An optimization method for AC / DC hybrid photovoltaic-storage distribution network

Abstract

This application discloses an optimization method for a hybrid AC / DC photovoltaic-storage distribution network. The objective function in the multi-objective robust optimization model comprehensively considers network losses, voltage deviations, and operating costs in the hybrid AC / DC distribution network. It also considers the operating parameters affected by flexible switching devices, energy storage systems, and voltage source converters during the operation of the hybrid AC / DC distribution network. Various control methods are applied in the coordinated optimization. Flexible interconnection devices, i.e., flexible switching devices, can effectively regulate the power flow between different parts of the hybrid AC / DC flexible distribution network. At the same time, the uncertainties of distributed generation and load are also considered. A multi-objective robust optimization method that simultaneously considers operating costs, voltage deviations, and network losses is proposed. Furthermore, the two-stage robust optimization method based on second-order cone relaxation and column constraint generation algorithms can handle load and renewable energy fluctuations more quickly and effectively.

Description

Technical Field

[0001] This invention relates to the field of distribution network resource management, and in particular to an AC / DC hybrid photovoltaic-storage distribution network optimization method. Background Technology

[0002] With increasing attention being paid to carbon emissions and distributed generation (DG), the utilization rate of renewable energy is improving, with photovoltaic (PV) and wind turbines already being fully utilized. Furthermore, energy storage systems (ESS), flexible loads, and numerous DC devices are continuously connected to the distribution network, making hybrid AC / DC distribution networks the future trend. Modern electronic devices (distributed generation, energy storage systems, and flexible interconnect devices) offer advantages such as fast response, wide control range, and low operating costs, providing flexible and controllable means for distribution system operation and control systems. However, this also significantly increases system uncertainty. Therefore, to improve energy efficiency and operational flexibility, it is necessary to research a novel optimal scheduling method for hybrid AC / DC distribution systems that considers multiple control methods and uncertainties.

[0003] Fluctuations in solar and wind power, as well as various loads, render traditional deterministic optimization inapplicable. To improve optimization accuracy, robust optimization has become an indispensable method in distribution networks, microgrids, and other fields, including voltage regulation, network reconfiguration, energy storage optimization, and cost reduction.

[0004] The continuous development of power electronics technology has brought flexible and controllable electronic devices into distribution networks, including flexible interconnection devices, distributed generation, and reactive power compensation devices. In AC / DC hybrid distribution networks, voltage source converters, as interconnection devices between AC and DC distribution networks, can also regulate active / reactive power in the AC network and active power in the DC network.

[0005] In existing research, robust optimization has been successfully applied to address the impact of uncertainty. However, existing robust optimization methods only include single-objective optimization models, and multi-objective models are rarely used in robust optimization methods. This means that robust optimization mostly only includes network loss, which cannot take into account both voltage deviation and network loss.

[0006] The introduction of flexible switches has significantly improved the system's economy and safety. It has been applied in AC systems, but the combined optimization of control methods such as flexible switches and energy storage systems is rarely considered in AC / DC hybrid distribution networks.

[0007] Therefore, there is a need for an optimization method for AC / DC hybrid photovoltaic-storage distribution networks to improve the flexibility and reliability of AC / DC hybrid distribution networks. Summary of the Invention

[0008] In view of this, the purpose of this invention is to provide an optimization method for AC / DC hybrid photovoltaic-storage distribution networks, thereby improving the flexibility and reliability of AC / DC hybrid distribution networks. The specific solution is as follows:

[0009] An optimization method for a hybrid AC / DC photovoltaic-storage distribution network includes:

[0010] Given a set of uncertainties, a pre-defined multi-objective robust optimization model is constructed; the set of uncertainties includes a collection of uncertainty variables corresponding to the output power of distributed generation devices and loads in an AC / DC hybrid distribution network.

[0011] The objective function value of the main problem is obtained by solving the objective function of the AC / DC hybrid distribution network with the network loss, voltage deviation and operation cost as the minimum objectives based on the uncertainty set in the main problem model of the multi-objective robust optimization model.

[0012] The objective function value of the main problem is substituted into the sub-problem model in the multi-objective robust optimization model to solve the objective function, resulting in a new uncertainty set and the objective function value of the sub-problem; it is then determined whether the difference between the objective function value of the sub-problem and the objective function value of the main problem is less than or equal to a preset threshold.

[0013] If not, the new uncertainty set is returned to the multi-objective robust optimization model for iterative calculation to determine the new objective function values ​​of the main problem and the sub-problems again.

[0014] If so, the target running parameters corresponding to the objective function are obtained;

[0015] The multi-objective robust optimization model is a two-stage robust optimization model based on the second-order cone relaxation algorithm and the column constraint generation algorithm.

[0016] Optionally, the objective function is: f = min(λ1P) loss +λ2ΔV+λ3C op );

[0017] in,

[0018]

[0019]

[0020]

[0021] In the formula, f is the objective function value, and λ1, λ2, and λ3 are the total daily network loss (P). loss Voltage deviation (ΔV) and operating costs (C) op The weighting factors of N are λ1+λ2+λ3=1. ac and N dc These represent the number of nodes in the AC and DC power distribution systems, respectively; and the power loss P. loss Ω i R is the set of all nodes connected to node i. ij It is the resistance of the branch between node i and node j, I ij Let be the current from node i to node j, and price(t) be the electricity price at time t; voltage deviation ΔV: V i (t) is the node voltage of node i at time t, V op Minimum value and V op The maximum value is the maximum and minimum value within the voltage optimization range; operating cost C op K, N, and J represent the number of voltage source converters, flexible switches, and energy storage systems, respectively. and These are the power losses of the k-th voltage source converter and the n-th flexible switch at time t, respectively. and K represents the charging / discharging power of the j-th energy storage system. The energy storage system absorbs positive power from the grid. ess It is the unit power charging / discharging cost coefficient of the energy storage system, which depends on the investment cost and maintenance cost.

[0022] Optionally, the constraints of the objective function include: power flow constraints, voltage source converter constraints, flexible switch constraints, energy storage system constraints, and safe operation constraints.

[0023] Optionally, the power flow constraints include:

[0024]

[0025]

[0026]

[0027] In the formula, R is the branch set with node i as the head node, φi is the branch set with node i as the ending node, and R is the branch set with node i as the ending node. ij and X ij P represents the resistance and reactance of branch ij. ih (t) and Q ih (t) represents the active and reactive power from node i to node h at time t, P i (t) and Qi P(t) represents the active and reactive power injected by node i at time t. ij (t) and Q ij V(t) represents the active and reactive power flow from node i to node j at time t. j (t) represents the voltage amplitude at node j at time t.

[0028] Optionally, the voltage source converter constraints include:

[0029]

[0030]

[0031]

[0032]

[0033]

[0034] In the formula, and These are the active and reactive power injected into the AC side of the k-th voltage source converter at time t. This represents the active power loss of the k-th voltage source converter at time t. It is the active power injected into the DC side of the k-th voltage source converter at time t. and These are the equivalent resistance and reactance of the k-th voltage source converter. This is the capacity limit of the k-th voltage source converter. It is the loss factor of the k-th voltage source converter. and It represents the upper limit of the active and reactive power of the k-th voltage source converter.

[0035] Optionally, the flexible switch constraint conditions include:

[0036]

[0037]

[0038]

[0039] In the formula, M is the number of the nth terminal of the flexible switch, and T m This represents the m-th terminal of the flexible switch. and These are the active power, reactive power, and active power loss at terminal m of the nth flexible switch at time t. It is the rated apparent power at the m-th terminal of the nth flexible switch. It is the loss coefficient of the nth flexible switch.

[0040] Optionally, the constraints of the energy storage system include:

[0041]

[0042]

[0043] In the formula, for the j-th energy storage system, It is the maximum charging / discharging power. It is a binary variable; the value is 0 when the energy storage system is in the charging state at time t, and 1 when it is in the discharging state. E ESS (0) and Let represent the minimum stored energy, initial stored energy, and maximum stored energy of the j-th energy storage system, respectively.

[0044] Optionally, the safe operation constraints include:

[0045] V i,min ≤V i (t)≤V i,max ;

[0046]

[0047] In the formula, V i,max and V i,min These are the upper and lower limits of the node voltage, I ij,max It is the maximum allowable current value for the branch.

[0048] Optionally, the uncertain set includes:

[0049]

[0050]

[0051] In the formula, u DG (t) and u L (t) represents the actual output power of distributed generation and loads at time t. and This is the predicted output power of distributed generation and load at time t. and It represents the maximum prediction deviation of distributed generation and load power at time t, where u represents the uncertainty variable of distributed generation and load.

[0052] Optionally, when returning the new uncertainty set to the multi-objective robust optimization model for iterative calculation, the method further includes:

[0053] The multi-objective robust optimization model is further enhanced by introducing variables of the main problem and corresponding constraints of the next iteration into the subproblem of the next iteration.

[0054] In this invention, the optimization method for AC / DC hybrid photovoltaic-storage distribution network includes: providing a set of uncertainties to a preset multi-objective robust optimization model; the uncertainties are a set of uncertain variables corresponding to the output power of distributed generation devices and loads in the AC / DC hybrid distribution network; using the main problem model in the multi-objective robust optimization model to solve the objective function with the network loss, voltage deviation, and operating cost of the AC / DC hybrid distribution network as the minimum objectives based on the uncertainties, obtaining the main problem objective function value; substituting the charging and discharging power state of the energy storage system into the sub-problem model in the multi-objective robust optimization model to solve the objective function, obtaining a new uncertainties and sub-problem objective function values; determining whether the difference between the sub-problem objective function value and the main problem objective function value is less than or equal to a preset threshold; if not, returning the new uncertainties to the multi-objective robust optimization model for iterative calculation to re-determine the new main problem objective function value and sub-problem objective function value; if yes, obtaining the target operating parameters corresponding to the objective function; wherein, the multi-objective robust optimization model is a two-stage robust optimization model based on a second-order cone relaxation algorithm and a column constraint generation algorithm.

[0055] The objective function of the multi-objective robust optimization model in this invention comprehensively considers network losses, voltage deviations, and operating costs in AC / DC hybrid distribution networks. It also takes into account the operating parameters affected by flexible switching devices, energy storage systems, and voltage source converters during the operation of AC / DC hybrid distribution networks. Multiple control methods are applied in the coordinated optimization. Flexible interconnection devices, i.e., flexible switching devices, can effectively regulate the power flow between different parts of the AC / DC hybrid flexible distribution network. At the same time, the uncertainties of distributed generation and load are also considered. A multi-objective robust optimization method that simultaneously considers operating costs, voltage deviations, and network losses is proposed. Furthermore, the two-stage robust optimization method based on second-order cone relaxation and column constraint generation algorithms can handle load and renewable energy fluctuations more quickly and effectively. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0057] Figure 1 This is a schematic diagram of a method for optimizing an AC / DC hybrid photovoltaic-storage distribution network according to an embodiment of the present invention.

[0058] Figure 2 This is a schematic diagram of another AC / DC hybrid photovoltaic-storage distribution network optimization method disclosed in an embodiment of the present invention;

[0059] Figure 3 This is a schematic diagram of an equivalent model of a voltage source converter disclosed in an embodiment of the present invention;

[0060] Figure 4 This is a schematic diagram of an equivalent model of a multi-port flexible switch disclosed in an embodiment of the present invention;

[0061] Figure 5 This is a schematic diagram of a multi-objective robust optimization model solution process disclosed in an embodiment of the present invention;

[0062] Figure 6 This is a structural diagram of an improved IEEE 33-node AC / DC hybrid power distribution system disclosed in an embodiment of the present invention;

[0063] Figure 7 This is a schematic diagram of time-of-use pricing for an AC / DC hybrid power distribution system disclosed in an embodiment of the present invention;

[0064] Figure 8 This is a schematic diagram illustrating the predicted values ​​of photovoltaic power and load according to an embodiment of the present invention;

[0065] Figure 9 This is a schematic diagram of the voltage curve of node 33 in Examples 1 and 2 of the present invention.

[0066] Figure 10 This is a schematic diagram of the power flow of a flexible switch at node 33 disclosed in an embodiment of the present invention. Detailed Implementation

[0067] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] This invention discloses an optimization method for a hybrid AC / DC photovoltaic-storage distribution network, see [link to relevant documentation]. Figure 1 As shown, the method includes:

[0069] S11: Given a set of uncertainties, optimize a pre-defined multi-objective robust optimization model.

[0070] Specifically, the preset multi-objective robust optimization model is a two-stage robust optimization model based on the second-order cone relaxation algorithm and the column and constraint generation (C&CG) algorithm. It is generated based on the objective function and related constraints of minimizing the network loss, voltage deviation and operation cost of the AC / DC hybrid distribution network. In order to solve the multi-objective robust optimization model, the multi-objective robust optimization model is split into a main problem model and a sub-problem model. First, a set of preset uncertainties can be given to the preset multi-objective robust optimization model as initial calculation values ​​so that the multi-objective robust optimization model can perform the first step of calculation.

[0071] Specifically, the uncertainty set is a set of uncertainty variables that correspond to the output power of distributed generation devices and loads in a hybrid AC / DC distribution network.

[0072] S12: Using the main problem model in the multi-objective robust optimization model, the objective function with network loss, voltage deviation and operation cost of AC / DC hybrid distribution network as the minimum objective is solved based on the uncertainty set, and the objective function value of the main problem is obtained.

[0073] Specifically, in order to compute the multi-objective robust optimization model, the multi-objective robust optimization model is split into two models to solve two problems respectively. The first is the main problem model, and the second is the sub-problem model, which is a mixed integer linear optimization model.

[0074] Specifically, by calculating the uncertain set through the main problem model, the objective function value of the main problem can be calculated through the objective function, and the objective function value of the main problem can be used as the lower limit in the iterative calculation so as to determine whether to exit the iteration.

[0075] Specifically, the objective function value of the main problem is the corresponding solution obtained when solving the main problem using the objective function.

[0076] S13: Substitute the objective function value of the main problem into the sub-problem model in the multi-objective robust optimization model to solve the objective function, and obtain a new set of uncertainties and the objective function value of the sub-problem.

[0077] Specifically, after calculating the objective function value of the main problem, it is substituted into the sub-problem model in the multi-objective robust optimization model to continue solving the objective function. A new set of uncertainties can be solved again, and the objective function value of the sub-problem can be obtained. The objective function value of the sub-problem is used as the upper limit in the iterative calculation so that it can be used as the iterative judgment condition in the future.

[0078] S14: Determine whether the difference between the objective function value of the subproblem and the objective function value of the main problem is less than or equal to a preset threshold.

[0079] Specifically, when the difference between the objective function values ​​of the subproblem model and the objective function value of the main problem model becomes closer and closer, it can be considered that they are getting closer to the optimal solution corresponding to the objective function. Therefore, a threshold is set in advance, and the subsequent iteration process is stopped only when the difference between the objective function value of the subproblem model and the objective function value of the main problem is less than or equal to the preset threshold. If it is not less than the preset threshold, the subsequent iteration process can be executed to promote the objective function values ​​of the subproblem model and the objective function value of the main problem to gradually approach each iteration calculation.

[0080] S15: If not, return the new uncertainty set to the multi-objective robust optimization model for iterative calculation to determine the new objective function values ​​of the main problem and the sub-problems again.

[0081] Specifically, if the difference between the objective function value of the subproblem and the objective function value of the main problem is greater than a preset threshold, the new uncertainty set is brought back to the main problem model in the multi-objective robust optimization model for calculation and the next iteration. That is, return to S12, repeat steps S12 to S14 to obtain new objective function values ​​of the main problem and subproblem, and then execute S15 again to determine whether to continue iterating.

[0082] S16: If so, the target running parameters corresponding to the objective function are obtained.

[0083] Specifically, if the difference between the objective function value of the sub-problem and the objective function value of the main problem is less than or equal to a preset threshold, it indicates that the current output calculation result meets expectations, and the target operating parameters corresponding to the objective function are obtained. That is, the target operating parameters with the network loss, voltage deviation and operating cost of the AC / DC hybrid distribution network as the minimum objective are obtained. After obtaining the target operating parameters, the operation of the AC / DC hybrid distribution network is corrected according to the target operating parameters, thereby improving the operating efficiency of the distribution network and reducing losses, thus achieving optimization.

[0084] The target operating parameters include the active and reactive power of flexible switching devices and voltage source converters, the charging and discharging power status of the energy storage system, and the output power of distributed generation devices and loads, among other sub-problems requiring optimization of variable solutions.

[0085] Specifically, a multi-objective optimization model for an AC / DC hybrid distribution network considering distributed generation and load uncertainties is established based on a two-stage robust optimization algorithm. To simultaneously optimize operating costs, voltage deviations, and network losses, a multi-objective coordinated optimization model based on various controllable methods is proposed. Compared to conventional single-objective optimization, the proposed multi-objective robust optimization considers the flexibility and security of the AC / DC hybrid distribution system. Flexible switches and voltage source converters are used to flexibly transfer energy between AC and DC distribution systems and improve the energy efficiency of the AC / DC hybrid flexible distribution network. Then, the proposed robust model considers the uncertainties of distributed generation and loads. By solving the two-stage robust optimization model, the distribution network can obtain the optimal solution under the "worst-case" scenario. Compared to traditional deterministic methods, the greater the deviation between actual and predicted values, the more significant the optimization effect of the proposed robust method. Furthermore, the proposed scheme has strong robustness and can effectively resist the risks of renewable energy fluctuations.

[0086] As can be seen, the objective function in the multi-objective robust optimization model of this invention comprehensively considers network losses, voltage deviations, and operating costs in the AC / DC hybrid distribution network. It also considers the operating parameters affected by flexible switching devices, energy storage systems, and voltage source converters during the operation of the AC / DC hybrid distribution network. Multiple control methods are applied in the coordinated optimization. Flexible interconnection devices, i.e., flexible switching devices, can effectively regulate the power flow between different parts in the AC / DC hybrid flexible distribution network. At the same time, the uncertainties of distributed generation and load are also considered. A multi-objective robust optimization method that simultaneously considers operating costs, voltage deviations, and network losses is proposed. Furthermore, the two-stage robust optimization method based on second-order cone relaxation and column constraint generation algorithms can handle load and renewable energy fluctuations more quickly and effectively.

[0087] This invention discloses a specific method for optimizing a hybrid AC / DC photovoltaic-storage distribution network. Compared to the previous embodiment, this embodiment further explains and optimizes the technical solution. See also... Figure 2 As shown, specifically:

[0088] S21: Given a set of uncertainties, a pre-defined multi-objective robust optimization model is established; the uncertainties are a set of variables corresponding to the output power of distributed generation devices and loads in the AC / DC hybrid distribution network.

[0089] S22: Using the main problem model in the multi-objective robust optimization model, the objective function with network loss, voltage deviation and operation cost of AC / DC hybrid distribution network as the minimum objective is solved based on the uncertainty set, and the objective function value of the main problem is obtained;

[0090] S23: Substitute the objective function value of the main problem into the sub-problem model in the multi-objective robust optimization model to solve the objective function, and obtain a new set of uncertainties and the objective function value of the sub-problem;

[0091] S24: Determine whether the difference between the objective function value of the subproblem and the objective function value of the main problem is less than or equal to a preset threshold;

[0092] S25: If not, return the new uncertainty set to the multi-objective robust optimization model, add the variables of the main problem and the corresponding constraints of the next iteration to the multi-objective robust optimization model, and perform iterative calculation.

[0093] Specifically, to accelerate the iteration speed, see Figure 5 As shown, during iteration, the variable (x) of the main problem (introducing subproblems in the next iteration) is added to the multi-objective robust optimization model. l+1 The corresponding next constraint condition (constraint formula (38) l=l+1) accelerates the convergence speed of the algorithm, improves the running efficiency of the model, and enables the target running parameters to be obtained more quickly.

[0094] S26: If so, then obtain the target running parameters corresponding to the objective function;

[0095] Among them, the multi-objective robust optimization model is a two-stage robust optimization model based on the second-order cone relaxation algorithm and the column constraint generation algorithm.

[0096] Specifically, in order to simultaneously optimize network loss, voltage deviation, and operating cost, the objective function is as follows:

[0097] The objective function is: f = min(λ1P) loss +λ2ΔV+λ3C op (1)

[0098]

[0099]

[0100]

[0101]

[0102] In the formula, f is the objective function value, and λ1, λ2, and λ3 are the total daily network loss (P). loss Voltage deviation (ΔV) and operating costs (C) op The weighting factor for N is λ1+λ2+λ3=1. ac and N dc These are the number of nodes in the AC and DC power distribution systems, respectively.

[0103] Power loss P loss Ω i R is the set of all nodes connected to node i. ij It is the resistance of the branch between node i and node j. ij Let be the current from node i to node j, and price(t) be the electricity price at time t.

[0104] Voltage deviation ΔV: V i (t) is the node voltage of node i at time t. op Minimum value and V op The maximum value is the maximum and minimum value within the voltage optimization range.

[0105] Operating Costs C op K, N, and J represent the number of voltage source converters, flexible switches, and energy storage systems, respectively. and These are the power losses of the k-th voltage source converter and the n-th flexible switch at time t, respectively. and K represents the charging / discharging power of the j-th energy storage system. The energy storage system absorbs positive power from the grid. ess It is the unit power charging / discharging cost coefficient of the energy storage system, which depends on the investment cost and maintenance cost.

[0106] It should be noted that the cost in the operating cost in the embodiments of the present invention can be added as an option. Here, it is only an example of a real-time method that can be added to reflect the comprehensiveness of the parameters that the objective function of the embodiments of the present invention can consider.

[0107] Specifically, the established multi-objective optimization model needs to satisfy constraints related to power flow, voltage source converter, flexible switching, energy storage system, and safe operation. These constraints can be described as follows.

[0108] Specifically, the DistFlow model is used for AC / DC hybrid distribution networks. The power flow constraints are:

[0109]

[0110]

[0111] V j (t) 2 =V i (t) 2 -2(R ij P ij (t)+X ij Q ij (t))+(R ij 2 +X ij 2)×I ij (t) 2 (8)

[0112] In the formula, R is the branch set with node i as the head node, φi is the branch set with node i as the ending node, and R is the branch set with node i as the ending node. ij and X ij P represents the resistance and reactance of branch ij. ih (t) and Q ih (t) represents the active and reactive power from node i to node h at time t, P i (t) and Q i P(t) represents the active and reactive power injected by node i at time t. ij (t) and Q ij V(t) represents the active and reactive power flow from node i to node j at time t. j (t) represents the voltage amplitude at node j at time t. In a DC system, reactive power and reactance are equal to zero in formulas (6)-(8).

[0113] Specifically, the equivalent model of a voltage source converter is as follows: Figure 3 As shown, it is equivalent to the form of the converter and the series impedance.

[0114] The constraints of the voltage source converter include:

[0115]

[0116]

[0117]

[0118]

[0119]

[0120] In the formula, and These are the active and reactive power injected into the AC side of the k-th voltage source converter at time t. This represents the active power loss of the k-th voltage source converter at time t. It is the active power injected into the DC side of the k-th voltage source converter at time t. and These are the equivalent resistance and reactance of the k-th voltage source converter. This is the capacity limit of the k-th voltage source converter. It is the loss factor of the k-th voltage source converter. and It represents the upper limit of the active and reactive power of the k-th voltage source converter.

[0121] in, Figure 3 China Q k VSC This represents the reactive power on the DC side of the k-th voltage source converter.

[0122] Specifically, a flexible switch is a soft-switching device used to regulate energy transfer between AC and AC systems. The equivalent model of a multi-terminal flexible switch is as follows: Figure 4 As shown. The constraints of the nth multi-terminal flexible switch include:

[0123]

[0124]

[0125]

[0126] In the formula, M is the number of the nth terminal of the flexible switch, and T m This represents the m-th terminal of the flexible switch. and These are the active power, reactive power, and active power loss at terminal m of the nth flexible switch at time t. It is the rated apparent power at the m-th terminal of the nth flexible switch. It is the loss coefficient of the nth flexible switch.

[0127] Specifically, the constraints of energy storage systems include:

[0128]

[0129]

[0130] In the formula, for the j-th energy storage system, It is the maximum charging / discharging power. It is a binary variable; the value is 0 when the energy storage system is in the charging state at time t, and 1 when it is in the discharging state. E ESS (0) and Let represent the minimum stored energy, initial stored energy, and maximum stored energy of the j-th energy storage system, respectively.

[0131] Specifically, the constraints for safe operation include:

[0132] V i,min ≤V i (t)≤V i,max (19)

[0133]

[0134] Among them, V i,max and V i,min These are the upper and lower limits of the node voltage. ij,max It is the maximum allowable current value for the branch.

[0135] Specifically, the original objective optimization model based on the aforementioned objective function and constraints contains many nonlinear components. Therefore, a second-order cone and alternative methods are used to linearize the system.

[0136] ① Replace formulas (2), (4), (6-8), and (20) with formula (21):

[0137]

[0138] In the formula, V i,2 (t) and I ij,2 (t) represents the square of the voltage at node i at time t and the square of the current from node i to node j, respectively.

[0139] ② Process the absolute value term to make μ i (t)=|V i,2 (t)-1|:

[0140]

[0141] ③ Perform second-order cone transformations on formulas (7), (13), and (16):

[0142]

[0143]

[0144]

[0145] ④ Convert circular constraints to regular octagonal constraints:

[0146]

[0147]

[0148] Furthermore, by using convex relaxation and linearization, the original multi-objective optimization model is reformulated as the following SOCP model, as shown in Equation (28).

[0149]

[0150] Specifically, considering the uncertainties of distributed generation and load output, this embodiment of the invention constructs a multi-objective robust optimization model based on column constraint generation for the robust optimization problem of AC / DC hybrid flexible distribution networks.

[0151] Specifically, formula (28) can be written in a compact form:

[0152]

[0153] Where x represents a binary variable vector, including the charging / discharging state of the energy storage system. y is a continuous variable vector, including the active and reactive power of the flexible switch, the energy storage system, and the voltage source converter. In formula (29), A, B, C, D, F, and I... u It is the coefficient matrix corresponding to the variables of the constraint. a, c, d, f and u are constant column vectors. The second row of formula (29) corresponds to formula (2), formula (3), formula (5), formula (6), formula (8)-(9) and formula (14), the third row includes formula (9), formula (11), formula (17)-(20), formula (22) and formula (26)-(27), the fourth row indicates that uncertainty is ignored in the deterministic model, and the output power of distributed generation and load at each time step is equal to the predicted value, and the last row includes formula (23)-(25).

[0154] The deterministic optimization model (29) can be solved by second-order cone optimization. However, due to the existence of prediction errors, this method is not entirely applicable. Therefore, in this embodiment of the invention, the uncertainties of distributed generation and load are considered as shown in formula (30):

[0155]

[0156] Among them, u DG (t) and u L (t) represents the actual output power of distributed generation and loads at time t. and It is the predicted output power of distributed generation and load at time t. and It represents the maximum prediction deviation of distributed generation and load power at time t. Then, a two-stage robust optimization model is proposed to handle the uncertainty in formula (31) in order to seek the optimal solution in the worst case. u represents the uncertainty variables of distributed generation and load.

[0157]

[0158] Specifically, in the process of solving the multi-objective robust optimization model, column constraints are generated to solve the two-stage robust optimization model, represented by equation (31). This method decomposes the model into a main problem and sub-problems, i.e., a main problem model and sub-problem models, and then solves them iteratively. The main problem model is expressed as:

[0159]

[0160] In the formula, α represents the objective function value of the main problem. l is the number of iterations, and y l The variable u represents the subproblem introduced into the main problem for the lth time. l This is the worst-case scenario obtained in the l-th iteration.

[0161] The sub-problem model is expressed as follows:

[0162]

[0163] Where γ, λ, ν, ωi and It is the dual variable corresponding to the constraint. x l This represents the variable in the main problem that introduces a subproblem in the l-th iteration.

[0164] For each set of given u, equation (33) can be simplified to a deterministic optimization model. The above formula has a max-min form, where the inner minimization problem is linear for fixed x and u. Therefore, (33) can be rewritten as (34) based on strong duality theory:

[0165]

[0166] The optimal solution of equation (34) is obtained only at the boundary points of the uncertainty set. In this embodiment of the invention, the worst case occurs at the upper limit of the load and the lower limit of distributed generation. Therefore, the uncertainty set of distributed generation and load can be rewritten as shown in equation (35).

[0167]

[0168] Among them, Г DG and Γ L This is named "uncertainty," an integer between 0 and T, used to adjust the conservatism of the optimal solution. Here, we can let:

[0169]

[0170] Where, ξ DG and ξ L It is the fluctuation range coefficient of distributed generation and load.

[0171] After the above transformation, formula (34) becomes a form with binary and continuous variables, which can be transformed using linearization techniques. Then, the subproblem will be transformed into a mixed-integer linear optimization model:

[0172]

[0173] in, It is the upper limit of the dual variable of π, and is a sufficiently large value.

[0174] After the above process, the two-stage robust optimization model is decomposed into a main problem and sub-problems, and solved using a column constraint generation algorithm. The flowchart is as follows: Figure 3 As shown, where U B and L B These are the upper and lower limits of the loop, as shown in formula (38):

[0175]

[0176] Accordingly, this invention also discloses a specific application scenario of an AC / DC hybrid photovoltaic-storage distribution network optimization method:

[0177] Specifically, the verification was conducted in an improved IEEE 33-node AC / DC hybrid distribution network, such as... Figure 6 As shown. The network is divided into AC systems and DC systems via voltage source converters (VSC1, VSC2). The reference voltage for both AC and DC components is 12.66 kV. Node 1 is a relaxed node with an optimized voltage range of [0.985, 1.015]. In this embodiment, distributed generation is considered photovoltaic (PV). There are four PV systems (PV1, PV2, PV3, PV4) connected to nodes 11, 13, 20, and 31, respectively. Three energy storage systems (ESS1, ESS2, ESS3) with a maximum power of 1 MW and a rated capacity of 5 MW·h are connected to nodes 15, 24, and 30, respectively. Additionally, a multi-terminal flexible switch is connected to nodes 21, 25, and 33. Three 24-hour variable loads are connected to nodes 18, 23, and 32. It is assumed that the power direction of the voltage source converters is positive from the AC section to the DC section. The system scheduling step is 1 hour, and the system implements time-of-use pricing. The electricity price for each period is as follows: Figure 7 As shown. The power curves of the photovoltaic system and the load are as follows. Figure 8 As shown in Table 1, the parameters of the voltage source converter and the flexible switch are as follows.

[0178] Table 1

[0179]

[0180]

[0181] Specifically, a 24-hour simulation was conducted in this embodiment of the invention. To verify the performance of the proposed two-stage robust optimization method, simulations were performed under five different conditions. These five conditions are set as follows:

[0182] Case 1: Optimization only applied to the voltage source converter;

[0183] Case 2: Optimization of voltage source converter and flexible switch;

[0184] Case 3: The voltage source converter, flexible switch and energy storage system were optimized, but the uncertainties of photovoltaics and loads were not taken into account;

[0185] Case 4: Optimize the voltage source converter, flexible switch, and energy storage system, considering the uncertainties of photovoltaics and load, and predict the fluctuation range as ξ = ξ DG =ξ L =15%, Г PV =6 and Г L =6;

[0186] Case 5: Optimization of voltage source converter, flexible switch and energy storage system, considering the uncertainties of photovoltaic and load, predicting the fluctuation range as ξ = ξ DG =ξ L =15%, Г PV =6 and Г L =12;

[0187] Table 2 shows the daily operation optimization results for different cases. Comparing the results of Case 1 and Case 2, it can be found that the addition of the flexible switch reduces network losses and significantly improves the voltage curve. Taking node 33 as an example, the voltage curves with and without the flexible switch (Case 1 and Case 2) are as follows. Figure 9 and Figure 10 As shown. Compared to Case 1, the voltage curves in Case 2 are improved during the 1-8h and 19-24h periods because the flexible switch transfers power from terminals T1 and T2 to T3 during this period. The addition of the flexible switch makes the system power flow pattern more flexible, allowing for better power distribution between AC and DC networks, and increasing the economy and stability of the AC / DC hybrid distribution network.

[0188] Table 2

[0189]

[0190]

[0191] Compared to Cases 2 and 3, although the energy storage system increases operating costs, its effect on voltage deviation regulation is evident. This is because the energy storage system can absorb power when the relative power is sufficient to compensate for severe voltage drops caused by power source defects. It can be seen that voltage source converters, energy storage systems, and flexible switches can significantly improve system optimization.

[0192] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0193] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0194] The technical content provided by the present invention has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for optimizing a hybrid AC / DC photovoltaic-storage distribution network, characterized in that, include: Given a set of uncertainties, a pre-defined multi-objective robust optimization model is constructed; the set of uncertainties includes a collection of uncertainty variables corresponding to the output power of distributed generation devices and loads in an AC / DC hybrid distribution network. The objective function value of the main problem is obtained by solving the objective function of the AC / DC hybrid distribution network with the network loss, voltage deviation and operation cost as the minimum objectives based on the uncertainty set in the main problem model of the multi-objective robust optimization model. Substitute the objective function value of the main problem into the sub-problem model in the multi-objective robust optimization model to solve the objective function, and obtain a new uncertainty set and the objective function value of the sub-problem; Determine whether the difference between the objective function value of the sub-problem and the objective function value of the main problem is less than or equal to a preset threshold; If not, the new uncertainty set is returned to the multi-objective robust optimization model for iterative calculation to determine the new objective function values ​​of the main problem and the sub-problems again. If so, the target running parameters corresponding to the objective function are obtained; The multi-objective robust optimization model is a two-stage robust optimization model based on the second-order cone relaxation algorithm and the column constraint generation algorithm. When returning the new uncertainty set to the multi-objective robust optimization model for iterative calculation, the method further includes: The multi-objective robust optimization model is further enhanced by adding variables from the main problem that introduce subproblems in the next iteration and corresponding constraints for the next iteration.

2. The AC / DC hybrid photovoltaic-storage distribution network optimization method according to claim 1, characterized in that, The objective function is: f = min(λ1P) loss +λ2ΔV+λ3C op ); in, In the formula, f is the objective function value, and λ1, λ2, and λ3 are the total daily network loss (P). loss Voltage deviation (ΔV) and operating costs (C) op The weighting factors of N are λ1+λ2+λ3=1. ac and N dc These represent the number of nodes in the AC and DC power distribution systems, respectively; and the power loss P. loss Ω i R is the set of all nodes connected to node i. ij It is the resistance of the branch between node i and node j, I ij Let be the current from node i to node j, and price(t) be the electricity price at time t; voltage deviation ΔV: V i (t) is the node voltage of node i at time t, V op Minimum value and V op The maximum value is the maximum and minimum value within the voltage optimization range; operating cost C op K, N, and J represent the number of voltage source converters, flexible switches, and energy storage systems, respectively. and These are the power losses of the k-th voltage source converter and the n-th flexible switch at time t, respectively. and K represents the charging / discharging power of the j-th energy storage system. The energy storage system absorbs positive power from the grid. ess It is the unit power charging / discharging cost coefficient of the energy storage system, which depends on the investment cost and maintenance cost.

3. The AC / DC hybrid photovoltaic-storage distribution network optimization method according to claim 2, characterized in that, The constraints of the objective function include: power flow constraints, voltage source converter constraints, flexible switch constraints, energy storage system constraints, and safe operation constraints.

4. The AC / DC hybrid photovoltaic-storage distribution network optimization method according to claim 3, characterized in that, The power flow constraints include: In the formula, R is the branch set with node i as the head node, φi is the branch set with node i as the ending node, and R is the branch set with node i as the ending node. ij and X ij P represents the resistance and reactance of branch ij. ih (t) and Q ih (t) represents the active and reactive power from node i to node h at time t, P i (t) and Q i P(t) represents the active and reactive power injected by node i at time t. ij (t) and Q ij V(t) represents the active and reactive power flow from node i to node j at time t. j (t) represents the voltage amplitude at node j at time t.

5. The AC / DC hybrid photovoltaic-storage distribution network optimization method according to claim 3, characterized in that, The voltage source converter constraints include: In the formula, and These are the active and reactive power injected into the AC side of the k-th voltage source converter at time t. This represents the active power loss of the k-th voltage source converter at time t. It is the active power injected into the DC side of the k-th voltage source converter at time t. and These are the equivalent resistance and reactance of the k-th voltage source converter. This is the capacity limit of the k-th voltage source converter. It is the loss factor of the k-th voltage source converter. and It represents the upper limit of the active and reactive power of the k-th voltage source converter.

6. The AC / DC hybrid photovoltaic-storage distribution network optimization method according to claim 3, characterized in that, The constraints of the flexible switch include: In the formula, M is the number of the nth terminal of the flexible switch, and T m This represents the m-th terminal of the flexible switch. and These are the active power, reactive power, and active power loss at terminal m of the nth flexible switch at time t. It is the rated apparent power at the m-th terminal of the nth flexible switch. It is the loss coefficient of the nth flexible switch.

7. The AC / DC hybrid photovoltaic-storage distribution network optimization method according to claim 3, characterized in that, The constraints of the energy storage system include: In the formula, for the j-th energy storage system, It is the maximum charging / discharging power. It is a binary variable; the value is 0 when the energy storage system is in the charging state at time t, and 1 when it is in the discharging state. E ESS (0) and Let represent the minimum stored energy, initial stored energy, and maximum stored energy of the j-th energy storage system, respectively.

8. The AC / DC hybrid photovoltaic-storage distribution network optimization method according to claim 3, characterized in that, The safe operation constraints include: V i,min ≤V i (t)≤V i,max ; In the formula, V i,max and V i,min These are the upper and lower limits of the node voltage, I ij,max It is the maximum allowable current value for the branch.

9. The AC / DC hybrid photovoltaic-storage distribution network optimization method according to any one of claims 1 to 8, characterized in that, The uncertain set includes: In the formula, u DG (t) and u L (t) represents the actual output power of distributed generation and loads at time t. and This is the predicted output power of distributed generation and load at time t. and It represents the maximum prediction deviation of distributed generation and load power at time t, where u represents the uncertainty variable of distributed generation and load.

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