij These represent the road's maximum capacity, current traffic flow, and average road speed, respectively.

[0103] Finally, based on the established model and the simulation process of EV charging load, the spatiotemporal distribution information of charging load generated under the daily travel load of EV is simulated.

[0104] 2. Dynamic economic dispatch model for medium and low voltage distribution networks

[0105] First, considering that the traditional DistFlow power flow model contains quadratic terms, making the optimization problem non-convex, and distributed optimization algorithms struggle to obtain the global optimal solution for non-convex problems. Therefore, it is necessary to transform the DistFlow power flow model into a convex optimization problem. Based on this, this invention adopts a reasonable simplification method to solve this problem. Its simplification assumptions mainly include two points: (1) The power transmitted through the lines in the distribution network is much greater than the power lost on the lines; (2) The voltage of a single node in the distribution network is much greater than the voltage difference between two nodes. Based on the above two assumptions, the improved power flow model can be obtained as shown in the following equation:

[0106]

[0107] in U i =V 2i V1 is the balance node voltage, V ref This is the reference value for V1, V j P is the voltage amplitude at node j. ij and Q ij Let r represent the active and reactive power transmitted in branch ij, respectively. k:j→k represents the set of terminal nodes for all lines with node j as the starting point. ij and x ij p represents the resistance and reactance on line ij, respectively. j,l and q j,l It represents the active and reactive power demand at node j, p j,g and q j,g It represents the active and reactive power generated by the generator at node j, and ε represents the allowable voltage deviation, which is generally set to 0.05pu.

[0108] Secondly, the objective function for the optimal scheduling of the medium-voltage distribution network is to minimize the sum of the generation cost of distributed power sources, the network loss cost of the medium-voltage distribution network, and the interaction cost with the low-voltage distribution network. The objective function is as follows:

[0109] minF M =F G,M -F sell +Floss,M

[0110] Where F M It is the total operating cost of the medium-voltage distribution network, F G,M It is the generation cost of distributed power sources in medium-voltage distribution networks, F sell This refers to the revenue generated from the sale of electricity from the medium-voltage distribution network to the low-voltage distribution network, F. loss,M It is the network loss cost of medium-voltage distribution networks.

[0111]

[0112]

[0113]

[0114] Where T is the scheduling period, P G,i (t) represents the output power of the i-th distributed power source during time period t, and n represents the number of distributed power sources in the medium-voltage distribution network. j,L λ(t) represents the power sold by the medium-voltage distribution network to the j-th low-voltage distribution network during time period t. When its value is positive, it indicates that the medium-voltage distribution network sells electricity to the low-voltage distribution network. When its value is negative, it indicates that the medium-voltage distribution network purchases electricity from the low-voltage distribution network. λ(t) is the base electricity price during time period t, and m represents the number of low-voltage distribution networks.

[0115] The objective function for optimizing the scheduling of low-voltage distribution networks is similar to that of medium-voltage distribution networks, and its expression is shown in the following formula.

[0116] minF S =F G,s +F buy +F loss,s

[0117] Meanwhile, the optimized operation of medium and low voltage distribution networks also needs to meet the following constraints:

[0118] (1) Power balance constraints of the system:

[0119]

[0120] (2) Upper and lower limits of distributed power source output power constraints:

[0121] P G,i,min ≤P G,i (t)≤P G,i,max

[0122] (3) Ramp-up constraints on the output power of distributed power sources:

[0123] -R≤P G,i (t)-P G,i (t-1)≤R

[0124] (4) Operational constraints of energy storage systems:

[0125]

[0126] Among them, P G,i (t), P PV (t), P WT (t), P dis,ess (t), P Load (t), P ch,ess (t) and P ch,ev (t) represents the output power of the i-th distributed power source, photovoltaic, wind turbine, discharge and charge power of energy storage, and charge power of EV, respectively. G,i,max ,P G,i,min These represent the maximum and minimum output power of the distributed power source, respectively. R represents the maximum output power increment of the distributed power source. E(t) represents the real-time capacity of the energy storage. max and E min U represents the upper and lower limits of energy storage capacity. ch (t) and U dis (t) represents the state of charge / discharge quantity, which takes the value of 0 or 1.

[0127] 3. Hierarchical Distributed Optimization Solution Strategy for Medium and Low Voltage Distribution Networks Based on ADMM

[0128] (1) First, considering the characteristics of the ADMM distributed algorithm and the characteristics of the medium and low voltage distribution network operating in layers according to voltage level, this invention establishes a layered decoupling optimization architecture for the medium and low voltage distribution network, the structure of which is shown in the figure.

[0129] (2) Secondly, the virtual boundary variable between low-voltage distribution network i and medium-voltage distribution network j is X. ij’ ={P ij’ Q ij’ V ij’ The virtual boundary variable between medium-voltage distribution network j and low-voltage distribution network i is X. i’j ={P i’j Q i’j V i’j The reference value for the virtual boundary variable in the current iteration is the average value of the virtual boundary variable in the previous iteration, and its expression is as follows:

[0130]

[0131] Where m is the number of iterations, X i’j,m+1,ref and X ij’,m+1,ref X is the virtual boundary variable reference value for medium-voltage distribution network j and low-voltage distribution network i in the (m+1)th iteration. i’j,m and X ij’,m It is the virtual boundary variable for medium-voltage distribution network j and low-voltage distribution network i in the m-th iteration.

[0132] (3) Then, the virtual boundary variables of medium-voltage distribution network j and low-voltage distribution network i need to be updated respectively. The update rule is to find the variable value that minimizes the augmented Lagrangian function of the medium- and low-voltage distribution network optimization scheduling model. The expression is as follows:

[0133] X ij′,m+1 =argminL ij′ (X ij′,m ,X ij′,m,ref ,λ ij′,m )

[0134] X i′j,m+1 =argminL i′j (X i′j,m ,X i′j,m,ref ,λ i′j,m )

[0135]

[0136]

[0137] Among them, L i’j (X i’j,m ,X i’j,m,ref ,λ i’j,m ) and L ij’ (X ij’,m ,X ij’,m,ref ,λ ij’,m ) represent the augmented Lagrangian functions corresponding to the optimal scheduling models of medium-voltage distribution network j and low-voltage distribution network i, respectively, ρ is the penalty coefficient of the ADMM algorithm, and λ i’j,m and λ ij’,m These represent the Lagrange multipliers of medium- and low-voltage distribution networks, which are mainly composed of active power, reactive power, and voltage on the interconnecting lines of the medium- and low-voltage distribution networks. λ ij’,m ={λ P,ij',m ,λ Q,ij',m ,λ V,ij',m}, λ i’j,m ={λ P,i'j,m ,λ Q,i'j,m ,λ V,i'j,m}

[0138] (4) Subsequently, the Lagrange multipliers need to be updated, and their expression is as follows:

[0139] λ ij′,m+1 =λ ij′,m +(X ij′,m -X ij′,m,ref )

[0140] λ i′j,m+1 =λ i′j,m +(X i′j,m -Xi′j,m,ref )

[0141] (5) Finally, the convergence criterion of the ADMM algorithm is that the residuals of the virtual boundary variables in medium and low pressure converge to 0, as shown below:

[0142]

[0143] Simulation verification:

[0144] I. The parameters and conditions for the simulation experiment are as follows:

[0145] This invention uses the actual traffic network of Sioux Falls, USA, for simulation testing. EVs generate charging loads while driving through the traffic network and connect to various low-voltage distribution networks via charging stations. Considering the load demand of each low-voltage distribution area and the different traffic network topologies they supply, three low-voltage distribution networks with different numbers of nodes and different distribution structures are set up: an 11-node low-voltage distribution network for residential areas, and a 17-node low-voltage distribution network with different topologies for commercial and work areas. Finally, the upper-level medium-voltage distribution network is an improved IEEE 33-node network. Simultaneously, various distributed resources, including EV charging stations, wind turbines, photovoltaic systems, and energy storage systems, are also connected to the medium and low-voltage distribution networks. Finally, the system architecture of the simulation model is as follows: Figure 6 As shown.

[0146] II. Simulation test results:

[0147] Depend on Figure 4 It can be seen that the spatiotemporal distribution of EV charging load exhibits distinct regional characteristics. First, the charging load in residential areas is mainly concentrated in the early morning and evening hours, with very low charging load during the day, as electric vehicles primarily travel to workplaces and commercial areas during the day. Second, the charging load in workplaces shows two distinct charging peaks, consistent with the characteristic of EV users visiting workplaces twice a day. Finally, the charging load in commercial areas exhibits a clear single-peak characteristic, concentrated between 10:00 and 17:00, which coincides with the time when users go to commercial areas for dining and entertainment, consistent with the actual situation in commercial areas.

[0148] Depend on Figure 5 It can be seen that the active and reactive power of the tie lines in medium and low voltage distribution networks converge to a consistent level after a finite number of iterations. Furthermore, for different low-voltage distribution substations, the stable power obtained after convergence varies due to differences in load demand and network topology. Additionally, the residual convergence plots of active and reactive power show that the active and reactive power residuals of each low-voltage distribution substation and the medium-voltage distribution network converge to 0 after a finite number of iterations, indicating the convergence consistency of the tie line power in medium and low voltage distribution networks.

[0149] Depend on Figure 6 (a) It can be seen that for residential areas, since their charging load is higher in the early morning (1:00-5:00) and at night (18:00-23:00), residential areas need to purchase electricity from the medium-voltage distribution network during these periods to ensure the load demand during this period. During the daytime (7:00-15:00), the charging load and base load of residential areas are relatively small, so there is a power surplus in residential areas during this period. Therefore, they sell electricity to the upstream medium-voltage distribution network to ensure the system's economy, charge the energy storage system, and discharge during the high electricity price period (19:00-21:00) to reduce the amount of electricity purchased by the system and improve the system's economy.

[0150] Depend on Figure 6 (b) It can be seen that for commercial areas, the charging load and basic load are both high during the daytime period (10:00-18:00). Therefore, during this period, the distributed power supply in commercial areas basically outputs at maximum power to ensure the load demand. At the same time, energy storage is charged during the low electricity price period (0:00-7:00) and discharged during the high electricity price period (10:00-13:00) to reduce the system's electricity purchase and improve the system's economy.

[0151] Depend on Figure 6 (c) It can be seen that the charging load of the working area is relatively high between 7:00-12:00 and 16:00-20:00. At the same time, the basic load of the working area also reaches its peak at 10:00 and 16:00. Therefore, the distributed power supply of the working area outputs to the outside at maximum power between (8:00-12:00) and (16:00-20:00) to ensure the load demand. At the same time, the working energy storage system also charges during the low electricity price period (0:00-5:00) and discharges during the high electricity price period (9:00-11:00).

[0152] Depend on Figure 6 (d) It can be seen that for medium-voltage distribution networks, energy storage systems charge during periods when renewable energy output power is abundant and load is low (0:00-8:00) and discharge during periods when renewable energy output power is weak (17:00-22:00) to reduce load pressure. At the same time, various distributed power sources in the medium-voltage distribution network also output large-scale power during periods when renewable energy output power is weak to make up for the renewable energy output power deficit.

[0153] Depend on Figure 7Analysis of node voltage states in the four scenarios reveals that nodes with significant voltage drops are located at the far ends of the distribution network, far from distributed power sources, photovoltaics, and wind turbines. From a temporal perspective, the temporal distribution of node voltages in each low-voltage distribution area exhibits distinct regional characteristics. In residential areas, voltage drops are more severe in the early morning and evening due to higher loads during these times. In commercial areas, the voltage distribution primarily shows a single trough, consistent with the single-peak load characteristic of commercial areas. In work areas, the nodes with the most significant voltage drops show a double trough, consistent with the double-peak load characteristic of work areas.

[0154] Depend on Figure 8 It can be seen that before the proposed optimization strategy was adopted, the node voltages of each low-voltage distribution network experienced significant drops, with the lowest node voltage dropping below 0.95V, which had a significant impact on the safe operation of the distribution network. After the optimization strategy was adopted, the voltage drop of the distribution network nodes was significantly reduced and returned to the safe operating range. Secondly, comparing the distribution network losses before and after the optimization strategy, it can be found that the network losses were significantly reduced after the optimization strategy was adopted, which can effectively reduce the system operating costs and improve the system economy.

[0155] Furthermore, to demonstrate the superiority of the proposed strategy, this invention compares the optimization results using centralized optimization with those using the ADMM distributed algorithm, and the results are shown in Table 1.

[0156] Table 1 Comparison of centralized and distributed computing results

[0157]

[0158] As shown in Table 1, the cost error between the ADMM algorithm proposed in this invention and the centralized algorithm is 1.41%, indicating that the ADMM algorithm can guarantee the global optimality of the interests of all stakeholders and the system operating cost with high accuracy. Furthermore, since the ADMM algorithm proposed in this invention is implemented using a serial iterative solution method on a single PC, meaning that the PC needs to serially solve four decoupled independent optimization problems in each iteration, whereas in actual parallel iterative solutions, each sub-optimization problem is solved by an independent controller, its solution time is much shorter than that of serial iterative calculation. Moreover, when the type, number, and communication volume of sub-units in the low-voltage distribution substation area increase, the ADMM algorithm will have a significant solution advantage because the branch-and-bound method used in the centralized method has O(2^3) time complexity. nThe time complexity of centralized methods is significantly reduced by the increase in integer variables, which leads to an exponential increase in solution time. In contrast, the ADMM algorithm can be solved in a multi-machine parallel environment, reducing the number of integer variables and greatly shortening the solution time of centralized methods. Furthermore, centralized methods place a high burden on the communication of medium- and low-voltage distribution networks, while the ADMM algorithm only requires data communication at the tie lines of the medium- and low-voltage distribution networks, greatly reducing the data communication pressure and ensuring the data privacy of various entities within the medium- and low-voltage distribution network.

[0159] The embodiments described above merely illustrate specific implementation methods of this application, and while the descriptions are detailed and specific, they should not be construed as limiting the scope of protection of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the technical solution of this application, and these modifications and improvements all fall within the scope of protection of this application.

Claims

1. A hierarchical distributed optimization method for distribution networks considering the spatiotemporal distribution of charging load, characterized in that, Includes the following steps: S1: Establish a multi-level collaborative operation architecture for transportation-medium and low voltage distribution networks. Based on the current operating characteristics of urban transportation networks and distribution networks, the scenario of coupled operation of transportation networks and distribution networks, and the characteristics of distribution networks operating in layers according to voltage levels, establish a multi-level collaborative operation architecture for transportation-medium and low voltage distribution networks. S2: Simulate charging load. Based on the multi-layer collaborative operation architecture of transportation-medium and low voltage power distribution network, firstly, a travel probability model of EV residents is established; secondly, considering road congestion, a real-time vehicle dynamic transfer model is established; then, based on actual road network data, an abstract urban traffic network model is established; the three models are run together to simulate the charging load generated by EVs during a day's travel. S3: Establish a dynamic economic dispatch model for medium and low voltage distribution networks. Based on the charging load and operation of medium and low voltage distribution networks in S2, and according to the power flow distribution characteristics of the distribution network, an improved power flow model is proposed. Considering the operating characteristics of new energy units, energy storage systems, distributed power sources and EV charging stations, a dynamic economic dispatch model for medium and low voltage distribution networks is established. S4: A distributed algorithm is used to solve the problem. Based on the dynamic economic dispatch model of the medium and low voltage distribution network obtained in S3, a hierarchical distributed optimization solution strategy for the medium and low voltage distribution network is proposed. The specific steps for establishing the travel probability model for EV residents in S2 are as follows: To describe the probability distribution characteristics of EV travel times, based on the NHTS2017 dataset, the first departure time of EVs under all travel demands was statistically analyzed, and the generalized extreme value distribution was used to describe the probability distribution of EV travel times; the obtained probability density function is shown in the following equation: ； In the formula, μ, σ and ξ represent the mean, standard deviation and shape parameter of GEV, respectively, z is an intermediate variable and t is time; The establishment of the real-time vehicle dynamic transfer model in S2 is specifically as follows: To describe the traffic network in which EVs actually travel, a graph theory method is used to abstractly model the actual traffic network, resulting in a simplified directed graph of the road network, as shown in the following equation: ； ； Here, the adjacency matrix D represents the connection relationship between two traffic network nodes. This represents the distance between two nodes. Indicates the length of the road directly connecting node i and node j; inf indicates that there is no road directly connecting node i and node j. The specific steps for establishing the city's traffic network model in S2 are as follows: The Dijstra algorithm is adopted, with the shortest passage time of EVs as the guiding objective. Its expression is as follows: ； Where a and b correspond to the departure node and the destination node, respectively; Let R represent the travel time required from node a to node b, and let R represent the set of all possible roads from node a to node b. Meanwhile, based on research by the U.S. Highway Bureau, the relationship between vehicle travel time and traffic volume is shown in the following formula: ； in, and This indicates the time required for an EV to travel on a road under current traffic flow and zero traffic flow conditions. , ,and These represent the road's maximum capacity, current traffic flow, and average road speed, respectively.

2. The hierarchical distributed optimization method for distribution networks considering the spatiotemporal distribution of charging load as described in claim 1, characterized in that, The multi-level collaborative operation architecture for transportation and power distribution networks established in S1 is specifically as follows: Considering the respective operating characteristics of urban transportation networks and distribution networks, as well as the characteristics of the coupled operation of urban transportation networks and distribution networks, a multi-level collaborative operation architecture of transportation-medium and low voltage distribution networks is established. First, EVs drive in urban transportation networks and generate charging loads. Then, the charging loads are connected to the low voltage distribution network. The low voltage distribution network integrates local distributed resources and absorbs new energy sources while meeting the load requirements. Then, when the power supply capacity of the low-voltage distribution network is insufficient or excessive, it is connected to the medium-voltage distribution network for power transmission.

3. The hierarchical distributed optimization method for distribution networks considering the spatiotemporal distribution of charging load according to claim 1, characterized in that, The specific process of S3 is as follows: The traditional DistFlow power flow model is simplified by two simplification assumptions: 1) The power transmitted through the lines in the distribution network is much greater than the power lost along the lines; 2) The voltage at a single node in the distribution network is much greater than the voltage difference between two nodes; The improved power flow model is shown in the following equation: ； in, , , It is the balance node voltage. and Let represent the active and reactive power transmitted in branch ij, respectively, and k:j→k represent the set of terminal nodes of all lines with node j as the head. and These represent the resistance and reactance on line ij, respectively. and It represents the active and reactive power of the load demand at node j. and ε represents the active and reactive power generated by the generator at node j, and ε represents the allowable voltage deviation of the distribution network, which is generally set to 0.05pu. Secondly, the objective function for the optimal scheduling of the medium-voltage distribution network is to minimize the sum of the generation cost of distributed power sources, the network loss cost of the medium-voltage distribution network, and the interaction cost with the low-voltage distribution network. The objective function is as follows: ； in This is the total operating cost of the medium-voltage distribution network. It refers to the generation cost of distributed power sources in medium-voltage distribution networks. This refers to the revenue generated from the sale of electricity from the medium-voltage distribution network to the low-voltage distribution network. This refers to the network loss cost of the medium-voltage distribution network; ； Where T is the scheduling period. This represents the output power of the i-th distributed generation source during time period t, where n represents the number of distributed generation sources in the medium-voltage distribution network. Let λ(t) be the power sold by the medium-voltage distribution network to the j-th low-voltage distribution network during time period t. When its value is positive, it indicates that the medium-voltage distribution network sells electricity to the low-voltage distribution network. When its value is negative, it indicates that the medium-voltage distribution network purchases electricity from the low-voltage distribution network. λ(t) is the base electricity price during time period t, and m represents the number of low-voltage distribution networks. The objective function for optimal scheduling of low-voltage distribution networks is similar to that of medium-voltage distribution networks, and its expression is shown in the following formula: ； Meanwhile, the optimized operation of medium and low voltage distribution networks also needs to meet the following constraints: (1) Power balance constraints of the system: ； (2) Upper and lower limits of distributed power source output power constraints: ； (3) Ramp-up constraints on the output power of distributed power sources: ； (4) Operational constraints of energy storage systems: ； in, Let represent the output power of the i-th distributed power source, photovoltaic, wind turbine, discharge and charging power of energy storage, and charging power of EV, respectively. These represent the maximum and minimum output power of the distributed power source, respectively; R represents the maximum output power increment of the distributed power source. This indicates the real-time capacity of the energy storage. These represent the upper and lower limits of energy storage capacity; This represents the state of charge / discharge, and its value is either 0 or 1.

4. The hierarchical distributed optimization method for distribution networks considering the spatiotemporal distribution of charging load as described in claim 1, characterized in that, The specific process of S4 is as follows: Considering the characteristics of the ADMM distributed algorithm and the hierarchical operation of medium and low voltage distribution networks according to voltage levels, a hierarchical decoupling optimization architecture for medium and low voltage distribution networks is established. The virtual boundary variable between low-voltage distribution network i and medium-voltage distribution network j is The virtual boundary variable between medium-voltage distribution network j and low-voltage distribution network i is The reference value for the virtual boundary variable in this iteration is the average value of the virtual boundary variable in the previous iteration, and its expression is as follows: ； Where m is the number of iterations. and These are the virtual boundary variable reference values ​​for medium-voltage distribution network j and low-voltage distribution network i in the (m+1)th iteration. and It is the virtual boundary variable for medium-voltage distribution network j and low-voltage distribution network i in the m-th iteration; The virtual boundary variables of medium-voltage distribution network j and low-voltage distribution network i are updated respectively. The update rule is to find the variable values ​​that minimize the augmented Lagrangian function of the medium- and low-voltage distribution network optimization scheduling model. The expression is as follows: ； The updated Lagrange multipliers are expressed as follows: ； The convergence criterion for the ADMM algorithm is that the residuals of the virtual boundary variables in medium and low pressure converge to 0, as shown below: ； in, Let represent the augmented Lagrangian functions corresponding to the optimal scheduling models of medium-voltage distribution network j and low-voltage distribution network i, respectively, and ρ be the penalty coefficient of the ADMM algorithm. and These represent the Lagrange multipliers of medium and low voltage distribution networks, which are mainly composed of active power, reactive power, and voltage on the interconnecting lines of medium and low voltage distribution networks. .

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