Urban power grid toughness improving and optimizing method for configuring solid-state super capacitor

Abstract

The invention discloses an urban power grid toughness improvement optimization method configured with a solid-state super capacitor, and the method comprises the steps: obtaining the basic power of the solid-state super capacitor according to the output power of the solid-state super capacitor and the output power considering the power loss; constructing an urban power grid toughness improvement model based on the basic power of the solid-state super capacitor and the urban power grid loss model under the extreme disaster, constructing a balance model according to the urban power grid toughness improvement model, the total cost model and the urban power grid income model, and finally calculating the balance model by using a multi-objective optimization algorithm to obtain the urban power grid toughness improvement model. And an optimization result is obtained, so that personnel can configure the solid-state super capacitor according to the optimization result. According to the method, the planning rationality in disaster prevention and reduction construction can be improved while power supply is restored in a short time after the urban power grid suffers from extreme disasters.

Description

Technical Field

[0001] The present invention relates to the technical field of power grid planning, and particularly to an optimization method for improving the resilience of urban power grids configured with solid-state supercapacitors. Background Art

[0002] The development of China's economy today has driven the electricity demand from all sectors of society, and the load borne by urban power grids is increasing day by day. As the proportion of new energy is getting larger and larger, the system complexity of urban power grids is increasing day by day; in this scenario, even a minor fault in the urban power grid may trigger a chain reaction and even paralyze the power system. Once a major power outage occurs, it will have a huge impact on the city. With the deterioration of the global climate environment, extreme natural disasters such as typhoons and floods occur more frequently, and the probability of power systems being damaged due to their influence will increase significantly compared with before; the potential safety hazards of power grid systems caused by extreme natural disasters are seriously related to the safety of the country and people's lives and property. It is particularly important to promptly repair damaged equipment in areas affected by extreme natural disasters or to carry out disaster prevention and mitigation construction of power systems locally.

[0003] When carrying out disaster prevention and mitigation construction of urban power grids under the background of extreme natural disasters, three aspects need to be considered: one is how to select the construction method for resilience improvement, the second is how to consider the economy of power grid disaster prevention and mitigation construction, and the third is how to balance the quantitative results of the first and second problems to make the overall benefit of urban power grid disaster prevention construction optimal. In terms of improving the resilience of urban power grids, supercapacitors can be used as emergency power supply devices for urban power grids. As an efficient energy storage device, supercapacitors have performance advantages such as high power density, fast response ability, high charge and discharge efficiency, long life, high cycle times, and good durability and stability; compared with conventional supercapacitors, solid-state supercapacitors have the advantages of being easy to transfer and high reliability, and can play a key role in rapid response, frequency regulation, voltage support, energy balance, peak shaving and valley filling, and enhancing system stability in urban power grids. For the first aspect of the problem, solid-state supercapacitors can be used to regulate the frequency and support the voltage of the urban power grid after an accident, and a model for improving the resilience of urban power grids after natural disasters based on solid-state supercapacitors can be established.

[0004] In terms of the economy of urban power grid disaster prevention and mitigation construction, the costs of solid-state supercapacitors include investment costs, operation and maintenance costs, replacement costs, and salvage values, and the benefits include the economic benefits brought by peak shaving and frequency modulation during daily operation. For the second aspect of the problem, an economic benefit model can be used to quantify the comprehensive economic benefits generated by solid-state supercapacitors. However, how to solve the balance problem between the resilience improvement effect and economic benefits of urban power grids after configuring solid-state supercapacitors, so as to provide accurate reference for power grid companies when carrying out power grid planning is an urgent problem to be solved. Summary of the Invention

[0005] To solve the above technical problems, an embodiment of the present invention provides an optimization method for improving the resilience of urban power grids by configuring solid-state supercapacitors, so as to solve the technical problems in the prior art that power supply cannot be restored within a short time after an urban power grid undergoes an extreme disaster and the planning in disaster prevention and mitigation construction is unreasonable.

[0006] A first aspect of an embodiment of the present invention provides an optimization method for improving the resilience of urban power grids by configuring solid-state supercapacitors. The method includes:

[0007] Based on the output power of the solid-state supercapacitor and the output power considering power loss, obtain the basic power of the solid-state supercapacitor, and construct an urban power grid resilience improvement model based on the basic power of the solid-state supercapacitor and the urban power grid loss model under extreme disasters;

[0008] Construct the total cost model of the solid-state supercapacitor, construct the first power output model and the second power output model of the solid-state supercapacitor under peak shaving and frequency modulation, obtain the urban power grid revenue model according to the first power output model and the second power output model, and construct an equilibrium model according to the urban power grid resilience improvement model, the total cost model and the urban power grid revenue model;

[0009] Use a multi-objective optimization algorithm to calculate the equilibrium model to obtain an optimization result, so that the personnel configure the solid-state supercapacitor according to the optimization result.

[0010] In a possible implementation manner of the first aspect, constructing an urban power grid resilience improvement model based on the basic power of the solid-state supercapacitor and the urban power grid loss model under extreme disasters includes:

[0011] Based on the risk value theory, obtain the urban power grid loss model under extreme disasters, where the urban power grid loss model under extreme disasters is:

[0012]

[0013] In the formula, S(i) is the urban power grid loss model under extreme disasters, x i is the power supply state of the i-th emergency power supply, 0 means there is power supply from the i-th emergency power supply, 1 means there is no power supply from the i-th emergency power supply, Δt i is the power outage time at the i-th place, Z i is the power outage loss power at the i-th place, and C0 is the unit load power outage loss;

[0014] According to the initial power and equivalent parameter values of the solid-state supercapacitor in the emergency power supply state, obtain the power consumption of the solid-state supercapacitor in the emergency power supply state, where the power consumption expression is:

[0015] Z(t) = Z0·(1 - SOC)

[0016]

[0017] Wherein, Z(t) is the voltage of the solid supercapacitor at time t, Z0 is the initial charge, t is the time, P out (t) is the basic power of the solid supercapacitor, V(t) is the voltage of the solid supercapacitor at time t, R ESR is the internal resistance value, is the capacitance value, P out (t) is the power output by the solid supercapacitor at time t, and SOC is the state of charge of the solid supercapacitor;

[0018] According to the power consumption and the urban power grid loss model under extreme disasters, an urban power grid resilience improvement model is constructed, wherein the urban power grid resilience improvement model is:

[0019]

[0020] Wherein, S(i) is the urban power grid loss model under extreme disasters, x i is the power supply state of the i-th emergency power supply, 0 indicates that there is power supply from the i-th emergency power supply, 1 indicates that there is no power supply from the i-th emergency power supply, Δt i is the power outage time at the i-th place, Z i is the power outage loss power at the i-th place, and C0 is the power outage loss per unit load.

[0021] In a possible implementation manner of the first aspect, a total cost model of the solid supercapacitor is constructed, including:

[0022] According to the cost of the solid supercapacitor module, the cost of the power conversion system and the installation cost, the initial investment cost of the solid supercapacitor is obtained;

[0023] According to the initial investment cost and the maintenance cost, the total cost model of the solid supercapacitor is obtained, wherein the total cost model is:

[0024] F C = C inv,supercap + C O&M,supercap + C replace,supercap - C salvage,supercap

[0025] Wherein, C inv,supercap is the initial investment cost, C o&M,supercap is the operation and maintenance cost, C replace,supercap is the replacement cost, C salvage,supercap is the salvage value.

[0026] In a possible implementation of the first aspect, the maintenance cost is obtained based on the operation and maintenance cost, the replacement cost, and the salvage value, where the expression for the operation and maintenance cost is:

[0027] C o&M,supercap = α supercap ·C inv,supercap ·T

[0028] In the formula, C o&M,supercap is the operation and maintenance cost, α supercap is the annual operation and maintenance rate, and T is the life cycle of the solid-state supercapacitor;

[0029] The expression for the replacement cost is:

[0030] C replace,supercap = N replace,supercap ·C supercap

[0031] In the formula, C replace,supercap is the operation and maintenance cost, N replace,supercap is the number of replacements, T is the life cycle of the solid-state supercapacitor, and C supercap is the cost of the solid-state supercapacitor module;

[0032] The expression for the salvage value is:

[0033]

[0034] In the formula, T life,supercap is the actual service life of the solid-state supercapacitor, and T design,supercap is the designed life of the solid-state supercapacitor.

[0035] In a possible implementation of the first aspect, constructing the first power output model and the second power output model of the solid-state supercapacitor under peak shaving and frequency modulation includes:

[0036] Constructing the first power output model and the second power output model of the solid-state supercapacitor under peak shaving and frequency modulation, and the first power output model is:

[0037]

[0038] Among them, P(t) is the output power of the solid-state supercapacitor, V(t) is the voltage across the solid-state supercapacitor, C is the rated capacitance of the solid-state supercapacitor, and k1 is a constant related to the system characteristics;

[0039] The second power output model is:

[0040]

[0041] In the formula, P(t) is the output power of the solid-state supercapacitor, V(t) is the voltage across the solid-state supercapacitor, C is the rated capacitance value of the solid-state supercapacitor, k2 is a constant related to the load regulation ability, and ΔP load (t) is the change in load power.

[0042] In a possible implementation of the first aspect, a total revenue model is obtained according to the first power output model and the second power output model, including:

[0043] A total power output model is obtained according to the first power output model and the second power output model, where the total power output model is:

[0044]

[0045] In the formula, P total (t) is the total output power of the solid-state supercapacitor at time t, is the basic capacitance power output part, k1·ΔV grid (t) is the power provided by the solid-state supercapacitor for the voltage support across the solid-state supercapacitor, k2·ΔP load (t) is the power provided by the solid-state supercapacitor for peak shaving, and k3·Δf(t) is the power provided by the solid-state supercapacitor for frequency modulation, is the internal resistance loss of the solid-state supercapacitor;

[0046] A urban power grid revenue model is obtained according to the total power output model and the revenue per unit of electricity, where the urban power grid revenue model is:

[0047]

[0048] In the formula, P total is the revenue model, and e0 is the economic benefit per unit of electricity.

[0049] In a possible implementation of the first aspect, an equilibrium model is constructed according to the urban power grid resilience improvement model, the total cost model, and the urban power grid revenue model, including:

[0050] An equilibrium model is constructed according to the urban power grid resilience improvement model, the total cost model, and the urban power grid revenue model, where the objective function of the equilibrium model is:

[0051]

[0052] In the formula, d1 and d1 are the negotiation breakdown points respectively, and F E is the urban power grid revenue model, and F CThis is the urban power grid resilience improvement model.

[0053] In a possible implementation manner of the first aspect, a multi-objective optimization algorithm is used to calculate the equilibrium model to obtain an optimization result, so that the personnel configure the solid-state supercapacitor according to the optimization result, including:

[0054] Initialize the population, and calculate the objective function value of each individual according to the individuals in the population and the objective function of the equilibrium model;

[0055] Perform non-dominated sorting according to the objective function values of each individual to obtain a non-dominated sorting result. Based on the non-dominated sorting result, divide the population into multiple levels to obtain the non-dominated sorting levels of each individual, and calculate the crowding distance of each individual within the same non-dominated front;

[0056] Select the optimal solution among all individuals according to the non-dominated sorting level and the crowding distance to obtain a Pareto optimal solution set. Use the crossover and mutation operations of the genetic algorithm to generate an offspring population, and calculate the new objective function value according to the offspring population and the objective function of the equilibrium model;

[0057] Merge the parent population and the offspring population to obtain a temporary population. Perform non-dominated sorting on the temporary population, and select the next-generation population according to the population size and the sorting level. If the maximum number of generations is reached or the population converges, stop the calculation and determine the Pareto optimal solution set as the optimization result.

[0058] The second aspect of the embodiments of the present invention provides an urban power grid resilience improvement optimization system for configuring solid-state supercapacitors. The system includes:

[0059] A resilience improvement model construction module, configured to obtain the basic power of the solid-state supercapacitor according to the output power of the solid-state supercapacitor and the output power considering power loss, and construct an urban power grid resilience improvement model based on the basic power of the solid-state supercapacitor and the urban power grid loss model under extreme disasters;

[0060] An equilibrium model construction module, configured to construct the total cost model of the solid-state supercapacitor, construct the first power output model and the second power output model of the solid-state supercapacitor under peak shaving and frequency modulation, obtain the urban power grid revenue model according to the first power output model and the second power output model, and construct an equilibrium model according to the urban power grid resilience improvement model, the total cost model, and the urban power grid revenue model;

[0061] A solving module, configured to use a multi-objective optimization algorithm to calculate the equilibrium model to obtain an optimization result, so that the personnel configure the solid-state supercapacitor according to the optimization result.

[0062] In a possible implementation of the second aspect, the resilience improvement model construction module includes a loss model construction unit, a power consumption model construction unit, and a resilience model construction unit.

[0063] Among them, the loss model construction unit is used to obtain the urban power grid loss model under extreme disasters based on the risk value theory. Among them, the urban power grid loss model under extreme disasters is:

[0064]

[0065] In the formula, S(i) is the urban power grid loss model under extreme disasters, and x i is the power supply state of the i-th emergency power supply. 0 means that there is emergency power supply at the i-th place, and 1 means that there is no emergency power supply at the i-th place. Δt i is the power outage time at the i-th place, and Z i is the power outage loss power at the i-th place, and C0 is the unit load power outage loss;

[0066] The power consumption model construction unit is used to obtain the power consumption of the solid-state supercapacitor in the emergency power supply state according to the starting power and equivalent parameter values of the solid-state supercapacitor in the emergency power supply state. Among them, the power consumption expression is:

[0067] Z(t) = Z0·(1 - SOC)

[0068]

[0069] In the formula, Z(t) is the voltage of the solid-state supercapacitor at time t, Z0 is the starting power, t is the time, P out (t) is the basic power of the solid-state supercapacitor, V(t) is the voltage of the solid-state supercapacitor at time t, and R ESR is the internal resistance value, is the capacitance value, and P out (t) is the power output by the solid-state supercapacitor at time t, and SOC is the state of charge of the solid-state supercapacitor;

[0070] The resilience model construction unit is used to construct an urban power grid resilience improvement model according to the power consumption and the urban power grid loss model under extreme disasters. Among them, the urban power grid resilience improvement model is:

[0071]

[0072] In the formula, S(i) is the urban power grid loss model under extreme disasters, and x iThe power supply status of the i-th emergency power supply, where 0 indicates that there is emergency power supply at the i-th location and 1 indicates that there is no emergency power supply at the i-th location, Δt i The power outage time at the i-th location, Z i The power outage loss power at the i-th location, and C0 is the power outage loss per unit load.

[0073] The technical solution of the present invention has the following advantages:

[0074] The method for optimizing the resilience improvement of the urban power grid with solid-state supercapacitors provided by the embodiment of the present invention obtains the basic power of the solid-state supercapacitor by according to the output power of the solid-state supercapacitor and the output power considering power loss, constructs an urban power grid resilience improvement model based on the basic power of the solid-state supercapacitor and the urban power grid loss model under extreme disasters, constructs an equilibrium model according to the urban power grid resilience improvement model, the total cost model and the urban power grid revenue model, and finally uses a multi-objective optimization algorithm to calculate the equilibrium model to obtain an optimization result, so that personnel can configure the solid-state supercapacitor according to the optimization result. The above method can restore power supply in a short time after the urban power grid undergoes extreme disasters, while improving the planning rationality in disaster prevention and mitigation construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0076] Figure 1 It is the flowchart of the auditing method for the method for optimizing the resilience improvement of the urban power grid with solid-state supercapacitors in the embodiment of the present invention;

[0077] Figure 2 It is the introduction diagram of the equipment performance of the solid-state supercapacitor for the method for optimizing the resilience improvement of the urban power grid with solid-state supercapacitors in the embodiment of the present invention;

[0078] Figure 3 It is the introduction diagram of the application scenario of the equipment performance of the solid-state supercapacitor for the method for optimizing the resilience improvement of the urban power grid with solid-state supercapacitors in the embodiment of the present invention;

[0079] Figure 4 It is the schematic diagram of the construction process of the urban power grid resilience improvement model for the method for optimizing the resilience improvement of the urban power grid with solid-state supercapacitors in the embodiment of the present invention;

[0080] Figure 5Schematic diagram of the equilibrium model for the urban power grid resilience improvement optimization method with solid-state supercapacitors configured in the embodiments of the present invention;

[0081] Figure 6 Flowchart of the NSGA-II algorithm solution for the urban power grid resilience improvement optimization method with solid-state supercapacitors configured in the embodiments of the present invention;

[0082] Figure 7 System block diagram of the urban power grid resilience improvement optimization system with solid-state supercapacitors configured in the embodiments of the present invention. Detailed implementation manners

[0083] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0084] Please refer to Figure 1 , which is a schematic flowchart of an embodiment of the urban power grid resilience improvement optimization method with solid-state supercapacitors provided in the embodiments of the present invention, including steps S101 to S103.

[0085] S101. Obtain the basic power of the solid-state supercapacitor based on the output power of the solid-state supercapacitor and the output power considering power loss, and construct an urban power grid resilience improvement model based on the basic power of the solid-state supercapacitor and the urban power grid loss model under extreme disasters.

[0086] In this embodiment, the solid-state supercapacitor performs excellently in scenarios with instantaneous power demand, requiring it to provide a high enough power density to meet short-term high-power demands. Generally, the power density of the solid-state supercapacitor needs to reach the level of several kilowatts per kilogram (kW / kg) to ensure a quick response to urban power grid fluctuations. Moreover, the frequency and voltage regulation in the urban power grid require the equipment to respond within milliseconds. Therefore, the solid-state supercapacitor must have a fast charge-discharge response ability. The response time should be controlled within milliseconds to ensure immediate intervention and regulation when there are instantaneous fluctuations in the urban power grid. The solid-state supercapacitor should remain efficient during frequent charge and discharge cycles, and the charge-discharge efficiency is generally required to be above 90% to reduce energy loss and ensure that energy is not wasted during the fast charge-discharge process. The scenarios such as frequency modulation and peak shaving, and frequency stability in the urban power grid system have extremely high requirements for the charge-discharge cycles of energy storage devices. Due to its long cycle life (usually up to more than 1 million times), the solid-state supercapacitor can adapt to frequent power regulation demands, thereby reducing the replacement frequency and long-term maintenance costs. The urban power grid system may operate under different climate and environmental conditions. Therefore, the solid-state supercapacitor needs to maintain efficient operation within a wide temperature range. Generally, its operating temperature range is required to be between -40°C and 65°C to meet the operating requirements in different environments. Good durability and stability: The solid-state supercapacitor needs to maintain stable performance during long-term operation. Especially when it withstands frequent power changes and extreme operating conditions, it can still maintain efficient charge-discharge characteristics and structural stability. The main advantages of the solid-state supercapacitor in the urban power grid lie in its fast response, high-power output, and long life. It performs excellently in scenarios such as frequency modulation and peak shaving, frequency and voltage regulation, and instantaneous power support, and can significantly enhance the dynamic stability and operating reliability of the urban power grid. To ensure its best performance in the urban power grid, the solid-state supercapacitor needs to possess key performance such as high power density, fast response ability, long life, and high efficiency.

[0087] The improvement of the resilience of the urban power grid can be specifically divided into two aspects: the supporting mechanism for the improvement of the resilience of the urban power grid and the output power modeling of the solid-state supercapacitor under the emergency power supply mode, which are as follows:

[0088] The solid-state supercapacitor has a fast response ability within milliseconds. When there are frequency fluctuations or instantaneous voltage drops in the urban power grid system, the solid-state supercapacitor can immediately provide or absorb electrical energy to maintain the power balance of the urban power grid. Its output power is proportional to the voltage change rate:

[0089]

[0090] In the formula, P(t) is the output power of the solid-state supercapacitor, V(t) is the voltage across the solid-state supercapacitor, and C is the rated capacitance value of the solid-state supercapacitor.

[0091] Frequency fluctuations in the urban power grid system can lead to system instability, and solid-state supercapacitors regulate the output power to balance power fluctuations. When the load increases and power generation is insufficient, the solid-state supercapacitor smooths out the power difference through rapid discharge to help restore the system frequency. When the load decreases, it can regulate the frequency by absorbing excess power and keep the frequency within a safe range. This process can be achieved through the fast power response characteristics of the solid-state supercapacitor. In the urban power grid system, load changes and faults may cause voltage fluctuations or voltage sags. The solid-state supercapacitor can quickly provide reactive power support and stabilize the voltage through its high response speed. The voltage support ability of the solid-state supercapacitor is related to its voltage response characteristics. The voltage deviation is adjusted through fast charge and discharge, and the expression is:

[0092] Q(t)=k1·ΔV grid (t)

[0093] In the formula, Q(t) is the charge of the solid-state supercapacitor, k1 is a constant related to the system characteristics, and ΔV grid (t) is the voltage deviation across the solid-state supercapacitor.

[0094] The output power of the solid-state supercapacitor mainly depends on the voltage, charge and discharge current (i.e., the rate of change of voltage), capacitance value, and equivalent series resistance. In practical applications, in order to obtain accurate output power, the power loss caused by its internal resistance also needs to be considered. On this basis, the capacitance expression of the double-layer solid-state supercapacitor is substituted into the output power formula:

[0095]

[0096] In the formula, P(t) is the output power of the solid-state supercapacitor, and V(t) is the voltage across the solid-state supercapacitor.

[0097] The above formula shows that the output power of the double-layer solid-state supercapacitor not only depends on the voltage and the rate of change of voltage, but is also closely related to the capacitance value. And the capacitance value is determined by the dielectric constant, electrode area, and electrode spacing. By increasing the electrode area or reducing the electrode distance, the capacitance value can be increased, thereby increasing the power output of the solid-state supercapacitor. Considering the influence of the internal resistance, the basic power expression of the solid-state supercapacitor is obtained:

[0098]

[0099] In the formula, P out (t) is the basic power of the solid-state supercapacitor, V(t) is the voltage of the solid-state supercapacitor at time t, R ESR is the internal resistance value, is the capacitance value.

[0100] The capacitance of a double-layer solid-state supercapacitor can be expressed as Among them, the dielectric constant, electrode area, and electrode spacing are the key factors affecting capacitance. After substituting the capacitance expression into the output power formula, the output power not only depends on the voltage change rate but also is related to the material parameters of the solid-state supercapacitor. The internal resistance R ESR will reduce the actual output power. Therefore, when designing a high-performance solid-state supercapacitor, reducing the internal resistance R ESR is an important consideration.

[0101] After obtaining the basic power of the solid-state supercapacitor, a model of the urban power grid loss under extreme disasters is constructed, and then a model for improving the resilience of the urban power grid is obtained.

[0102] In some embodiments, a model for improving the resilience of the urban power grid is constructed based on the basic power of the solid-state supercapacitor and the model of the urban power grid loss under extreme disasters, including:

[0103] Based on the risk value theory, a model of the urban power grid loss under extreme disasters is obtained, where the model of the urban power grid loss under extreme disasters is:

[0104]

[0105] In the formula, S(i) is the model of the urban power grid loss under the extreme disaster, and x i is the power supply state of the i-th emergency power supply. 0 means there is power supply from the i-th emergency power supply, and 1 means there is no power supply from the i-th emergency power supply. Δt i is the power outage time at the i-th location, Z i is the power outage loss power at the i-th location, and C0 is the unit load power outage loss;

[0106] According to the initial charge and equivalent parameter values of the solid-state supercapacitor in the emergency power supply state, the power consumption of the solid-state supercapacitor in the emergency power supply state is obtained, where the power consumption expression is:

[0107] Z(t) = Z0·(1 - SOC)

[0108]

[0109] In the formula, Z(t) is the voltage of the solid-state supercapacitor at time t, Z0 is the initial charge, t is the time, P out (t) is the basic power of the solid-state supercapacitor, V(t) is the voltage of the solid-state supercapacitor at time t, R ESR is the internal resistance value, is the capacitance value, P out (t) is the power output by the solid-state supercapacitor at time t, and SOC is the state of charge of the solid-state supercapacitor;

[0110] The urban power grid resilience improvement model is constructed based on the power consumption and the urban power grid loss model under extreme disasters. Among them, the urban power grid resilience improvement model is as follows:

[0111]

[0112] In the formula, S(i) is the urban power grid loss model under the extreme disaster, and x i is the power supply state of the i-th emergency power supply. 0 indicates that there is emergency power supply at the i-th place, and 1 indicates that there is no emergency power supply at the i-th place. Δt i is the power outage time at the i-th place, and Z i is the power outage loss power at the i-th place, and C0 is the power outage loss per unit load.

[0113] In this embodiment, based on the risk value theory, the urban power grid loss can be expressed as the failure consequences of all possible damaged power grid equipment. Using S to represent the weighted load loss during the entire power outage process reflects the urban power grid failure consequences. The expression is:

[0114]

[0115] In the formula, S(i) is the urban power grid loss model under the extreme disaster, and x i is the power supply state of the i-th emergency power supply. 0 indicates that there is emergency power supply at the i-th place, and 1 indicates that there is no emergency power supply at the i-th place. Δt i is the power outage time at the i-th place, and Z i is the power outage loss power at the i-th place, and C0 is the power outage loss per unit load;

[0116] During the emergency power supply process of the urban power grid under extreme disasters, the energy supplied by the solid-state supercapacitor energy storage system can be reflected by the state of charge (SOC). According to the calculation formula of the SOC value at a certain moment based on the ampere-hour measurement method; combining the fitting parameter expression of the battery equivalent model, and assuming that the initial charge of the energy storage device is Z0, the power consumption of the solid-state supercapacitor energy storage system during the emergency power supply process can be obtained by integrating according to the time-varying equivalent parameter values such as voltage and resistance. The specific expression is:

[0117] Z(t) = Z0·(1 - SOC)

[0118]

[0119] In the formula, Z(t) is the voltage of the solid-state supercapacitor at time t, Z0 is the initial charge, t is the time, P out (t) is the basic power of the solid-state supercapacitor, V(t) is the voltage of the solid-state supercapacitor at time t, R ESR is the internal resistance value, is the capacitance value, P out(t) is the power output by the solid-state supercapacitor at time t, and SOC is the state of charge of the solid-state supercapacitor;

[0120] This process can be equivalent to the process of the solid-state supercapacitor energy storage device restoring the urban power grid during a power grid fault, that is, the reduction of the solid-state supercapacitor's electric quantity measures the reduction of the urban power grid fault consequences. The specific expression is:

[0121]

[0122] In the formula, S(i) is the urban power grid loss model under the extreme disaster, and x i is the power supply state of the i-th emergency power supply. 0 indicates that there is an emergency power supply at the i-th place, and 1 indicates that there is no emergency power supply at the i-th place. Δt i is the power outage time at the i-th place, and Z i is the power outage loss power at the i-th place, and C0 is the unit load power outage loss.

[0123] S102. Construct the total cost model of the solid-state supercapacitor, construct the first power output model and the second power output model of the solid-state supercapacitor under peak shaving and frequency modulation, obtain the urban power grid revenue model according to the first power output model and the second power output model, and construct an equilibrium model according to the urban power grid resilience improvement model, the total cost model and the urban power grid revenue model.

[0124] In this embodiment, the urban power grid revenue model configured with the solid-state supercapacitor can be divided into two aspects: the solid-state supercapacitor cost modeling and the solid-state supercapacitor revenue modeling. After measuring the economy of the urban power grid according to the peak shaving and valley filling effect after the solid-state supercapacitor is put into operation and the operation cost of the solid-state supercapacitor during the normal operation of the urban power grid, the Nash bargaining game model is selected as the main model for solving the equilibrium problem of the urban power grid resilience and economy based on the configuration of the solid-state supercapacitor, and an equilibrium model is constructed.

[0125] In some embodiments, constructing the total cost model of the solid-state supercapacitor includes:

[0126] According to the solid-state supercapacitor module cost, the power conversion system cost and the installation cost, obtain the initial investment cost of the solid-state supercapacitor;

[0127] According to the initial investment cost and the maintenance cost, obtain the total cost model of the solid-state supercapacitor, where the total cost model is:

[0128] F C = C inv,supercap + C O&M,supercap + C replace,supercap - C salvage,supercap

[0129] Wherein, C inv,supercap is the initial investment cost, C o&M,supercap is the operation and maintenance cost, C replace,supercap is the replacement cost, C salvage,supercap is the salvage value.

[0130] In this embodiment, the initial investment cost of the solid-state supercapacitor generally includes the cost of the solid-state supercapacitor module, the cost of the power conversion system, and the installation cost. According to the initial investment cost and the maintenance cost, the total cost model of the solid-state supercapacitor is obtained, wherein the total cost model is:

[0131] F C = C inv,supercap + C O&M,supercap + C replace,supercap - C salvage,supercap

[0132] Wherein, C inv,supercap is the initial investment cost, C o&M,supercap is the operation and maintenance cost, C replace,supercap is the replacement cost, C salvage,supercap is the salvage value.

[0133] In some embodiments, the maintenance cost is obtained based on the operation and maintenance cost, the replacement cost, and the salvage value. Among them, the expression of the operation and maintenance cost is:

[0134] C o&M,supercap = α supercap ·C inv,supercap ·T

[0135] Wherein, C o&M,supercap is the operation and maintenance cost, α supercap is the annual operation and maintenance rate, and T is the life cycle of the solid-state supercapacitor;

[0136] The expression of the replacement cost is:

[0137] C replace,supercap = N replace,supercap ·C supercap

[0138] Wherein, C replace,supercap is the operation and maintenance cost, N replace,supercap is the number of replacements, T is the life cycle of the solid-state supercapacitor, and C supercap is the cost of the solid-state supercapacitor module;

[0139] The expression of the salvage value is:

[0140]

[0141] Wherein, T life,supercap is the actual service life of the solid-state supercapacitor, T design,supercapFor the designed life of the solid-state supercapacitor.

[0142] In this embodiment, the operation and maintenance cost of the solid-state supercapacitor is lower than that of the storage battery. The annual operation and maintenance cost usually accounts for 0.5%-2% of the initial investment. The expression of the operation and maintenance cost is:

[0143] C o&M,supercap =α supercap ·C inv,supercap ·T

[0144] In the formula, C o&M,supercap is the operation and maintenance cost, α supercap is the annual operation and maintenance rate, and T is the life cycle of the solid-state supercapacitor;

[0145] The life of the solid-state supercapacitor is usually longer than that of the storage battery. During its designed life, considering that some modules may need to be replaced, the replacement cost can be calculated according to the actual usage. The expression of the replacement cost is:

[0146] C replace,supercap =N replace,supercap ·C supercap

[0147] In the formula, C replace,supercap is the operation and maintenance cost, N replace,supercap is the number of replacements, T is the life cycle of the solid-state supercapacitor, usually 20 years, and C supercap is the cost of the solid-state supercapacitor module.

[0148] The solid-state supercapacitor may still have residual value at the end of its service life, usually calculated according to its depreciated salvage value. The expression of the salvage value is:

[0149]

[0150] In the formula, T life,supercap is the actual service life of the solid-state supercapacitor, and T design,supercap is the designed life of the solid-state supercapacitor.

[0151] In some embodiments, constructing the first power output model and the second power output model of the solid-state supercapacitor under peak shaving and frequency modulation includes:

[0152] Constructing the first power output model and the second power output model of the solid-state supercapacitor under peak shaving and frequency modulation, the first power output model is:

[0153]

[0154] Among them, P(t) is the output power of the solid-state supercapacitor, V(t) is the voltage across the solid-state supercapacitor, C is the rated capacitance value of the solid-state supercapacitor, and k1 is a constant related to the system characteristics;

[0155] The second power output model is as follows:

[0156]

[0157] In the formula, P(t) is the output power of the solid-state supercapacitor, V(t) is the voltage across the solid-state supercapacitor, C is the rated capacitance value of the solid-state supercapacitor, k2 is a constant related to the load regulation ability, and ΔP load (t) is the change in load power.

[0158] In this embodiment, based on the basic power of the above-mentioned solid-state supercapacitor, in order to further improve the power output equation of the solid-state supercapacitor, it is necessary to consider its various functional roles in the power system, especially the requirements in practical applications such as voltage support, peak shaving and frequency modulation. As an energy storage device, solid-state supercapacitors play an important role in these applications. They not only provide energy, but also make a significant contribution to the dynamic stability of the system.

[0159] In the power system, the solid-state supercapacitor maintains the voltage stability of the system through rapid response. The voltage support function requires the solid-state supercapacitor to discharge or charge rapidly when the voltage fluctuates, so as to keep the system voltage within a stable range. This means that the output power of the solid-state supercapacitor needs to be associated with the voltage change. During voltage support, the output power of the solid-state supercapacitor not only depends on its own voltage change rate, but also is related to the voltage fluctuation of the external urban power grid. Assuming that the voltage fluctuation amount of the urban power grid is, the solid-state supercapacitor needs to adjust its output power to maintain voltage stability. The power output formula at this time is:

[0160]

[0161] Among them, P(t) is the output power of the solid-state supercapacitor, V(t) is the voltage across the solid-state supercapacitor, C is the rated capacitance value of the solid-state supercapacitor, k1 is a constant related to the system characteristics, reflecting the support strength of the solid-state supercapacitor for the voltage fluctuation of the urban power grid.

[0162] The solid-state supercapacitor realizes the voltage support function by quickly charging and discharging to smooth the voltage fluctuation.

[0163] The peak shaving function means that the solid-state supercapacitor stores excess electrical energy during low load periods through energy storage and releases electrical energy during high load periods to smooth out load fluctuations. The key to peak shaving lies in the energy storage and release strategies of the solid-state supercapacitor at different time periods, which involves the charge-discharge cycle and charge balance issues of the solid-state supercapacitor. During the peak shaving process, the output power of the solid-state supercapacitor needs to be adjusted according to the peak and trough of the urban power grid load. Assuming the system load fluctuation amount is, the power output of the solid-state supercapacitor should match the load fluctuation. The power output formula at this time can be expressed as:

[0164]

[0165] In the formula, P(t) is the output power of the solid-state supercapacitor, V(t) is the voltage across the solid-state supercapacitor, C is the rated capacitance value of the solid-state supercapacitor, k2 is a constant related to the load regulation ability, and ΔP load (t) is the change in load power.

[0166] The frequency modulation function means that the solid-state supercapacitor helps to maintain the frequency stability of the power system by quickly responding to frequency deviations. The solid-state supercapacitor can correct the change in system frequency by increasing or decreasing the output power, thereby maintaining the frequency stability of the system. The frequency modulation function requires that the power output of the solid-state supercapacitor be related to the system frequency deviation. Assuming the deviation of the system frequency is, the solid-state supercapacitor needs to adjust the power according to the frequency deviation. The power output formula during frequency modulation can be rewritten as:

[0167]

[0168] Among them, P(t) is the output power of the solid-state supercapacitor, V(t) is the voltage across the solid-state supercapacitor, C is the rated capacitance value of the solid-state supercapacitor, k3 is a constant related to the system frequency stability, reflecting the response ability of the solid-state supercapacitor during frequency modulation. When the frequency of the solid-state supercapacitor deviates from the normal value, it balances the power of the system through charge and discharge, thereby quickly correcting the frequency deviation. By balancing the power of the system through charge and discharge, thereby quickly correcting the frequency deviation.

[0169] In an embodiment, a total revenue model is obtained according to the first power output model and the second power output model, including:

[0170] A total power output model is obtained according to the first power output model and the second power output model, where the total power output model is:

[0171]

[0172] In the formula, P total (t) is the total output power of the solid-state supercapacitor at time, is the basic capacitor power output part, k1·ΔV grid (t) is the power provided by the solid-state supercapacitor for voltage support at both ends of the solid-state supercapacitor, k2·ΔP load (t) is the power provided by the solid-state supercapacitor for peak shaving, and k3·Δf(t) is the power provided by the solid-state supercapacitor for frequency modulation. is the internal resistance loss of the solid-state supercapacitor;

[0173] According to the total power output model and the unit power benefit, an urban power grid benefit model is obtained. Among them, the urban power grid benefit model is:

[0174]

[0175] In the formula, P total is the benefit model, and e0 is the economic benefit per unit of power.

[0176] In this embodiment, considering the various functions of the solid-state supercapacitor in the power system, such as voltage support, peak shaving and frequency modulation, these functions can be integrated into a complete power output equation to obtain the benefit model. Among them, the benefit model is:

[0177]

[0178] In the formula, P total (t) is the total output power of the solid-state supercapacitor at time t, is the basic capacitor power output part, k1·ΔV grid (t) is the power provided by the solid-state supercapacitor for voltage support, k2·ΔP load (t) is the power provided by the solid-state supercapacitor for peak shaving, and k3·Δf(t) is the power provided by the solid-state supercapacitor for frequency modulation. is the internal resistance loss of the solid-state supercapacitor.

[0179] Therefore, the total economic benefit F E is:

[0180]

[0181] In the formula, P total is the said benefit model, and e0 is the economic benefit per unit of power.

[0182] In some embodiments, an equilibrium model is constructed according to the urban power grid resilience improvement model, the total cost model and the urban power grid benefit model, including:

[0183] An equilibrium model is constructed according to the urban power grid resilience improvement model, the total cost model and the urban power grid benefit model. Among them, the objective function of the equilibrium model is:

[0184]

[0185] where d1 and d1 are the negotiation breakdown points respectively, and F E is the urban power grid revenue model, and F C is the urban power grid resilience improvement model.

[0186] In this embodiment, the Nash bargaining game belongs to the category of cooperative games, mainly simulating the negotiation agreement process between the two parties of the game, and having the property of independence from linear transformation. In the negotiation, both parties will conduct consultations in the direction of increasing their own interests. When neither of them can make concessions, an equilibrium situation is reached. The following are the main advantages of the Nash bargaining model:

[0187] (1) Fairness and rationality: The Nash bargaining model takes fairness as the core, ensuring that the agreements reached are reasonable for the participating parties. By maximizing the product of the utilities of both parties, the model achieves "Pareto Optimality" in the distribution of interests, that is, the highest efficiency in resource allocation, and there is no possibility of making one party better without harming the other party.

[0188] (2) Rigorous mathematical foundation: The Nash bargaining model is based on a set of clear mathematical axioms (symmetry, efficiency, independence, and invariance of the disagreement point), which provide theoretical support for its rationality.

[0189] (3) Wide range of applications: The model can solve various equilibrium problems and is applicable to scenarios ranging from simple bilateral negotiations to complex multi-party collaborations.

[0190] (4) Symmetry principle: The model assumes symmetry between the two parties (in the absence of external biases), making the bargaining result independent of external identities or backgrounds, highlighting the essential issues of the negotiation. This feature makes the model particularly applicable in applications that emphasize fairness, such as social distribution and public welfare projects.

[0191] (5) Simplicity and flexibility: The Nash bargaining model transforms the optimization problem into a utility function maximization problem, with a clear mathematical expression, which is convenient for analysis and calculation; at the same time, the definitions of the disagreement point and the utility function can be set flexibly, enabling the model to adapt to different fields and problems.

[0192] The general expression of the Nash bargaining model is as follows:

[0193]

[0194] Wherein, x is an independent variable vector, F0 is the comprehensive benefit, u1(x) and u2(x) are the benefit vectors of the two parties in the game, d=(d1, d2)∈U is the negotiation breakdown critical point. If the two parties fail to reach an agreement under this condition, the negotiation breaks down, and U is the set of all benefit vectors.

[0195] This game model belongs to a two-objective optimization model, corresponding to the two mutually constrained optimization objectives of the urban power grid resilience improvement model and the benefit model in the invention. At the same time, the change direction of the independent variables of each optimization objective and the positive and negative of each objective function value directly affect the optimization direction of the comprehensive benefit, and then affect the equilibrium solution. Considering converting each objective function value into the same sign of positive and negative, the obtained combination of independent variables is the equilibrium solution under the optimal comprehensive benefit. It is intended to establish a Nash bargaining game equilibrium model for balancing urban power grid resilience improvement and economy, which mathematically describes how the two parties of urban power grid resilience and economic benefits based on solid-state supercapacitors reach a fair and reasonable agreement in cooperation.

[0196] Regarding the economy and resilience of the urban power grid as two game players, and defining F E 、F C as the sub-objectives of economy and resilience. Taking the value of the negotiation breakdown point (d1, d2) as the value of F E 、F C corresponding to the maximum value of the independent variable, and combining with the general expression of the Nash bargaining model, the objective function of the equilibrium model for the urban power grid resilience improvement model and the urban power grid benefit model is obtained as:

[0197]

[0198] Wherein, d1 and d1 are the negotiation breakdown points respectively, F E is the urban power grid benefit model, and F C is the urban power grid resilience improvement model.

[0199] It can be seen from the above formula that if the benefit and resilience can reach an equilibrium point, the benefit functions of both parties should be the farthest from the negotiation breakdown point (d1, d2). When the above objective function takes the maximum value, the corresponding resilience and economy values are the equilibrium solutions of the Nash negotiation. If there is a difference in the order of magnitude of the two product terms, the objective function with a larger order of magnitude has a greater impact on the final equilibrium solution of the game. Since the traditional multi-objective optimization method adds subjective weights to the optimization objectives, it weakens the influence between the magnitudes of each optimization objective. Under the condition of different magnitudes, the set subjective weights may conflict significantly with the magnitude differences of the objectives, and then significantly affect the equilibrium result. The Nash bargaining game takes multiple optimization objectives as game participants, more truly reflects the relationship of magnitude differences between each optimization objective, and thus more appropriately obtains the equilibrium solution.

[0200] S103. Use a multi-objective optimization algorithm to calculate the equilibrium model to obtain an optimization result, so that personnel can configure solid-state supercapacitors according to the optimization result.

[0201] In this embodiment, first, establish a risk value model of the product of the urban power grid failure rate and the load power outage loss as the urban power grid failure loss; then, take the reduction of the failure loss after the solid-state supercapacitor energy storage device is connected to the grid as the urban power grid resilience improvement amount, and measure the economy of the urban power grid according to the peak shaving and valley filling effect after the solid-state supercapacitor is put into operation during the normal operation of the urban power grid and the operating cost of the solid-state supercapacitor.

[0202] The NSGA-II algorithm is widely used to solve multi-objective optimization problems due to its efficient non-dominated sorting, crowding degree calculation, and fast selection operation. Its core idea is based on natural selection. Through non-dominated sorting and crowding degree operations, the diversity and superiority of solutions are balanced, and gradually iterated to achieve the Pareto optimal solution. Compared with other multi-objective optimization algorithms, NSGA-II has the advantages of fast non-dominated sorting (adopting a computational optimization strategy to reduce the time complexity), crowding distance operation (ensuring the diversity of the Pareto solution set), and elitist strategy (ensuring the retention of excellent solutions by combining the selection of parents and offspring), and can better solve the equilibrium model.

[0203] In one embodiment, using a multi-objective optimization algorithm to calculate the equilibrium model to obtain an optimization result, so that personnel can configure solid-state supercapacitors according to the optimization result, includes:

[0204] Initialize the population, and calculate the objective function value of each individual according to the individuals in the population and the objective function of the equilibrium model;

[0205] Perform non-dominated sorting according to the objective function values of each individual to obtain the non-dominated sorting result. Based on the non-dominated sorting result, divide the population into multiple levels to obtain the non-dominated sorting levels of each individual, and calculate the crowding distance of each individual within the same non-dominated front;

[0206] Select the optimal solutions from all individuals according to the non-dominated sorting levels and crowding distances to obtain the Pareto optimal solution set. Use the crossover and mutation operations of the genetic algorithm to generate the offspring population, and calculate the new objective function values according to the offspring population and the objective function of the equilibrium model;

[0207] Merge the parent population and the offspring population to obtain a temporary population, perform non-dominated sorting on the temporary population, and select the next generation population according to the population size and sorting levels. If the maximum number of generations is reached or the population converges, stop the calculation and determine the Pareto optimal solution set as the optimization result.

[0208] In this embodiment, the specific solution process steps of the NSGA-II algorithm are:

[0209] (1) Population initialization: Randomly generate a population P0 containing N individuals, where each individual represents a solution; for each individual, calculate its objective function value.

[0210] (2) Non-dominated sorting: Divide the population into multiple levels according to the non-dominated relationship, i.e., non-dominated fronts. The sorting principle is: If all objectives of solution A are not worse than those of solution B, and at least one objective value is better than B, then A dominates B.

[0211] (3) Crowding degree calculation: Within the same non-dominated front, calculate the crowding distance of each solution to measure the distribution density of the solutions; the crowding degree formula is based on the objective value range and calculates the distance between two adjacent solutions in ascending order of the objective function values.

[0212] (4) Selection operation: Preferentially select solutions according to the non-dominated sorting level, and secondarily according to the crowding distance to ensure the uniform distribution of solutions on the Pareto front; use the crowding degree sorting to solve the solution selection problem within the sorting level.

[0213] (5) Crossover and mutation: Use the crossover and mutation operations of the genetic algorithm to generate new solutions (offspring population Q t ); the objective function values of the offspring population are updated accordingly.

[0214] (6) Population merging and elimination: Merge the parent population P t and the offspring population Q t to form a temporary population R t ; perform non-dominated sorting on R t and select the next generation population P t+1 according to the population size N and the sorting level.

[0215] (7) Termination: If the maximum number of generations is reached or the population converges, stop the algorithm and output the set of Pareto optimal solutions in the population.

[0216] Solve using the NSGA-II algorithm. The basic idea is: First, randomly generate an initial population of size N1. After non-dominated sorting, through the three basic operations of selection, crossover, and mutation of the genetic algorithm, obtain the offspring population; starting from the second iteration, merge the parent population and the offspring population, perform fast non-dominated sorting, and at the same time calculate the crowding degree of the individuals in the non-dominated layer, and select appropriate individuals according to the above indicators to form a new parent population; finally, generate a new offspring population. When the number of iterations is reached, the calculation ends, and the obtained offspring population is the optimal solution of the objective function.

[0217] It should be understood that although Figure 1The steps in the flowchart are shown in sequence according to the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise clearly stated in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1 At least a portion of the steps may include multiple steps or multiple stages. These steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be executed alternately or in turn with at least a portion of other steps or steps or stages in other steps.

[0218] In one embodiment, as Figure 7 shown, it shows a block diagram of an urban power grid resilience improvement optimization system 700 for configuring solid-state supercapacitors provided by an embodiment of the present application, including a resilience improvement model construction module 701, an equilibrium model construction module 702, and a solution module 703, where:

[0219] The resilience improvement model construction module 701 is used to obtain the basic power of the solid-state supercapacitor based on the output power of the solid-state supercapacitor and the output power considering power loss, and construct an urban power grid resilience improvement model based on the basic power of the solid-state supercapacitor and the urban power grid loss model under extreme disasters;

[0220] The equilibrium model construction module 702 is used to construct a total cost model of the solid-state supercapacitor, construct a first power output model and a second power output model of the solid-state supercapacitor under peak shaving and frequency modulation, obtain an urban power grid revenue model according to the first power output model and the second power output model, and construct an equilibrium model according to the urban power grid resilience improvement model, the total cost model, and the urban power grid revenue model;

[0221] The solution module 703 is used to calculate the equilibrium model using a multi-objective optimization algorithm to obtain an optimization result, so that personnel can configure the solid-state supercapacitor according to the optimization result.

[0222] In some embodiments, the resilience improvement model construction module includes a loss model construction unit, a power consumption model construction unit, and a resilience model construction unit.

[0223] Among them, the loss model construction unit is used to obtain an urban power grid loss model under extreme disasters based on the risk value theory, where the urban power grid loss model under extreme disasters is:

[0224]

[0225] In the formula, S(i) is the urban power grid loss model under extreme disasters, x iThe power supply status of the i-th emergency power supply, where 0 indicates that there is emergency power supply at the i-th location and 1 indicates that there is no emergency power supply at the i-th location, Δt i The power outage time at the i-th location, Z i The power outage loss power at the i-th location, and C0 is the power outage loss per unit load;

[0226] The power consumption model construction unit is used to obtain the power consumption of the solid-state supercapacitor in the emergency power supply state according to the starting power and equivalent parameter values of the solid-state supercapacitor in the emergency power supply state. Among them, the power consumption expression is:

[0227] Z(t) = Z0·(1 - SOC)

[0228]

[0229] In the formula, Z(t) is the voltage of the solid-state supercapacitor at time t, Z0 is the starting power, t is the time, P out (t) is the basic power of the solid-state supercapacitor, V(t) is the voltage of the solid-state supercapacitor at time t, R ESR is the internal resistance value, is the capacitance value, P out (t) is the power output by the solid-state supercapacitor at time t, and SOC is the state of charge of the solid-state supercapacitor;

[0230] The resilience model construction unit is used to construct the urban power grid resilience improvement model according to the power consumption and the urban power grid loss model under extreme disasters. Among them, the urban power grid resilience improvement model is:

[0231]

[0232] In the formula, S(i) is the urban power grid loss model under extreme disasters, x i is the power supply status of the i-th emergency power supply, where 0 indicates that there is emergency power supply at the i-th location and 1 indicates that there is no emergency power supply at the i-th location, Δt i is the power outage time at the i-th location, Z i is the power outage loss power at the i-th location, and C0 is the power outage loss per unit load.

[0233] The specific implementation manner of the urban power grid resilience improvement optimization system configured with the solid-state supercapacitor is basically the same as the specific embodiments of the above-mentioned urban power grid resilience improvement optimization method configured with the solid-state supercapacitor, and will not be elaborated here.

[0234] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered that the scope described in this specification.

[0235] The specific embodiments described above further elaborate on the objectives, technical solutions, and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the protection scope of the present invention. In particular, for those skilled in the art, any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for optimizing the resilience of a city power grid equipped with solid-state supercapacitors, characterized in that: include: According to the output power of the solid-state supercapacitor and the output power considering power loss, the basic power of the solid-state supercapacitor is obtained, and the urban power grid resilience improvement model is constructed based on the basic power of the solid-state supercapacitor and the urban power grid loss model under extreme disasters; Constructing a total cost model of the solid-state supercapacitor, constructing a first power output model and a second power output model of the solid-state supercapacitor under peak regulation and frequency regulation, obtaining an urban power grid revenue model according to the first power output model and the second power output model, and constructing an equilibrium model according to the urban power grid resilience improvement model, the total cost model and the urban power grid revenue model; The equilibrium model is calculated using a multi-objective optimization algorithm to obtain an optimization result, so that personnel can configure the solid-state supercapacitor according to the optimization result.

2. The method for optimizing the resilience of a city power grid equipped with a solid-state supercapacitor according to claim 1, characterized in that: The urban power grid resilience improvement model is constructed based on the basic power of the solid-state supercapacitor and the urban power grid loss model under extreme disasters, including: Based on the risk value theory, the urban power grid loss model under extreme disasters is obtained, wherein the urban power grid loss model under extreme disasters is: Where S(i) is the urban power grid loss model under extreme disasters, x i is the power supply status of the emergency power supply at the i-th location, 0 means that the i-th location has emergency power supply, 1 means that the i-th location has no emergency power supply, Δt i is the power outage time at the i-th location, Z i is the power loss at the i-th power outage, C0 is the power outage loss per unit load; According to the starting power and equivalent parameter value of the solid-state supercapacitor in the emergency power supply state, the power consumption of the solid-state supercapacitor in the emergency power supply state is obtained, wherein the power consumption expression is: Z(t)=Z0·(1-SOC) Where Z(t) is the voltage of the solid-state supercapacitor at time t, Z0 is the starting charge, t is the time, P out (t) is the basic power of the solid-state supercapacitor, V(t) is the voltage of the solid-state supercapacitor at time t, R ESR is the internal resistance value, is the capacitance value, P out (t) is the power output by the solid-state supercapacitor at time t, and SOC is the state of charge of the solid-state supercapacitor; According to the power consumption and the urban power grid loss model under the extreme disaster, a model for improving the resilience of the urban power grid is constructed, wherein the model for improving the resilience of the urban power grid is: Where S(i) is the urban power grid loss model under extreme disasters, x i is the power supply status of the emergency power supply at the i-th location, 0 means that the i-th location has emergency power supply, 1 means that the i-th location has no emergency power supply, Δt i is the power outage time at the i-th location, Z i is the power loss caused by power outage at the i-th location, and C0 is the power outage loss per unit load.

3. The method for optimizing the resilience of a city power grid equipped with solid-state supercapacitors according to claim 1, characterized in that: The total cost model of constructing the solid-state supercapacitor includes: Obtaining the initial investment cost of the solid-state supercapacitor according to the solid-state supercapacitor module cost, the power conversion system cost and the installation cost; According to the initial investment cost and maintenance cost, the total cost model of the solid-state supercapacitor is obtained, wherein the total cost model is: F C =C inv,supercap +C O&M,supercap +C replace,supercap -C salvage,supercap In the formula, C inv,supercap is the initial investment cost, C o&M,supercap is the operation and maintenance cost, C replace,supercap is the replacement cost, C salvage,supercap For the residual value.

4. The method for optimizing the resilience of a city power grid equipped with solid-state supercapacitors according to claim 3, characterized in that: The maintenance cost is obtained based on the operation and maintenance cost, the replacement cost and the residual value, wherein the expression of the operation and maintenance cost is: C o&M,supercap =α supercap ·C inv,supercap ·T In the formula, C o&M,supercap is the operation and maintenance cost, α supercap is the annual operation and maintenance rate, T is the life cycle of the solid-state supercapacitor; The expression of the replacement cost is: C replace,supercap =N replace,supercap ·C supercap In the formula, C replace,supercap is the operation and maintenance cost, N replace,supercap is the number of replacements, T is the life cycle of the solid-state supercapacitor, C supercap is the cost of solid-state supercapacitor module; The expression of the residual value is: Where, T life,supercap is the actual service life of the solid-state supercapacitor, T design,supercap is the design life of solid-state supercapacitors.

5. The method for optimizing the resilience of a city power grid equipped with solid-state supercapacitors according to claim 1, characterized in that: The constructing of the first power output model and the second power output model of the solid-state supercapacitor under peak regulation and frequency regulation includes: Constructing a first power output model and a second power output model of the solid-state supercapacitor under peak regulation and frequency regulation, wherein the first power output model is: Wherein, P(t) is the output power of the solid-state supercapacitor, V(t) is the voltage across the solid-state supercapacitor, C is the rated capacitance of the solid-state supercapacitor, and k1 is a constant related to system characteristics; The second power output model is: Where P(t) is the output power of the solid-state supercapacitor, V(t) is the voltage across the solid-state supercapacitor, C is the rated capacitance of the solid-state supercapacitor, k2 is a constant related to the load regulation capability, and ΔP load (t) is the change in load power.

6. The method for optimizing the resilience of a city power grid equipped with solid-state supercapacitors according to claim 1, characterized in that: The obtaining of a total benefit model according to the first power output model and the second power output model comprises: A total power output model is obtained according to the first power output model and the second power output model, wherein the total power output model is: Where P total (t) is the total output power of the solid-state supercapacitor at time, For the basic capacitor power output part, k1·ΔV grid (t) is the power provided by the solid-state supercapacitor for the voltage support at both ends of the solid-state supercapacitor, k2·ΔP load (t) is the power provided by the solid-state supercapacitor for peak regulation, k3·Δf(t) is the power provided by the solid-state supercapacitor for frequency regulation, is the internal resistance loss of the solid-state supercapacitor; The urban power grid revenue model is obtained according to the total power output model and the unit power revenue, wherein the urban power grid revenue model is: Where P total is the profit model, and e0 is the economic benefit per unit of electricity.

7. The method for optimizing the resilience of a city power grid equipped with solid-state supercapacitors according to claim 1, characterized in that: The constructing of the equilibrium model according to the urban power grid resilience improvement model, the total cost model and the urban power grid revenue model includes: An equilibrium model is constructed according to the urban power grid resilience improvement model, the total cost model and the urban power grid revenue model, wherein the objective function of the equilibrium model is: In the formula, d1 and d2 are the negotiation breakdown points, F E is the urban power grid revenue model, F C A model for improving the resilience of the urban power grid.

8. The method for optimizing the resilience of a city power grid equipped with solid-state supercapacitors according to claim 1, characterized in that: The method of calculating the equilibrium model using a multi-objective optimization algorithm to obtain an optimization result so that the personnel can configure the solid-state supercapacitor according to the optimization result includes: Initializing a population, and calculating an objective function value of each individual according to individuals in the population and an objective function of the equilibrium model; Performing non-dominated sorting according to the objective function value of each of the individuals to obtain a non-dominated sorting result, dividing the population into multiple levels based on the non-dominated sorting result, obtaining a non-dominated sorting level of each of the individuals, and calculating the crowding distance of each of the individuals within the same non-dominated frontier; Selecting the optimal solution from all the individuals according to the non-dominated sorting level and the crowding distance to obtain a Pareto optimal solution set, generating a progeny population using crossover and mutation operations of a genetic algorithm, and calculating a new objective function value according to the progeny population and the objective function of the equilibrium model; The parent population and the child population are merged to obtain a temporary population, and the temporary population is non-dominated sorted. The next generation population is selected according to the population size and sorting level. If the maximum number of generations is reached or the population converges, the calculation is stopped and the Pareto optimal solution set is determined as the optimization result.

9. A system for improving the resilience of urban power grids using solid-state supercapacitors, characterized in that: include: A resilience enhancement model construction module is used to obtain the basic power of the solid-state supercapacitor according to the output power of the solid-state supercapacitor and the output power considering power loss, and to obtain a city power grid resilience enhancement model based on the basic power of the solid-state supercapacitor and the city power grid loss model under extreme disasters; A balance model construction module, used to construct a total cost model of the solid-state supercapacitor, construct a first power output model and a second power output model of the solid-state supercapacitor under peak regulation and frequency regulation, obtain an urban power grid revenue model according to the first power output model and the second power output model, and construct a balance model according to the urban power grid resilience improvement model, the total cost model and the urban power grid revenue model; A solution module is used to calculate the equilibrium model using a multi-objective optimization algorithm to obtain an optimization result so that the personnel can configure the solid-state supercapacitor according to the optimization result.

10. The urban power grid resilience improvement optimization system configured with solid-state supercapacitors according to claim 9, characterized in that: The resilience enhancement model building module includes a loss model building unit, a power consumption model building unit and a resilience model building unit. The loss model construction unit is used to obtain a city power grid loss model under extreme disasters based on the risk value theory, wherein the city power grid loss model under extreme disasters is: Where S(i) is the urban power grid loss model under extreme disasters, x i is the power supply status of the emergency power supply at the i-th location, 0 means that the i-th location has emergency power supply, 1 means that the i-th location has no emergency power supply, Δt i is the power outage time at the i-th location, Z i is the power loss at the i-th power outage, C0 is the power outage loss per unit load; The power consumption model building unit is used to obtain the power consumption of the solid-state supercapacitor in the emergency power supply state according to the starting power and equivalent parameter values ​​of the solid-state supercapacitor in the emergency power supply state, wherein the power consumption expression is: Z(t)=Z0·(1-SOC) Where Z(t) is the voltage of the solid-state supercapacitor at time t, Z0 is the starting charge, t is the time, P out (t) is the basic power of the solid-state supercapacitor, V(t) is the voltage of the solid-state supercapacitor at time t, R ESR is the internal resistance value, is the capacitance value, P out (t) is the power output by the solid-state supercapacitor at time t, and SOC is the state of charge of the solid-state supercapacitor; The resilience model building unit is used to build a city power grid resilience improvement model according to the power consumption and the city power grid loss model under extreme disasters, wherein the city power grid resilience improvement model is: Where S(i) is the urban power grid loss model under extreme disasters, x i is the power supply status of the emergency power supply at the i-th location, 0 means that the i-th location has emergency power supply, 1 means that the i-th location has no emergency power supply, Δt i is the power outage time at the i-th location, Z i is the power loss caused by power outage at the i-th location, and C0 is the power outage loss per unit load.

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