Multi-microgrid collaborative optimization scheduling method based on improved ADMM

Abstract

The invention relates to the technical field of electric power system dispatching, in particular to a multi-microgrid collaborative optimization dispatching method based on an improved ADMM, and the method comprises the steps: constructing a microgrid operation cost minimization objective function based on a microgrid mathematical model, and carrying out the operation constraint of each microgrid; iteratively updating a local variable, a global variable and a Lagrange multiplier by using an ADMM model to solve the operation cost of the micro-grid; and income distribution is carried out based on the asymmetric Nash negotiation model. According to the method, the problem that the convergence speed and the calculation complexity need to be further improved when an existing model is used for multi-microgrid dispatching optimization is solved.

Description

Technical Field

[0001] This invention relates to the field of power system dispatching technology, and in particular to a multi-microgrid collaborative optimization dispatching method based on an improved ADMM. Background Technology

[0002] Multi-microgrid coordinated optimization scheduling is an important direction for the development of smart grids. It aims to improve the renewable energy absorption capacity and system operating efficiency through the interconnection and complementarity of multiple microgrids. It involves distributed generation, energy storage systems, flexible load management and communication control technologies. Through centralized or distributed optimization algorithms (such as model predictive control, game theory and reinforcement learning), it coordinates the energy flow between microgrids to achieve multi-objective optimization of economy, environmental protection and reliability. It addresses challenges such as renewable energy volatility, network constraints and market mechanism integration, and provides flexible and efficient regional energy management solutions for new power systems.

[0003] Wang Chengshan et al.'s "Microgrid Optimization Operation and Control Technology" achieves efficient energy allocation through global optimization, but this method requires all microgrids to share detailed operating data, which poses a risk of privacy leakage. Huang Haitao's "Research on Distributed Collaborative Optimization of Multi-Agent Integrated Energy System Based on ADMM Algorithm" introduces distributed optimization algorithms, such as the Alternating Direction Multiplier Method (ADMM), which reduces data sharing by decomposing the global problem into local subproblems, but there is still room for improvement in terms of convergence speed and computational complexity. Summary of the Invention

[0004] To address the shortcomings of existing methods, this invention solves the problem that existing models, when optimizing multi-microgrid scheduling, require further improvement in convergence speed and computational complexity.

[0005] The technical solution adopted in this invention is: a multi-microgrid cooperative optimization scheduling method based on improved ADMM, comprising the following steps: Step 1: Construct an objective function to minimize the operating cost of the microgrid based on the microgrid mathematical model, and apply operational constraints to each microgrid; In a preferred embodiment of the present invention, the formula for the objective function of minimizing the operating cost of a microgrid is: (1) In the formula, microgrid Operating costs express Moment Microgrid The corresponding costs of demand, express Moment Microgrid The equipment operation and maintenance costs, express Moment Microgrid Energy storage leasing costs, express Moment Microgrid Energy purchase cost, express Moment Microgrid Energy sales costs.

[0006] In a preferred embodiment of the present invention, the operating constraints include: power balance constraints and charge / discharge constraints.

[0007] In a preferred embodiment of the present invention, the microgrid includes distributed power sources, energy storage, loads, and interaction with the main grid.

[0008] Step 2: Use the ADMM model to iteratively update local variables, global variables, and Lagrange multipliers to solve for the microgrid operating cost; In a preferred embodiment of the present invention, the ADMM model is improved by using the BB method to calculate the adaptive step size based on the variable changes and gradient changes between two iterations, as shown in the formula: (15) (16) In the formula, Indicates the multiplier change term; Represents the consistency residual term; Represents the norm; Represents the dot product; For the first k+ Step size before the first correction; For the first k Secondary Lagrange multipliers; For the first k Secondary local variables; For the first k Secondary global variable.

[0009] In a preferred embodiment of the present invention, the step size before correction is selected based on the residual value, and the step size after correction is calculated based on the step size before correction.

[0010] In a preferred embodiment of the present invention, the formula for selecting the step size before step size correction based on the residual value is as follows: (18) in, The residual threshold; This represents the original residual.

[0011] In a preferred embodiment of the present invention, the formula for the corrected step size is: (19) in, The weight factor represents the step size update; These represent the lower and upper bounds of the step size, respectively.

[0012] In a preferred embodiment of the present invention, whether the original residual and the dual residual satisfy the convergence accuracy is used as the termination condition of the ADMM model or the improved ADMM model.

[0013] Step 3: Distribute the benefits based on the asymmetric Nash negotiation model.

[0014] As a preferred embodiment of the present invention, a multi-microgrid cooperative optimization scheduling system based on improved ADMM includes: a memory for storing instructions executable by a processor; and a processor for executing the instructions to implement a multi-microgrid cooperative optimization scheduling method based on improved ADMM.

[0015] The beneficial effects of this invention are: 1. Construct a target function for the operating cost of microgrids to reveal the key characteristics of microgrids in terms of renewable energy generation, energy storage system operation, and energy trading demand; formulate differentiated optimization scheduling strategies to optimize resource allocation by controlling the scale and timing of energy trading between microgrids; 2. Distributed optimization is achieved through the improved Alternating Directional Multiplier Method (ADMM) algorithm, which efficiently coordinates the generation, energy storage, and trading behaviors of each microgrid; and the mode of participation in the main grid dispatch is dynamically adjusted according to the energy supply capacity and demand characteristics of each microgrid. 3. By adopting an asymmetric Nash negotiation model, the economic benefits of cooperation are fairly distributed based on the contributions of each microgrid in electricity and heat trading, ensuring that all microgrids benefit from collaborative optimization. This optimized scheduling scheme not only improves the overall operating efficiency of multi-microgrid systems, but also enhances the reliability and economy of the power system through collaborative interaction with the main grid, providing a practical solution for the optimized operation of modern power systems. Attached Figure Description

[0016] Figure 1 This is a flowchart of the multi-microgrid collaborative optimization scheduling method based on the improved ADMM of the present invention; Figure 2 Here is a flowchart of the improved ADMM method for solving the multi-microgrid collaborative optimization problem; Figure 3 It is a comparison chart of the original residuals and step size of the power of the improved ADMM and the ADMM. Figure 4 It is a comparison chart of the original thermal residuals and step size between the improved ADMM and ADMM; Figure 5It is a comparison chart of the energy duality residuals and step size between the improved ADMM and the ADMM; Figure 6 It is a comparison chart of the thermal dual residuals and step size of the improved ADMM and ADMM; Figure 7 This is a comparison chart of the costs of each microgrid before and after system optimization, taking one day as an example. Detailed Implementation

[0017] The present invention will be further described below with reference to the accompanying drawings and embodiments. The drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0018] like Figure 1 As shown, a multi-microgrid cooperative optimization scheduling method based on improved ADMM includes the following steps: Step 1: Construct a mathematical model for multiple microgrids. The mathematical model for multiple microgrids includes distributed power sources (wind power, photovoltaic, etc.), energy storage, loads, and their interaction with the main grid; define the operating constraints of each microgrid (such as power balance and capacity limitations); and construct an objective function to minimize the operating cost of the microgrids. The objective function formula is: (1) In the formula, microgrid Operating costs express Moment Microgrid The corresponding costs of demand, express Moment Microgrid The equipment operation and maintenance costs, express Moment Microgrid Energy storage leasing costs, express Moment Microgrid Energy purchase cost, express Moment Microgrid Energy sales costs.

[0019] The formula is: (2) In the formula, Indicates the excitation coefficient for transferable electrical / thermal loads; This represents the excitation factor that can reduce electrical load. microgrid exist Electrical load that can be transferred at any time; microgrid exist The heat load can be transferred at any time.

[0020] The formula is: (3) In the formula, , This indicates the operation and maintenance coefficient of electric boilers and new energy equipment; express Moment Microgrid Output power of electric boiler; express Moment Microgrid Output power of new energy equipment.

[0021] The power balance constraint is calculated using the following formula: (4) in, express Moment Microgrid The output of new energy sources; express Moment Microgrid Electricity purchased from operators; express Moment Microgrid Purchase energy from energy storage; express Moment Microgrid Energy storage and discharge; express Moment Microgrid To microgrids Electricity purchased; express Moment Microgrid The amount of charge given to the energy storage system; express Moment Microgrid Input the electrical power of the electric boiler; express Moment Microgrid Electrical load after demand response; express Moment Microgrid To microgrids Electricity sold; express Moment Microgrid Output power of electric boiler; express Moment Microgrid Purchase heat from operators; express Moment Microgrid To microgrids Purchase of calories; express Moment Microgrid Heat load after demand response; express Moment Microgrid To microgrids It sells calories.

[0022] The charging and discharging constraints include ES charging constraints and ES discharging constraints. The ES charging constraint formula is as follows: (5) (6) in, microgrid The initial energy storage capacity; express Final value of energy storage in a microgrid during a dispatch cycle; microgrid The upper limit of energy storage charging power; microgrid The upper limit of energy storage discharge power; express Moment Microgrid The amount of charge given to the energy storage system; express Real-time energy storage system to microgrid The amount of discharge; express Moment Microgrid Energy storage capacity.

[0023] like Figure 2 Step 2: Optimize the ADMM algorithm by introducing adaptive penalty parameters and approximate linearization techniques, and design a distributed computing framework to ensure that each microgrid only shares boundary interaction information, thereby reducing computational complexity. The ADMM algorithm breaks down the complex global optimization problem into local subproblems for each microgrid; each microgrid independently calculates its own optimization scheme, taking into account the generation, energy storage, and trading decisions of each microgrid; to protect privacy, microgrids do not share internal data, but only share boundary interaction information, namely the planned electricity or heat to be sold or purchased to other microgrids.

[0024] Energy exchange between microgrids typically involves power exchange between multiple microgrids, with the goal of minimizing total operating costs (including generation costs, electricity purchase costs, etc.) while simultaneously satisfying the supply-demand balance and interaction constraints of each microgrid. Existing... For a microgrid, the optimization problem can be formalized as follows: (7) in, It is the first The operating cost function of a microgrid microgrid Decision variables; It can be an existing microgrid operating cost function: ; It can also be the microgrid of this invention. Operating costs ; In addition, each microgrid must meet its own supply and demand balance and operational constraints, as shown in the formula: (8) (9) in, Indicates the microgrid in system operation Inequality constraints; Indicates the microgrid in system operation Equality constraints; microgrid The interactive energy.

[0025] The ADMM algorithm decomposes the global optimization problem into multiple sub-problems by introducing auxiliary variables and consistency constraints; for the energy interaction problem of multiple microgrids, auxiliary variables are introduced. microgrid If the interaction energy is the value from a global perspective, then the optimization problem is rewritten as: (10) The ADMM algorithm updates local variables iteratively. global variables and Lagrange multipliers ; The augmented Lagrangian function is: (11) In the formula, Indicates the penalty parameter; penalty term Used to encourage and Towards consensus; It represents the Lagrange multiplier.

[0026] Local subproblem (updated) ): (12) Global subproblem (updated) ): (13) Multiplier Update: (14) This invention utilizes the Barzilai-Borwein (BB) method to obtain gradient information during the iteration process and dynamically adjusts the step size. To accelerate convergence; BB performs gradient descent, using the inverse of the approximate Hessian matrix to select the step size; in ADMM, the penalty parameter... The step size affects the iteration direction and convergence speed and can be considered as the reciprocal of the step size. The Black-Scholes method calculates the adaptive step size based on the variable changes and gradient changes between two iterations, as shown in the formula: (15) (16) In the formula, This indicates the term of change of the multiplier, used to reflect the change of the multiplier; This represents the consistency residual term, reflecting the changes in the consistency residual; The appropriate step size for updating is selected based on the magnitude of the residual, as shown in the formula: (18) (19) in, The residual threshold; For the first k Step size after the next correction; For the first k+ Step size before first correction The original residual; The weight factor represents the step size update; These represent the lower and upper bounds of the step size, respectively.

[0027] Update the model using a step size, and add upper and lower bounds to the step size.

[0028] In response to the randomness (such as wind power output fluctuations and load changes), physical constraints (such as energy storage capacity and boiler capacity limitations) and real-time requirements in microgrid operation, formula (18) is used to adapt to the needs of different stages in the optimization process and effectively address the nonlinearity and uncertainty of the system. This method can accelerate the convergence speed of residuals in the early stage, and effectively address nonlinear uncertainty by gradually reducing the step size in the later stage. On this basis, formula (19) smooths the step size update process, avoids drastic fluctuations, and improves the stability and reliability of the overall optimization process.

[0029] In the ADMM algorithm, convergence is evaluated using two key residuals to ensure the feasibility of the solution in satisfying both the primal and dual problems: Original residual With dual residual The formula is: (20) The algorithm terminates when both residuals meet the convergence accuracy. (twenty one) in, , These represent the convergence accuracy of the original residual and the dual residual, respectively.

[0030] Step 3: Construct a multi-microgrid collaborative optimization framework, realize distributed iterative optimization based on the improved ADMM algorithm, integrate the Nash negotiation mechanism, and balance the economic interests of each microgrid by fairly distributing the benefits generated by collaborative optimization. After maximizing the overall benefits of the alliance, a reasonable profit distribution plan needs to be formulated to ensure that each participating microgrid can benefit from the alliance and avoid the breakdown of cooperation due to unfair distribution.

[0031] Through energy trading, microgrids can reduce their dependence on the main grid, utilize each other's surplus renewable energy or energy storage, and lower overall costs. The total cost after cooperation is lower than the sum of the costs of each microgrid operating independently; this saving is called "cooperation gain," which is the core value of collaborative optimization. The weight of each microgrid is calculated based on its contribution to electricity and heat. This weight reflects its bargaining power in revenue distribution; the greater the contribution of a microgrid, the higher its weight. Therefore, this invention designs an asymmetric Nash negotiation model for profit distribution, specifically including: To reflect the differences in the contributions of each microgrid within the consortium, supply and reception are assessed from two dimensions: electrical energy and thermal energy, and weights are assigned accordingly. (twenty two) in, These represent the contributions of electrical energy and thermal energy, respectively. microgrid Bargaining weight in asymmetric Nash negotiations; They represent microgrids The total amount of electricity supplied to and received by other microgrids during the cooperation period; They represent microgrids The total amount of heat energy supplied to and received by other microgrids during the cooperation period; These represent the maximum power supply and reception within the alliance, respectively. These represent the maximum heat energy supply and reception within the alliance, respectively. The cooperative benefits of each microgrid are defined as follows: (twenty three) in, microgrid Cost savings through participation in alliances, i.e., the benefits of cooperation; microgrid The optimal cost when running independently; based on The cooperative gain is used to construct an asymmetric Nash negotiation benefit distribution model, with the following formula: (twenty four) in, microgrid Operating costs.

[0032] Experimental procedure: This invention applies an improved ADMM algorithm to the collaborative optimization scheduling of multiple microgrids, combining Nash negotiation to minimize the total system cost and maximize the revenue of each microgrid. It collects transaction data during the cooperation period, such as the total daily or weekly electricity and heat supplied by each microgrid; simulates the independent operation of each microgrid, calculates its independent cost, and considers its renewable energy, energy storage, and main grid purchases; uses the optimization results of the improved ADMM algorithm to determine the cooperation cost and calculate the gain of each microgrid; calculates the contribution weight based on the transaction data, and compares the energy supply and reception of each microgrid with the maximum value in the alliance; and runs the Nash negotiation optimization program to adjust the revenue distribution, ensuring that each microgrid receives a positive revenue and that the distribution is fair.

[0033] Table 1. Parameter configuration of the improved ADMM algorithm

[0034] like Figure 3-6 As shown, after collaborative optimization scheduling of multiple microgrids, the results show that the BB-ADMM algorithm consistently outperforms the traditional ADMM algorithm in terms of convergence speed, stability, and residual suppression. Specifically, BB-ADMM achieves fast and stable convergence with double residuals in the first 20 iterations, and the electrical coordination is as follows: Thermal coordination is And maintain these low residual levels in subsequent iterations; in contrast, the ADMM algorithm exhibits oscillations: the electrical dual residuals initially drop to It fluctuates around, but the price is quite volatile and cannot be stabilized. Below, the thermal dual residual remains unchanged after the initial decrease. The above results indicate poor convergence. Furthermore, the adaptive step size in BB-ADMM, i.e. and They quickly stabilized at approximately 1.5 times. and 1.5 times In contrast, the step size in traditional ADMM exhibits significant volatility, indicating inefficient adaptation to coordination complexity. This demonstrates that BB-ADMM provides a more robust and efficient mechanism for handling both electrical and thermal updates, effectively improving the overall algorithm's stability and convergence accuracy. Optimization effect analysis shows that the multi-microgrid collaborative optimization scheduling method based on improved ADMM and Nash negotiation significantly reduces the operating costs of each microgrid. like Figure 7 The cost of microgrid 1 decreased from 100,169 yuan to 88,494 yuan (a decrease of 11.66%), microgrid 2 from 65,980 yuan to 22,919 yuan (a decrease of 65.27%), and microgrid 3 from 35,829 yuan to 29,869 yuan (a decrease of 16.63%), with an overall cost reduction of 30.05%, verifying the effectiveness of the method.

[0035] This invention employs an improved ADMM algorithm combined with a Nash negotiation strategy, using multi-microgrid collaborative optimization as a framework to construct a system total cost minimization objective, thereby achieving the effects of reducing operating costs, fairly distributing the benefits of each microgrid, and enhancing system stability.

[0036] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A multi-microgrid cooperative optimization scheduling method based on an improved ADMM, characterized in that, Includes the following steps: Step 1: Construct an objective function to minimize the operating cost of the microgrid based on the microgrid mathematical model, and apply operational constraints to each microgrid; Step 2: Use the ADMM model to iteratively update local variables, global variables, and Lagrange multipliers to solve for the microgrid operating cost; Step 3: Distribute the benefits based on the asymmetric Nash negotiation model.

2. The multi-microgrid cooperative optimization scheduling method based on improved ADMM according to claim 1, characterized in that, The formula for the objective function of minimizing the operating cost of a microgrid is: (1) In the formula, microgrid Operating costs express Moment Microgrid The corresponding costs of demand, express Moment Microgrid The equipment operation and maintenance costs, express Moment Microgrid Energy storage leasing costs, express Moment Microgrid Energy purchase cost, express Moment Microgrid Energy sales costs.

3. The multi-microgrid cooperative optimization scheduling method based on improved ADMM according to claim 1, characterized in that, The ADMM model is improved by using the Black-Brow method to calculate the adaptive step size based on the variable changes and gradient changes between two iterations. The formula is as follows: (15) (16) In the formula, Indicates the multiplier change term; Represents the consistency residual term; Represents the norm; Represents the dot product; For the first k+ Step size before the first correction; For the first k Secondary Lagrange multipliers; For the first k Secondary local variables; For the first k Secondary global variable.

4. The multi-microgrid cooperative optimization scheduling method based on improved ADMM according to claim 3, characterized in that, The step size before correction is selected based on the residual value, and the step size after correction is calculated based on the step size before correction.

5. The multi-microgrid cooperative optimization scheduling method based on improved ADMM according to claim 4, characterized in that, The formula for selecting the step size before correction based on the residual value is: (18) in, The residual threshold; This represents the original residual.

6. The multi-microgrid cooperative optimization scheduling method based on improved ADMM according to claim 5, characterized in that, The formula for the corrected step size is: (19) in, The weight factor represents the step size update; These represent the lower and upper bounds of the step size, respectively.

7. The multi-microgrid cooperative optimization scheduling method based on improved ADMM according to claim 1 or 2, characterized in that, Whether the original residual and the dual residual satisfy the convergence accuracy can be used as the termination condition for the ADMM model or the improved ADMM model.

8. The multi-microgrid cooperative optimization scheduling method based on improved ADMM according to claim 1, characterized in that, Operational constraints include: power balance constraints and charge / discharge constraints.

9. The multi-microgrid cooperative optimization scheduling method based on improved ADMM according to claim 1, characterized in that, Microgrids include distributed power sources, energy storage, loads, and interaction with the main grid.

10. A multi-microgrid collaborative optimization scheduling system based on an improved ADMM, characterized in that, include: Memory is used to store instructions that can be executed by the processor; A processor for executing instructions to implement the multi-microgrid collaborative optimization scheduling method based on the improved ADMM as described in any one of claims 1-9.

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