Hydrogen energy equipment multi-state model-based reliability evaluation method for electric hydrogen energy system

Abstract

The present invention relates to the technical field of power system reliability assessment, specifically a reliability assessment method for an electric-hydrogen regional integrated energy system based on a multi-state model of hydrogen energy equipment. The method comprises describing the electric-hydrogen regional integrated energy system and establishing a multi-state Markov space or a two-state Markov space for the equipment; using the Markov Chain Monte Carlo method to sample and generate a sequence of equipment operating states to form the system operating state; establishing a model for load reduction of the system's optimal quality energy; constructing a heterogeneous energy reliability assessment index system; solving the optimal quality energy load reduction model under all system operating states, calculating heterogeneous energy reliability assessment indexes, and evaluating the reliability level of the electric-hydrogen regional integrated energy system. This method addresses the technical problem that the existing system reliability assessment index system for heterogeneous energy within the system is still incomplete.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system reliability evaluation, in particular to a hydrogen energy equipment multi-state model-based reliability evaluation method for an electric-hydrogen regional integrated energy system. BACKGROUND

[0002] With the continuous maturity of hydrogen production, storage, transportation and utilization technologies, the coupling between hydrogen energy systems and electricity, gas and heat energy systems is becoming closer. The electric-hydrogen regional integrated energy system can effectively tap the coordination and complementary potential between heterogeneous energy systems and fully play the advantages of zero-carbon and flexible operation of hydrogen energy systems, and is considered an important part of realizing a green and low-carbon energy system. However, there is a lack of research on the reliability evaluation of electric-hydrogen regional integrated energy systems.

[0003] In terms of hydrogen energy equipment reliability modeling, existing research mainly uses a two-state model of electrolyzers and a multi-state model of fuel cells in power generation mode, ignoring the non-normal operating state of electrolyzers caused by auxiliary component failures that reduce hydrogen production efficiency, and the coupling relationship between different component failures and fuel cell heat-electricity conversion efficiency in cogeneration mode. Moreover, no research has established a reliability evaluation model for hydrogen refueling equipment. Therefore, the existing hydrogen energy equipment reliability model cannot accurately reflect the reliability level of the electric-hydrogen regional integrated energy system.

[0004] In terms of reliability evaluation of electric-hydrogen regional integrated energy systems, existing research only analyzes the priority of device failure risks in a photovoltaic-heat-fuel cell integrated system and the improvement of hydrogen energy systems on microgrid power supply reliability. It can be seen that the supply-demand imbalance mechanism of the electric-hydrogen regional integrated energy system is not clear, and the heterogeneous energy reliability evaluation index system within the system has not been perfected.

[0005] In summary, it is necessary to analyze the mechanism of hydrogen energy equipment, establish an accurate hydrogen energy equipment reliability evaluation model, and propose a reliability evaluation index system and evaluation method for electric-hydrogen regional integrated energy systems. SUMMARY

[0006] The purpose of the present application is to solve the technical problem that the heterogeneous energy reliability evaluation index system within the system has not been perfected in the prior art.

[0007] The hydrogen energy equipment multi-state model-based reliability evaluation method for an electric-hydrogen regional integrated energy system in the present application mainly includes the following steps:

[0008] Step 1) Describe the electric-hydrogen regional integrated energy system and establish a multi-state Markov space for electrolyzers, fuel cells and hydrogen refueling machines in the system, and a two-state Markov space for other energy equipment;

[0009] Step 2) According to the Markov space of all devices, a sequence of device operating states is generated by using the Markov chain Monte Carlo method to sample and form the system operating state;

[0010] Step 3) An optimal heterogeneous energy load reduction model is established by taking the sum of the penalty cost of wind and light abandonment and the penalty cost of heterogeneous energy load reduction as the objective function, and considering the system operation constraints;

[0011] Step 4) A heterogeneous energy reliability evaluation index system is constructed by using the heterogeneous energy load reduction probability, the heterogeneous energy load reduction time expectation, the heterogeneous energy load energy shortage expectation, the heterogeneous energy load energy shortage comprehensive loss and the device reliability contribution degree;

[0012] Step 5) The optimal heterogeneous energy load reduction model under all system operating states is solved, the heterogeneous energy reliability evaluation index is calculated, and the reliability level of the electric-hydrogen regional integrated energy system is evaluated.

[0013] Further, the electric-hydrogen regional integrated energy system in step 1) comprises electric energy devices, hydrogen energy devices and thermal energy devices;

[0014] The electric energy devices include power lines, wind turbine generators, photovoltaic generators and storage batteries;

[0015] The hydrogen energy devices include electrolytic cells, hydrogen storage tanks, fuel cells and several hydrogen filling machines;

[0016] The thermal energy devices include gas boilers and fuel cells;

[0017] The fuel cell generates heat and electricity through consumption of hydrogen from the hydrogen storage tank;

[0018] The electric load of the electric-hydrogen regional integrated energy system is supplied by the external power grid, wind and light generators and storage batteries, and the hydrogen load is supplied by hydrogen released from the electrolytic cell and the hydrogen storage tank through several hydrogen filling machines;

[0019] The thermal load is supplied by the gas boiler consuming natural gas to produce heat and the fuel cell consuming hydrogen to produce heat.

[0020] Further, in step 1), a three-state Markov space is established for the electrolytic cell,

[0021] The states include a normal operating state;

[0022] A fault outage state caused by a fault of an alkaline electrolytic cell or a gas separation device, a circulating water pump;

[0023] A reduced capacity operating state caused by a fault of a heater tube;

[0024] A four-state Markov space is established for the fuel cell,

[0025] its state includes, normal operation state;

[0026] fuel cell failure shutdown state caused by fuel cell stack failure or insufficient oxygen supply leading to proton membrane failure;

[0027] fuel cell output power reduction and output heat power increase state caused by heat exchanger failure leading to fuel cell operating temperature rise;

[0028] fuel cell output power reduction and output heat power increase state caused by proton membrane dryness when humidifier fails, which increases its ohmic resistance;

[0029] Taking into account the independent failure of each hydrogen dispenser, a multi-state Markov space is established for the whole hydrogen dispenser, including the normal operation state,

[0030] and a variety of failure operation / shutdown states caused by simultaneous failure of different numbers of hydrogen dispensers;

[0031] A two-state Markov space is established for the other energy equipment, taking into account the normal operation state and failure shutdown state.

[0032] Further, in step 2), the system operation state generation specifically includes the following steps:

[0033] Step 2.1) Determine the device state s x,0 of device x at the initial time;

[0034] Step 2.2) According to the device state s x,t at the current time, according to the probability of occurrence of each state transition path in its Markov space, randomly sample to determine the state s x,t+1 at the next time;

[0035] Step 2.3) Repeat step 2.2) until the state of device x at all times in the period is determined, and the time sequence state sequence of device x is generated;

[0036] Step 2.4) Repeat steps 2.1) to 2.3) for all devices in the electric-hydrogen regional integrated energy system to generate the state sequence set of all devices in the system, i.e. the system operation state.

[0037] Further, in step 3), the objective function expression of the optimal heterogeneous energy load reduction model is:

[0038]

[0039] In the formula, c DG is the unit penalty cost of abandoned wind and light; Ω WG , ΩPV respectively are the wind and solar power installation node set; ΔP WG,it , ΔP PV,it respectively are the abandoned wind and solar power; T is the scheduling period; n is the number of nodes; Z is the supply load type set, including electricity, heat, and hydrogen three types of load; c z is the unit reduction penalty cost of the zth load; L z,it is the reduction power of the zth load, and subscripts i and t represent node i and time t, respectively.

[0040] Further, in step 3), the system operation constraints include power balance constraints, load reduction constraints, device operation constraints, and interactive power constraints:

[0041] The power balance constraints include electrical, thermal, and hydrogen power balance constraints.

[0042] The electrical power balance constraint is as follows:

[0043] P Grid,it +P WG,it +P PV,it +P dis,it +P F,it =P EL,it +P ch,it +P load,it -L p,it

[0044]

[0045] In the formula, P Grid,it is the interactive power of the energy coupling node and the power grid; P WG,it , P PV,it are the actual output powers of wind and solar power units; P ch,it , P dis,it are the charge and discharge powers of the battery; P FC,it is the power generation power of the fuel cell; P EL,it is the power consumption power of the electrolytic tank; P load,it is the electrical load demand power; L p,it is the electrical load reduction power; P ij,t is the active power transmitted by the power line ij; k ∈ j indicates that node k has node j as the head node; Ω EH is the energy coupling node set.

[0046] The thermal power balance constraint is as follows:

[0047] H GB,it +H FC,it =P load,it -L h,it

[0048] H GB,it is the heat production power of the gas boiler; H FC,it is the heat production power of the fuel cell; H load,it is the heat load demand power; L h,it is the heat load reduction power;

[0049] The hydrogen power balance constraint is as follows:

[0050]

[0051] Q EL,it is the hydrogen production of the electrolyzer; Q HT,in,it , Q HT,out,it are the hydrogen storage and hydrogen release of the hydrogen storage tank, respectively, Q FC,it is the hydrogen consumption of the fuel cell, Q EL2DP,it , Q HT2DP,it are the hydrogen supply of the electrolyzer and the hydrogen storage tank to the hydrogen refueling station, respectively, Q DP,in,t , Q DP,out,t are the hydrogen input and output of all hydrogen refueling stations, respectively, Q load,it is the hydrogen load demand, L q,it is the hydrogen load reduction;

[0052] The load reduction constraint is as follows:

[0053]

[0054] The equipment operation constraints include power line operation constraints, wind-solar unit operation constraints, battery operation constraints, gas boiler operation constraints, electrolyzer operation constraints, hydrogen storage tank operation constraints, fuel cell operation constraints, and hydrogen refueling station operation constraints;

[0055] The power line operation constraints are as follows:

[0056] -s ij,t P ij,max ≤ P ij,t ≤ s ij,t P ij,max ,

[0057] wherein s ij,t is the operation state of line ij, 1 indicating normal operation and 0 indicating failure shutdown; P ij,max is the upper limit of line transmission active power;

[0058] The wind-solar unit operation constraints are as follows:

[0059]

[0060] wherein, are the predicted output power of the wind-solar unit, respectively; sWG,it PV,it respectively represent the operation state of the wind-solar unit, 1 represents normal operation, and 0 represents failure shutdown;

[0061] The operation constraint of the battery is as follows:

[0062]

[0063] In the formula, SOCt represents the state of charge of the battery at time t, SOCt+1 represents the state of charge of the battery at time t+1, P represents the charging and discharging power of the battery, and η represents the charging and discharging efficiency. i,t i,t+1 In the formula, SOCt represents the state of charge of the battery at time t, SOCt+1 represents the state of charge of the battery at time t+1, P represents the charging and discharging power of the battery, and η represents the charging and discharging efficiency. ch,it dis,it In the formula, SOCt represents the state of charge of the battery at time t, SOCt+1 represents the state of charge of the battery at time t+1, P represents the charging and discharging power of the battery, and η represents the charging and discharging efficiency. ch dis In the formula, SOCt represents the state of charge of the battery at time t, SOCt+1 represents the state of charge of the battery at time t+1, P represents the charging and discharging power of the battery, and η represents the charging and discharging efficiency. ES is the capacity of the battery, and α and β represent the charging and discharging state of the battery, respectively, 0 represents no electric energy charging / discharging, and 1 represents electric energy charging / discharging. ch,it dis,it In the formula, SOCt represents the state of charge of the battery at time t, SOCt+1 represents the state of charge of the battery at time t+1, P represents the charging and discharging power of the battery, and η represents the charging and discharging efficiency. max min In the formula, SOCt represents the state of charge of the battery at time t, SOCt+1 represents the state of charge of the battery at time t+1, P represents the charging and discharging power of the battery, and η represents the charging and discharging efficiency. T In the formula, SOCt represents the state of charge of the battery at time t, SOCt+1 represents the state of charge of the battery at time t+1, P represents the charging and discharging power of the battery, and η represents the charging and discharging efficiency. ES , it respectively represent the operation state of the wind-solar unit, 1 represents normal operation, and 0 represents failure shutdown;

[0064] The operation constraint of the gas boiler is as follows:

[0065]

[0066] In the formula, G represents the gas consumption power of the gas boiler, η represents the efficiency of the gas boiler, and s represents the operation state of the gas boiler, 1 represents normal operation, and 0 represents failure shutdown. GB,it GB In the formula, G represents the gas consumption power of the gas boiler, η represents the efficiency of the gas boiler, and s represents the operation state of the gas boiler, 1 represents normal operation, and 0 represents failure shutdown. GB,it is the upper limit of the gas consumption power of the gas boiler.

[0067] The operation constraint of the electrolytic cell is as follows:

[0068]

[0069] In the formula, Q represents the hydrogen production amount of the electrolytic cell, ρ represents the standard density of hydrogen, k1 and k2 are unit conversion coefficients, F is the Faraday constant, and η represents the Faraday efficiency. EL,it H2 In the formula, Q represents the hydrogen production amount of the electrolytic cell, ρ represents the standard density of hydrogen, k1 and k2 are unit conversion coefficients, F is the Faraday constant, and η represents the Faraday efficiency. f is the operating voltage of a single electrolytic cell in state s EL,it ​​​​​​​​​​​The electrolytic cell is in state s EL,it Total power consumption; μ EL,it The start and stop status of the electrolytic cell, 1 is the start state, 0 is the stop state; P EL,max and P EL,min They are the upper and lower limits of the total power consumption of the electrolyzer respectively;

[0070] The operating constraints of the hydrogen storage tank are as follows:

[0071]

[0072] Where SOH i,t 、SOH i,t+1 are the hydrogen storage states of the hydrogen storage tank at time t and time t+1, that is, the ratio of stored hydrogen to capacity at that time; Q HT,in,it , Q HT,out,it are the hydrogen storage capacity and hydrogen release capacity of the hydrogen storage tank respectively; η HT,in ,η HT,out are the hydrogen charging and discharging efficiency; S HT is the capacity of the hydrogen storage tank; α in,it , β out,it They are the hydrogen storage tank charging and discharging status, 0 means no hydrogen charging / discharging, 1 means hydrogen charging / discharging; SOH max 、SOH min They are the upper and lower limit constraints of the hydrogen storage state of the hydrogen storage tank; SOH0, SOH T are the hydrogen storage states of the hydrogen storage tank at the initial and final moments of the research period; s HT,it The operating status of the hydrogen storage tank, 1 indicates normal operation, and 0 indicates failure and shutdown;

[0073] The fuel cell operating constraints are as follows:

[0074]

[0075] Where Q FC,it is the hydrogen consumption of the fuel cell, in kg; m FC,it is the hydrogen consumption of the fuel cell, in kW; P FC,it 、H FC,it are the electrical power and heat power of the fuel cell respectively; % is the fuel cell in state s FC,it The derating factor of the output power is RP1% = 0, RP4% = 1; U fc,it is the operating voltage of a single fuel cell; K fc is the heat recovery coefficient of the fuel cell; ΔH is the molar calorific value of hydrogen; μ FC,it The start and stop state of the fuel cell, 1 is the start state, 0 is the stop state; P FC,max 、P FC,minrespectively, are upper and lower limits of power generation of fuel cells; Q FC,max , Q FC,min respectively, are upper and lower limits of hydrogen consumption of fuel cells;

[0076] The operation constraints of the hydrogen refueling machines are as follows:

[0077]

[0078] In the formula, Q DP,in,it , Q DP,out,it respectively, are hydrogen input and output of all hydrogen refueling machines; η DP is hydrogen refueling efficiency; C DP,it respectively, are available capacities of all hydrogen refueling machines; s DP,it is an operation state of the hydrogen refueling equipment; c DP is an available capacity of a single hydrogen refueling machine.

[0079] The interaction power constraints are as follows:

[0080]

[0081] In the formula, is an upper limit of interaction power between the energy coupling node and the power grid; s GGrid,it is an operation state of the natural gas grid, 1 indicating normal operation and 0 indicating failure shutdown; is an upper limit of interaction power between the energy coupling node and the natural gas grid.

[0082] Further, in step 4), the heterogeneous energy reliability evaluation index system includes a heterogeneous energy load reduction probability, a heterogeneous energy load reduction time expectation, a heterogeneous energy load shortage energy expectation, a heterogeneous energy load shortage energy comprehensive loss, and a device reliability contribution degree.

[0083] The heterogeneous energy load reduction probability index is as follows:

[0084]

[0085] In the formula, x z,t is a reduction state variable of the zth type of load at t, 1 indicating that the system performs load reduction, and 0 otherwise; N y is a simulation time limit;

[0086] The heterogeneous energy load reduction time expectation index is as follows:

[0087] LOLE z = 8760LOLP z ,

[0088] The heterogeneous energy load shortage energy expectation index is as follows:

[0089]

[0090] The heterogeneous energy load energy shortage comprehensive loss index is as follows:

[0091]

[0092] The equipment reliability contribution degree index is as follows:

[0093] RCOE x,z =(EENS z -EENS z,x ) / EENS z ,

[0094] In the formula, RCOE x,z is the contribution degree index of equipment x to the energy shortage of the zth type of load; EENS z,x is the expected index of the energy shortage of the heterogeneous energy load of the zth type of load under the condition that only the failure scenario of equipment x is not considered.

[0095] Further, in step 5), the evaluation of the comprehensive energy system reliability level of the electricity-hydrogen regional comprehensive energy system specifically includes the following steps:

[0096] Step 5.1) input the electricity-hydrogen regional comprehensive energy system and its device parameter related data, and initialize the running state of all devices;

[0097] Step 5.2) divide the system running state obtained through Markov chain Monte Carlo simulation sampling into different sections in units of days;

[0098] Step 5.3) initialize the section count d = 1 and the simulation year N y = 1;

[0099] Step 5.4) obtain the system state under the dth section, solve the optimal heterogeneous energy load reduction problem under the section, and obtain the load reduction state and optimal load reduction amount of each period under the section;

[0100] Step 5.5) if d > 365, go to step 6), otherwise let d = d + 1, and go to step 5.4);

[0101] Step 5.6) calculate the system reliability evaluation index of the N y th year, and let N y = N y + 1;

[0102] Step 5.7) if N y > 15000 or the system EENS index variance ε < 0.05, go to step 8), otherwise let d = 1, and go to step 4);

[0103] Step 5.8) outputting the heterogeneous energy system reliability evaluation index.

[0104] Compared with the prior art, the present application has the following advantages:

[0105] The multi-state model of the electrolytic cell, the combined heat and power fuel cell and the hydrogen refueling machine provided by the present application helps to accurately evaluate the heterogeneous energy load supply reliability level of the electric-hydrogen regional integrated energy system, improves the energy utilization rate of the system through the combined heat and power fuel cell mode, and reduces the load energy shortage and system economic loss.

[0106] The present application constructs a heterogeneous energy reliability evaluation index system from different angles, combines an optimal heterogeneous energy load reduction model, quantitatively evaluates the reliability of the electric-hydrogen regional integrated energy system based on the Markov chain Monte Carlo method, reveals the supply-demand imbalance mechanism of the heterogeneous energy in the electric-hydrogen regional integrated energy system under the failure mode, effectively quantifies the system energy supply reliability level, economic loss and the reliability contribution degree of the equipment, and provides a scientific and reasonable decision basis for the planning, construction and safe operation of the system. BRIEF DESCRIPTION OF DRAWINGS

[0107] Figure 1 The figure is a structural schematic diagram of an exemplary electric-hydrogen regional integrated energy system in the implementation of the present application;

[0108] Figure 2 The figure is a structural schematic diagram of an electrolytic cell and its three-state Markov space in the implementation of the present application;

[0109] Figure 3 The figure is a structural schematic diagram of a fuel cell and its four-state Markov space in the implementation of the present application;

[0110] Figure 4 The figure is a multi-state Markov space schematic diagram of a hydrogen refueling machine in the implementation of the present application;

[0111] Figure 5 The figure is a reliability evaluation process schematic diagram in the implementation of the present application. DETAILED DESCRIPTION

[0112] The present application will be further described below in conjunction with the embodiments, but should not be understood as limiting the above-mentioned subject matter of the present application to the following embodiments. According to the ordinary technical knowledge and conventional means in the art, various substitutions and modifications can be made without departing from the above-mentioned technical idea of the present application, and all should be included in the protection scope of the present application.

[0113] The electric-hydrogen regional integrated energy system reliability evaluation method based on the hydrogen energy equipment multi-state model in the present embodiment mainly includes the following steps:

[0114] Step 1) The electricity-hydrogen regional integrated energy system is described, and a multi-state Markov space is established for the electrolyzer, fuel cell and hydrogen dispenser in the system, and a two-state Markov space is established for other energy equipment;

[0115] The exemplary electricity-hydrogen regional integrated energy system in this embodiment is substantially as shown in Figure 1 , which includes electric energy equipment, hydrogen energy equipment and thermal energy equipment;

[0116] The electric energy equipment includes power lines, wind turbine generators, photovoltaic generators and batteries;

[0117] The hydrogen energy equipment includes electrolyzers, hydrogen storage tanks, fuel cells and several hydrogen dispensers;

[0118] The thermal energy equipment includes gas boilers and fuel cells;

[0119] The fuel cell produces heat and electricity by consuming hydrogen from the hydrogen storage tank, the electricity load of the electricity-hydrogen regional integrated energy system is supplied by the external power grid, wind and light generators and batteries, the hydrogen load is supplied by hydrogen released from the electrolyzer and hydrogen storage tank through several hydrogen dispensers, and the heat load is supplied by the gas boiler consuming natural gas to produce heat and the fuel cell consuming hydrogen to produce heat.

[0120] As shown in part (a) of Figure 2 , the electrolyzer in this embodiment is composed of an alkaline electrolytic cell, a heat exchanger, a circulating water pump and a gas separation cooling device. When the alkaline electrolytic cell or the gas separation device, circulating water pump fails, the electrolyzer cannot operate normally and is in a fault shutdown state. When the tube side of the heat exchanger fails, alkali leakage occurs, resulting in a decrease in electrolyte concentration, thereby reducing hydrogen production efficiency, and the electrolyzer enters a reduced capacity operation state, thereby obtaining the three-state Markov space of the electrolyzer as shown in part (b) of Figure 2 .

[0121] As shown in part (a) of Figure 3 , the fuel cell is composed of a fuel cell stack, a humidifier, a heat exchanger, a water tank and a circulating water pump. When the fuel cell stack fails or the oxygen supply is insufficient to cause the proton membrane to fail, the fuel cell will be in a fault shutdown state. When the heat exchanger fails, the operating temperature of the fuel cell increases, the output electric power of the fuel cell decreases and the output thermal power increases. When the humidifier fails, the proton membrane becomes dry, causing the ohmic resistance to increase, the output electric power of the fuel cell decreases and the output thermal power increases, thereby obtaining the four-state Markov space of the cogeneration fuel cell as shown in part (b) of the figure.

[0122] Several hydrogenation machines jointly supply hydrogen load demand, taking into account the independent failure of each hydrogenation machine, so there are multiple operating states, and each operating state involves the simultaneous failure of a different number of hydrogenation machines; taking two hydrogenation machines as an example, there can be three operating states, namely no hydrogenation machine failure, 1 hydrogenation machine failure, and 2 hydrogenation machine failure, so a three-state Markov space as shown in Table 1 can be obtained, and similarly, a multi-state Markov space can be obtained for multiple hydrogenation machines. Figure 4

[0123] The hydrogen storage tank, the electric energy device and the thermal energy device take into account the normal operation-failure shutdown state, thereby obtaining their two-state Markov space.

[0124] Step 2) According to the Markov space of all devices, a sequence of device operating states is generated by using the Markov chain Monte Carlo method to sample and constitute the system operating state.

[0125] Generating a system operating state specifically includes the following steps:

[0126] Step 2.1) Determine the device state s x,0 of device x at the initial time;

[0127] Step 2.2) According to the device state s x,t at the current time, according to the probability of occurrence of each state transition path in its Markov space, the state s x,t+1 at the next time is determined by random sampling;

[0128] Taking a two-state Markov space as an example, the probabilities of occurrence of device state transitions according to different transition paths are as follows:

[0129]

[0130] In the formula, p x {·} represents the probability of event · occurrence; λ x , μ x are the failure rate and repair rate of device x, respectively.

[0131] Step 2.3) Perform step 2.2) for the next time until the state of device x at all times within the period is determined, and a time sequence state sequence of device x is generated.

[0132] Step 2.4) Repeat steps 2.1) to 2.3) for all devices in the electric-hydrogen regional integrated energy system to generate a set of state sequences of all devices in the system, i.e., the system operating state.

[0133] Step 3) Taking the sum of the penalty cost of abandoned wind and light and the penalty cost of heterogeneous energy load reduction as the objective function, taking into account the system operating constraints, an optimal heterogeneous energy load reduction model of the system is established. ​

[0134] The objective function expression of the optimal heterogeneous energy source load shedding model is:

[0135]

[0136] In the formula, c DG is the unit penalty cost of abandoned wind and light; Ω WG , Ω PV are wind and light unit installation node sets; ΔP WG,it , ΔP PV,it are abandoned wind and light power; T is a scheduling period; n is the number of nodes; Z is a supply load type set, including three types of loads, i.e., electricity, heat, and hydrogen; c z is the unit reduction penalty cost of the zth load; L z,it is the reduction power of the zth load. Subscripts i and t represent nodes i and t time, respectively.

[0137] The system operation constraints include power balance constraints, load reduction constraints, device operation constraints, and interactive power constraints:

[0138] The power balance constraints include electric, heat, and hydrogen power balance constraints.

[0139] The electric power balance constraint is as follows:

[0140] P Grid,it + P WG,it + P PV,it + P dis,it + P F,it = P EL,it + P ch,it + P load,it - L p,it (3)

[0141]

[0142] In the formula, P Grid,it is the interactive power of the energy coupling node and the power grid; P WG,it , P PV,it are actual output powers of wind and light units; P ch,it , P dis,it are charge and discharge powers of the battery; P FC,it is the power generation power of the fuel cell; P EL,it is the power consumption power of the electrolytic tank; P load,it is the electric load demand power; L p,it is the electric load reduction power; P ij,t is the active power transmitted by the electric power line ij; k∈j indicates that node k takes node j as the head node; Ω EH is an energy coupling node set.

[0143] The thermal power balance constraint is shown as follows:

[0144] H GB,it +H FC,it =H load,it -L h,it (5)

[0145] In the formula, H GB,it is the heat production power of the gas boiler; H FC,it is the heat production power of the fuel cell; H load,it is the heat load demand power; and L h,it is the heat load reduction power.

[0146] The hydrogen power balance constraint is shown as follows:

[0147]

[0148] In the formula, Q EL,it is the hydrogen production amount of the electrolyzer; Q HT,in,it and Q HT,out,it are the hydrogen storage amount and hydrogen release amount of the hydrogen storage tank, respectively; Q FC,it is the hydrogen consumption amount of the fuel cell; Q EL2DP,it and Q HT2DP,it are the hydrogen supply amounts of the electrolyzer and the hydrogen storage tank to the hydrogen refueling station, respectively; Q DP,in,t and Q DP,out,t are the hydrogen input and output amounts of all the hydrogen refueling stations, respectively; Q load,it is the hydrogen load demand amount; and L q,it is the hydrogen load reduction amount.

[0149] The load reduction constraint is shown as follows:

[0150]

[0151] The equipment operation constraints include power line operation constraints, wind-solar unit operation constraints, battery operation constraints, gas boiler operation constraints, electrolyzer operation constraints, hydrogen storage tank operation constraints, fuel cell operation constraints, and hydrogen refueling station operation constraints. The power line operation constraints are shown as follows:

[0152] -s ij,t P ij,max ≤P ij,t ≤s ij,t P ij,max (8)

[0153] In the formula, s ij,t is the operation state of the line ij, 1 indicating normal operation and 0 indicating fault shutdown; and P ij,max is the upper limit of the line transmission active power.

[0154] The wind-solar unit operation constraints are shown as follows:

[0155]

[0156] Where, are the predicted output power of wind and solar power units; s WG,it 、s PV,it They are the operating status of the wind and solar units respectively, 1 indicates normal operation, and 0 indicates failure and shutdown.

[0157] The battery operation constraints are as follows:

[0158]

[0159] Where, SOC i,t , SOC i,t+1 are the battery state of charge at time t and time t+1 respectively; P ch,it 、P dis,it are the charging and discharging power of the battery respectively; η ch ,η dis are charge and discharge efficiency; S ES is the battery capacity; α ch,it , β dis,it They are the battery charging and discharging status, 0 means no power charging / discharging, 1 means power charging / discharging; SOC max , SOC min They are the upper and lower limit constraints of the battery state of charge; SOC0, SOC T are the battery state of charge at the initial and final moments of the study period; s ES , it The operating status of the battery, 1 indicates normal operation, and 0 indicates failure and shutdown.

[0160] The operating constraints for gas boilers are as follows:

[0161]

[0162] Where G GB,it is the gas consumption power of the gas boiler; η GB is the gas boiler efficiency; s GB,it The operating status of the gas boiler, 1 indicates normal operation, 0 indicates failure and shutdown; It is the upper limit of gas consumption power of gas boiler.

[0163] The electrolyzer operating constraints are as follows:

[0164]

[0165] Where Q EL,it is the hydrogen production of the electrolyzer; ρ H2is the standard density of hydrogen; k1, k2 are unit conversion coefficients; F is Faraday constant; η is the hydrogen charging efficiency f is the Faraday efficiency; is the operating voltage of a single electrolyzer in state s EL,it ; is the total power consumption of the electrolyzer in state s EL,it ; μ is the hydrogen charging efficiency EL,it ; s is the start-stop state of the electrolyzer, 1 is the start state, and 0 is the stop state; P EL,max and P EL,min are the upper and lower limits of the total power consumption of the electrolyzer, respectively.

[0166] The operating constraints of the hydrogen storage tank are as follows:

[0167]

[0168] wherein SOH i,t and SOH i,t+1 are the hydrogen storage states of the hydrogen storage tank at time t and t+1, respectively, i.e., the ratio of the hydrogen stored at that time to the capacity; Q HT,in,it and Q HT,out,it are the hydrogen storage amount and hydrogen release amount of the hydrogen storage tank, respectively; η HT,in and η HT,out are the hydrogen charging and discharging efficiencies, respectively; S HT is the capacity of the hydrogen storage tank; α in,it and β out,it are the hydrogen charging and discharging states of the hydrogen storage tank, 0 indicating no hydrogen charging / discharging and 1 indicating hydrogen charging / discharging; SOH max and SOH min are the upper and lower constraints of the hydrogen storage state of the hydrogen storage tank; SOH0 and SOH T are the hydrogen storage states of the hydrogen storage tank at the initial time and the end time within the research period, respectively; s HT,it is the operating state of the hydrogen storage tank, 1 indicating normal operation and 0 indicating failure shutdown.

[0169] The operating constraints of the fuel cell are as follows:

[0170]

[0171] wherein Q FC,it is the hydrogen consumption of the fuel cell (kg); m FC,it is the hydrogen consumption of the fuel cell (kW); P FC,it and H FC,it are the power generation and heat generation of the fuel cell, respectively; RP is the derating coefficient of the output electric power of the fuel cell in state s FC,it , wherein RP1% = 0 and RP4% = 1; U fc,it is the operating voltage of a single fuel cell; Kfc is the thermal recovery utilization coefficient of fuel cell; ΔH is the molar heat value of hydrogen; μ FC,it is the start-stop state of fuel cell, 1 is start state, 0 is stop state; P FC,max , P FC,min are respectively the upper and lower limit values of power generated by fuel cell; Q FC,max , Q FC,min are respectively the upper and lower limit values of hydrogen consumption of fuel cell.

[0172] The operation constraints of hydrogen refueling station are as follows:

[0173]

[0174] In the formula, Q DP,in,it , Q DP,out,it are respectively the input and output hydrogen amount of all hydrogen refueling stations; η DP is the hydrogen refueling efficiency; C DP,it are respectively the available capacities of all hydrogen refueling stations; s DP,it is the operation state of hydrogen refueling equipment; c DP is the available capacity of a single hydrogen refueling station.

[0175] The interactive power constraints are as follows:

[0176]

[0177] In the formula, is the upper limit of the interactive power between the energy coupling node and the power grid; s GGrid,it is the operation state of natural gas network equivalent element, 1 represents normal operation, and 0 represents fault shutdown; is the upper limit of the interactive power between the energy coupling node and the natural gas network.

[0178] Step 4) constructing a heterogeneous energy reliability evaluation index system by using the heterogeneous energy load reduction probability, the heterogeneous energy load reduction time expectation, the heterogeneous energy load energy shortage expectation, the heterogeneous energy load energy shortage comprehensive loss and the equipment reliability contribution degree;

[0179] The heterogeneous energy load reduction probability index is as follows:

[0180]

[0181] In the formula, x z,t is the reduction state variable of the zth load at t time, 1 represents that the system carries out load reduction, and 0 represents otherwise; N y is the simulation life.

[0182] The heterogeneous energy load reduction time expectation index is as follows:

[0183] LOLEz 8760 LOLP z (17)

[0184] The heterogeneous energy load energy shortage expectation index is as follows:

[0185]

[0186] The heterogeneous energy load energy shortage comprehensive loss index is as follows:

[0187]

[0188] In the formula, x z,t is the reduction state variable of the zth type of load at time t, 1 indicates that the system carries out load reduction, otherwise 0; N y is the simulation year.

[0189] The equipment reliability contribution index is as follows:

[0190] RCOE x,z = (EENS z -EENS z,x ) / EENS z (20)

[0191] In the formula, RCOE x,z is the contribution index of equipment x to the energy shortage of the zth type of load; EENS z,x is the heterogeneous energy load energy shortage expectation index of the zth type of load only without considering the fault scene of equipment x.

[0192] Step 5) The optimal heterogeneous energy load reduction model under all system operating states is solved, the heterogeneous energy reliability evaluation index is calculated, and the reliability level of the electric hydrogen regional integrated energy system is evaluated.

[0193] In this embodiment, the process of evaluating the reliability level of the electric hydrogen regional integrated energy system is basically as shown in Figure 5 , and specifically includes the following steps:

[0194] Step 5.1) Input the electric hydrogen regional integrated energy system and its device parameter related data, and initialize the operating state of all devices;

[0195] Step 5.2) Divide the system operating state obtained by Markov chain Monte Carlo simulation sampling into different sections in units of days;

[0196] Step 5.3) Initialize the section count d = 1 and the simulation year N y = 1;

[0197] Step 5.4) Obtain the system state under the dth section, solve the optimal heterogeneous energy load shedding problem of the system under the section, and obtain the load shedding state and optimal load shedding amount of each time period of the section;

[0198] Step 5.5) If d > 365, turn to step 5.6), otherwise let d = d + 1, and turn to step 5.4);

[0199] Step 5.6) Calculate the system reliability evaluation index of the N y th year, and let N y = N y + 1;

[0200] Step 5.7) If N y > 15000 or the variance ε of the system EENS index is less than 0.05, turn to step 5.8), otherwise let d = 1, and turn to step 5.4);

[0201] Step 5.8) Output the heterogeneous energy reliability evaluation index of the system.

[0202] In the embodiment, the reliability evaluation method of the hydrogen energy equipment multi-state model-based electric-hydrogen regional comprehensive energy system is verified through a simulation example. In the simulation example, the electric-hydrogen regional comprehensive energy system composed of the IEEE14 node distribution network is taken as an example to prove the feasibility and effectiveness of the hydrogen energy equipment reliability model and the electric-hydrogen regional comprehensive energy system reliability evaluation method. In the system, node 7 and node 13 are energy coupling nodes, and the electric-hydrogen regional comprehensive energy system as shown in Figure 1 is configured. Scheme one is that the electrolyzer adopts the traditional two-state reliability evaluation model and the fuel cell adopts the power generation mode, scheme two is that the electrolyzer adopts the three-state reliability evaluation model and the fuel cell adopts the power generation mode, scheme three is that the electrolyzer adopts the traditional two-state reliability evaluation model and the fuel cell adopts the combined heat and power mode, and scheme four is that the electrolyzer adopts the three-state reliability evaluation model and the fuel cell adopts the combined heat and power mode.

[0203] Through the simulation and solution of the model, the system reliability evaluation indexes of each simulation scheme are obtained, as shown in Table 1.

[0204] Table 1: System reliability evaluation index calculation results of different schemes

[0205]

[0206]

[0207] As can be seen from Table 1, the reliability levels of the electric load and the thermal load of Scheme II are the same as those of Scheme I, but the hydrogen load supply reliability level of Scheme II is worse than that of Scheme I because Scheme II takes into account the reduced operation state of the electrolytic cell. Comparing Scheme IV with Scheme II, the electric load and the hydrogen load supply reliability indexes of Scheme IV almost do not change, but the thermal load supply reliability level of Scheme IV is greatly improved compared with that of Scheme II because the fuel cell in Scheme IV adopts a cogeneration operation mode. Comparing Scheme IV with Scheme III, the hydrogen load reliability level of Scheme IV decreases and the thermal load energy shortage of Scheme IV also increases compared with Scheme III because Scheme IV takes into account the reduced operation state of the electrolytic cell.

Claims

1. A reliability assessment method for an electric-hydrogen regional integrated energy system based on a multi-state model of hydrogen energy equipment, characterized by: The following steps are involved: Step 1) Describe the regional integrated energy system for electricity and hydrogen, and establish a multi-state Markov space for the electrolyzer, fuel cell, and hydrogenator in the system, and a two-state Markov space for other energy devices; Step 2) Based on the Markov space of all devices, the Markov Chain Monte Carlo method is used to sample and generate the device operation state sequence and form the system operation state; Step 3) Taking the minimization of the sum of the penalty costs for curtailing wind and solar power and the penalty costs for reducing heterogeneous energy loads as the objective function, taking into account the system operation constraints, establish the optimal heterogeneous energy load reduction model for the system; Step 4) Construct a heterogeneous energy reliability evaluation index system using heterogeneous energy load reduction probability, heterogeneous energy load reduction time expectation, heterogeneous energy load shortfall energy expectation, heterogeneous energy load shortfall energy comprehensive loss, and equipment reliability contribution; Step 5) Solve the optimal energy load reduction model under all system operating conditions, calculate the heterogeneous energy reliability evaluation index, and evaluate the reliability level of the electric-hydrogen regional integrated energy system.

2. The method according to claim 1, characterized in that The electric-hydrogen regional integrated energy system in step 1) includes electric energy equipment, hydrogen energy equipment, and thermal energy equipment; The electric energy equipment includes power lines, wind turbines, photovoltaic units and batteries; The hydrogen energy equipment includes an electrolyzer, a hydrogen storage tank, a fuel cell and several hydrogen refueling machines; The thermal energy equipment includes a gas boiler and a fuel cell; The fuel cell performs cogeneration of heat and power by consuming hydrogen from the hydrogen storage tank; The electric load of the electric-hydrogen regional integrated energy system is supplied by the external power grid, wind and solar power units, and batteries, while the hydrogen load is supplied by hydrogen released from electrolyzers and hydrogen storage tanks through several hydrogen refueling machines. The heat load is supplied by gas boilers consuming natural gas to generate heat and fuel cells consuming hydrogen to generate heat.

3. The method according to claim 1, characterized in that In step 1), a three-state Markov space is established for the electrolytic cell. Its status includes, Normal operating status; Failure and shutdown caused by failure of alkaline electrolytic cell, gas separation device or circulating water pump; Derating operation status caused by failure of the heat exchanger tube; A four-state Markov space is established for the fuel cell. Its status includes normal operating status; Fuel cell failure and shutdown due to fuel cell stack failure or insufficient oxygen supply causing proton membrane failure; The state where the fuel cell output electrical power decreases and the output thermal power increases due to the increase in the fuel cell operating temperature caused by heat exchanger failure; When the humidifier fails, the proton membrane dries out, causing its ohmic resistance to increase, which in turn causes the fuel cell's output electrical power to decrease and its output thermal power to increase; Taking into account the independent failure of each hydrogenation machine, a multi-state Markov space is established for the hydrogenation machine as a whole, and its states include normal operation state, and, multiple faulty operation / outage states caused by simultaneous failures of different numbers of hydrogenation units; A two-state Markov space is established for the other energy devices, taking into account the normal operation state and the fault shutdown state.

4. The method according to claim 1, wherein In step 2), generating the system operation status specifically includes the following steps: Step 2.1) Determine the device state s of device x at the initial time x,0 ; Step 2.2) Based on the current device status s x,t , randomly sample the state transition paths in the Markov space according to their probability of occurrence, and determine the state s at the next moment x,t+1 ; Step 2.3) Repeat step 2.2) until the state of device x at all moments in the cycle is determined, and the time sequence of device x's state is generated; Step 2.4) Repeat steps 2.1) to 2.3) for all devices in the electric-hydrogen regional integrated energy system to generate a state sequence set of all devices in the system, i.e., the system operating state.

5. The evaluation method according to claim 1, wherein: In step 3), the objective function expression of the optimal quality energy load reduction model is: ， Where c DG is the unit penalty cost for curtailing wind and solar power; Ω WG ,Ω PV are the installation node sets of wind and solar turbines respectively; △P WG,it , △P PV,it are the wind and solar power curtailment respectively; T is the scheduling period; n is the number of nodes; Z is the supply load type set, including electricity, heat and hydrogen loads; c z The penalty cost for unit reduction of load class z; L z,it is the power reduction of the z-th type load, and the subscripts i and t represent the node i and time t respectively.

6. The method according to claim 5, characterized in that In step 3), the system operation constraints include power balance constraints, load reduction constraints, equipment operation constraints, and interactive power constraints: The power balance constraints include electricity, heat and hydrogen power balance constraints; The electric power balance constraints are as follows: ， ， Where, P Grid,it is the interaction power between the energy coupling node and the grid; P WG,it 、P PV,it are the actual output power of wind and solar power units respectively; P ch,it 、P dis,it are the charging and discharging power of the battery respectively; P FC,it is the power generated by the fuel cell; P EL,it is the power consumption of the electrolytic cell; P load,it L is the power demanded by the electric load; p,it To reduce power for electrical load; P ij,t is the active power transmitted by power line ij; k∈j means node k takes node j as the head node; Ω EH is the set of energy coupling nodes; The thermal power balance constraints are as follows: ， Where H GB,it is the heating power of the gas boiler; H FC,it is the heat generation power of the fuel cell; H load,it is the required power of heat load; L h,it Cut power for thermal loads; The hydrogen power balance constraints are as follows: ， Where Q EL,it is the hydrogen production of the electrolyzer; Q HT,in,it , Q HT,out,it are the hydrogen storage capacity and hydrogen release capacity of the hydrogen storage tank, Q FC,it is the hydrogen consumption of the fuel cell, Q EL2DP,it , Q HT2DP,it The amount of hydrogen supplied to the hydrogen refueling machine by the electrolyzer and the hydrogen storage tank, Q DP,in,t , Q DP,out,t are the hydrogen input and output of all hydrogen refueling machines, Q load,it is the hydrogen load demand, L q,it is the hydrogen load reduction; The load shedding constraints are as follows: ； The equipment operation constraints include power line operation constraints, wind and solar unit operation constraints, battery operation constraints, gas boiler operation constraints, electrolyzer operation constraints, hydrogen storage tank operation constraints, fuel cell operation constraints and hydrogen refueling machine operation constraints; The power line operation constraints are as follows: ， Where s ij,t is the operating status of line ij, 1 indicates normal operation, 0 indicates fault outage; P ij,max The upper limit of active power transmitted by the line; The wind and solar power generation unit operation constraints are as follows: ； Where, 、 are the predicted output power of wind and solar power units; s WG,it 、s PV,it They are the operating status of the wind and solar generator sets, 1 indicates normal operation, and 0 indicates failure and shutdown; The battery operation constraints are as follows: ， Where, SOC i,t , SOC i,t+1 are the battery state of charge at time t and time t+1, P ch,it 、P dis,it are the charging and discharging power of the battery, η ch ,η dis are charge and discharge efficiency, S ES is the battery capacity, α ch,it , β dis,it They are the battery charging and discharging status, 0 means no energy charging / discharging, 1 means energy charging / discharging, SOC max , SOC min They are the upper and lower limits of the battery state of charge, SOC0 and SOC T are the battery charge states at the initial and final moments of the study period; s ES, it The operating status of the battery, 1 indicates normal operation, 0 indicates failure and shutdown; The gas boiler operation constraints are as follows: ， Where G GB,it is the gas consumption power of the gas boiler; η GB is the gas boiler efficiency; s GB,it The operating status of the gas boiler, 1 indicates normal operation, 0 indicates failure and shutdown; The upper limit of gas consumption power of gas boiler; The electrolyzer operating constraints are as follows: ， Where Q EL,it is the hydrogen production of the electrolyzer; ρ H2 is the standard density of hydrogen; k1 and k2 are unit conversion coefficients; F is the Faraday constant; η f is the Faraday efficiency; For a single electrolytic cell in state s EL, it The operating voltage under The electrolytic cell is in state s EL, it Total power consumption; μ EL, it The start and stop status of the electrolytic cell, 1 is the start state, 0 is the stop state; P EL,max and P EL,min They are the upper and lower limits of the total power consumption of the electrolyzer respectively; The operating constraints of the hydrogen storage tank are as follows: ， Where SOH i,t 、SOH i,t+1 are the hydrogen storage states of the hydrogen storage tank at time t and time t+1, that is, the ratio of stored hydrogen to capacity at that time; Q HT,in,it , Q HT,out,it are the hydrogen storage capacity and hydrogen release capacity of the hydrogen storage tank respectively; η HT,in ,η HT,out are the hydrogen charging and discharging efficiency; S HT is the capacity of the hydrogen storage tank; α in,it , β out,it They are the hydrogen storage tank charging and discharging status, 0 means no hydrogen charging / discharging, 1 means hydrogen charging / discharging; SOH max 、SOH min They are the upper and lower limit constraints of the hydrogen storage state of the hydrogen storage tank; SOH0, SOH T are the hydrogen storage states of the hydrogen storage tank at the initial and final moments of the research period; s HT,it The operating status of the hydrogen storage tank, 1 indicates normal operation, and 0 indicates failure and shutdown; The fuel cell operating constraints are as follows: ， Where Q FC,it is the hydrogen consumption of the fuel cell, in kg; m FC,it is the hydrogen consumption of the fuel cell, in kW; P FC,it 、H FC,it are the electricity generation power and heat generation power of the fuel cell respectively; RP sFC,it % is the fuel cell in state s FC,it The derating factor of the output power is RP1%=0, RP4%=1; U fc,it is the operating voltage of a single fuel cell; K fc is the heat recovery coefficient of the fuel cell; △H is the molar calorific value of hydrogen; μ FC,it The start and stop state of the fuel cell, 1 is the start state, 0 is the stop state; P FC,max 、P FC,min are the upper and lower limits of fuel cell power generation respectively; Q FC,max , Q FC,min They are the upper and lower limits of hydrogen consumption of fuel cells; The operating constraints of the hydrogenation machine are as follows: ， Where Q DP,in,it , Q DP,out,it are the hydrogen input and output volumes of all hydrogen refueling machines respectively; η DP is the hydrogenation efficiency; C DP,it are the available capacities of all hydrogen refueling machines; DP,it is the operating status of the hydrogenation equipment; c DP is the available capacity of a single hydrogen refueling machine; The interaction power constraints are as follows: ， Where, is the upper limit of the interaction power between the energy coupling node and the grid; s GGrid,it It is the operating status of the equivalent component of the natural gas grid, 1 indicates normal operation, and 0 indicates failure and shutdown; It is the upper limit of the interaction power between the energy coupling node and the natural gas grid.

7. The method according to claim 5, characterized in that In step 4), the heterogeneous energy reliability evaluation index system includes heterogeneous energy load reduction probability, heterogeneous energy load reduction time expectation, heterogeneous energy load shortfall energy expectation, heterogeneous energy load shortfall energy comprehensive loss and equipment reliability contribution; The heterogeneous energy load reduction probability index is as follows: ， Where x z,t is the load shedding state variable of the zth type at time t, 1 indicates that the system is shedding load, otherwise it is 0; N y is the simulation years; The expected indicators of heterogeneous energy load reduction time are as follows: ， The expected indicators of the heterogeneous energy load shortfall energy are as follows: ， The comprehensive energy loss index of the heterogeneous energy load shortage is as follows: ， Among them, c z Reduction of penalty costs for units with class z load; The equipment reliability contribution index is as follows: ， Where, RCOE x,z EENS is the contribution index of equipment x to the energy shortage of load type z; z,x is the expected index of the energy shortage of heterogeneous energy loads of type z without considering the failure scenario of device x.

8. The method according to claim 1, characterized in that In step 5), the reliability level of the electric-hydrogen regional integrated energy system is assessed, including the following steps: Step 5.1) Input the relevant data of the electric-hydrogen regional integrated energy system and its equipment parameters, and initialize the operating status of all equipment; Step 5.2) Divide the system operating state obtained by Markov Chain Monte Carlo simulation sampling into different sections on a daily basis; Step 5.3) Initialize the cross-section count d = 1 and the number of simulation years N y =1; Step 5.4) Obtain the system state at the d-th section, solve the optimal quality energy load reduction problem for the system at this section, and obtain the load reduction state and optimal load reduction amount for each period of the section; Step 5.5) If d > 365, go to Step 6). Otherwise, set d = d + 1 and go to Step 5.4); Step 5.6) Calculate the Nth y The system reliability evaluation index of the year, and let N y = N y +1; Step 5.7) If N y >15000 or the system EENS index variance ε <0.05, go to step 8); otherwise, set d = 1 and go to step 4); Step 5.8) Output the system heterogeneous energy reliability evaluation index.

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