Methods and equipment for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints

Abstract

This invention discloses a coordinated optimization method for distribution networks and microgrids with embedded frequency security constraints. The method treats the distribution network and microgrids as independent entities, establishing separate models for each. The distribution network model is constructed based on a second-order cone programming model with embedded frequency security constraints; the microgrid model is constructed based on inertia and frequency regulation constraints, with the objective of minimizing scheduling costs, and employs the stochastic-conditional value-at-risk (VAT) method to assess uncertain costs. A cooperative game theory system model for the distribution network and microgrids is established, determining the reserve capacity and corresponding price provided by each microgrid through cooperative bargaining. Furthermore, the cooperative game theory system model is transformed into two sub-problems: cost minimization and benefit allocation within the cooperative game system. The optimal bargaining strategy is obtained through distributed solution using the ADMM algorithm. This invention, through the cooperative optimization of the distribution network and microgrids, leverages the frequency regulation function of microgrid energy storage, achieving more economical operation.

Description

Technical Field

[0001] This invention relates to a method for coordinating and optimizing distribution networks and microgrids, and particularly to a method and device for coordinating and optimizing distribution networks and microgrids with embedded frequency security constraints. Background Technology

[0002] Currently, with the growth of wind and solar power installed capacity, traditional thermal power is gradually being replaced, driving the green energy transition. However, the limited inertia and primary frequency regulation capabilities of wind and solar power lead to a shortage of power system inertia reserves and frequency regulation resources, posing challenges to frequency stability. The large-scale integration of solar power into the distribution network exacerbates active power fluctuations in local areas, particularly for distributed solar power, which is significantly affected by weather, increasing frequency fluctuation risks and frequency regulation pressure. To address the challenges brought about by the increasing proportion of renewable energy, it is necessary to optimize dispatch strategies, improve the frequency response capabilities of renewable energy sources, and introduce technologies such as energy storage systems.

[0003] Traditional power dispatch models primarily rely on centralized generator units on the transmission side to provide inertia and frequency regulation response, neglecting the frequency regulation potential of microgrid energy storage systems. With the rapid development of microgrids and distributed energy storage, these systems now possess strong frequency regulation capabilities. They can adjust frequency deviations through rapid charging and discharging, compensating for insufficient inertia in wind and solar power and improving system frequency stability. Therefore, optimizing the frequency regulation model and fully utilizing the frequency regulation capabilities of distributed energy storage resources is particularly important. This not only enhances the grid's frequency response but also reduces the frequency regulation pressure on the transmission side, promoting a more flexible and reliable grid development. Summary of the Invention

[0004] This invention provides a method and device for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints to solve the technical problems existing in the prior art.

[0005] The technical solution adopted by this invention to solve the technical problems existing in the prior art is as follows:

[0006] A method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints is characterized by treating the distribution network and microgrid as independent entities, establishing separate models for the distribution network and microgrid. The distribution network model is constructed based on a second-order cone programming model with embedded frequency security constraints; the microgrid model is constructed based on inertia and frequency regulation constraints with the objective of minimizing scheduling costs, and uses the stochastic-conditional value-at-risk (VAT) method to assess uncertain costs. A cooperative game system model for the distribution network and microgrid is established, and the reserve capacity and corresponding price provided by each microgrid are determined through cooperative bargaining. Furthermore, the cooperative game system model is transformed into two sub-problems: cost minimization and benefit allocation within the cooperative game system. The optimal bargaining strategy is obtained by distributed solution of the model using the ADMM algorithm.

[0007] Furthermore, the objective function for the distribution network model is established as follows:

[0008] C DN =min(C P,DN +C R,DN (1)

[0009]

[0010] In the formula:

[0011] t is the time period number;

[0012] Δt represents the size of the scheduling period;

[0013] N T Number of time periods;

[0014] i represents the microgrid serial number;

[0015] m represents the microgrid collection;

[0016] C DN For distribution network operating costs;

[0017] C P,DN The cost of purchasing and selling electricity in the power distribution network;

[0018] C R,DN For distribution network backup costs;

[0019] P g,t The amount of electricity purchased by the distribution network from the transmission network during time period t;

[0020] Let be the electricity sold by the microgrid to the distribution network during time period t;

[0021] Let t represent the amount of electricity purchased by the microgrid from the distribution network during the i-th time period;

[0022] The electricity price of the distribution network during time period t;

[0023] The electricity purchase price of the distribution network during time period t;

[0024] R g,t Reserve capacity provided for the transmission network during time period t;

[0025] R i,t The reserve capacity provided for the i-th microgrid during time period t;

[0026] The standby price for providing standby services to the power grid during time period t;

[0027] The standby price for providing standby services to the i-th microgrid during time period t;

[0028] H g,t The inertia provided to the transmission network during time period t;

[0029] H i,t The inertia provided by the i-th microgrid during time period t;

[0030] D g,t The droop factor provided for the transmission network during time period t;

[0031] D i,t The droop factor provided for the i-th microgrid in time period t;

[0032] P g This is the maximum output of the equivalent motor in the power transmission network;

[0033] P i This represents the maximum output of the i-th microgrid;

[0034] This refers to the maximum permissible rate of frequency change in a power distribution network system.

[0035] This represents the maximum permissible frequency variation in a power distribution network system.

[0036] Furthermore, the constraints of the distribution network model include line operation constraints and frequency security constraints.

[0037] Furthermore, the distribution network model is configured with photovoltaic and reactive power compensation devices (SVCs). At time t, the line operation constraints adopt the Distflow equation after second-order cone relaxation. The line operation constraints include the following equations:

[0038]

[0039] In the formula:

[0040] j is the node number;

[0041] k is the node number;

[0042] u is the node number;

[0043] N bus For the set of nodes in the distribution network;

[0044] N line For the line set in the distribution network;

[0045] N PV A set of photovoltaic nodes in a power distribution network;

[0046] p j,t Let be the active power flowing out of node j during time period t;

[0047] q j,t The reactive power flowing out of node j during time period t;

[0048] v j,t Let be the square of the voltage at node j during time period t;

[0049] P jk,t Let be the active power flowing from node j to node k during time period t;

[0050] Q jk,t Let t be the reactive power flowing from node j to node k during time period t;

[0051] P uj,t Let t be the active power flowing from node u to node j during time period t;

[0052] Q uj,t Let t be the reactive power flowing from node u to node j during time period t;

[0053] l uj,t The square of the line current between nodes u and j during time period t;

[0054] r uj Here are the line impedance parameters between nodes u and j;

[0055] x uj The line reactance parameters between nodes u and j;

[0056] p u This is the lower limit of the active power of node u in the distribution network;

[0057] q u This is the lower limit of the reactive power of node u in the distribution network;

[0058] v u This is the lower limit of the square of the voltage u at a distribution network node;

[0059] p u,t Let t be the active power flowing out of node u during time period t;

[0060] q u,t The reactive power flowing out of node u during time period t;

[0061] v u,t The square of the voltage at node u during time period t;

[0062] This represents the upper limit of the active power of node u in the distribution network;

[0063] This represents the upper limit of reactive power at node u in the distribution network.

[0064] This is the upper limit of the square of the voltage u at a distribution network node;

[0065] l uj The square of the line current between nodes u and j in the distribution network;

[0066] This is the upper limit of the square of the line current between nodes u and j in the distribution network;

[0067] P j,g,t The active power injected into the transmission network connected to node j during time period t;

[0068] Let t be the electricity sold by the distribution network to the i-th microgrid connected to node j during time period t;

[0069] Let t be the power purchased by the distribution network to the i-th microgrid connected to node j during time period t;

[0070] Let be the power generation capacity of the photovoltaic system connected to node j during time period t;

[0071] Let be the active load power of node j during time period t;

[0072] Q j,g,t The reactive power injected into the transmission network connected to node j during time period t;

[0073] The reactive power compensated by the SVC connected to node j during time period t;

[0074] Let be the reactive load power of node j during time period t;

[0075] The maximum power of the photovoltaic system connected to node k during time period t;

[0076] The arrows in j→k indicate the direction of power flow.

[0077] Furthermore, the equivalent motor model of the distribution network frequency response is constructed as follows:

[0078]

[0079] In the formula:

[0080] i represents the microgrid serial number;

[0081] m represents the microgrid collection;

[0082] H total The equivalent inertia of a cooperative game system;

[0083] D total The equivalent downward coefficient of the cooperative game system;

[0084] H g The inertia provided to the power transmission network;

[0085] P g This is the maximum output of the equivalent motor in the power transmission network;

[0086] D g This represents the droop coefficient of the power transmission network.

[0087] P d This represents the maximum load demand of the distribution network.

[0088] H i The inertia provided for the i-th microgrid;

[0089] P i This represents the maximum output of the i-th microgrid;

[0090] D i Let be the droop coefficient of the i-th microgrid;

[0091] Based on the equivalent motor model of the distribution network frequency response, the following frequency security constraints are constructed:

[0092]

[0093] In the formula:

[0094] F(H total D total ) is H total and D total Nonlinear functions;

[0095] K α The upper quantile of the perturbation;

[0096] This represents the maximum permissible quasi-steady-state deviation in a cooperative game system.

[0097] The maximum allowed rate of change of frequency in a cooperative game system;

[0098] This represents the maximum allowed frequency variation in a cooperative game system.

[0099] D0 represents the damping of the power distribution network system;

[0100] h is the hyperplane index;

[0101] For the h-th approximation F(H) total D total The intercept of the hyperplane;

[0102] For the h-th approximation F(H) totalD total The hyperplane of H total The fitting coefficient;

[0103] For the h-th approximation F(H) total D total The hyperplane of ) about D total Fit coefficients.

[0104] Furthermore, minimizing the scheduling cost is taken as the optimization objective of the i-th microgrid operation. CVaR is used to quantify the risk cost caused by uncertainties in the microgrid. The objective function of the microgrid model is set as follows:

[0105]

[0106]

[0107] In the formula:

[0108] t is the time period number;

[0109] Δt represents the size of the scheduling period;

[0110] N T Number of time periods;

[0111] i represents the microgrid serial number;

[0112] ω represents the scene number;

[0113] S represents the total number of scenes;

[0114] σ i This is a risk coefficient used to weigh the relationship between scheduling costs and risk costs.

[0115] C i Let be the scheduling cost of the i-th microgrid;

[0116] Let be the expected scheduling cost for all scenarios of the i-th microgrid;

[0117] Let be the scheduling risk cost of the i-th microgrid;

[0118] Let the reserve revenue be that of the i-th microgrid;

[0119] Let $t$ be the reserve price for the $i$-th microgrid during time period $t$.

[0120] R i,t Let be the reserve capacity of the i-th microgrid during time period t;

[0121] Let be the energy storage degradation cost of the i-th microgrid;

[0122] Let be the electricity purchase and sale cost of the i-th microgrid;

[0123] Let be the degradation cost of the thermal storage system of the i-th microgrid;

[0124] ρ i,ω Let ω be the probability of the i-th microgrid occurring in scenario ω.

[0125] K ESS The degradation coefficient of the energy storage system;

[0126] The charging power of the energy storage system under the i-th microgrid scenario ω in time period t;

[0127] Let ω be the discharge power of the energy storage system in the i-th microgrid scenario during time period t;

[0128] The amount of electricity purchased by the distribution network from the i-th microgrid during time period t;

[0129] Let t be the amount of electricity sold by the distribution network to the i-th microgrid during time period t;

[0130] The electricity price sold in the distribution network;

[0131] The purchase price of electricity for the power distribution network;

[0132] K HSS The degradation coefficient of a thermal storage electric boiler;

[0133] Let be the thermal storage power of the thermal storage electric boiler in the i-th microgrid during time period t;

[0134] Let be the heat release power of the thermal storage electric boiler in the i-th microgrid during time period t;

[0135] ζ is an auxiliary variable, and its optimal value is the value at risk.

[0136] α represents the CVaR confidence level;

[0137] [ ] + Indicates a positive value, [x] + =max{x,0};

[0138] C i,ω Let ω be the scheduling cost for the i-th microgrid scenario;

[0139] Let be the energy interaction cost of the i-th microgrid during time period t;

[0140] Let be the degradation cost of the thermal storage electric boiler during the i-th microgrid time period t.

[0141] Furthermore, the constraints of the microgrid model include operational constraints; these constraints include load balancing constraints for cooling, heating, and electricity; operational constraints for battery energy storage systems; operational constraints for thermal storage electric boiler systems; and electricity purchase and sale constraints.

[0142] The following constraints are set for balancing cooling, heating, and electrical loads:

[0143]

[0144] In the formula:

[0145] Let be the predicted photovoltaic power of the i-th microgrid in time period t;

[0146] Let be the photovoltaic power prediction error for the i-th microgrid scenario ω during time period t;

[0147] Let ω represent the curtailed solar power in the i-th microgrid scenario during time period t.

[0148] Let be the predicted wind power output of the i-th microgrid during time period t;

[0149] Let be the wind power prediction error for the i-th microgrid scenario ω during time period t;

[0150] Let ω represent the wind curtailment power in the i-th microgrid scenario during time period t.

[0151] Let be the predicted electrical load power of the i-th microgrid during time period t;

[0152] Let be the power load prediction error for the i-th microgrid scenario ω during time period t;

[0153] Let be the electrical power of the thermal storage electric boiler in the i-th microgrid during time period t;

[0154] Let t be the predicted heat load power of the i-th microgrid during time period t;

[0155] Let be the input power of the absorption chiller in the i-th microgrid during time period t;

[0156] η HSSFor heat storage and heat release efficiency;

[0157] η EB The electro-thermal conversion efficiency of a thermal storage electric boiler;

[0158] Let be the predicted cooling load power of the i-th microgrid during time period t;

[0159] η AC The working efficiency of the absorption chiller;

[0160] The operating constraints for the battery energy storage system are set as follows:

[0161]

[0162] SOC min ≤SOC i,t,ω ≤SOC max (34)

[0163]

[0164] In the formula:

[0165] SOC i,t,ω The state of charge of the battery energy storage system under the i-th microgrid scenario ω in time period t;

[0166] SOC i,t-1,ω The state of charge of the battery energy storage system under the i-th microgrid scenario ω in time period t-1;

[0167] SOC min This represents the minimum charge value for the battery energy storage system.

[0168] SOC max This represents the maximum charge of the battery energy storage system.

[0169] η represents the charge / discharge efficiency of the battery energy storage system;

[0170] Let be the maximum capacity of the i-th microgrid battery energy storage system;

[0171] Let be the binary variable representing the charging and discharging state of the battery energy storage system under the i-th microgrid scenario ω in time period t;

[0172] λ ESS This refers to the maximum charge / discharge rate of the battery energy storage system.

[0173] The backup capacity provided by the battery energy storage system for the i-th microgrid in time period t;

[0174] Δt fr This is the frequency modulation response time;

[0175] The operating constraints of the thermal storage electric boiler thermal storage system are as follows:

[0176] The thermal storage system of the thermal storage electric boiler is not subject to frequency regulation and no standby capacity is set. It only needs to ensure that the thermal storage value is within the upper and lower limits and is continuous.

[0177] The constraints for purchasing and selling electricity are set as follows:

[0178] The value of the electricity purchase or sale of the i-th microgrid within a time period should meet the upper and lower limit constraints.

[0179] Furthermore, the following cooperative game system model for the distribution network and microgrid is established:

[0180]

[0181] In the formula:

[0182] C DN,0 Costs incurred by the distribution network that did not participate in the cooperation;

[0183] C DN,co The costs associated with the distribution network's participation in the cooperation;

[0184] The cost for the i-th microgrid that did not participate in the cooperation;

[0185] Let be the cost of the i-th microgrid participating in the cooperation.

[0186] Furthermore, the equilibrium solution problem of the cooperative game system model is decomposed into two sub-problems: minimizing system costs and allocating benefits. The optimal bargaining strategy is obtained through sequential optimization. Where R i The reserve capacity provided for the i-th microgrid; The standby price for providing standby services to the i-th microgrid;

[0187] The objective function for the subproblem of minimizing system cost is set as follows:

[0188]

[0189] In the formula:

[0190] t is the time period number;

[0191] Δt represents the size of the scheduling period;

[0192] N T Number of time periods;

[0193] i represents the microgrid serial number;

[0194] m represents the microgrid collection;

[0195] C P,DN The cost of purchasing and selling electricity in the power distribution network;

[0196] C s Costs of cooperative game systems;

[0197] Reserve costs paid by the distribution network to the transmission network;

[0198] Let be the expected scheduling cost for all scenarios of the i-th microgrid;

[0199] σ i This is a risk coefficient used to weigh the relationship between scheduling costs and risk costs.

[0200] The risk cost of the i-th microgrid;

[0201] R g,t Reserve capacity provided for the transmission network during time period t;

[0202] c g,t The reserve price of the transmission network during time period t;

[0203] For the subproblem of minimizing system cost, let... Let i be the reserve capacity that the distribution network expects the i-th microgrid to provide during time period t. Let R be the reserve capacity that the i-th microgrid is willing to provide to the distribution network during time period t; introduce the reserve capacity R provided by the i-th microgrid during time period t. i,t Couple the components and introduce consistency constraints. To achieve decoupling; using the ADMM algorithm for decomposition and computation, the following optimization model for minimizing the system cost subproblem is obtained:

[0204]

[0205] In the formula:

[0206] For the augmented Lagrangian function of the distribution network with respect to the subproblem of minimizing system cost;

[0207] λ i,t,pr1 The Lagrange multiplier for the reserve power exchanged between the distribution network and the i-th microgrid during time period t in the subproblem of minimizing system cost;

[0208] ρ pr1 The penalty factor for the subproblem of minimizing system cost;

[0209] L i,pr1 Let be the augmented Lagrangian function of the i-th microgrid with respect to the subproblem of minimizing system cost;

[0210] The constraints are the respective operational constraints for the distribution network and the microgrid;

[0211] The formula for updating variables during iteration is:

[0212]

[0213] The convergence condition is:

[0214]

[0215] In the formula:

[0216] w is the sequence number of the step-by-step iteration;

[0217] argmin represents the variable that minimizes the function;

[0218] This represents the reserve capacity that the distribution network expects the i-th microgrid to provide during the (w+1)-th iteration.

[0219] The backup capacity that the distribution network expects the i-th microgrid to provide at the w-th iteration;

[0220] This represents the reserve capacity that the distribution network expects the i-th microgrid to provide during the (w-1)-th iteration.

[0221] Let be the reserve capacity that the i-th microgrid is willing to provide to the distribution network at the w-th iteration;

[0222] This represents the reserve capacity that the i-th microgrid is willing to provide to the distribution network at the (w+1)-th iteration.

[0223] r pr1 (w) represents the original residual of the subproblem of minimizing system cost at the w-th iteration;

[0224] s pr1 (w) represents the dual residual of the subproblem minimizing the system cost at the w-th iteration;

[0225] ε pr1,pri The original residual convergence accuracy of the subproblem minimizing system cost at the w-th iteration;

[0226] ε pr1,dual Let be the convergence accuracy of the dual residual of the subproblem minimizing the system cost at the w-th iteration;

[0227] L i Let be the augmented Lagrangian function of the i-th microgrid with respect to the subproblem of minimizing system cost;

[0228] λi,pr1 (w) is the Lagrange multiplier of the reserve power exchanged between the distribution network and the i-th microgrid in the w-th iteration of the subproblem of minimizing system cost;

[0229] λ i,pr1 (w+1) is the Lagrange multiplier of the reserve power exchanged between the distribution network and the i-th microgrid in the (w+1)-th iteration of the subproblem of minimizing system cost;

[0230] The reserve capacity after the interaction between the distribution network and each microgrid is obtained by solving the subproblem of minimizing system cost. The reserve capacity is then substituted into formula 39 to solve for the reserve price.

[0231] The objective function for the benefit allocation subproblem is set as follows:

[0232]

[0233] Taking the logarithm of the objective function of the benefit allocation subproblem, we get:

[0234]

[0235] In the formula:

[0236] C P,DN,* The result is the solution for the cost of purchasing and selling electricity;

[0237] The solution for the reserve costs paid by the distribution network to the transmission network;

[0238] This represents the solution for the reserve capacity negotiated between the i-th microgrid and the distribution network during time period t.

[0239] This represents the solution for the expected scheduling cost for all scenarios of the i-th microgrid.

[0240] This represents the solution for the risk cost of the i-th microgrid.

[0241] Let be the reserve price of the i-th microgrid in time period t;

[0242] Similarly, the ADMM algorithm is used to solve the objective function of the benefit allocation subproblem, introducing... As a coupling variable, the optimization model after decoupling by introducing consistency constraints is as follows:

[0243]

[0244] In the formula:

[0245] For the augmented Lagrangian function of the distribution network with respect to the benefit allocation problem;

[0246] The standby capacity quotation from the distribution network to the i-th microgrid during time period t;

[0247] The reserve capacity bid of the i-th microgrid to the distribution network during time period t;

[0248] L i,pr2 Let be the augmented Lagrangian function of the i-th microgrid with respect to the benefit distribution subproblem;

[0249] λ i,t,pr2 For the Lagrange multiplier of the interaction power between the distribution network and the i-th microgrid in time period t in the benefit allocation subproblem;

[0250] ρ pr2 The penalty factor for the sub-problem of allocating benefits.

[0251] The present invention also provides an apparatus for a method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints, comprising a memory and a processor, wherein the memory is used to store a computer program; and the processor is used to execute the computer program and, when executing the computer program, implement the steps of the method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints as described above.

[0252] The advantages and positive effects of this invention are:

[0253] (1) A second-order cone programming model of distribution network with embedded frequency security constraints was constructed. Combined with the equivalent frequency response model, the constraints such as the maximum rate of change of frequency, the maximum deviation and the steady-state frequency were considered. The optimal combination of inertia and droop coefficient of distribution network can be determined, thereby optimizing the reserve requirements of distribution network and improving frequency security.

[0254] (2) The model optimizes the collaboration between the distribution network and the microgrid, giving full play to the frequency regulation role of the microgrid energy storage, thereby reducing the dependence on the frequency regulation resources of the transmission network and achieving more economical operation.

[0255] (3) The complex non-convex nonlinear problem is decomposed into two sub-problems: maximizing social benefits and distributing income. By iteratively solving the reserve capacity and reserve price step by step, the global optimal solution is achieved. The optimization process is more efficient than traditional complex solution methods. Attached Figure Description

[0256] Figure 1 This is a frequency response model aggregated on the distribution network side in an embodiment of the distribution network and microgrid coordination optimization method with embedded frequency security constraints of the present invention.

[0257] Figure 2This is a diagram illustrating the frequency response process of a distribution network in an embodiment of a method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints, according to the present invention.

[0258] Figure 3 This is an embodiment of the distribution network disturbance and the provision of reserve capacity for each part in a method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints according to the present invention.

[0259] Figure 4 This is an embodiment of the distribution network and microgrid coordination optimization method with embedded frequency security constraints of the present invention, which specifies the standby capacity price negotiated between the distribution network and the microgrid.

[0260] Figure 1 Chinese: F H T represents the proportion of electricity generated by high-pressure turbines. R The generator reheat time constant is represented by ΔP; the disturbance in the distribution network is represented by ΔP; the distribution network system damping is represented by D0; s is the differential operator; Δf is the frequency deviation; H total D is the equivalent inertia of a cooperative game system. total This is the equivalent downward coefficient of the cooperative game system.

[0261] Figure 2 In the diagram: Microgrid 1 represents the first microgrid; Microgrid 2 represents the second microgrid; Microgrid 3 represents the third microgrid. Detailed Implementation

[0262] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0263] The following are the Chinese definitions of English words, abbreviations, and phrases:

[0264] SVC: Static Var Compensator.

[0265] Distflow equation: Second-order cone power flow equation. The DistFlow model can accurately reflect the actual operation of the distribution network and can be used to simulate and optimize the situation after the distribution network is reconfigured.

[0266] Nash bargaining is a game theory model proposed by John Nash, primarily used to solve the problem of finding the optimal solution in a bargaining process between two players. The core idea of ​​the Nash bargaining model is to find an allocation method that allows each player to obtain the maximum utility under given constraints.

[0267] ADMM Algorithm: The Alternating Direction Method of Multipliers (ADMM) is an iterative algorithm for solving optimization problems, particularly those that can be decomposed into multiple subproblems. ADMM combines the characteristics of the Lagrange multiplier method and the splitting method, approximating the global optimum by alternately optimizing the splitting subproblems of the original problem and updating the multipliers. It is especially effective in handling large-scale and distributed optimization problems and is widely used in machine learning, signal processing, statistical learning, image processing, and other fields.

[0268] Please see Figures 1 to 4 A method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints is proposed. The distribution network and microgrid are treated as independent entities, and separate distribution network and microgrid models are established. The distribution network model is constructed based on a second-order cone programming model with embedded frequency security constraints; the microgrid model is constructed based on inertia and frequency regulation constraints with the objective of minimizing scheduling costs, and uses the stochastic-conditional value-at-risk (VAT) method to assess uncertain costs. A cooperative game system model of the distribution network and microgrid is established, and the reserve capacity and corresponding price provided by each microgrid are determined through cooperative bargaining. Furthermore, the cooperative game system model is transformed into two sub-problems: cost minimization and benefit allocation within the cooperative game system. The optimal bargaining strategy is obtained through distributed solution of the model using the ADMM algorithm.

[0269] Preferably, the objective function for the distribution network model can be established as follows:

[0270] C DN =min(C P,DN +C R,DN (1)

[0271]

[0272] In the formula:

[0273] t is the time period number;

[0274] Δt represents the size of the scheduling period;

[0275] N T Number of time periods;

[0276] i represents the microgrid serial number;

[0277] m represents the microgrid collection;

[0278] C DN For distribution network operating costs;

[0279] C P,DN The cost of purchasing and selling electricity in the power distribution network;

[0280] CR,DN For distribution network backup costs;

[0281] P g,t The amount of electricity purchased by the distribution network from the transmission network during time period t;

[0282] Let be the electricity sold by the microgrid to the distribution network during time period t;

[0283] Let t represent the amount of electricity purchased by the microgrid from the distribution network during the i-th time period;

[0284] The electricity price of the distribution network during time period t;

[0285] The electricity purchase price of the distribution network during time period t;

[0286] R g,t Reserve capacity provided for the transmission network during time period t;

[0287] R i,t The reserve capacity provided for the i-th microgrid during time period t;

[0288] The standby price for providing standby services to the power grid during time period t;

[0289] The standby price for providing standby services to the i-th microgrid during time period t;

[0290] H g,t The inertia provided to the transmission network during time period t;

[0291] H i,t The inertia provided by the i-th microgrid during time period t;

[0292] D g,t The droop factor provided for the transmission network during time period t;

[0293] D i,t The droop factor provided for the i-th microgrid in time period t;

[0294] P g This is the maximum output of the equivalent motor in the power transmission network;

[0295] P i This represents the maximum output of the i-th microgrid;

[0296] This refers to the maximum permissible rate of frequency change in a power distribution network system.

[0297] This represents the maximum permissible frequency variation in a power distribution network system.

[0298] Preferably, the constraints of the distribution network model may include line operation constraints and frequency security constraints.

[0299] Preferably, the distribution network model can be configured with photovoltaic and reactive power compensation devices (SVCs). At time t, the line operation constraints can adopt the Distflow equation after second-order cone relaxation. The line operation constraints can include the following equations:

[0300]

[0301]

[0302] In the formula:

[0303] j is the node number;

[0304] k is the node number;

[0305] u is the node number;

[0306] N bus For the set of nodes in the distribution network;

[0307] N line For the line set in the distribution network;

[0308] N PV A set of photovoltaic nodes in a power distribution network;

[0309] p j,t Let be the active power flowing out of node j during time period t;

[0310] q j,t The reactive power flowing out of node j during time period t;

[0311] v j,t Let be the square of the voltage at node j during time period t;

[0312] P jk,t Let be the active power flowing from node j to node k during time period t;

[0313] Q jk,t Let t be the reactive power flowing from node j to node k during time period t;

[0314] P uj,t Let t be the active power flowing from node u to node j during time period t;

[0315] Q uj,t Let t be the reactive power flowing from node u to node j during time period t;

[0316] l uj,t The square of the line current between nodes u and j during time period t;

[0317] r ujHere are the line impedance parameters between nodes u and j;

[0318] x uj The line reactance parameters between nodes u and j;

[0319] p u This is the lower limit of the active power of node u in the distribution network;

[0320] q u This is the lower limit of the reactive power of node u in the distribution network;

[0321] v u This is the lower limit of the square of the voltage u at a distribution network node;

[0322] p u,t Let t be the active power flowing out of node u during time period t;

[0323] q u,t The reactive power flowing out of node u during time period t;

[0324] v u,t The square of the voltage at node u during time period t;

[0325] This represents the upper limit of the active power of node u in the distribution network;

[0326] This represents the upper limit of reactive power at node u in the distribution network.

[0327] This is the upper limit of the square of the voltage u at a distribution network node;

[0328] l uj The square of the line current between nodes u and j in the distribution network;

[0329] This is the upper limit of the square of the line current between nodes u and j in the distribution network;

[0330] P j,g,t The active power injected into the transmission network connected to node j during time period t;

[0331] Let t be the electricity sold by the distribution network to the i-th microgrid connected to node j during time period t;

[0332] Let t be the power purchased by the distribution network to the i-th microgrid connected to node j during time period t;

[0333] Let be the power generation capacity of the photovoltaic system connected to node j during time period t;

[0334] Let be the active load power of node j during time period t;

[0335] Q j,g,t The reactive power injected into the transmission network connected to node j during time period t;

[0336] The reactive power compensated by the SVC connected to node j during time period t;

[0337] Let be the reactive load power of node j during time period t;

[0338] The maximum power of the photovoltaic system connected to node k during time period t;

[0339] The arrows in j→k indicate the direction of power flow.

[0340] Preferably, the equivalent motor model of the distribution network frequency response can be constructed as follows:

[0341]

[0342] In the formula:

[0343] i represents the microgrid serial number;

[0344] m represents the microgrid collection;

[0345] H total The equivalent inertia of a cooperative game system;

[0346] D total The equivalent downward coefficient of the cooperative game system;

[0347] H g The inertia provided to the power transmission network;

[0348] P g This is the maximum output of the equivalent motor in the power transmission network;

[0349] D g This represents the droop coefficient of the power transmission network.

[0350] P d This represents the maximum load demand of the distribution network.

[0351] H i The inertia provided for the i-th microgrid;

[0352] P i This represents the maximum output of the i-th microgrid;

[0353] D i Let be the droop coefficient of the i-th microgrid;

[0354] The following frequency security constraints can be constructed based on the equivalent motor model of the distribution network frequency response:

[0355]

[0356] In the formula:

[0357] F(H total D total ) is H total and D total Nonlinear functions;

[0358] K α The upper quantile of the perturbation;

[0359] This represents the maximum permissible quasi-steady-state deviation in a cooperative game system.

[0360] The maximum allowed rate of change of frequency in a cooperative game system;

[0361] This represents the maximum allowed frequency variation in a cooperative game system.

[0362] D0 represents the damping of the power distribution network system;

[0363] h is the hyperplane index;

[0364] For the h-th approximation F(H) total D total The intercept of the hyperplane;

[0365] For the h-th approximation F(H) total D total The hyperplane of H total The fitting coefficient;

[0366] For the h-th approximation F(H) total D total The hyperplane of ) about D total Fit coefficients.

[0367] F(H total D total ) is H total and D total The nonlinear function forms a surface in space. It is processed using the piecewise linear method, which uses multiple hyperplanes to approximate this surface.

[0368] Preferably, minimizing the scheduling cost can be used as the optimization objective for the i-th microgrid operation. CVaR is used to quantify the risk cost caused by uncertainties in the microgrid. The objective function of the microgrid model can be set as follows:

[0369]

[0370]

[0371] In the formula:

[0372] t is the time period number;

[0373] Δt represents the size of the scheduling period;

[0374] N T Number of time periods;

[0375] i represents the microgrid serial number;

[0376] ω represents the scene number;

[0377] S represents the total number of scenes;

[0378] σ i This is a risk coefficient used to weigh the relationship between scheduling costs and risk costs.

[0379] C i Let be the scheduling cost of the i-th microgrid;

[0380] Let be the expected scheduling cost for all scenarios of the i-th microgrid;

[0381] Let be the scheduling risk cost of the i-th microgrid;

[0382] Let the reserve revenue be that of the i-th microgrid;

[0383] Let $t$ be the reserve price for the $i$-th microgrid during time period $t$.

[0384] R i,t Let be the reserve capacity of the i-th microgrid during time period t;

[0385] Let be the energy storage degradation cost of the i-th microgrid;

[0386] Let be the electricity purchase and sale cost of the i-th microgrid;

[0387] Let be the degradation cost of the thermal storage system of the i-th microgrid;

[0388] ρ i,ω Let ω be the probability of the i-th microgrid occurring in scenario ω.

[0389] K ESS The degradation coefficient of the energy storage system;

[0390] The charging power of the energy storage system under the i-th microgrid scenario ω in time period t;

[0391] Let ω be the discharge power of the energy storage system in the i-th microgrid scenario during time period t;

[0392] The amount of electricity purchased by the distribution network from the i-th microgrid during time period t;

[0393] Let t be the amount of electricity sold by the distribution network to the i-th microgrid during time period t;

[0394] The electricity price sold in the distribution network;

[0395] The purchase price of electricity for the power distribution network;

[0396] K HSS The degradation coefficient of a thermal storage electric boiler;

[0397] Let be the thermal storage power of the thermal storage electric boiler in the i-th microgrid during time period t;

[0398] Let be the heat release power of the thermal storage electric boiler in the i-th microgrid during time period t;

[0399] ζ is an auxiliary variable, and its optimal value is the value at risk.

[0400] α represents the CVaR confidence level;

[0401] [ ] + Indicates a positive value, [x] + =max{x,0};

[0402] G i,ω Let ω be the scheduling cost for the i-th microgrid scenario;

[0403] Let be the energy interaction cost of the i-th microgrid during time period t;

[0404] Let be the degradation cost of the thermal storage electric boiler during the i-th microgrid time period t.

[0405] Preferably, the constraints of the microgrid model may include operational constraints; the operational constraints of the microgrid may include load balance constraints for cooling, heating, and electricity, operational constraints for battery energy storage systems, operational constraints for thermal storage electric boiler systems, and electricity purchase and sale constraints; wherein:

[0406] The following load balance constraints for cooling, heating, and electricity can be set:

[0407]

[0408] In the formula:

[0409] Let be the predicted photovoltaic power of the i-th microgrid in time period t;

[0410] Let be the photovoltaic power prediction error for the i-th microgrid scenario ω during time period t;

[0411] Let ω represent the curtailed solar power in the i-th microgrid scenario during time period t.

[0412] Let be the predicted wind power output of the i-th microgrid during time period t;

[0413] Let be the wind power prediction error for the i-th microgrid scenario ω during time period t;

[0414] Let ω represent the wind curtailment power in the i-th microgrid scenario during time period t.

[0415] Let be the predicted electrical load power of the i-th microgrid during time period t;

[0416] Let be the power load prediction error for the i-th microgrid scenario ω during time period t;

[0417] Let be the electrical power of the thermal storage electric boiler in the i-th microgrid during time period t;

[0418] Let t be the predicted heat load power of the i-th microgrid during time period t;

[0419] Let be the input power of the absorption chiller in the i-th microgrid during time period t;

[0420] η HSS For heat storage and heat release efficiency;

[0421] η EB The electro-thermal conversion efficiency of a thermal storage electric boiler;

[0422] Let be the predicted cooling load power of the i-th microgrid during time period t;

[0423] η AC The working efficiency of the absorption chiller;

[0424] The following operating constraints can be set for the battery energy storage system:

[0425]

[0426] SOC min≤SOC i,t,ω ≤SOC max (34)

[0427]

[0428] In the formula:

[0429] SOC i,t,ω The state of charge of the battery energy storage system under the i-th microgrid scenario ω in time period t;

[0430] SOC i,t-1,ω The state of charge of the battery energy storage system under the i-th microgrid scenario ω in time period t-1;

[0431] SOC min This represents the minimum charge value for the battery energy storage system.

[0432] SOC max This represents the maximum charge of the battery energy storage system.

[0433] η represents the charge / discharge efficiency of the battery energy storage system;

[0434] Let be the maximum capacity of the i-th microgrid battery energy storage system;

[0435] Let be the binary variable representing the charging and discharging state of the battery energy storage system under the i-th microgrid scenario ω in time period t;

[0436] λ ESS This refers to the maximum charge / discharge rate of the battery energy storage system.

[0437] The backup capacity provided by the battery energy storage system for the i-th microgrid in time period t;

[0438] Δt fr This is the frequency modulation response time;

[0439] The operating constraints of a thermal storage electric boiler thermal storage system can be as follows:

[0440] The thermal storage system of the thermal storage electric boiler is not subject to frequency regulation and no standby capacity is set. It only needs to ensure that the thermal storage value is within the upper and lower limits and is continuous.

[0441] The following can be used to set constraints on electricity purchase and sale:

[0442] The value of the electricity purchase or sale of the i-th microgrid within a time period should meet the upper and lower limit constraints.

[0443] Preferably, the following cooperative game system model between the distribution network and the microgrid can be established:

[0444]

[0445] In the formula:

[0446] C DN,0 Costs incurred by the distribution network that did not participate in the cooperation;

[0447] C DN,co The costs associated with the distribution network's participation in the cooperation;

[0448] The cost for the i-th microgrid that did not participate in the cooperation;

[0449] Let be the cost of the i-th microgrid participating in the cooperation.

[0450] Preferably, the equilibrium solution problem of the cooperative game system model is decomposed into two sub-problems: minimizing system costs and allocating benefits. The optimal bargaining strategy is obtained through sequential optimization. Where R i The reserve capacity provided for the i-th microgrid; The standby price for providing standby services to the i-th microgrid;

[0451] The objective function for the subproblem of minimizing system cost can be set as follows:

[0452]

[0453] In the formula:

[0454] t is the time period number;

[0455] Δt represents the size of the scheduling period;

[0456] N T Number of time periods;

[0457] i represents the microgrid serial number;

[0458] m represents the microgrid collection;

[0459] C P,DN The cost of purchasing and selling electricity in the power distribution network;

[0460] C s Costs of cooperative game systems;

[0461] Reserve costs paid by the distribution network to the transmission network;

[0462] Let be the expected scheduling cost for all scenarios of the i-th microgrid;

[0463] σ i This is a risk coefficient used to weigh the relationship between scheduling costs and risk costs.

[0464] The risk cost of the i-th microgrid;

[0465] R g,t Reserve capacity provided for the transmission network during time period t;

[0466] c g,t The reserve price of the transmission network during time period t;

[0467] For the subproblem of minimizing system cost, we can set... Let i be the reserve capacity that the distribution network expects the i-th microgrid to provide during time period t. Let R be the reserve capacity that the i-th microgrid is willing to provide to the distribution network during time period t; the reserve capacity R provided by the i-th microgrid during time period t can be introduced. i,t Couple the components and introduce consistency constraints. To achieve decoupling; by using the ADMM algorithm for decomposition and calculation, the following optimization model for the system cost minimization subproblem can be obtained:

[0468]

[0469] In the formula:

[0470] For the augmented Lagrangian function of the distribution network with respect to the subproblem of minimizing system cost;

[0471] λ i,t,pr1 The Lagrange multiplier for the reserve power exchanged between the distribution network and the i-th microgrid during time period t in the subproblem of minimizing system cost;

[0472] ρ pr1 The penalty factor for the subproblem of minimizing system cost;

[0473] L i,pr1 Let be the augmented Lagrangian function of the i-th microgrid with respect to the subproblem of minimizing system cost;

[0474] The constraints are the respective operational constraints for the distribution network and the microgrid;

[0475] The formula for updating variables during iteration is:

[0476]

[0477] The convergence condition is:

[0478]

[0479] In the formula:

[0480] w is the sequence number of the step-by-step iteration;

[0481] argmin represents the variable that minimizes the function;

[0482] This represents the reserve capacity that the distribution network expects the i-th microgrid to provide during the (w+1)-th iteration.

[0483] The backup capacity that the distribution network expects the i-th microgrid to provide at the w-th iteration;

[0484] This represents the reserve capacity that the distribution network expects the i-th microgrid to provide during the (w-1)-th iteration.

[0485] Let be the reserve capacity that the i-th microgrid is willing to provide to the distribution network at the w-th iteration;

[0486] This represents the reserve capacity that the i-th microgrid is willing to provide to the distribution network at the (w+1)-th iteration.

[0487] r pr1 (w) represents the original residual of the subproblem of minimizing system cost at the w-th iteration;

[0488] s pr1 (w) represents the dual residual of the subproblem minimizing the system cost at the w-th iteration;

[0489] ε pr1,pri The original residual convergence accuracy of the subproblem minimizing system cost at the w-th iteration;

[0490] ε pr1,dual Let be the convergence accuracy of the dual residual of the subproblem minimizing the system cost at the w-th iteration;

[0491] L i Let be the augmented Lagrangian function of the i-th microgrid with respect to the subproblem of minimizing system cost;

[0492] λ i,pr1 (w) is the Lagrange multiplier of the reserve power exchanged between the distribution network and the i-th microgrid in the w-th iteration of the subproblem of minimizing system cost;

[0493] λ i,pr1 (w+1) is the Lagrange multiplier of the reserve power exchanged between the distribution network and the i-th microgrid in the (w+1)-th iteration of the subproblem of minimizing system cost;

[0494] The reserve capacity after the interaction between the distribution network and each microgrid is obtained by solving the subproblem of minimizing system cost. The reserve capacity is then substituted into formula 39 to solve for the reserve price.

[0495] The objective function for the benefit allocation subproblem can be set as follows:

[0496]

[0497] Taking the logarithm of the objective function of the benefit allocation subproblem, we get:

[0498]

[0499] In the formula:

[0500] C P,DN,* The result is the solution for the cost of purchasing and selling electricity;

[0501] The solution for the reserve costs paid by the distribution network to the transmission network;

[0502] This represents the solution for the reserve capacity negotiated between the i-th microgrid and the distribution network during time period t.

[0503] This represents the solution for the expected scheduling cost for all scenarios of the i-th microgrid.

[0504] This represents the solution for the risk cost of the i-th microgrid.

[0505] Let be the reserve price of the i-th microgrid in time period t;

[0506] Similarly, the ADMM algorithm can be used to solve the objective function of the benefit allocation subproblem, and can introduce... As a coupling variable, the optimization model after decoupling by introducing consistency constraints is as follows:

[0507]

[0508] In the formula:

[0509] For the augmented Lagrangian function of the distribution network with respect to the benefit allocation problem;

[0510] The standby capacity quotation from the distribution network to the i-th microgrid during time period t;

[0511] The reserve capacity bid of the i-th microgrid to the distribution network during time period t;

[0512] L i,pr2 Let be the augmented Lagrangian function of the i-th microgrid with respect to the benefit distribution subproblem;

[0513] λ i,t,pr2 For the Lagrange multiplier of the interaction power between the distribution network and the i-th microgrid in time period t in the benefit allocation subproblem;

[0514] ρpr2 The penalty factor for the sub-problem of allocating benefits.

[0515] The aforementioned transmission network is the upper-level power grid of the distribution network.

[0516] The present invention also provides an apparatus for a method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints, comprising a memory and a processor, wherein the memory is used to store a computer program; and the processor is used to execute the computer program and, when executing the computer program, implement the steps of the method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints as described above.

[0517] The workflow and working principle of the present invention will be further described below with reference to a preferred embodiment:

[0518] This invention relates to a coordinated frequency security constraint scheduling system for distribution networks and microgrids based on Nash bargaining, and its structural framework is as follows: Figure 1 As shown, the coordinated optimization model mainly consists of two parts:

[0519] 1) Two-layer optimization model for distribution network and microgrid: The distribution network and microgrid are treated as independent entities. The distribution network model is a second-order cone programming model with embedded frequency security constraints, while the microgrid is economically dispatched based on inertia and frequency regulation requirements, and the stochastic-conditional value-at-risk method is used to address uncertainty. Finally, a cooperative game model for distribution network and microgrid is established.

[0520] 2) Solution process based on ADMM algorithm: Problem transformation and solution process based on ADMM algorithm: The non-convex nonlinear optimization problem of reserve capacity and price is transformed into two sub-problems of system cost minimization and benefit allocation through ADMM algorithm, and solved step by step iteratively, so as to finally achieve the global optimal coordinated scheduling of distribution network and microgrid.

[0521] Nash bargaining is a game theory model proposed by John Nash, primarily used to solve the problem of finding the optimal solution in a bargaining process between two players. The core idea of ​​the Nash bargaining model is to find an allocation method that allows each player to obtain the maximum utility under given constraints.

[0522] The Nash bargaining problem can be described as follows: two parties each demand a portion of a certain property. If the sum of their demands is less than the total property, both parties get what they want; however, if the sum exceeds the total property, neither party gets anything. Nash proposed an axiomatic solution where a solution satisfying certain axioms maximizes each party's current and cooperative gains.

[0523] 1. Two-layer optimization model

[0524] This patent treats the distribution network and microgrid as independent optimization entities, each with different optimization objectives. Unlike traditional models that only involve power exchange, this patent introduces frequency security constraints into the distribution network model to address disturbances. The microgrid incorporates its provided reserve capacity into energy storage constraints for optimized scheduling.

[0525] (1) Distribution network model

[0526] (1.1) Objective function of distribution network:

[0527] The distribution network cost function is:

[0528] C DN =min(C P,DN +C R,DN (1)

[0529]

[0530]

[0531] The relationship between active power reserve in power transmission networks and active power reserve in microgrids and inertia and droop coefficient is as follows:

[0532]

[0533] (1.2) Distribution network operation constraints:

[0534] 1) Line constraints

[0535] In the distribution network model, photovoltaic and reactive power compensation devices (SVCs) are configured. At time t, the line operation constraints adopt the Distflow equation after second-order cone relaxation:

[0536]

[0537] 2) Frequency security constraints

[0538] Figure 1 This is an equivalent motor model for the frequency response of a power distribution network. Where F... H and T R ΔP represents the proportion of high-voltage turbine power generation, Δf represents the generator reheat time constant, and Δp represents the disturbance in the distribution network. Δf represents the frequency deviation. total D is the equivalent inertia of the system. total The equivalent droop coefficient of the system is calculated using formulas (17) and (18), respectively:

[0539]

[0540] Using the equivalent system frequency response model, the dynamic frequency index of the frequency response can be transformed into the following constraints:

[0541]

[0542]

[0543] Formula (21) is the result after piecewise linearization. This indicates approximation of F(H) total D total A set of hyperplane coefficients.

[0544] (2) Microgrid Model

[0545] (2.1) Objective function of microgrid

[0546] The optimization objective of microgrid i is to minimize scheduling costs. CVaR is used to quantify the impact of uncertainty risks, and the objective function is shown below:

[0547]

[0548] Energy storage degradation costs Degradation costs of thermal storage systems Electricity purchase and sale costs Calculate using the following formula:

[0549]

[0550] Dispatch risk cost Calculate using the following formula:

[0551]

[0552] [ ] + Indicates a positive value, [x] + =max{x,0}.

[0553] (2.2) Operational constraints of microgrids

[0554] 1) Balance constraints of cooling, heating and electricity loads

[0555]

[0556] The power of absorption chillers and thermal storage electric boilers must be within their operating range.

[0557] 2) Constraints on the operation of energy storage

[0558]

[0559] SOC min ≤SOC i,t,ω ≤SOC max (34)

[0560]

[0561]

[0562] 3) Operational constraints of the thermal storage system in thermal storage electric boilers

[0563] Thermal storage electric boilers operate similarly to electric energy storage systems, but they do not participate in frequency regulation, do not need to consider standby capacity, and only need to ensure that the HOC is within the upper and lower limits and is continuous.

[0564] 4) Electricity purchase and sale constraints

[0565] The value of the electricity purchase or sale of the i-th microgrid within a time period should meet the upper and lower limit constraints.

[0566] 3. Problem transformation and solution process based on ADMM algorithm

[0567] The cooperative game system model of distribution networks and microgrids can be described as follows:

[0568]

[0569] By solving the equilibrium solution of problem (39), the optimal bargaining strategy can be derived for the distribution network and microgrid. To simplify the solution, this invention decomposes it into two sub-problems: minimizing system cost and allocating benefits. The optimal solution of formula (39) is obtained through sequential optimization.

[0570] 1) Subproblem 1: The subproblem of minimizing system cost, with the following objective function:

[0571]

[0572] Introduce a reserve capacity R for problem 1. i,t Couple the components and introduce consistency constraints. To achieve decoupling. The backup capacity that the distribution network expects the microgrid to provide. This refers to the reserve capacity that a microgrid is willing to provide to the distribution network.

[0573] This invention utilizes the ADMM algorithm for decomposition calculation to obtain an optimized model for Problem 1.

[0574]

[0575] and L i,pr1 The augmented Lagrangian functions of the distribution network and microgrid i with respect to question 1 are ρ and ρ, respectively. pr1 λ is the penalty factor for subproblem 1. i,t,pr1 Let be the Lagrange multiplier of the interactive power between the distribution network and microgrid i in time period t in subproblem 1, and let the constraints be the respective operating constraints of the distribution network and the microgrid.

[0576] The formula for updating variables during the iteration process is:

[0577]

[0578] argmin represents the variable that minimizes the function. The convergence condition is:

[0579]

[0580] 2) Sub-problem 2: Profit distribution

[0581] By solving subproblem 1, the reserve capacity after the interaction between the distribution network and each microgrid can be obtained. Substituting the reserve capacity into (39), the reserve price can be solved.

[0582] The objective function for the benefit allocation subproblem is set as follows:

[0583]

[0584] The superscript * indicates the solution obtained from solving problem 1. It is also solved using the ADMM algorithm.

[0585] Taking the logarithm of the objective function of the benefit allocation subproblem, we get:

[0586]

[0587] Similarly, the ADMM algorithm is used to solve the objective function of the benefit allocation subproblem, introducing... As a coupling variable, the optimization model after decoupling by introducing consistency constraints is as follows:

[0588]

[0589] The variable updates during the iteration process are similar to those in Problem 1, and will not be repeated here.

[0590] The definitions of the expressions in formulas (1) to (49) above are consistent with the definitions shown in other parts of the specification.

[0591] The following is a specific embodiment of the application of the distribution network and microgrid coordination optimization method with embedded frequency security constraints of the present invention:

[0592] Assuming the upper-level power grid is an equivalent generator with a capacity of 5MW, an inertia range of 2-20s, and a droop factor of 25-60p.u., T R and F HThe values ​​are 8s and 0.25, respectively. The distribution network adopts IEEE 33 nodes. Microgrids 1 to 3 are located at nodes 24, 30, and 12, respectively. Nodes 6, 17, 30, and 33 are equipped with SVCs, and nodes 2, 7, and 11 are equipped with 300kW, 600kW, and 400kW photovoltaics, respectively. We take values ​​of 0.5 Hz / s, 0.25 Hz, and 0.5 Hz respectively.

[0593] Microgrid 1 is equipped with 1200kW photovoltaic power, 500kW wind turbines, 1000kW electric boilers, and 500kW chillers, with cooling, heating, and power loads of 120kW, 120kW, and 650kW respectively. Microgrid 2 is identical to Microgrid 1. Microgrid 3 has 400kW wind turbines, and its cooling, heating, and power loads are 0.9 times that of Microgrid 1. Microgrids 1 and 2 are equipped with 500kWh of energy storage, and Microgrid 3 has 400kWh, with a charge / discharge rate of 0.5 for both. The electricity price is 1.14 yuan / kWh during peak hours, 0.75 yuan / kWh during normal hours, and 0.475 yuan / kWh during off-peak hours. The power purchase price from the distribution network is 0.8 times the electricity price, and the standby cost is 20% of the electricity price. Peak hours are 18:00-20:00, normal hours are 9:00-17:00 and 21:00-22:00, and off-peak hours are 1:00-8:00 and 23:00-24:00.

[0594] (1) Interaction results of standby capacity

[0595] The distribution network disturbance risk coefficient is set to 0.05. The period when the maximum disturbance is likely to occur is selected. The inertia and droop coefficient when additional backup is provided are generated by distribution network optimization.

[0596] Figure 2 This is a graph showing the frequency response results after the disturbance. (From...) Figure 2 It can be seen that without optimization, the maximum frequency deviation exceeds the system's operating range (1.12Hz), and the quasi-steady-state frequency deviation is also lower than the system's allowable standard (0.42Hz). In contrast, the optimized distribution network has a better frequency response (quasi-steady-state deviation of 0.2Hz, maximum frequency deviation of 0.48Hz), and can ensure frequency safety even when encountering the largest frequency disturbances.

[0597] Figure 3 The magnitude of disturbances and the required reserve capacity are given for each time period. During periods 1-26 and 77-96, the photovoltaic power generation in the distribution network is relatively small, resulting in smaller disturbances and lower required additional reserves. During periods 28-76, the distribution network load level is high, and photovoltaic power generation is also involved, leading to larger active power fluctuations. The additional reserves provided by the microgrid are insufficient to meet the requirements, and the transmission network also participates in additional frequency regulation reserves.

[0598] (2) Cost calculation results

[0599] The goal of cooperation between distribution networks and microgrids is to reduce their respective costs, which can be reflected in electricity price negotiations.

[0600] Figure 4 This refers to the electricity price negotiated between each microgrid and the distribution network. Figure 4 It can be seen that the negotiated electricity price is 0 during periods when no additional backup is required. The negotiated electricity price between the distribution network and the microgrid is lower than the price of obtaining backup from the transmission network, enabling the distribution network to achieve cost savings through microgrid backup.

[0601] Table 1 shows the cost situation of the microgrid group and the distribution network before and after cooperation, with negative values ​​representing profits. As can be seen from Table 1, each microgrid reduced its revenue from electricity trading to obtain more revenue from standby services. Through cooperation, the overall revenue of all three microgrids increased. The standby cost of the distribution network decreased by 125 yuan, resulting in a final system cost reduction of 208 yuan. This indicates that the distribution network successfully reduced its operating costs.

[0602] Table 1: Costs of Each Part Before and After Participation in Cooperation

[0603]

[0604] (3) Conclusion

[0605] The case results show that:

[0606] 1) The proposed frequency security constraint scheduling method for distribution network and microgrid based on Nash bargaining takes into account the disturbances of the distribution network at different times, uses the risk coefficient to transform the uncertain model into a deterministic model for modeling, and uses the equivalent motor model to construct frequency security constraints, which effectively improves the frequency security of the system.

[0607] 2) The cost results after interaction show that using microgrids for backup can effectively reduce distribution network backup costs and improve microgrid revenue. Ultimately, the total revenue of the microgrid is increased (11%, 16.9%, and 15.3% for microgrid 1, 2, and 3 respectively); distribution network backup costs are reduced by 9.2%, and total costs are reduced by 0.73%.

[0608] The aforementioned second-order cone programming model, stochastic-conditional value at risk method, ADMM algorithm, Nash bargaining, equivalent system frequency response model and other functional modules, models and methods can all adopt applicable functional modules, models and methods in the existing technology, or adopt functional modules, models and methods in the existing technology and construct them using conventional technical means.

[0609] The embodiments described above are only used to illustrate the technical ideas and features of the present invention. Their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The patent scope of the present invention should not be limited by these embodiments. That is, any equivalent changes or modifications made in accordance with the spirit disclosed in the present invention still fall within the patent scope of the present invention.

Claims

1. A method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints, characterized in that, The distribution network and microgrids are treated as independent entities, and separate models are established for the distribution network and microgrids. The distribution network model is constructed based on a second-order cone programming model with embedded frequency security constraints. The microgrid model is constructed based on inertia and frequency regulation constraints with the goal of minimizing scheduling costs, and the stochastic-conditional value-at-risk method is used to evaluate uncertain costs. A cooperative game system model for the distribution network and microgrids is established, and the reserve capacity and corresponding price provided by each microgrid are determined through cooperative bargaining. Furthermore, the cooperative game system model is transformed into two sub-problems: cost minimization and benefit allocation within the cooperative game system. The optimal bargaining strategy is obtained by distributed solution of the model using the ADMM algorithm. The objective function for the following power distribution network model is established: C DN =min(C P,DN +C R,DN ) (1) In the formula: t is the time period number; Δt represents the size of the scheduling period; N T Number of time periods; i represents the microgrid serial number; m represents the microgrid collection; C DN For distribution network operating costs; C P,DN The cost of purchasing and selling electricity in the power distribution network; C R,DN For distribution network backup costs; P g,t The amount of electricity purchased by the distribution network from the transmission network during time period t; Let be the electricity sold by the microgrid to the distribution network during time period t; Let t represent the amount of electricity purchased by the microgrid from the distribution network during the i-th time period; The electricity price of the distribution network during time period t; The electricity purchase price of the distribution network during time period t; R g,t Reserve capacity provided for the transmission network during time period t; R i,t The reserve capacity provided for the i-th microgrid during time period t; The standby price for providing standby services to the power grid during time period t; The standby price for providing standby services to the i-th microgrid during time period t; H g,t The inertia provided by the power grid during time period t; H i,t The inertia provided by the i-th microgrid during time period t; D g,t The droop factor provided for the transmission network during time period t; D i,t The droop factor provided for the i-th microgrid in time period t; P g This is the maximum output of the equivalent motor in the power transmission network; P i This represents the maximum output of the i-th microgrid. This refers to the maximum permissible rate of frequency change in a power distribution network system. This represents the maximum permissible frequency variation in a power distribution network system.

2. The method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints according to claim 1, characterized in that, The constraints of the distribution network model include line operation constraints and frequency security constraints.

3. The method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints according to claim 2, characterized in that, In the distribution network model, photovoltaic and reactive power compensation devices (SVCs) are configured. At time t, the line operation constraints adopt the Distflow equation after second-order cone relaxation. The line operation constraints include the following equations: In the formula: j is the node number; k is the node number; u is the node number; N bus For the set of nodes in the distribution network; N line For the line set in the distribution network; N PV A set of photovoltaic nodes in a power distribution network; p j,t Let be the active power flowing out of node j during time period t; q j,t The reactive power flowing out of node j during time period t; v j,t Let be the square of the voltage at node j during time period t; P jk,t Let be the active power flowing from node j to node k during time period t; Q jk,t Let t be the reactive power flowing from node j to node k during time period t; P uj,t Let t be the active power flowing from node u to node j during time period t; Q uj,t Let t be the reactive power flowing from node u to node j during time period t; l uj,t The square of the line current between nodes u and j during time period t; r uj Here are the line impedance parameters between nodes u and j; x uj The line reactance parameters between nodes u and j; p u This is the lower limit of the active power of node u in the distribution network; q u This is the lower limit of the reactive power of node u in the distribution network; v u This is the lower limit of the square of the voltage u at a distribution network node; p u,t Let t be the active power flowing out of node u during time period t; q u,t The reactive power flowing out of node u during time period t; v u,t The square of the voltage at node u during time period t; This represents the upper limit of the active power of node u in the distribution network; This represents the upper limit of reactive power at node u in the distribution network. This is the upper limit of the square of the voltage u at a distribution network node; l uj The square of the line current between nodes u and j in the distribution network; This is the upper limit of the square of the line current between nodes u and j in the distribution network; P j,g,t The active power injected into the transmission network connected to node j during time period t; Let t be the electricity sold by the distribution network to the i-th microgrid connected to node j during time period t; Let t be the power purchased by the distribution network to the i-th microgrid connected to node j during time period t; Let be the power generation capacity of the photovoltaic system connected to node j during time period t; Let be the active load power of node j during time period t; Q j,g,t The reactive power injected into the transmission network connected to node j during time period t; The reactive power compensated by the SVC connected to node j during time period t; Let be the reactive load power of node j during time period t; The maximum power of the photovoltaic system connected to node k during time period t; The arrows in j→k indicate the direction of power flow.

4. The method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints according to claim 2, characterized in that, Construct an equivalent motor model for the frequency response of the distribution network as follows: In the formula: i represents the microgrid serial number; m represents the microgrid collection; H total The equivalent inertia of a cooperative game system; D total The equivalent downward coefficient of the cooperative game system; H g The inertia provided to the power transmission network; P g This is the maximum output of the equivalent motor in the power transmission network; D g This represents the droop coefficient of the power transmission network. P d This represents the maximum load demand of the distribution network. H i The inertia provided for the i-th microgrid; P i This represents the maximum output of the i-th microgrid. D i Let be the droop coefficient of the i-th microgrid; Based on the equivalent motor model of the distribution network frequency response, the following frequency security constraints are constructed: In the formula: F(H total D total ) is H total and D total Nonlinear functions; K α The upper quantile of the perturbation; This represents the maximum permissible quasi-steady-state deviation in a cooperative game system. The maximum allowed rate of change of frequency in a cooperative game system; This represents the maximum allowed frequency variation in a cooperative game system. D0 represents the damping of the power distribution network system; h is the hyperplane index; For the h-th approximation F(H) total D total The intercept of the hyperplane; For the h-th approximation F(H) total D total The hyperplane about H total The fitting coefficient; For the h-th approximation F(H) total D total The hyperplane of ) about D total Fit coefficients.

5. The method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints according to claim 1, characterized in that, Minimizing scheduling cost is taken as the optimization objective of the i-th microgrid operation. CVaR is used to quantify the risk cost caused by uncertainties in the microgrid. The objective function of the microgrid model is set as follows: In the formula: t is the time period number; Δt represents the size of the scheduling period; N T Number of time periods; i represents the microgrid serial number; ω represents the scene number; S represents the total number of scenes; σ i This is a risk coefficient used to weigh the relationship between scheduling costs and risk costs. C i Let be the scheduling cost of the i-th microgrid; Let be the expected scheduling cost for all scenarios of the i-th microgrid; Let be the scheduling risk cost of the i-th microgrid; Let the reserve revenue be that of the i-th microgrid; Let $t$ be the reserve price for the $i$-th microgrid during time period $t$. R i,t Let be the reserve capacity of the i-th microgrid during time period t; Let be the energy storage degradation cost of the i-th microgrid; Let be the electricity purchase and sale cost of the i-th microgrid; Let be the degradation cost of the thermal storage system of the i-th microgrid; ρ i,ω Let ω be the probability of the i-th microgrid occurring in scenario ω. K ESS The degradation coefficient of the energy storage system; The charging power of the energy storage system under the i-th microgrid scenario ω in time period t; Let ω be the discharge power of the energy storage system in the i-th microgrid scenario during time period t; The amount of electricity purchased by the distribution network from the i-th microgrid during time period t; Let t be the amount of electricity sold by the distribution network to the i-th microgrid during time period t; The electricity price sold in the distribution network; The purchase price of electricity for the power distribution network; K HSS The degradation coefficient of a thermal storage electric boiler; Let be the thermal storage power of the thermal storage electric boiler in the i-th microgrid during time period t; Let denot be the thermal power released by the thermal storage electric boiler in the i-th microgrid during time period t; ζ is an auxiliary variable, the optimal value of which is the risk value. α represents the CVaR confidence level; [] + Indicates a positive value, [x] + =max{x,0}; C i,ω Let ω be the scheduling cost for the i-th microgrid scenario; Let be the energy interaction cost of the i-th microgrid during time period t; Let be the degradation cost of the thermal storage electric boiler during the i-th microgrid time period t.

6. The method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints according to claim 5, characterized in that, The constraints of the microgrid model include operational constraints; these constraints include load balancing constraints for cooling, heating, and electricity; operational constraints for battery energy storage systems; operational constraints for thermal storage electric boiler systems; and electricity purchase and sale constraints. The following constraints are set for balancing cooling, heating, and electrical loads: In the formula: Let be the predicted photovoltaic power of the i-th microgrid in time period t; Let be the photovoltaic power prediction error for the i-th microgrid scenario ω during time period t; Let ω represent the curtailed solar power in the i-th microgrid scenario during time period t. Let be the predicted wind power output of the i-th microgrid during time period t; Let be the wind power prediction error for the i-th microgrid scenario ω during time period t; Let ω represent the wind curtailment power in the i-th microgrid scenario during time period t. Let be the predicted electrical load power of the i-th microgrid during time period t; Let be the power load prediction error for the i-th microgrid scenario ω during time period t; Let be the electrical power of the thermal storage electric boiler in the i-th microgrid during time period t; Let t be the predicted heat load power of the i-th microgrid during time period t; Let be the input power of the absorption chiller in the i-th microgrid during time period t; η HSS For heat storage and heat release efficiency; η EB The electro-thermal conversion efficiency of a thermal storage electric boiler; Let be the predicted cooling load power of the i-th microgrid during time period t; η AC The working efficiency of the absorption chiller; The operating constraints for the battery energy storage system are set as follows: SOC min ≤SOC i,t,ω ≤SOC max (34) In the formula: SOC i,t,ω The state of charge of the battery energy storage system under the i-th microgrid scenario ω in time period t; SOC i,t-1,ω The state of charge of the battery energy storage system under the i-th microgrid scenario ω in time period t-1; SOC min This represents the minimum charge value for the battery energy storage system. SOC max This represents the maximum charge of the battery energy storage system. η represents the charge / discharge efficiency of the battery energy storage system; Let be the maximum capacity of the i-th microgrid battery energy storage system; Let be the binary variable representing the charging and discharging state of the battery energy storage system under the i-th microgrid scenario ω in time period t; λ ESS This refers to the maximum charge / discharge rate of the battery energy storage system. The backup capacity provided by the battery energy storage system for the i-th microgrid in time period t; Δt fr This is the frequency modulation response time; The operating constraints of the thermal storage electric boiler thermal storage system are as follows: The thermal storage system of the thermal storage electric boiler is not subject to frequency regulation and no standby capacity is set. It only needs to ensure that the thermal storage value is within the upper and lower limits and is continuous. The constraints for purchasing and selling electricity are set as follows: The value of the electricity purchase or sale of the i-th microgrid within a time period should meet the upper and lower limit constraints.

7. The method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints according to claim 1, characterized in that, Establish the following cooperative game system model between the distribution network and the microgrid: In the formula: C DN,0 Costs incurred by the distribution network that did not participate in the cooperation; C DN,co The costs associated with the distribution network's participation in the cooperation; The cost for the i-th microgrid that did not participate in the cooperation; Let be the cost of the i-th microgrid participating in the cooperation.

8. The method for coordinated optimization of distribution networks and microgrids with embedded frequency security constraints according to claim 7, characterized in that, The equilibrium solution problem of the cooperative game system model is decomposed into two sub-problems: minimizing system costs and allocating benefits. The optimal bargaining strategy is obtained through sequential optimization. Where R i The reserve capacity provided for the i-th microgrid; The standby price for providing standby services to the i-th microgrid; The objective function for the subproblem of minimizing system cost is set as follows: In the formula: t is the time period number; Δt represents the size of the scheduling period; N T Number of time periods; i represents the microgrid serial number; m represents the microgrid collection; C P,DN The cost of purchasing and selling electricity in the power distribution network; C s Costs of cooperative game systems; Reserve costs paid by the distribution network to the transmission network; Let be the expected scheduling cost for all scenarios of the i-th microgrid; σ i This is a risk coefficient used to weigh the relationship between scheduling costs and risk costs. The risk cost of the i-th microgrid; R g,t Reserve capacity provided for the transmission network during time period t; c g,t The reserve price of the transmission network during time period t; For the subproblem of minimizing system cost, let... Let i be the reserve capacity that the distribution network expects the i-th microgrid to provide during time period t. Let R be the reserve capacity that the i-th microgrid is willing to provide to the distribution network during time period t; introduce the reserve capacity R provided by the i-th microgrid during time period t. i,t Couple the components and introduce consistency constraints. To achieve decoupling; using the ADMM algorithm for decomposition and computation, the following optimization model for minimizing the system cost subproblem is obtained: In the formula: For the augmented Lagrangian function of the distribution network with respect to the subproblem of minimizing system cost; λ i,t,pr1 The Lagrange multiplier for the reserve power exchanged between the distribution network and the i-th microgrid during time period t in the subproblem of minimizing system cost; ρ pr1 The penalty factor for the subproblem of minimizing system cost; L i,pr1 Let be the augmented Lagrangian function of the i-th microgrid with respect to the subproblem of minimizing system cost; The constraints are the respective operational constraints for the distribution network and the microgrid; The formula for updating variables during iteration is: The convergence condition is: In the formula: w is the sequence number of the step-by-step iteration; argmin represents the variable that minimizes the function; This represents the reserve capacity that the distribution network expects the i-th microgrid to provide during the (w+1)-th iteration. The backup capacity that the distribution network expects the i-th microgrid to provide at the w-th iteration; This represents the reserve capacity that the distribution network expects the i-th microgrid to provide during the (w-1)-th iteration. Let be the reserve capacity that the i-th microgrid is willing to provide to the distribution network at the w-th iteration; This represents the reserve capacity that the i-th microgrid is willing to provide to the distribution network at the (w+1)-th iteration; r pr1 (w) represents the original residual of the subproblem of minimizing system cost at the w-th iteration; s pr1 (w) represents the dual residual of the subproblem minimizing the system cost at the w-th iteration; ε pr1,pri The original residual convergence accuracy of the subproblem minimizing system cost at the w-th iteration; ε pr1,dual Let be the convergence accuracy of the dual residual of the subproblem minimizing the system cost at the w-th iteration; L i Let be the augmented Lagrangian function of the i-th microgrid with respect to the subproblem of minimizing system cost; λ i,pr1 (w) is the Lagrange multiplier of the reserve power exchanged between the distribution network and the i-th microgrid in the w-th iteration of the subproblem of minimizing system cost; λ i,pr1 (w+1) is the Lagrange multiplier of the reserve power exchanged between the distribution network and the i-th microgrid in the (w+1)-th iteration of the subproblem of minimizing system cost; The reserve capacity after the interaction between the distribution network and each microgrid is obtained by solving the subproblem of minimizing system cost. The reserve capacity is then substituted into formula 39 to solve for the reserve price. The objective function for the benefit allocation subproblem is set as follows: Taking the logarithm of the objective function of the benefit allocation subproblem, we get: In the formula: The result is the solution for the cost of purchasing and selling electricity; The solution for the reserve costs paid by the distribution network to the transmission network; This represents the solution for the reserve capacity negotiated between the i-th microgrid and the distribution network during time period t. This represents the solution for the expected scheduling cost for all scenarios of the i-th microgrid. This represents the solution for the risk cost of the i-th microgrid. The reserve price for the I-th microgrid during time period T; Similarly, the ADMM algorithm is used to solve the objective function of the benefit allocation subproblem, introducing... As a coupling variable, the optimization model after decoupling by introducing consistency constraints is as follows: In the formula: For the augmented Lagrangian function of the distribution network with respect to the benefit allocation problem; The standby capacity quotation from the distribution network to the i-th microgrid during time period t; The reserve capacity bid of the i-th microgrid to the distribution network during time period t; L i,pr2 Let be the augmented Lagrangian function of the i-th microgrid with respect to the benefit distribution subproblem; λ i,t,pr2 For the Lagrange multiplier of the interaction power between the distribution network and the i-th microgrid in time period t in the benefit allocation subproblem; ρ pr2 The penalty factor for the sub-problem of allocating benefits.

9. A device for a coordinated optimization method of distribution networks and microgrids with embedded frequency security constraints, comprising a memory and a processor, characterized in that, The memory is used to store a computer program; the processor is used to execute the computer program and, when executing the computer program, implement the steps of the distribution network and microgrid coordinated optimization method with embedded frequency security constraints as described in any one of claims 1 to 8.

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