Novel equipment maintenance plan optimization method considering distribution and micro cooperation under power system

Abstract

The invention discloses a novel power system equipment maintenance plan optimization method considering distribution and micro cooperation, and the method comprises the steps: constructing a first-stage optimization model of an equipment maintenance plan, and enabling the first-stage optimization model to determine a maintenance plan decision variable with the minimum sum of maintenance cost, unit start-stop cost and expected operation cost as a target; a second-stage optimization model of the equipment maintenance plan is constructed, and the second-stage optimization model carries out optimization scheduling for different typical operation scenes with the purpose of minimizing the comprehensive operation cost of the distribution micro-grid system on the premise that maintenance plan decision variables are fixed; performing second-order cone relaxation processing on power flow constraints of the power distribution network in the first-stage optimization model and the second-stage optimization model, and converting an original nonlinear model into a mixed integer second-order cone programming model; and solving the mixed integer second-order cone programming model, and outputting an optimal equipment maintenance plan.

Description

Technical Field

[0001] This invention relates to the field of power system equipment maintenance and optimized scheduling technology, and more specifically, to a novel method for optimizing equipment maintenance plans in a power system that considers distribution-micro-coordination. Background Technology

[0002] With the large-scale integration of distributed generators (DG) and microgrids, the power system is gradually evolving from centralized to distributed, profoundly changing the structure and operation of the distribution system and exhibiting more significant hierarchical and localized characteristics. Against this backdrop, a distribution-microgrid collaborative structure is gradually taking shape. Microgrids, as an important component of the distribution network, are no longer merely a collection of controlled loads or generation units, but rather secondary network systems with autonomous operation capabilities, flexible dispatch capabilities, and bidirectional power flow interaction capabilities. While this nested structure improves the system's operational resilience and the utilization of clean energy, it also introduces more complexity and uncertainty into the formulation and execution of equipment maintenance plans.

[0003] Firstly, from an operational perspective, microgrids can connect to the distribution network and operate in parallel under normal conditions, and can also switch to islanded operation under special circumstances to achieve local supply and demand balance. However, during maintenance, especially when critical feeders, tie points, or transformers are out of service, the islanding switching capability of a microgrid directly affects its stability and power supply reliability. If the reserve capacity, energy storage response capability, and protection strategies required for microgrid islanded operation are not fully considered, voltage collapse and power quality degradation are highly likely to occur. Therefore, developing a reasonable equipment maintenance plan supported by a distribution-microgrid coordination mechanism can fully mobilize the distributed flexibility resources on the microgrid side during maintenance, providing operational compensation and support to the distribution network, thereby maximizing the safety of equipment and system operation, effectively optimizing resource input and maintenance sequence, reducing the impact of uncertainty on the system, and achieving economic improvement in the maintenance process and coordinated optimization among multiple entities while ensuring power supply reliability. Currently, the optimization of existing distribution system equipment maintenance plans suffers from insufficient handling of photovoltaic output uncertainty and a lack of full reflection of the coordinated regulation capabilities of the distribution network and microgrid. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a novel method for optimizing equipment maintenance plans in power systems that considers distribution-micro-coordination.

[0005] According to one aspect of the present invention, a novel method for optimizing equipment maintenance plans in a power system considering distribution micro-coordination is provided, comprising:

[0006] A first-stage optimization model for the equipment maintenance plan is constructed, in which the first-stage optimization model aims to minimize the sum of maintenance cost, unit start-up and shutdown cost and expected operating cost, and determines the decision variables for the maintenance plan.

[0007] A second-stage optimization model for equipment maintenance planning is constructed. Under the premise that the decision variables of the maintenance plan are fixed, the second-stage optimization model optimizes scheduling for different typical operating scenarios with the goal of minimizing the overall operating cost of the microgrid system.

[0008] The power flow constraints of the distribution network in the first-stage optimization model and the second-stage optimization model are subjected to second-order cone relaxation treatment, and the original nonlinear model is transformed into a mixed-integer second-order cone programming model.

[0009] Solve the mixed-integer second-order cone programming model and output the optimal equipment maintenance plan.

[0010] Optionally, the objective function expression for the first-stage optimization model is:

[0011]

[0012] In the formula, F represents the sum of equipment maintenance costs, unit start-up and shutdown costs, and expected system operating costs; f1 represents the sum of equipment maintenance costs and unit start-up and shutdown costs; N s ω represents the number of typical scenarios; s f represents the probability of a typical scenario s; 2,s The system's overall operating cost under scenario s; J is the number of devices to be inspected; T is the total research period; X represents the maintenance cost corresponding to equipment j being repaired during time period t; j,t G represents the maintenance status of equipment j during time period t; G represents the total number of units in the system. The cost corresponding to the start-up of the i-th generating unit in time period t; The main grid electricity purchase cost coefficient for time period t; Power purchased during time period t under scenario s; N DN This refers to the number of nodes in the distribution network. The load outage loss cost coefficient for period t; Let N be the load outage loss power of the i-th distribution network node during time period t in scenario s; M N HS and N PSH These are the numbers of small thermal power units, small hydropower units, and small pumped storage units, respectively. and These are the operating cost coefficients for the i-th small thermal power unit, small hydropower unit, and small pumped storage unit, respectively. and These represent the active power output of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t. and respectively are the charging and discharging power of the ith small pumped storage power station in time period t under scenario s.

[0013] Optionally, the constraint conditions of the first-stage optimization model include:

[0014] Maintenance time window constraint:

[0015]

[0016] wherein e j and l j are the time periods in which device j can complete maintenance;

[0017] Device start and stop maintenance state constraint:

[0018]

[0019] wherein q j,t is a state variable indicating whether device j starts maintenance from time period t;

[0020] Maintenance total duration constraint:

[0021]

[0022] wherein: is the maintenance duration of device j;

[0023] Device continuous maintenance constraint:

[0024]

[0025] Maintenance resource constraint:

[0026]

[0027] wherein σ k,j,t is the number of resource k required by device j for maintenance in time period t; R k,t is the available number of resource k in time period t; R k is the total available amount of resource k in the study period;

[0028] Unit minimum start-stop time constraint:

[0029]

[0030]

[0031] wherein I i,t is the operation state of unit i, and the value 1 indicates that the unit is in operation state, and 0 indicates that the unit is in shutdown state; T i,on and T i,offrespectively, are the minimum allowed on / off durations of unit i;

[0032] Unit start-up cost constraint

[0033]

[0034] wherein: is the start-up cost of unit i.

[0035] Optionally, the objective function expression of the second-stage optimization model is:

[0036]

[0037] wherein, N s is the number of typical scenarios; ω s is the probability of typical scenario s; f 2,s is the total operation cost of the system under scenario s.

[0038] Optionally, the constraint conditions of the second-stage optimization model include:

[0039] Load loss constraint:

[0040]

[0041] wherein: is the load loss power of the i-th distribution network node in time period t under scenario s; is the maximum output of the i-th node load in time period t of the distribution network; N DN is the number of distribution network nodes.

[0042] Unit power upper and lower limit constraint:

[0043]

[0044] wherein: and are the upper limits of the active power output of the small thermal power unit and the small hydropower unit i, respectively; and are the lower limits of the active power output of the small thermal power unit and the small hydropower unit i, respectively; and are the active power outputs of the i-th small thermal power unit and the small hydropower unit in time period t under scenario s;

[0045] Unit ramping constraint:

[0046]

[0047] wherein: and are the up / down ramping capabilities of the small thermal power unit i, respectively; and respectively the up / down ramping capability of the ith small hydropower unit; and respectively the active power output of the ith small thermal power unit and small hydropower unit in scenario s at time period t; and respectively the active power output of the ith small thermal power unit and small hydropower unit in scenario s at time period t-1;

[0048] Small pumped storage charging / discharging power constraints:

[0049]

[0050] wherein: and respectively the upper limit of the charging / discharging power of the ith small pumped storage; and respectively the lower limit of the charging / discharging power of the ith small pumped storage; and respectively the charging power and discharging power of the ith small pumped storage in scenario s at time period t;

[0051] Distributional photovoltaic power output constraints:

[0052]

[0053] wherein: is the active power output of the mth distributional photovoltaic at time t in scenario s; is the predicted value of the active power output of the mth distributional photovoltaic at time t;

[0054] Distributional microgrid tie-line transmission capacity constraints:

[0055]

[0056] wherein: is the transmission power of the kth microgrid and distributional grid tie-line in scenario s; and respectively represent the maximum and minimum values of the active power allowed to flow through the branch connected to the distributional grid by the kth microgrid.

[0057] Microgrid distributional power source operation constraints:

[0058]

[0059] wherein: is the active power output of the ith distributional power source in the kth microgrid at time t in scenario s; and respectively represent the upper limit and lower limit of the active power output of the ith distributional power source in the kth microgrid;

[0060] Microgrid energy storage charging and discharging constraints:

[0061]

[0062] wherein: and are the charging state and discharging state of the energy storage i in the microgrid k at time t, both of which are 0-1 variables; and are the charging power and discharging power of the energy storage i in the microgrid k at time t under scenario s; and are the upper limit of the charging power and the upper limit of the discharging power of the energy storage i in the microgrid k; is the active power output of the energy storage i in the microgrid k at time t under scenario s; is the state of charge of the energy storage i in the microgrid k at time t under scenario s; η ch and η dis are the charging efficiency and discharging efficiency, respectively;

[0063] Distribution network power flow constraints:

[0064]

[0065] wherein: P ij,t,s and Q ij,t,s are the active power and reactive power flowing into the branch ij in the distribution network at time t under scenario s; P jn,t,s and Q jn,t,s are the active power and reactive power flowing into the branch jn in the distribution network at time t under scenario s; I ij,t,s is the current amplitude of the branch ij in the distribution network at time t under scenario s; r ij and x ij are the resistance and reactance of the line ij, respectively; P L,j,t,s and Q L,j,t,s are the active power and reactive power of the load at node j in the distribution network at time t under scenario s; V i,t,s is the voltage amplitude of node i in the distribution network at time t under scenario s; V i,max and V i,min are the upper limit and lower limit of the voltage at node i in the distribution network, respectively.

[0066] Optionally, the first-stage optimization model and the second-stage optimization model are processed by using a second-order cone relaxation technique, and the expression of the new variable introduced is:

[0067]

[0068] wherein: l ij,t,s is the square of the current amplitude of the branch ij in the distribution network at time t under scenario s; u i,t,sI represents the square of the voltage amplitude at node i at time t under scenario s in the distribution network. ij,t,s V represents the amplitude of the branch current ij at time t under scenario s in the distribution network; i,t,s Let be the voltage amplitude of node i at time t under scenario s in the distribution network.

[0069] According to another aspect of the present invention, a novel device for optimizing equipment maintenance plans in a power system considering distribution micro-coordination is provided, comprising:

[0070] The first construction module is used to build the first-stage optimization model of the equipment maintenance plan. The first-stage optimization model aims to minimize the sum of maintenance cost, unit start-up and shutdown cost and expected operating cost, and determines the decision variables of the maintenance plan.

[0071] The second construction module is used to build the second-stage optimization model of the equipment maintenance plan. Under the premise that the decision variables of the maintenance plan are fixed, the second-stage optimization model optimizes the scheduling for different typical operating scenarios with the goal of minimizing the comprehensive operating cost of the microgrid system.

[0072] The processing module is used to perform second-order cone relaxation processing on the power flow constraints of the distribution network in the first-stage optimization model and the second-stage optimization model, and to transform the original nonlinear model into a mixed-integer second-order cone programming model.

[0073] The solver module is used to solve the mixed-integer second-order cone programming model and output the optimal equipment maintenance plan.

[0074] According to another aspect of the present invention, a computer-readable storage medium is provided, the storage medium storing a computer program for performing the methods described in any of the above aspects of the present invention.

[0075] According to another aspect of the present invention, an electronic device is provided, the electronic device comprising: a processor; a memory for storing executable instructions of the processor; the processor being configured to read the executable instructions from the memory and execute the instructions to implement the method described in any of the preceding aspects of the present invention.

[0076] Therefore, this invention proposes an optimization method for equipment maintenance plans that takes into account the uncertainty of photovoltaic output and considers distribution-microgrid collaboration. By constructing a two-stage optimization model to comprehensively characterize the maintenance plan and operation scheduling logic, and employing appropriate mathematical descriptions of uncertainty and power flow constraint relaxation techniques, the method ensures that the maintenance plan is feasible, safe, and economical at the system operation level under conditions of stochastic photovoltaic output. This method can effectively reduce system operating costs, improve the utilization level of renewable energy, and enhance the system's ability to cope with uncertain risks during maintenance, while ensuring the reliability of power supply under distribution-microgrid collaboration. Attached Figure Description

[0077] Exemplary embodiments of the present invention can be more fully understood by referring to the following figures:

[0078] Figure 1 This is a flowchart illustrating a novel equipment maintenance plan optimization method considering distribution micro-coordination in a power system, provided by an exemplary embodiment of the present invention.

[0079] Figure 2 This is an improved IEEE 33-node power distribution system topology diagram provided by an exemplary embodiment of the present invention;

[0080] Figure 3 This is a schematic diagram of a 72-hour load curve of a microgrid provided in an exemplary embodiment of the present invention;

[0081] Figure 4 This is a schematic diagram of a typical photovoltaic output curve provided by an exemplary embodiment of the present invention;

[0082] Figure 5 This is a schematic diagram of a typical scenario distribution network load curve provided by an exemplary embodiment of the present invention;

[0083] Figure 6 This is a schematic diagram of the power purchase capacity of the distribution network during different time periods of 1-24 hours under different scenarios provided by an exemplary embodiment of the present invention;

[0084] Figure 7 This is a schematic diagram of the unit output during 72 hours in scenario 1 provided by an exemplary embodiment of the present invention;

[0085] Figure 8 This is a schematic diagram of the unit output during 72 hours in scenario 2 provided by an exemplary embodiment of the present invention;

[0086] Figure 9 This is a schematic diagram of the power purchase and equivalent net load of the distribution network during the 1-24 time period under scenario 2 provided by an exemplary embodiment of the present invention;

[0087] Figure 10 This is a schematic diagram of the power purchase and equivalent net load of the distribution network during the 1-24 time period under scenario 3 provided by an exemplary embodiment of the present invention;

[0088] Figure 11 This is a schematic diagram of the structure of a novel equipment maintenance plan optimization device considering distribution micro-coordination in a power system, provided by an exemplary embodiment of the present invention.

[0089] Figure 12 This is the structure of an electronic device provided in an exemplary embodiment of the present invention. Detailed Implementation

[0090] Hereinafter, exemplary embodiments according to the present invention will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments of the present invention. It should be understood that the present invention is not limited to the exemplary embodiments described herein.

[0091] It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention.

[0092] Those skilled in the art will understand that the terms "first," "second," etc., in the embodiments of the present invention are only used to distinguish different steps, devices, or modules, and do not represent any specific technical meaning, nor do they indicate a necessary logical order between them.

[0093] It should also be understood that in the embodiments of the present invention, "multiple" can refer to two or more, and "at least one" can refer to one, two or more.

[0094] It should also be understood that any component, data or structure mentioned in the embodiments of the present invention can generally be understood as one or more unless explicitly defined or given contrary instructions in the context.

[0095] Furthermore, the term "and / or" in this invention is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this invention generally indicates that the preceding and following related objects have an "or" relationship.

[0096] It should also be understood that the description of the various embodiments in this invention emphasizes the differences between the various embodiments, and the similarities or similarities can be referred to each other. For the sake of brevity, they will not be described in detail.

[0097] At the same time, it should be understood that, for ease of description, the dimensions of the various parts shown in the accompanying drawings are not drawn according to actual scale.

[0098] The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the invention or its application or use.

[0099] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, they should be considered part of the specification.

[0100] It should be noted that similar labels and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be discussed further in subsequent figures.

[0101] The embodiments of this invention can be applied to electronic devices such as terminal devices, computer systems, and servers, and can operate together with a wide range of other general-purpose or special-purpose computing system environments or configurations. Well-known examples of terminal devices, computing systems, environments, and / or configurations suitable for use with electronic devices such as terminal devices, computer systems, and servers include, but are not limited to: personal computer systems, server computer systems, thin clients, thick clients, handheld or laptop devices, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputer systems, mainframe computer systems, and distributed cloud computing environments including any of the above systems, etc.

[0102] Electronic devices such as terminal devices, computer systems, and servers can be described in the general context of computer system executable instructions (such as program modules) executed by a computer system. Typically, program modules can include routines, programs, object programs, components, logic, data structures, etc., which perform specific tasks or implement specific abstract data types. Computer systems / servers can be implemented in distributed cloud computing environments, where tasks are executed by remote processing devices linked through communication networks. In distributed cloud computing environments, program modules can reside on local or remote computing system storage media, including storage devices.

[0103] Exemplary method

[0104] Figure 1 This is a flowchart illustrating a novel equipment maintenance plan optimization method considering distribution micro-coordination in a power system, provided by an exemplary embodiment of the present invention. This embodiment can be applied to electronic devices, such as… Figure 1 As shown, the equipment maintenance plan optimization method 100 considering distribution micro-coordination under the new power system includes the following steps:

[0105] Step 101: Construct the first-stage optimization model for the equipment maintenance plan. The first-stage optimization model aims to minimize the sum of maintenance cost, unit start-up and shutdown cost, and expected operating cost, and determines the decision variables for the maintenance plan.

[0106] Step 102: Construct the second-stage optimization model for the equipment maintenance plan. Under the premise that the decision variables of the maintenance plan are fixed, the second-stage optimization model optimizes the scheduling for different typical operating scenarios with the goal of minimizing the overall operating cost of the microgrid system.

[0107] Step 103: Perform second-order cone relaxation on the power flow constraints of the distribution network in the first-stage optimization model and the second-stage optimization model to transform the original nonlinear model into a mixed-integer second-order cone programming model.

[0108] Step 104: Solve the mixed integer second-order cone programming model and output the optimal equipment maintenance plan.

[0109] Specifically, this invention addresses the shortcomings in existing power distribution system equipment maintenance plan optimization, namely insufficient handling of photovoltaic (PV) output uncertainty and inadequate reflection of the coordinated regulation capabilities of the distribution network and microgrid. Existing methods generally only consider deterministic operating conditions or single types of uncertainty scenarios, lacking systematic modeling of PV stochastic fluctuations. This fails to effectively reflect the impact of distributed generation (DG) on system power balance, power flow feasibility, and reserve capacity during maintenance. Furthermore, the coordinated operation relationship between the distribution network and microgrid is not incorporated into the maintenance decision-making process, resulting in maintenance strategies failing to reflect the regulation potential of distributed flexibility resources during maintenance, thus reducing dispatch economy and renewable energy absorption capacity. In addition, some maintenance models still primarily focus on static economic objectives, failing to guarantee the robustness of maintenance strategies to system security under uncertainty.

[0110] To address this, this invention proposes an optimization method for equipment maintenance plans that considers the uncertainty of photovoltaic (PV) output and the coordination between distribution and microgrids. By constructing a two-stage optimization model to comprehensively characterize the maintenance plan and operational scheduling logic, and employing appropriate mathematical descriptions of uncertainty and power flow constraint relaxation techniques, the method ensures that the maintenance plan is feasible, safe, and economical at the system operation level under conditions of stochastic PV output. This method can effectively reduce system operating costs, improve the utilization level of renewable energy, and enhance the system's ability to cope with uncertain risks during maintenance, while ensuring the reliability of power supply under the coordination of distribution and microgrids.

[0111] This invention proposes a method and system for optimizing equipment maintenance plans that takes into account load, photovoltaic uncertainties, and the coordinated operation of distribution microgrids. The method constructs a two-stage optimization model and introduces uncertainty modeling and scenario simulation techniques to comprehensively characterize photovoltaic output fluctuations and the interactive regulation capabilities of distribution microgrids. While ensuring system operational safety and power supply reliability during maintenance, it achieves economic optimization of maintenance plans and enhances the coordinated utilization capability of distributed generation (DG).

[0112] The specific contents of this invention are as follows:

[0113] 1. Considering a two-stage optimization model for equipment maintenance with micro-coordination

[0114] 1.1 First-stage optimization model

[0115] The first-stage optimization model of the equipment maintenance plan considering micro-coordination is shown in Equation (1), with the goal of minimizing the sum of equipment maintenance cost, unit start-up and shutdown cost and system comprehensive operating cost.

[0116]

[0117] In the formula: f1 is the sum of equipment maintenance costs and unit start-up and shutdown costs; N s ω represents the number of typical scenarios; s f represents the probability of a typical scenario s; 2,s The overall operating cost of the system under scenario s.

[0118] J represents the number of equipment to be inspected; T represents the total research period. X represents the maintenance cost corresponding to equipment j being repaired during time period t; j,t G represents the maintenance status of equipment j during time period t; G represents the total number of units in the system. This represents the cost corresponding to the start-up of the i-th generating unit during time period t.

[0119] The main grid electricity purchase cost coefficient for time period t; Power purchased during time period t under scenario s; N DN This refers to the number of nodes in the distribution network. The load outage loss cost coefficient for period t; Let N be the load outage loss power of the i-th distribution network node during time period t in scenario s; M N HS and N PSH These are the numbers of small thermal power units, small hydropower units, and small pumped storage units, respectively. and These are the operating cost coefficients for the i-th small thermal power unit, small hydropower unit, and small pumped storage unit, respectively. and These represent the active power output of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t. and These represent the charging power and discharging power of the i-th small pumping unit in scenario s during time period t, respectively.

[0120] The first-stage model considers constraints related to equipment maintenance and unit combination, as detailed below:

[0121] 1) Maintenance time window constraints

[0122]

[0123] In the formula: e j and l j Let be the time period during which equipment j can complete maintenance, i.e., the research period. This constraint means that maintenance must be scheduled within the maintenance window.

[0124] 2) Constraints on the start and stop of equipment maintenance:

[0125]

[0126] In the formula: q j,tLet j be the state variable indicating whether equipment j will begin maintenance from time period t.

[0127] 3) Total maintenance time constraint:

[0128]

[0129] In the formula: The constraint specifies the maintenance duration for equipment j, meaning the equipment must be maintained in one go.

[0130] 4) Constraints on continuous equipment maintenance:

[0131]

[0132] 5) Maintenance resource constraints:

[0133]

[0134] In the formula: σ k,j,t R represents the amount of resource k required for equipment j to be repaired during time period t; k,t R represents the available quantity of resource k during time period t; k To study the total available amount of resource k within the research period.

[0135] 6) Minimum start-up and shutdown time constraints for the unit

[0136]

[0137] In the formula: I i,t This represents the operating status of unit i. A value of 1 indicates that the unit is in operation, and 0 indicates that the unit is out of operation; T i,on and T i,off These represent the minimum allowed start-up and shutdown durations for unit i, respectively.

[0138] 7) Unit start-up cost constraints

[0139]

[0140] In the formula: Let be the startup cost of unit i.

[0141] 1.2 Second-stage optimization model

[0142] The second-stage optimization model for the equipment maintenance plan considering the micro-system is shown in Equation (11), with the goal of minimizing the overall operating cost of the micro-system.

[0143]

[0144] The second-stage model considers the constraints related to the operation of the microsystem, as follows:

[0145] 1) Unload constraint

[0146]

[0147] In the formula: Let t be the maximum load output of the i-th node in the distribution network during time period t.

[0148] 2) Upper and lower limits of unit power constraints

[0149]

[0150] In the formula: and The upper limit of active power output for small thermal power units and small hydropower units is set respectively. and The lower limit of the active power output of small thermal power units and small hydropower units is respectively set as the i-th limit.

[0151] 3) Unit ramping constraints

[0152]

[0153] In the formula: and These refer to the uphill / downhill climbing capabilities of small thermal power unit i; and These represent the uphill / downhill climbing capabilities of small hydropower unit i, respectively. and These represent the active power outputs of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t. and These represent the active power output of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t-1.

[0154] 4) Power constraints for charging and discharging of small-scale pumped storage hydroelectric power

[0155]

[0156] In the formula: and These are the upper limits of the charging and discharging power of the small pumped storage unit i; and These are the lower limits of the charging and discharging power of the small pumped storage unit i.

[0157] 5) Distribution network distributed photovoltaic output constraints

[0158]

[0159] In the formula: The active power output of distributed photovoltaic m at time t under scenario s; Let m be the predicted active power output of the distributed photovoltaic system at time t.

[0160] 6) Transmission capacity constraints of microgrid interconnect lines

[0161]

[0162] In the formula: Let be the power transmitted between the k-th microgrid and the distribution network in scenario s; and These represent the maximum and minimum active power allowed to flow through the branches connected to the microgrid k and the distribution network, respectively.

[0163] 7) Operating constraints of distributed generation in microgrids

[0164]

[0165] In the formula: Let i be the active power output of distributed power source i in microgrid k at time t under scenario s; and These are the upper and lower limits of the active power output of distributed generation i in microgrid k, respectively.

[0166] 8) Constraints on charging and discharging of microgrid energy storage

[0167]

[0168] In the formula: and Let be the charging state and discharging state of energy storage i in microgrid k at time t, respectively, both being 0-1 variables; and These represent the charging power and discharging power of energy storage i in microgrid k at time t under scenario s, respectively. and These are the upper limits of charging power and discharging power of energy storage i in microgrid k, respectively; Let i be the active power output of energy storage i in microgrid k at time t under scenario s; Let η be the state of charge of energy storage i in microgrid k at time t under scenario s; ch and η dis These are the charging efficiency and the discharging efficiency, respectively.

[0169] 9) Distribution network power flow constraints

[0170]

[0171]

[0172] In the formula: P ij,t,s and Q ij,t,s (P jn,t,s and Q jn,t,s) represent the active and reactive power flowing into branch ij(jn) in the distribution network at time t under scenario s; I ij,t,s Let r be the amplitude of the branch current ij at time t under scenario s in the distribution network; ij and x ij These represent the resistance and reactance of line ij, respectively; P L,j,t,s and Q L,j,t,s These represent the active and reactive power of the load at node j at time t in scenario s of a distribution network; V i,t,s V represents the voltage amplitude at node i at time t in scenario s of a power distribution network. i,max and V i,min These are the upper and lower voltage limits for node i in the distribution network, respectively.

[0173] 2. Model transformation and solution

[0174] This invention proposes an optimization model for equipment maintenance plans considering micro-coordination, which is a MINP model that cannot be solved quickly. Therefore, it is necessary to linearize the nonlinear terms and reconstruct the model as a mixed-integer second-order cone programming (MISOCP). The model is then processed using second-order cone relaxation techniques, introducing new variables as shown below.

[0175]

[0176] In the formula: l ij,t,s u is the square of the current amplitude of branch ij at time t under scenario s in the distribution network; i,t,s Let be the square of the voltage amplitude of node i at time t under scenario s in the distribution network.

[0177] The expressions for the original DistFlow power flow constraints (20)-(21) after second-order cone relaxation are shown in equations (23)-(25).

[0178]

[0179] The two-stage optimization model for the equipment maintenance plan of the distribution microgrid after second-order cone relaxation belongs to MISOCP and can be solved directly based on the YALMIP optimization platform and GUROBI solver.

[0180] In a specific embodiment of the present invention, the specific implementation method is as follows:

[0181] 1. Example Introduction

[0182] This invention uses an improved IEEE 33-node power distribution system for the computational example, such as... Figure 2As shown in Table 1, the system has 32 normally closed lines and 4 normally open lines, with a base voltage of 12.66 kV and an allowable voltage fluctuation range of 0.95 to 1.05 pu. Three small thermal power units with a total capacity of 9 MW are connected at node 22, and three small hydropower units with total capacities of 7.5 MW and 4.5 MW are connected at nodes 6 and 18, respectively. The relevant parameters for the small thermal and hydropower units are shown in Table 1. A small pumped storage hydropower station with a capacity of 3.8 MW and a charge / discharge efficiency of 0.9 is connected at node 33.

[0183] Table 1 Parameters of Small Thermal Power Plants and Small Hydropower Units

[0184]

[0185] This invention connects a microgrid to 14 nodes of a distribution network. The microgrid includes a micro gas turbine, distributed power sources, and energy storage. The predicted load data within the microgrid is as follows: Figure 3 As shown in the figure. The impact of photovoltaic (PV) uncertainties was also considered, with distributed PV installed at nodes 10, 24, and 31, with a rated capacity of 5.3MW. The maximum system load during the study period was set to 42MW. First, the Latin hypercube sampling method was used to generate 500 sample scenarios for both PV and load data. Then, K-means scenario clustering was used to cluster the sample scenarios into four typical scenarios, resulting in the PV active power output curves and load curves for each typical scenario, as shown in the figure. Figure 4 , Figure 5 As shown, this example uses 24 hours.

[0186] The maintenance cycle is set to T = 72 hours. The lines to be maintained are 11-12, 20-21, and 23-24. The generating units to be maintained are small thermal power unit 1 and small hydropower unit 1. The maintenance duration for the lines is 5 hours, and the maintenance duration for the small thermal power units and small hydropower units is 12 hours and 9 hours respectively. The maintenance cost for the small thermal power units and small hydropower units is 2000 yuan / hour and 1800 yuan / hour respectively. The maximum number of lines and units that can be maintained simultaneously is 1, and the maximum number of equipment that can be maintained simultaneously is 2.

[0187] 2. Analysis of the Calculation Results

[0188] 1) Analysis of Equipment Maintenance Decision Results

[0189] To demonstrate the effectiveness of the distribution-microgrid collaborative maintenance optimization model, this invention analyzes two scenarios within a 72-hour study period: Scenario 1: The microgrid is connected to the distribution network as a dynamic load, and the output of equipment within the microgrid is zero; Scenario 2: The distribution-microgrid collaborative scheduling operation makes equipment maintenance decisions, and the equipment within the microgrid flexibly outputs power to participate in the active power game between the distribution and microgrids. The equipment maintenance periods under different scenarios are shown in Table 2.

[0190] Table 2 Equipment Maintenance Plans in Different Scenarios

[0191]

[0192] In Scenario 1, since the microgrid is considered a passive load and cannot provide power support to the distribution network, Table 2 shows that the maintenance plan for lines 11-12 is postponed to the 39-43 time period. This is because the 8th-12th hour is the initial stage of the system load increase during the daytime, and the power supply pressure gradually increases. Moreover, this period coincides with the maintenance period of small hydropower unit 1, which cannot provide sufficient compensation for the power supply gap caused by the maintenance. Therefore, scheduling the maintenance of lines 11-12 during the 8th-12th time period in Scenario 1 will lead to uneven power flow distribution in the distribution network, increased node voltage deviation, and local branch power flow approaching its limit, putting significant pressure on the system to maintain its safety margin.

[0193] In Scenario 2, the system comprehensively considers the output characteristics and load response capabilities of adjustable equipment within the microgrid, and enables bidirectional power interaction with the distribution network via tie lines. Compared to Scenario 1, the maintenance period for lines 11-12 is proactively scheduled to the 8th-12th time period. Although this period coincides with the maintenance period of small hydropower unit 1, and the overall load level is in a daytime upward trend, due to the discreteness and complexity of the entire problem, maintenance should not be avoided during periods of high load. In fact, the system load level on the second day is lower than that on the first day. Scenario 2 proactively avoids this period, thus effectively reducing the system's operating costs. Especially under the condition of bidirectional power interaction between the microgrid and the distribution network, the microgrid can transform from a "load unit" to a "local power source" during the maintenance period, proactively undertaking power supply tasks and effectively mitigating the power imbalance caused by maintenance.

[0194] 2) Economic analysis of system operation

[0195] Table 3 shows the equipment maintenance and scheduling costs under different scenarios.

[0196] Table 3 Total System Operation and Scheduling Costs in Different Scenarios

[0197]

[0198] In Scenario 1, the microgrid is equivalent to a variable load connected to the distribution network and cannot participate in active power support and optimized allocation. The system needs to rely more on external power purchase and conventional unit output to meet power supply demand. In Scenario 2, by optimizing and coordinating the power exchange relationship between the microgrid and the distribution network in the region, the complementary consumption of local energy and economic operation are realized. The total cost of the system is reduced from RMB 1,275,485.06 to RMB 1,108,135.64, a reduction of about 13.1%, and the economic benefits are significantly improved.

[0199] From the perspective of cost composition, the cost of load outage losses remains consistent in both scenarios, with no load outage losses, indicating that distribution-microgrid collaboration primarily affects the economic aspects of the distribution network operation. Compared to scenario 1, the electricity purchase cost in scenario 2 decreased from RMB 635,163.10 to RMB 486,499.46, a reduction of approximately 23.4%. This is mainly due to the flexible output adjustment capability of the distributed generation (DG) within the microgrid, enabling the system to share the external electricity purchase pressure during high-load periods by combining the local output of small thermal power plants, small hydropower plants, small pumped storage units, and distributed photovoltaic power, thereby significantly reducing the amount of external electricity purchased. Simultaneously, the distribution network operating cost decreased from RMB 598,321.96 to RMB 579,636.18, a reduction of approximately 3.1%, indicating that under collaborative conditions, through the local balance between DG and load, electricity is utilized more efficiently within the distribution network, the system power flow distribution is more rational, and the output of small thermal power plants and small hydropower units is reduced to some extent. Therefore, the equipment maintenance optimization method proposed in this invention can improve the economics of the power system.

[0200] From the perspective of the temporal characteristics of power purchase in the distribution network, the output of distributed photovoltaic power also affects the optimized dispatch results. In both scenarios, the power purchase shows a significant increase after 17:00. Figure 6 This explanation primarily uses the 1-24 hour period as an example. This is because photovoltaic (PV) power output gradually decreases or even drops to zero during the night, forcing the system to rely on small thermal power plants, small hydropower plants, small pumped storage units, and the external power grid to maintain power balance. However, in a distribution-microgrid coordinated operation scenario, the system load level decreases at night, and the microgrid can support the distribution network through its internal energy storage units and distributed generation (DG), resulting in a significantly lower power purchase rate during the same period compared to the non-coordinated scenario. During the nighttime hours when PV output is zero, coordinated operation enables bidirectional power flow between the distribution network and the microgrid, ensuring system supply and demand balance while avoiding excessive reliance on the upper-level grid, thus improving operational stability and economy.

[0201] Furthermore, from the perspective of unit operation, the differences in operating characteristics between small hydropower and small thermal power are a significant reason for cost variations. The 72-hour unit output under the two scenarios is as follows: Figure 7 , Figure 8 As shown in the diagram, small hydropower units are prioritized for utilization in dispatching due to their lower operating costs and high renewability. Only after the output of small hydropower units reaches their maximum capacity are small thermal power units activated to compensate for the system's power deficit. Compared to Scenario 1, the average active power output of small thermal power units has decreased, indicating that coordinated operation effectively reduces the proportion of conventional units with higher fuel costs and increases the proportion of clean and low-carbon energy in the system. Furthermore, during unit maintenance periods 2-10 and 51-62, the microgrid can reduce dependence on the external grid through internal power regulation and small-scale pumped storage coordination, further reducing electricity purchase costs and unit operating costs.

[0202] 3) The impact of maintenance on the equivalent net load and regulation capacity of the distribution network

[0203] To illustrate the impact of distribution network maintenance plans on the equivalent net load and regulation capacity of the distribution network, this invention sets up scenarios 2 and 3 for comparative analysis. Scenario 3: During the study period, no equipment maintenance plan is formulated for the distribution network, but the equipment within the microgrid flexibly contributes power to participate in the active power game between the distribution and microgrids. The system optimization scheduling costs under different scenarios are shown in Table 4.

[0204] Table 4 Total System Operation and Scheduling Costs in Different Scenarios

[0205]

[0206] Introducing equipment maintenance constraints under the condition of distribution network coordination increased the total system cost from RMB 1,036,864.48 to RMB 1,066,135.64, an increase of approximately 2.82%. This indicates that while equipment maintenance at the distribution network level ensures system security, it also has a certain impact on system economy. This impact is mainly reflected in the reduced availability of some lines and distributed generation (DG) during maintenance, as well as the weakened system power flow flexibility and regulation capability.

[0207] The power purchase capacity and equivalent net load of the distribution network in the two scenarios are as follows: Figure 9 , Figure 10 As shown in the diagram, period 2-10 represents the maintenance period for small hydropower unit 1. During this time, the output of the small hydropower station is zero, and the system loses the support of low-cost renewable energy. Although other small thermal power plants and small pumped storage facilities increase their output to compensate for the shortfall, their compensation capacity is limited. Therefore, the net load of the distribution network during this period is higher than that in scenario 3, where no maintenance plan was set, leading to an increase in the system's power purchase. As small hydropower unit 1 gradually resumes operation, the participation of renewable energy sources in the system increases, and the power purchase gap between scenario 2 and scenario 3 gradually narrows, indicating that the impact of maintenance on system operation has obvious phased and localized characteristics.

[0208] pass Figure 9 and Figure 10As shown in Table 4, the maintenance of lines 11-12 and small hydropower unit 1 altered the power flow path. Furthermore, line maintenance resulted in power flow constraints during certain periods, reducing the distribution network's adjustability margin, i.e., weakening the system's ability to feed power back to the main grid. Although the distribution network did not actively feed power back to the main grid in this example, the increase in purchased power during maintenance essentially reflects this weakening of adjustability. In other words, when lines or distributed units are under maintenance, the distribution network cannot fully support regional load demand solely through internal coordination of small thermal power plants, small hydropower plants, small pumped storage units, photovoltaic systems, and microgrids. It must increase power purchases from the main grid, causing the power purchase cost to rise from 439,489.50 yuan to 486,499.46 yuan, an increase of approximately 10.7%, and consequently, the total cost to rise from 1,036,864.48 yuan to 1,066,135.64 yuan, an increase of approximately 2.82%.

[0209] Therefore, this invention proposes a method for optimizing equipment maintenance plans that considers micro-coordination, which has the following beneficial effects:

[0210] 1) By simultaneously considering the random fluctuations in photovoltaic output, changes in load levels, and the coordinated adjustment capabilities among distribution microgrids in the maintenance model, the multi-source uncertainty of the system's operating status during maintenance can be more accurately characterized, significantly improving the applicability and engineering consistency of the maintenance model.

[0211] 2) The microgrid's collaborative mechanism is explicitly embedded into the maintenance decision-making and operation scheduling process, enabling the microgrid's local flexibility resources to form adjustment and compensation during maintenance, thereby improving the distributed resources' ability to support maintenance risks and achieving system-level collaborative optimization.

[0212] 3) By integrating two-stage optimization modeling with power flow constraints, the maintenance plan is no longer limited to static economic cost comparison, but can ensure operational feasibility under uncertain conditions, thereby improving the robustness of the maintenance plan to extreme photovoltaic deviations and the operational safety margin.

[0213] 4) By employing mathematical modeling techniques such as second-order cone relaxation, the original mixed-integer nonlinear maintenance problem can be transformed into a convex programming form that can be solved efficiently. This significantly improves the solution efficiency while ensuring the accuracy of the solution, making it easier to implement in engineering scenarios.

[0214] 5) The calculation results show that the method of the present invention can effectively alleviate the system operation pressure during maintenance, reduce the overall operating cost, and improve the local absorption level of DG, thereby enhancing the economy and flexibility of the power distribution system under maintenance conditions.

[0215] Exemplary apparatus

[0216] Figure 11This is a schematic diagram of a novel equipment maintenance plan optimization device considering distribution micro-coordination in a power system, provided by an exemplary embodiment of the present invention. Figure 11 As shown, the device 1100 includes:

[0217] The first construction module 1110 is used to construct the first-stage optimization model of the equipment maintenance plan. The first-stage optimization model aims to minimize the sum of maintenance cost, unit start-up and shutdown cost and expected operating cost, and determines the decision variables of the maintenance plan.

[0218] The second construction module 1120 is used to construct the second-stage optimization model of the equipment maintenance plan. Under the premise that the decision variables of the maintenance plan are fixed, the second-stage optimization model optimizes the scheduling for different typical operating scenarios with the goal of minimizing the comprehensive operating cost of the microgrid system.

[0219] Processing module 1130 is used to perform second-order cone relaxation processing on the power flow constraints of the distribution network in the first-stage optimization model and the second-stage optimization model, and to transform the original nonlinear model into a mixed-integer second-order cone programming model.

[0220] Solver module 1140 is used to solve the mixed integer second-order cone programming model and output the optimal equipment maintenance plan.

[0221] Optionally, the objective function expression for the first-stage optimization model is:

[0222]

[0223] In the formula, F represents the sum of equipment maintenance costs, unit start-up and shutdown costs, and expected system operating costs; f1 represents the sum of equipment maintenance costs and unit start-up and shutdown costs; N s ω represents the number of typical scenarios; s f represents the probability of a typical scenario s; 2,s The system's overall operating cost under scenario s; J is the number of devices to be inspected; T is the total research period; X represents the maintenance cost corresponding to equipment j being repaired during time period t; j,t G represents the maintenance status of equipment j during time period t; G represents the total number of units in the system. The cost corresponding to the start-up of the i-th generating unit in time period t; The main grid electricity purchase cost coefficient for time period t; Power purchased during time period t under scenario s; N DN This refers to the number of nodes in the distribution network. The load outage loss cost coefficient for period t; Let N be the load outage loss power of the i-th distribution network node during time period t in scenario s; M N HS and N PSHThese are the numbers of small thermal power units, small hydropower units, and small pumped storage units, respectively. and These are the operating cost coefficients for the i-th small thermal power unit, small hydropower unit, and small pumped storage unit, respectively. and These represent the active power output of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t. and These represent the charging power and discharging power of the i-th small pumping unit in scenario s during time period t, respectively.

[0224] Optionally, the constraints of the first-stage optimization model include:

[0225] Maintenance time window constraints:

[0226]

[0227] In the formula: e j and l j These represent the time periods during which equipment j can complete maintenance;

[0228] State constraints for starting and stopping equipment maintenance:

[0229]

[0230] In the formula: q j,t Let j be the state variable indicating whether maintenance begins from time period t.

[0231] Total maintenance time constraint:

[0232]

[0233] In the formula: For the duration of equipment maintenance;

[0234] Constraints of continuous equipment maintenance:

[0235]

[0236] Maintenance resource constraints:

[0237]

[0238] In the formula: σ k,j,t R represents the amount of resource k required for equipment j to be repaired during time period t; k,t R represents the available quantity of resource k during time period t; k To study the total available amount of resource k within the research period;

[0239] Minimum start-up and shutdown time constraints for the unit:

[0240]

[0241] In the formula: I i,t This represents the operating status of unit i. A value of 1 indicates that the unit is in operation, and 0 indicates that the unit is out of operation; T i,on and T i,off These are the minimum allowed start-up and shutdown durations for unit i, respectively.

[0242] Unit start-up cost constraints

[0243]

[0244] In the formula: Let be the startup cost of unit i.

[0245] Optionally, the objective function expression for the second-stage optimization model is:

[0246]

[0247] In the formula, N s ω represents the number of typical scenarios; s f represents the probability of a typical scenario s; 2,s The overall operating cost of the system under scenario s.

[0248] Optionally, the constraints of the second-stage optimization model include:

[0249] Unload constraint:

[0250]

[0251] In the formula: Let be the load outage power loss of the i-th distribution network node during time period t in scenario s; N represents the maximum load output of the i-th node in the distribution network during time period t; DN This represents the number of nodes in the distribution network.

[0252] Unit power upper and lower limit constraints:

[0253]

[0254] In the formula: and The upper limit of active power output for small thermal power units and small hydropower units is set respectively. and The lower limit of active power output for small thermal power units and small hydropower units is set respectively. and These represent the active power output of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t.

[0255] Unit ramp-up constraints:

[0256]

[0257] In the formula: and These refer to the uphill / downhill climbing capabilities of small thermal power unit i; and These represent the uphill / downhill climbing capabilities of small hydropower unit i, respectively. and These represent the active power outputs of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t. and These represent the active power outputs of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t-1.

[0258] Small-scale pumped storage charging and discharging power constraints:

[0259]

[0260] In the formula: and These are the upper limits of the charging and discharging power of the small pumped storage unit i; and These are the lower limits of the charging and discharging power of the small pumped storage unit i; and These are the charging power and discharging power of the i-th small pumping unit in scenario s during time period t, respectively.

[0261] Distribution grid distributed photovoltaic output constraints:

[0262]

[0263] In the formula: The active power output of distributed photovoltaic m at time t under scenario s; Let m be the predicted active power output of the distributed photovoltaic system at time t.

[0264] Microgrid tie-line transmission capacity constraints:

[0265]

[0266] In the formula: Let be the power transmitted between the k-th microgrid and the distribution network in scenario s; and These represent the maximum and minimum active power allowed to flow through the branches connected to the microgrid k and the distribution network, respectively.

[0267] Operating constraints of distributed generation in microgrids:

[0268]

[0269] In the formula: Let i be the active power output of distributed power source i in microgrid k at time t under scenario s; and These are the upper and lower limits of the active power output of distributed generation i in microgrid k, respectively;

[0270] Microgrid energy storage charging and discharging constraints:

[0271]

[0272] In the formula: and Let be the charging state and discharging state of energy storage i in microgrid k at time t, respectively, both being 0-1 variables; and These represent the charging power and discharging power of energy storage i in microgrid k at time t under scenario s, respectively. and These are the upper limits of charging power and discharging power of energy storage i in microgrid k, respectively; Let i be the active power output of energy storage i in microgrid k at time t under scenario s; Let η be the state of charge of energy storage i in microgrid k at time t under scenario s; ch and η dis These are charging efficiency and discharging efficiency, respectively.

[0273] Distribution network power flow constraints:

[0274]

[0275] In the formula: P ij,t,s and Q ij,t,s These represent the active and reactive power flowing into branch ij in the distribution network at time t under scenario s; P jn,t,s and Q jn,t,s These represent the active and reactive power flowing into branch jn of the distribution network at time t under scenario s; I ij,t,s Let r be the amplitude of the branch current ij at time t under scenario s in the distribution network; ij and x ij These represent the resistance and reactance of line ij, respectively; P L,j,t,s and Q L,j,t,s These represent the active and reactive power of the load at node j at time t in scenario s of a distribution network; V i,t,s V represents the voltage amplitude at node i at time t in scenario s of a power distribution network. i,max and V i,min These are the upper and lower voltage limits for node i in the distribution network, respectively.

[0276] Optionally, the first-stage optimization model and the second-stage optimization model are processed using the second-order cone relaxation technique, and the expression for the introduced new variable is:

[0277]

[0278] In the formula: l ij,t,s u is the square of the current amplitude of branch ij at time t under scenario s in the distribution network; i,t,s I represents the square of the voltage amplitude at node i at time t under scenario s in the distribution network. ij,t,s V represents the amplitude of the branch current ij at time t under scenario s in the distribution network; i,t,s Let be the voltage amplitude of node i at time t under scenario s in the distribution network.

[0279] Exemplary electronic device

[0280] Figure 12 This is the structure of an electronic device provided in an exemplary embodiment of the present invention. For example... Figure 12 As shown, the electronic device 120 includes one or more processors 121 and memory 122.

[0281] The processor 121 may be a central processing unit (CPU) or other form of processing unit with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions.

[0282] The memory 122 may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may include, for example, random access memory (RAM) and / or cache memory. The non-volatile memory may include, for example, read-only memory (ROM), hard disk, flash memory, etc. One or more computer program instructions may be stored on the computer-readable storage medium, and the processor 121 may execute the program instructions to implement the methods of the software programs of the various embodiments of the present invention described above, and / or other desired functions. In one example, the electronic device may also include an input device 123 and an output device 124, which are interconnected via a bus system and / or other forms of connection mechanisms (not shown).

[0283] In addition, the input device 123 may also include, for example, a keyboard, a mouse, etc.

[0284] The output device 124 can output various information to the outside. The output device 124 may include, for example, a display, a speaker, a printer, and a communication network and its connected remote output devices, etc.

[0285] Of course, for the sake of simplicity, Figure 12Only some of the components of this electronic device relevant to the present invention are shown, omitting components such as buses, input / output interfaces, etc. In addition, the electronic device may include any other suitable components depending on the specific application.

[0286] Exemplary computer program product and computer readable storage medium

[0287] In addition to the methods and apparatus described above, embodiments of the present invention may also be computer program products, which include computer program instructions that, when executed by a processor, cause the processor to perform the steps in the methods according to various embodiments of the present invention described in the "Exemplary Methods" section above.

[0288] The computer program product can be written in any combination of one or more programming languages ​​to perform the operations of the embodiments of the present invention. The programming languages ​​include object-oriented programming languages ​​such as Java and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server.

[0289] Furthermore, embodiments of the present invention may also be computer-readable storage media storing computer program instructions thereon, which, when executed by a processor, cause the processor to perform the steps of the methods according to various embodiments of the present invention described in the "Exemplary Methods" section above.

[0290] The computer-readable storage medium may be any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or any combination thereof. More specific examples (a non-exhaustive list) of readable storage media include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0291] The basic principles of the present invention have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in the present invention are merely examples and not limitations, and should not be considered as essential features of each embodiment of the present invention. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the present invention to the necessity of employing the aforementioned specific details.

[0292] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For system embodiments, since they largely correspond to method embodiments, the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments.

[0293] The block diagrams of devices, systems, devices, and systems involved in this invention are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, systems, devices, and systems can be connected, arranged, and configured in any manner. Words such as “comprising,” “including,” “having,” etc., are open-ended terms meaning “including but not limited to,” and are used interchangeably with them. The terms “or” and “and” as used herein refer to the terms “and / or,” and are used interchangeably with them unless the context clearly indicates otherwise. The term “such as” as used herein refers to the phrase “such as but not limited to,” and is used interchangeably with it.

[0294] The methods and systems of the present invention may be implemented in many ways. For example, they may be implemented by software, hardware, firmware, or any combination of software, hardware, and firmware. The above-described order of steps for the methods is for illustrative purposes only, and the steps of the methods of the present invention are not limited to the order specifically described above unless otherwise specifically stated. Furthermore, in some embodiments, the present invention may also be implemented as a program recorded on a recording medium, the program comprising machine-readable instructions for implementing the methods according to the present invention. Thus, the present invention also covers recording media storing programs for performing the methods according to the present invention.

[0295] It should also be noted that in the systems, apparatus, and methods of the present invention, the components or steps can be disassembled and / or recombined. These disassemblies and / or recombinations should be considered equivalents of the present invention. The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the invention. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other aspects without departing from the scope of the invention. Therefore, the invention is not intended to be limited to the aspects shown herein, but rather to be carried out within the widest scope consistent with the principles and novel features disclosed herein.

[0296] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of the invention to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations thereof.

Claims

1. A novel method for optimizing equipment maintenance plans in a power system, considering distribution micro-coordination, characterized in that... include: A first-stage optimization model for the equipment maintenance plan is constructed, wherein the first-stage optimization model aims to minimize the sum of maintenance cost, unit start-up and shutdown cost and expected operating cost, and determines the decision variables for the maintenance plan. A second-stage optimization model for equipment maintenance planning is constructed, wherein the second-stage optimization model optimizes scheduling for different typical operating scenarios with the goal of minimizing the overall operating cost of the microgrid system, under the premise that the decision variables of the maintenance plan are fixed. The power flow constraints of the distribution network in the first-stage optimization model and the second-stage optimization model are subjected to second-order cone relaxation treatment, and the original nonlinear model is transformed into a mixed-integer second-order cone programming model. Solve the mixed-integer second-order cone programming model and output the optimal equipment maintenance plan.

2. The method according to claim 1, characterized in that, The objective function expression of the first-stage optimization model is: In the formula, F is the sum of equipment maintenance costs, unit start-up and shutdown costs, and expected system operating costs; f1 is the sum of equipment maintenance costs and unit start-up and shutdown costs; N s ω represents the number of typical scenarios; s f represents the probability of a typical scenario s; 2,s The system's overall operating cost under scenario s; J is the number of devices to be inspected; T is the total research period; X represents the maintenance cost corresponding to equipment j being repaired during time period t; j,t G represents the maintenance status of equipment j during time period t; G represents the total number of units in the system. The cost corresponding to the start-up of the i-th generating unit in time period t; The main grid electricity purchase cost coefficient for time period t; Power purchased during time period t under scenario s; N DN This refers to the number of nodes in the distribution network. The load outage loss cost coefficient for period t; Let N be the load outage loss power of the i-th distribution network node during time period t in scenario s; M N HS and N PSH These are the numbers of small thermal power units, small hydropower units, and small pumped storage units, respectively. and These are the operating cost coefficients for the i-th small thermal power unit, small hydropower unit, and small pumped storage unit, respectively. and These represent the active power output of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t. and These represent the charging power and discharging power of the i-th small pumping unit in scenario s during time period t, respectively.

3. The method according to claim 2, characterized in that, The constraints of the first-stage optimization model include: Maintenance time window constraints: In the formula: e j and l j These represent the time periods during which equipment j can complete maintenance; State constraints for starting and stopping equipment maintenance: In the formula: q j,t Let j be the state variable indicating whether maintenance begins from time period t. Total maintenance time constraint: In the formula: For the duration of equipment maintenance; Constraints of continuous equipment maintenance: Maintenance resource constraints: Where: σ k,j,t R represents the amount of resource k required for equipment j to be repaired during time period t; k,t R represents the available quantity of resource k during time period t; k To study the total available amount of resource k within the research period; Minimum start-up and shutdown time constraints for the unit: In the formula: I i,t This represents the operating status of unit i. A value of 1 indicates that the unit is in operation, and 0 indicates that the unit is out of operation; T i,on and T i,off These are the minimum allowed start-up and shutdown durations for unit i, respectively. Unit start-up cost constraints In the formula: Let be the startup cost of unit i.

4. The method according to claim 1, characterized in that, The objective function expression for the second-stage optimization model is: In the formula, N s ω represents the number of typical scenarios; s f represents the probability of a typical scenario s; 2,s The overall operating cost of the system under scenario s.

5. The method according to claim 1, characterized in that, The constraints of the second-stage optimization model include: Unload constraint: In the formula: Let be the load outage loss power of the i-th distribution network node during time period t in scenario s; N represents the maximum load output of the i-th node in the distribution network during time period t; DN This represents the number of nodes in the distribution network. Unit power upper and lower limit constraints: In the formula: and The upper limit of active power output for small thermal power units and small hydropower units is set respectively. and The lower limit of the active power output of small thermal power units and small hydropower units are respectively set as the i-th output. and These represent the active power output of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t. Unit ramp-up constraints: In the formula: and These refer to the uphill / downhill climbing capabilities of small thermal power unit i; and These represent the uphill / downhill climbing capabilities of small hydropower unit i, respectively. and These represent the active power outputs of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t. and These represent the active power outputs of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t-1. Small-scale pumped storage charging and discharging power constraints: In the formula: and These are the upper limits of the charging and discharging power of the small pumped storage unit i; and These are the lower limits of the charging and discharging power of the small pumped storage unit i; and These are the charging power and discharging power of the i-th small pumping unit in scenario s during time period t, respectively. Distribution grid distributed photovoltaic output constraints: In the formula: The active power output of distributed photovoltaic m at time t under scenario s; Let m be the predicted active power output of the distributed photovoltaic system at time t. Microgrid tie-line transmission capacity constraints: In the formula: Let be the power transmitted between the k-th microgrid and the distribution network in scenario s; and These represent the maximum and minimum values ​​of active power allowed to flow through the branches connected to the microgrid k and the distribution network, respectively. Operating constraints of distributed generation in microgrids: In the formula: Let i be the active power output of distributed power source i in microgrid k at time t under scenario s; and These are the upper and lower limits of the active power output of distributed generation i in microgrid k, respectively; Microgrid energy storage charging and discharging constraints: In the formula: and Let be the charging state and discharging state of energy storage i in microgrid k at time t, respectively, both being 0-1 variables; and These represent the charging power and discharging power of energy storage i in microgrid k at time t under scenario s, respectively. and These are the upper limits of charging power and discharging power of energy storage i in microgrid k, respectively; Let i be the active power output of energy storage i in microgrid k at time t under scenario s; Let η represent the state of charge of energy storage i in microgrid k at time t under scenario s; ch and η dis These are charging efficiency and discharging efficiency, respectively. Distribution network power flow constraints: In the formula: P ij,t,s and Q ij,t,s These represent the active and reactive power flowing into branch ij in the distribution network at time t under scenario s; P jn,t,s and Q jn,t,s These represent the active and reactive power flowing into branch jn of the distribution network at time t under scenario s; I ij,t,s Let r be the amplitude of the branch current ij at time t under scenario s in the distribution network; ij and x ij These represent the resistance and reactance of line ij, respectively; P L,j,t,s and Q L,j,t,s These represent the active and reactive power of the load at node j at time t in scenario s of a distribution network; V i,t,s V represents the voltage amplitude at node i at time t in scenario s of a power distribution network. i,max and V i,min These are the upper and lower voltage limits for node i in the distribution network, respectively.

6. The method according to claim 1, characterized in that, The first-stage optimization model and the second-stage optimization model are processed using the second-order cone relaxation technique. The expression for the new variable introduced is as follows: In the formula: l ij,t,s u is the square of the current amplitude of branch ij at time t under scenario s in the distribution network; i,t,s I represents the square of the voltage amplitude at node i at time t under scenario s in the distribution network. ij,t,s V represents the amplitude of the branch current ij at time t under scenario s in the distribution network; i,t,s Let be the voltage amplitude of node i at time t under scenario s in the distribution network.

7. A novel equipment maintenance plan optimization device considering distribution micro-coordination in a power system, characterized in that, include: The first construction module is used to construct the first-stage optimization model of the equipment maintenance plan, wherein the first-stage optimization model aims to minimize the sum of maintenance cost, unit start-up and shutdown cost and expected operating cost, and determines the decision variables of the maintenance plan. The second construction module is used to construct the second-stage optimization model of the equipment maintenance plan. The second-stage optimization model optimizes the scheduling for different typical operating scenarios with the goal of minimizing the overall operating cost of the microgrid system, under the premise that the decision variables of the maintenance plan are fixed. The processing module is used to perform second-order cone relaxation processing on the power flow constraints of the distribution network in the first-stage optimization model and the second-stage optimization model, and to transform the original nonlinear model into a mixed-integer second-order cone programming model. The solution module is used to solve the mixed integer second-order cone programming model and output the optimal equipment maintenance plan.

8. The apparatus according to claim 7, characterized in that, The objective function expression of the first-stage optimization model is: In the formula, F is the sum of equipment maintenance costs, unit start-up and shutdown costs, and expected system operating costs; f1 is the sum of equipment maintenance costs and unit start-up and shutdown costs; N s ω represents the number of typical scenarios; s f represents the probability of a typical scenario s; 2,s The system's overall operating cost under scenario s; J is the number of devices to be inspected; T is the total research period; X represents the maintenance cost corresponding to equipment j being repaired during time period t; j,t G represents the maintenance status of equipment j during time period t; G represents the total number of units in the system. The cost corresponding to the start-up of the i-th generating unit in time period t; The main grid electricity purchase cost coefficient for time period t; Power purchased during time period t under scenario s; N DN This refers to the number of nodes in the distribution network. The load outage loss cost coefficient for period t; Let N be the load outage loss power of the i-th distribution network node during time period t in scenario s; M N HS and N PSH These are the numbers of small thermal power units, small hydropower units, and small pumped storage units, respectively. and These are the operating cost coefficients for the i-th small thermal power unit, small hydropower unit, and small pumped storage unit, respectively. and These represent the active power output of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t. and These represent the charging power and discharging power of the i-th small pumping unit in scenario s during time period t, respectively.

9. The apparatus according to claim 8, characterized in that, The constraints of the first-stage optimization model include: Maintenance time window constraints: In the formula: e j and l j These represent the time periods during which equipment j can complete maintenance; State constraints for starting and stopping equipment maintenance: In the formula: q j,t Let j be the state variable indicating whether maintenance begins from time period t. Total maintenance time constraint: In the formula: For the duration of equipment maintenance; Constraints of continuous equipment maintenance: Maintenance resource constraints: Where: σ k,j,t R represents the amount of resource k required for equipment j to be repaired during time period t; k,t R represents the available quantity of resource k during time period t; k To study the total available amount of resource k within the research period; Minimum start-up and shutdown time constraints for the unit: In the formula: I i,t This represents the operating status of unit i. A value of 1 indicates that the unit is in operation, and 0 indicates that the unit is out of operation; T i,on and T i,off These are the minimum allowed start-up and shutdown durations for unit i, respectively. Unit start-up cost constraints In the formula: Let be the startup cost of unit i.

10. The apparatus according to claim 7, characterized in that, The objective function expression for the second-stage optimization model is: In the formula, N s ω represents the number of typical scenarios; s f represents the probability of a typical scenario s; 2,s The overall operating cost of the system under scenario s.

11. The apparatus according to claim 7, characterized in that, The constraints of the second-stage optimization model include: Unload constraint: In the formula: Let be the load outage loss power of the i-th distribution network node during time period t in scenario s; N represents the maximum load output of the i-th node in the distribution network during time period t; DN This represents the number of nodes in the distribution network. Unit power upper and lower limit constraints: In the formula: and The upper limit of active power output for small thermal power units and small hydropower units is set respectively. and The lower limit of the active power output of small thermal power units and small hydropower units are respectively set as the i-th output. and These represent the active power output of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t. Unit ramp-up constraints: In the formula: and These refer to the uphill / downhill climbing capabilities of small thermal power unit i; and These represent the uphill / downhill climbing capabilities of small hydropower unit i, respectively. and These represent the active power outputs of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t. and These represent the active power outputs of the i-th small thermal power unit and the i-th small hydropower unit in scenario s during time period t-1. Small-scale pumped storage charging and discharging power constraints: In the formula: and These are the upper limits of the charging and discharging power of the small pumped storage unit i; and These are the lower limits of the charging and discharging power of the small pumped storage unit i; and These are the charging power and discharging power of the i-th small pumping unit in scenario s during time period t, respectively. Distribution grid distributed photovoltaic output constraints: In the formula: The active power output of distributed photovoltaic m at time t under scenario s; Let m be the predicted active power output of the distributed photovoltaic system at time t. Microgrid tie-line transmission capacity constraints: In the formula: Let be the power transmitted between the k-th microgrid and the distribution network in scenario s; and These represent the maximum and minimum values ​​of active power allowed to flow through the branches connected to the microgrid k and the distribution network, respectively. Operating constraints of distributed generation in microgrids: In the formula: Let i be the active power output of distributed power source i in microgrid k at time t under scenario s; and These are the upper and lower limits of the active power output of distributed generation i in microgrid k, respectively; Microgrid energy storage charging and discharging constraints: In the formula: and Let be the charging state and discharging state of energy storage i in microgrid k at time t, respectively, both being 0-1 variables; and These represent the charging power and discharging power of energy storage i in microgrid k at time t under scenario s, respectively. and These are the upper limits of charging power and discharging power of energy storage i in microgrid k, respectively; Let i be the active power output of energy storage i in microgrid k at time t under scenario s; Let η represent the state of charge of energy storage i in microgrid k at time t under scenario s; ch and η dis These are charging efficiency and discharging efficiency, respectively. Distribution network power flow constraints: In the formula: P ij,t,s and Q ij,t,s These represent the active and reactive power flowing into branch ij in the distribution network at time t under scenario s; P jn,t,s and Q jn,t,s These represent the active and reactive power flowing into branch jn of the distribution network at time t under scenario s; I ij,t,s Let r be the amplitude of the branch current ij at time t under scenario s in the distribution network; ij and x ij These represent the resistance and reactance of line ij, respectively; P L,j,t,s and Q L,j,t,s These represent the active and reactive power of the load at node j at time t in scenario s of a distribution network; V i,t,s V represents the voltage amplitude at node i at time t in scenario s of a power distribution network. i,max and V i,min These are the upper and lower voltage limits for node i in the distribution network, respectively.

12. The apparatus according to claim 7, characterized in that, The first-stage optimization model and the second-stage optimization model are processed using the second-order cone relaxation technique. The expression for the new variable introduced is as follows: In the formula: l ij,t,s u is the square of the current amplitude of branch ij at time t under scenario s in the distribution network; i,t,s I represents the square of the voltage amplitude at node i at time t under scenario s in the distribution network. ij,t,s V represents the amplitude of the branch current ij at time t under scenario s in the distribution network; i,t,s Let be the voltage amplitude of node i at time t under scenario s in the distribution network.

13. A computer-readable storage medium, characterized in that, The storage medium stores a computer program for performing the method described in any one of claims 1-6.

14. An electronic device, characterized in that, The electronic device includes: processor; Memory used to store the processor's executable instructions; The processor is configured to read the executable instructions from the memory and execute the instructions to implement the method described in any one of claims 1-6.

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