CN117200265B - Marine electro-hydrogen system capacity planning method considering uncertainty fault - Google Patents

Abstract

The invention provides a capacity planning method of an offshore electro-hydrogen system, which is used for considering uncertainty faults, and constructing an objective function of a capacity planning model of the offshore electro-hydrogen system, which is used for considering equipment capacity planning, normal operation of the system and fault operation of the system; an equipment fault model of the fuel cell, the electrolytic tank and the power transmission line is established, and a fault uncertainty set of the offshore hydrogen system is set; constructing constraint conditions of a capacity planning model of the offshore hydrogen system; writing out a linearization form of the capacity planning model, and converting the linearization form into a dual form; and solving the model by adopting a nested column constraint generation algorithm to obtain an optimized capacity planning result. According to the invention, a hydrogen energy system is added on the basis of a traditional offshore wind power system, a wind power consumption way is increased, an additional power supply source is provided in a wind power intermittent period, and the system stability is improved.

Description

A capacity planning method for offshore electric-hydrogen system considering uncertain faults

Technical Field

The present invention relates to the field of capacity planning, and in particular to a method for capacity planning of an offshore electric hydrogen system taking into account uncertain faults.

Background Art

Clean energy is gradually taking a leading position in power generation, among which wind power generation is one of the main forms of new energy power generation. Due to the abundant wind resources at sea, the planned capacity of offshore wind turbines is increasing and gradually developing towards COSCO SEA. However, due to the uncertainty and volatility of wind power, the output of wind power varies greatly under different wind speeds, which may lead to wind abandonment or load abandonment, affecting the stability of the power grid.

At present, as hydrogen production and hydrogen energy storage technologies continue to mature, the application of hydrogen energy systems in power supply security has become feasible. The system converts surplus wind power into hydrogen through an electrolyzer and stores it in a hydrogen storage tank. Hydrogen can be provided to hydrogen loads, or it can be converted into electricity through fuel cells to ensure power supply when wind power output is insufficient. The system can effectively improve wind power absorption capacity and power supply security capabilities. However, the offshore hydrogen system still has the following problems: when planning capacity, it does not consider whether the system can reliably supply power and achieve absorption after equipment failure.

Summary of the invention

Technical problem: The present invention proposes a capacity planning method for an offshore electric hydrogen system considering uncertain faults. The method proposed in the present invention focuses on the capacity planning of an offshore electric hydrogen system considering equipment failures, and takes into account the uncertainty of faulty equipment.

Technical solution: In order to solve the above technical problems, the present invention proposes a method for offshore electric hydrogen system capacity planning considering uncertain faults, the method comprising the following steps:

1. According to the capacity planning of electrolyzers, fuel cells, hydrogen storage tanks and transmission lines in the electric-hydrogen system and the normal operation and fault operation of the electric-hydrogen system, the objective function of the offshore electric-hydrogen system capacity planning model is constructed;

2. Establish equipment failure models for electrolyzers, fuel cells, and transmission lines;

3. Based on the equipment failure models of the electrolyzer, fuel cell and transmission line established in step 2, a failure uncertainty set of the offshore electric hydrogen system is constructed;

4. Obtain the constraint conditions of the offshore electric hydrogen system capacity planning model based on the objective function and the equipment failure model;

5 Take the objective function in step 1, the equipment failure model of the electrolyzer, fuel cell and transmission line in step 2, the failure uncertainty set of the offshore electric hydrogen system in step 3 and the constraint conditions in step 4 as the capacity planning model of the offshore electric hydrogen system, and write its linearized form;

6 Based on the linearized form of the offshore electric-hydrogen system capacity planning model proposed in step 5, write the dual form;

7 Based on the offshore electric-hydrogen system capacity planning model and its linearized form in step 5 and the dual form in step 6, the capacity planning model is solved using a nested column constraint generation algorithm, and capacity planning is performed on the model based on the solution results.

Furthermore, the specific process of step 1 is as follows:

The objective function of the offshore electric hydrogen system capacity planning model is constructed. The objective function is in the following form:

where _uf represents the uncertainty variable vector of all component states; U represents the uncertainty set of component states; s _e represents the uncertainty variable vector of all scenario states; S _sce represents the uncertainty set of scenario states; r is the discount rate; m is the operating life; P _ELmax , P _FCmax , V _hmax , and P _trans are the planned capacities of electrolyzer, fuel cell, hydrogen storage tank, and transmission line, respectively; L is the length of the submarine cable; e _k is the correlation coefficient of each equipment planning, k＝1,2,...,5, where k＝1 represents electrolyzer, k＝2 represents fuel cell, k＝3 represents hydrogen storage tank, k＝4 represents transmission line, and k＝5 represents infrastructure; e _HVDC1 and e _HVDC2 are the fixed coefficients of converter station planning and the coefficient related to the transmission line capacity, respectively; _Re1 , R _h1 , and _Re2 are the output generated by supplying power to the upper grid, the output generated by supplying hydrogen, and the output generated by supplying power to the load, respectively; C _com , C _wloss , and C _loss represents the maintenance cost required for the operation of the electric hydrogen system, the penalty caused by the unabsorbed wind power, and the penalty caused by the lost load power;

The specific expressions of some parameters in the objective function are as follows:

Wherein, s represents the scenario of system operation, and the output of wind turbines is different in different scenarios; the operation of all scenarios under s∈Ω _nor is defined as the normal operation of the electric hydrogen system, and the operation of all scenarios under s∈Ω _xtm is defined as the fault operation of the electric hydrogen system; Ω _nor is all scenarios of normal operation of the electric hydrogen system; Ω _xtm is all scenarios of fault operation of the electric hydrogen system; t represents the operation time, and T is the total number of operation times; _Ke1,t , _Kh , and _Ke2 are the relevant parameters for power supply to the upper power grid, the relevant parameters for hydrogen supply, and the relevant parameters for power supply to the load, respectively; μ _loss is the transmission consumption coefficient; P _net,s,t is the power transmitted to the upper power grid; V _hsell,s,t is the amount of hydrogen output to the hydrogen load; P _wload,s,t is the power supplied to the load by wind power; P _FC1,s,t is the power supplied to the load by the fuel cell; Q _k is the operation and maintenance coefficient of each device, k=1,2,...,5; Q _h1 is the operation and maintenance coefficient of the electrolyzer related to the hydrogen production; Q _h2 is the operation and maintenance coefficient of the fuel cell related to the hydrogen consumption; V _FC,s,t is the volume of hydrogen consumed by the fuel cell; V _EL,s,t is the volume of hydrogen produced by the electrolyzer at time t; P _loss,s,t and c _loss are the load loss power and the penalty coefficient for load loss, respectively; P _wloss,s,t is the wind power that is not absorbed when the scene is s and the time is t; c _wloss is the penalty coefficient for the wind power that is not absorbed; π ¹ ~π ⁶ are the dual variables corresponding to each formula.

Further, the specific process of step 2 is as follows:

(201) A fuel cell equipment failure model is established, which includes the relationship between the current and voltage in the fuel cell, the relationship between the hydrogen consumption and electricity production of the fuel cell, and the fuel cell operation constraints. The specific expression is as follows:

μ _FC,s,t ·P _{FC min} ≤P _FC,s,t ≤μ _FC,s,t ·P _{FC max}

Wherein, U _fc,s,t and I _fc,s,t represent the operating voltage and current of the fuel cell respectively; τ ₁ , τ ₂ , τ ₃ , τ ₄ are the correlation coefficients of the electromotive force of the fuel cell; T _fc is the operating temperature of the fuel cell; and are the partial pressures of the hydrogen interface and oxygen interface of the fuel cell respectively; ξ _i is the empirical coefficient, i＝1,2,...,4; is the oxygen concentration at the cathode gas-liquid surface; J _{fc max} is the maximum current density of the fuel cell; A _fc represents the active area of the fuel cell; B is a constant coefficient; R _m is the equivalent membrane impedance; R _c is the equivalent contact resistance of the membrane; P′ _FC,s,t and P _FC,s,t are the ideal output power and actual output power of the fuel cell respectively; k _f is the unit conversion coefficient; F is the Faraday constant; represents the state of the fuel cell in scenario s, q = 1, 2, ..., 5; is the working efficiency of the fuel cell under different operating conditions; P _{FC min} is the minimum output power of the fuel cell; μ _FC,s,t is the start and stop state of the fuel cell, Respectively represent the status of the four components of the fuel cell;

(202) An electrolytic cell equipment failure model is established, which includes the relationship between the electrolytic cell's power consumption and hydrogen production, the relationship between the electrolytic cell's operating power and current, and the electrolytic cell's operating constraints. The specific expression is as follows:

Where, I _el,s,t represents the operating current of the electrolytic cell; _Tel is the operating temperature of the electrolytic cell; A _el is the effective reaction area of the electrolytic cell; U _rev is the reversible voltage of the electrolytic cell; and They represent the ohmic resistance of the alkali solution under normal operation, the ohmic resistance of the alkali solution under derating operation, and the thermal resistance coefficient of the alkali solution respectively; is the electrode overvoltage coefficient obtained by fitting; η _f is the Faraday efficiency; P _EL,s,t represents the power consumption of the electrolytic cell at time t; Indicates the power consumption of the electrolytic cell under different operating conditions, z = 1, 2, 3; P _{EL min} indicates the minimum power consumption of the electrolytic cell; Indicates the operating status of the electrolytic cell; μ _EL,s,t indicates the start and stop status of the electrolytic cell; Respectively represent the status of the two components of the electrolyzer;

(203) Equipment Failure Model of Transmission Line

When the transmission line is not faulty, the power transmitted to the upper grid must not exceed its capacity. When the transmission line fails, the electric hydrogen system will no longer be connected to the upper grid, and the power transmitted to the upper grid is 0. The capacity constraints of the transmission line considering the fault are as follows:

0≤P _net,s,t ≤υ _jtrans,s ·P _trans

In the formula, jtrans represents the faulty component in the transmission line; υ _jtrans,s represents the state of the component jtrans in the transmission line under scenario s, υ _jtrans,s = 1 indicates that the component operates normally, and υ _jtrans,s = 0 indicates that the component fails.

Furthermore, the specific process of step 3 is as follows:

Construct an uncertain set of faults for the offshore electric hydrogen system, set limits on the number of component failures in each fault scenario and the total number of failures of each component throughout the year, and set limits on the number of fault scenarios in all scenarios:

u _f = [u _jel ; u _jfc ; u _jtrans ]

where Ω _s is a set of operating scenarios; jel, jfc represent the faulty components in the electrolyzer and fuel cell, respectively; n _el , n _fc , n _trans represent the number of components in the electrolyzer, fuel cell and transmission line, respectively; λ _jel,s represents the state of component jel in the electrolyzer under scenario s, λ _jel,s = 1 represents the normal operation of the component, and λ _jel,s = 0 represents the component failure; ζ _jfc,s represents the state of component jfc in the fuel cell under scenario s, ζ _jfc,s = 1 represents the normal operation of the component, and ζ _jfc,s = 0 represents the component failure; let the number of scenarios s in Ω _xtm be N _s ; N _xtm is the upper limit of component failure in the fault scenario, and N _sce is the upper limit of the total number of component failures within one year; u _jel , u _jfc , u _jtrans are the variable vector forms of λ _jel,s , ζ _jfc,s and υ _jtrans,s, respectively; s _sce,s represents the state of scenario s.

Furthermore, the specific process of step 4 is as follows:

Establish constraints for the offshore electric-hydrogen system capacity planning model considering uncertain faults:

(401) Power balance constraint:

Where P _load,s,t is the load power; P _w,s,t and P _wnet,s,t represent the wind power generation and the power transmitted to the upper grid at time t respectively; It is the dual variable corresponding to each formula in the power balance constraint;

(402) Hydrogen storage tank constraints:

Where V _h,s,t is the gas capacity in the hydrogen storage tank; V _hload,s,t is the hydrogen load demand; V _h0 and V _hT are the hydrogen volumes in the hydrogen storage tank at the beginning and end of the period; It is the dual variable corresponding to each formula in the hydrogen storage tank constraint.

Furthermore, the specific process of step 5 is as follows:

The above-mentioned offshore electric hydrogen system capacity planning model is a nonlinear mixed integer programming problem, in which the equipment failure models of the electrolyzer, fuel cell and transmission line contain nonlinear variables. The linear form of the offshore electric hydrogen system capacity planning model is written using linear fitting and linearization processing methods;

(501) The linearized form of the equipment failure model of the electrolytic cell is as follows:

Where bigM is a constant; N _el is the number of electrolytic cells; For N _el and The result of multiplication; For N _el and The result of multiplication; for The result of multiplication with μ _EL,s,t ; for The result of multiplying μ _EL,s,t ; I _{el min} and I _{el max} are the minimum operating current and maximum operating current of the electrolytic cell respectively; and They represent the product of I _el,s,t and N _el under different operating conditions of the electrolytic cell; and Respectively After linear fitting with and The coefficient of correlation; and Respectively After linear fitting with and The coefficient of correlation; and is the dual variable corresponding to each formula in the linearized form of the equipment failure model of the electrolyzer;

(502) The linearized form of the fuel cell equipment failure model is as follows:

P _{FC max} =(k _fc1 ·I _{fc max} +k _fc2 )·N _fc

Where _kfc1 and _kfc2 represent the linear relationship between _PFC,s,t and INfc _s,t after linear fitting. The relevant coefficient; N _fc represents the number of fuel cells; INfc _s,t represents the product of I _fc,s,t and N _fc ; I _fcmin and I _fcmax represent the minimum operating current and maximum operating current of the fuel cell respectively; V′ _FC,s,t represents the volume of hydrogen consumed by the fuel cell under ideal conditions; represents μ _FC,s,t and The product of express The product of _Nfc ; express The product of V′ _FC,s,t ; express The product of V′ _FC,s,t ; express The product of V′ _FC,s,t ; is the dual variable corresponding to each formula in the linearized form of the equipment failure model of the fuel cell;

(503) The linearized form of the equipment failure model of the transmission line is as follows:

In the formula, represents the product of P _trans and υ _jtrans,s ; and It is the dual variable corresponding to each formula in the linearized form of the equipment failure model of the transmission line.

Furthermore, the specific process of step 6 is as follows:

(601) The part of the capacity planning model that is not affected by u _f and s _e is defined as the planning stage. The objective function of the offshore electric hydrogen system capacity planning model is as follows:

(602) The capacity planning method is a two-stage robust optimization problem, including an upper model and a lower model. The upper model is defined as an outer main problem, and the lower model is defined as an outer sub-problem. The outer main problem is as follows:

RESULT _MP ≤(R _e1 +R _h1 +R _e2 -C _com -C _wloss -C _loss )

Where, RESULT _MP is the auxiliary variable of the outer main problem, which is used to relax the objective function of the outer sub-problem; the constraints of the outer main problem include the equipment failure model of the electrolyzer, fuel cell and transmission line, power balance constraint and hydrogen storage tank constraint;

(603) The lower model is in the following form:

The constraints of the lower model include the linearized form of the equipment failure model of the electrolyzer, fuel cell and transmission line, the power balance constraint, the hydrogen storage tank constraint and the fault uncertainty set of the offshore hydrogen system. The lower model is a min-max problem. In order to solve it, the problem is transformed into a dual form based on the strong duality theory. The dual form of the lower model is defined as the inner master problem. The dual form is as follows:

π ¹ ≥1

π ² ≥1

π ³ ≥1

π ⁴ ≥ -1

π ⁵ ≥ -1π ⁶ ≥ -1

In the formula, RESULT _SP-MP is the auxiliary variable of the inner master problem. μ _EL,s,t 、μ _FC,s,t and All are integer variables, and the dual problem cannot be solved. For these variables, the initial values are given and The new dual form is as follows:

The new dual form is linearized, and after solving it, the set of fault scenarios is determined to obtain the form of the new lower-level model, which is defined as the inner-level sub-problem:

RESULT _SP-SP =max(R _e1 +R _h1 +R _e2 -C _com -C _wloss -C _loss )

Where RESULT _SP-SP is the auxiliary variable of the inner subproblem.

Furthermore, in step 7, a nested column constraint generation algorithm is used to solve the capacity planning model. The specific steps of the nested column constraint generation algorithm are as follows:

(1) Let the initial lower bound of the upper model OTL _down = -∞, the initial upper bound OTL _up = ∞, the initial number of iterations of the upper model num _OTL = 1, and the convergence gap of the upper iteration be δ _OTL ; let the initial lower bound of the lower model INL _down = -∞, the initial upper bound INL _up = ∞, the initial number of iterations of the lower model num _INL = 1, and the convergence gap of the lower iteration be δ _INL ;

(2) Given an initial fault scenario, merge it into the scenario uncertainty set, solve the outer main problem, obtain the capacity planning solution for each device, and use OTL _up = min{OTL _up ,RESULT _MP } to update the upper bound of the upper model;

(3) Input the capacity planning results obtained from the upper model into the inner main problem, set a set of preset initial values for the integer variables in the inner main problem, merge them into the set of integer variable scenarios, solve the inner main problem, use INL _down = max{INL _down ,RESULT _SP-MP } to determine the lower bound of the lower model, bring the capacity planning results and the fault scenarios solved by the inner main problem into the inner sub-problem for solution, and obtain the upper bound of the lower model INL _up = min{INL _up ,RESULT _SP-SP };

(4) Determine whether the lower model converges based on |INL _up -INL _down |≤δ _INL. If the condition is met, the optimal solution of the lower model is obtained and used as the lower bound OTL _down of the upper model, and process (5) is performed; if not, num _INL = num _INL + 1, the integer variables obtained from the inner subproblem are merged into the integer variable scenario set, and new variables and constraints are generated, and the process is returned to process (3);

(5) According to |OTL _up -OTL _down |≤δ _OTL , determine whether the upper model has converged. If the condition is not met, num _OTL = num _OTL + 1, merge the fault scenarios solved by the lower model into the scenario uncertainty set, add new variables and constraints, and return to process (2); if the condition is met, obtain the optimal solution of the upper model and proceed to process (6);

(6) Output the capacity planning results and the solution is completed.

Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

This invention applies hydrogen energy equipment to offshore wind power systems, which can store surplus wind power in the form of hydrogen energy, and can ensure power supply through fuel cells when wind power output is insufficient, which is conducive to solving the problems caused by large fluctuations in wind power output and improving the power supply guarantee capability. This invention takes into account uncertain failures during capacity planning, so that when a failure occurs in the system, the amount of load loss can be reduced as much as possible, further improving the reliability of power supply. The present invention takes into account the uncertain failures of equipment during capacity planning, reduces the load loss caused by equipment failure, and improves the reliability of power supply.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 is a flow chart of the method of the present invention;

Figure 2 is a schematic diagram of the structure of an offshore electric hydrogen system;

Figure 3 is a load diagram for fault scenario 1;

Figure 4 is a load diagram for fault scenario 2;

Figure 5 is the load diagram for fault scenario 3.

DETAILED DESCRIPTION

As shown in FIG1 , the present invention proposes a method for capacity planning of an offshore electric hydrogen system considering uncertain faults, the method comprising the following steps:

1. According to the capacity planning of electrolyzers, fuel cells, hydrogen storage tanks and transmission lines in the electric-hydrogen system and the normal operation and fault operation of the electric-hydrogen system, the objective function of the offshore electric-hydrogen system capacity planning model is constructed;

2. Establish equipment failure models for electrolyzers, fuel cells, and transmission lines;

3. Based on the equipment failure models of the electrolyzer, fuel cell and transmission line established in step 2, a failure uncertainty set of the offshore electric hydrogen system is constructed;

4. Obtain the constraint conditions of the offshore electric hydrogen system capacity planning model based on the objective function and the equipment failure model;

5 Take the objective function in step 1, the equipment failure model of the electrolyzer, fuel cell and transmission line in step 2, the failure uncertainty set of the offshore electric hydrogen system in step 3 and the constraint conditions in step 4 as the capacity planning model of the offshore electric hydrogen system, and write its linearized form;

6 Based on the linearized form of the offshore electric-hydrogen system capacity planning model proposed in step 5, write the dual form;

7 Based on the offshore electric-hydrogen system capacity planning model and its linearized form in step 5 and the dual form in step 6, the capacity planning model is solved using a nested column constraint generation algorithm, and capacity planning is performed on the model based on the solution results.

Furthermore, the specific process of step 1 is as follows:

The objective function of the offshore electric hydrogen system capacity planning model is constructed. The objective function is in the following form:

where _uf represents the uncertainty variable vector of all component states; U represents the uncertainty set of component states; s _e represents the uncertainty variable vector of all scenario states; S _sce represents the uncertainty set of scenario states; r is the discount rate; m is the operating life; P _ELmax , P _FCmax , V _hmax , and P _trans are the planned capacities of electrolyzer, fuel cell, hydrogen storage tank, and transmission line, respectively; L is the length of the submarine cable; e _k is the correlation coefficient of each equipment planning, k＝1,2,...,5, where k＝1 represents electrolyzer, k＝2 represents fuel cell, k＝3 represents hydrogen storage tank, k＝4 represents transmission line, and k＝5 represents infrastructure; e _HVDC1 and e _HVDC2 are the fixed coefficients of converter station planning and the coefficient related to the transmission line capacity, respectively; _Re1 , R _h1 , and _Re2 are the output generated by supplying power to the upper grid, the output generated by supplying hydrogen, and the output generated by supplying power to the load, respectively; C _com , C _wloss , and C _loss represents the maintenance cost required for the operation of the electric hydrogen system, the penalty caused by the unabsorbed wind power, and the penalty caused by the lost load power;

The specific expressions of some parameters in the objective function are as follows:

Wherein, s represents the scenario of system operation, and the output of wind turbines is different in different scenarios; the operation of all scenarios under s∈Ω _nor is defined as the normal operation of the electric hydrogen system, and the operation of all scenarios under s∈Ω _xtm is defined as the fault operation of the electric hydrogen system; Ω _nor is all scenarios of normal operation of the electric hydrogen system; Ω _xtm is all scenarios of fault operation of the electric hydrogen system; t represents the operation time, and T is the total number of operation times; _Ke1,t , _Kh , and _Ke2 are the relevant parameters for power supply to the upper grid, the relevant parameters for hydrogen supply, and the relevant parameters for power supply to the load, respectively; μ _loss is the transmission consumption coefficient; P _net,s,t is the power transmitted to the upper grid; V _hsell,s,t is the amount of hydrogen output to the hydrogen load; P _wload,s,t is the power supplied to the load by wind power; P _FC1,s,t is the power supplied to the load by the fuel cell; Q _k is the operation and maintenance coefficient of each device, k=1,2,...,5; Q _h1 is the operation and maintenance coefficient of the electrolyzer related to the hydrogen production; Q _h2 is the operation and maintenance coefficient of the fuel cell related to the hydrogen consumption; V _FC,s,t is the volume of hydrogen consumed by the fuel cell; V _EL,s,t is the volume of hydrogen produced by the electrolyzer at time t; P _loss,s,t and c _loss are the load loss power and the penalty coefficient for load loss, respectively; P _wloss,s,t is the wind power that is not absorbed when the scene is s and the time is t; c _wloss is the penalty coefficient for the wind power that is not absorbed; π ¹ ~π ⁶ are the dual variables corresponding to each formula.

Further, the specific process of step 2 is as follows:

(201) A fuel cell equipment failure model is established, which includes the relationship between the current and voltage in the fuel cell, the relationship between the hydrogen consumption and electricity production of the fuel cell, and the fuel cell operation constraints. The specific expression is as follows:

P′ _FC,s,t ＝2·k _f ·F·U _fc,s,t ·V _FC,s,t

μ _FC,s,t ·P _{FC min} ≤P _FC,s,t ≤μ _FC,s,t ·P _{FC max}

Wherein, U _fc,s,t and I _fc,s,t represent the operating voltage and current of the fuel cell respectively; τ ₁ , τ ₂ , τ ₃ , τ ₄ are the correlation coefficients of the electromotive force of the fuel cell; T _fc is the operating temperature of the fuel cell; and are the partial pressures of the hydrogen interface and oxygen interface of the fuel cell respectively; ξ _i is the empirical coefficient, i＝1,2,...,4; is the oxygen concentration at the cathode gas-liquid surface; J _{fc max} is the maximum current density of the fuel cell; A _fc represents the active area of the fuel cell; B is a constant coefficient; R _m is the equivalent membrane impedance; R _c is the equivalent contact resistance of the membrane; P′ _FC,s,t and P _FC,s,t are the ideal output power and actual output power of the fuel cell respectively; k _f is the unit conversion coefficient; F is the Faraday constant; represents the state of the fuel cell in scenario s, q = 1, 2, ..., 5; is the working efficiency of the fuel cell under different operating conditions; P _{FC min} is the minimum output power of the fuel cell; μ _FC,s,t is the start and stop state of the fuel cell, Respectively represent the status of the four components of the fuel cell;

(202) An electrolytic cell equipment failure model is established, which includes the relationship between the electrolytic cell's power consumption and hydrogen production, the relationship between the electrolytic cell's operating power and current, and the electrolytic cell's operating constraints. The specific expression is as follows:

Where, I _el,s,t represents the operating current of the electrolytic cell; _Tel is the operating temperature of the electrolytic cell; A _el is the effective reaction area of the electrolytic cell; U _rev is the reversible voltage of the electrolytic cell; and They represent the ohmic resistance of the alkali solution under normal operation, the ohmic resistance of the alkali solution under derating operation, and the thermal resistance coefficient of the alkali solution respectively; is the electrode overvoltage coefficient obtained by fitting; η _f is the Faraday efficiency; P _EL,s,t represents the power consumption of the electrolytic cell at time t; Indicates the power consumption of the electrolytic cell under different operating conditions, z = 1, 2, 3; P _{EL min} indicates the minimum power consumption of the electrolytic cell; Indicates the operating status of the electrolytic cell; μ _EL,s,t indicates the start and stop status of the electrolytic cell; Respectively represent the status of the two components of the electrolyzer;

(203) Equipment Failure Model of Transmission Line

When the transmission line is not faulty, the power transmitted to the upper grid must not exceed its capacity. When the transmission line fails, the electric hydrogen system will no longer be connected to the upper grid, and the power transmitted to the upper grid is 0. The capacity constraints of the transmission line considering the fault are as follows:

0≤P _net,s,t ≤υ _jtrans,s ·P _trans

Wherein, jtrans represents the faulty component in the transmission line; υ _jtrans,s represents the state of the component jtrans in the transmission line under scenario s, υ _jtrans,s = 1 indicates that the component operates normally, and υ _jtrans,s = 0 indicates that the component fails.

Furthermore, the specific process of step 3 is as follows:

Construct an uncertain set of faults for the offshore electric hydrogen system, set limits on the number of component failures in each fault scenario and the total number of failures of each component throughout the year, and set limits on the number of fault scenarios in all scenarios:

u _f = [u _jel ; u _jfc ; u _jtrans ]

where Ω _s is a set of operating scenarios; jel, jfc represent the faulty components in the electrolyzer and fuel cell, respectively; n _el , n _fc , n _trans represent the number of components in the electrolyzer, fuel cell and transmission line, respectively; λ _jel,s represents the state of component jel in the electrolyzer under scenario s, λ _jel,s = 1 represents the normal operation of the component, and λ _jel,s = 0 represents the component failure; ζ _jfc,s represents the state of component jfc in the fuel cell under scenario s, ζ _jfc,s = 1 represents the normal operation of the component, and ζ _jfc,s = 0 represents the component failure; let the number of scenarios s in Ω _xtm be N _s ; N _xtm is the upper limit of component failure in the fault scenario, and N _sce is the upper limit of the total number of component failures within one year; u _jel , u _jfc , u _jtrans are the variable vector forms of λ _jel,s , ζ _jfc,s and υ _jtrans,s, respectively; s _sce,s represents the state of scenario s.

Furthermore, the specific process of step 4 is as follows:

Establish constraints for the offshore electric-hydrogen system capacity planning model considering uncertain faults:

(401) Power balance constraint:

Where P _load,s,t is the load power; P _w,s,t and P _wnet,s,t represent the wind power generation and the power transmitted to the upper grid at time t respectively; It is the dual variable corresponding to each formula in the power balance constraint;

(402) Hydrogen storage tank constraints:

Where V _h,s,t is the gas capacity in the hydrogen storage tank; V _hload,s,t is the hydrogen load demand; V _h0 and V _hT are the hydrogen volumes in the hydrogen storage tank at the beginning and end of the period; It is the dual variable corresponding to each formula in the hydrogen storage tank constraint.

Furthermore, the specific process of step 5 is as follows:

The above-mentioned offshore electric hydrogen system capacity planning model is a nonlinear mixed integer programming problem, in which the equipment failure models of the electrolyzer, fuel cell and transmission line contain nonlinear variables. The linear form of the offshore electric hydrogen system capacity planning model is written using linear fitting and linearization processing methods;

(501) The linearized form of the equipment failure model of the electrolytic cell is as follows:

Where bigM is a constant; N _el is the number of electrolytic cells; For N _el and The result of multiplication; For N _el and The result of multiplication; for The result of multiplication with μ _EL,s,t ; for The result of multiplying μ _EL,s,t ; I _{el min} and I _{el max} are the minimum operating current and maximum operating current of the electrolytic cell respectively; and They represent the product of I _el,s,t and N _el under different operating conditions of the electrolytic cell; and Respectively After linear fitting with and The coefficient of correlation; and Respectively After linear fitting with and The coefficient of correlation; and is the dual variable corresponding to each formula in the linearized form of the equipment failure model of the electrolyzer;

(502) The linearized form of the fuel cell equipment failure model is as follows:

P _{FC max} =(k _fc1 ·I _{fc max} +k _fc2 )·N _fc

Where _kfc1 and _kfc2 represent the linear relationship between _PFC,s,t and INfc _s,t after linear fitting. The relevant coefficient; N _fc represents the number of fuel cells; INfc _s,t represents the product of I _fc,s,t and N _fc ; I _{fc min} and I _{fc max} represent the minimum operating current and maximum operating current of the fuel cell respectively; V′ _FC,s,t represents the volume of hydrogen consumed by the fuel cell under ideal conditions; represents μ _FC,s,t and The product of express The product of _Nfc ; express The product of V′ _FC,s,t ; express The product of V′ _FC,s,t ; express The product of V′ _FC,s,t ; is the dual variable corresponding to each formula in the linearized form of the equipment failure model of the fuel cell;

(503) The linearized form of the equipment failure model of the transmission line is as follows:

In the formula, represents the product of P _trans and υ _jtrans,s ; and It is the dual variable corresponding to each formula in the linearized form of the equipment failure model of the transmission line.

Furthermore, the specific process of step 6 is as follows:

(601) The part of the capacity planning model that is not affected by u _f and s _e is defined as the planning stage. The objective function of the offshore electric hydrogen system capacity planning model is as follows:

(602) The capacity planning method is a two-stage robust optimization problem, including an upper model and a lower model. The upper model is defined as an outer main problem, and the lower model is defined as an outer sub-problem. The outer main problem is as follows:

RESULT _MP ≤(R _e1 +R _h1 +R _e2 -C _com -C _wloss -C _loss )

Where, RESULT _MP is the auxiliary variable of the outer main problem, which is used to relax the objective function of the outer sub-problem; the constraints of the outer main problem include the equipment failure model of the electrolyzer, fuel cell and transmission line, power balance constraint and hydrogen storage tank constraint;

(603) The lower model is in the following form:

The constraints of the lower model include the linearized form of the equipment failure model of the electrolyzer, fuel cell and transmission line, the power balance constraint, the hydrogen storage tank constraint and the fault uncertainty set of the offshore hydrogen system. The lower model is a min-max problem. In order to solve it, the problem is transformed into a dual form based on the strong duality theory. The dual form of the lower model is defined as the inner master problem. The dual form is as follows:

π ¹ ≥1

π ² ≥1

π ³ ≥1

π ⁴ ≥ -1

π ⁵ ≥ -1

π ⁶ ≥ -1

In the formula, RESULT _SP-MP is the auxiliary variable of the inner master problem. μ _EL,s,t 、μ _FC,s,t and All are integer variables, and the dual problem cannot be solved. For these variables, the initial values are given and The new dual form is as follows:

The new dual form is linearized, and after solving it, the set of fault scenarios is determined to obtain the form of the new lower-level model, which is defined as the inner-level sub-problem:

RESULT _SP-SP =max(R _e1 +R _h1 +R _e2 -C _com -C _wloss -C _loss )

Where RESULT _SP-SP is the auxiliary variable of the inner subproblem.

Furthermore, in step 7, a nested column constraint generation algorithm is used to solve the capacity planning model. The specific steps of the nested column constraint generation algorithm are as follows:

(1) Let the initial lower bound of the upper model OTL _down = -∞, the initial upper bound OTL _up = ∞, the initial number of iterations of the upper model num _OTL = 1, and the convergence gap of the upper iteration be δ _OTL ; let the initial lower bound of the lower model INL _down = -∞, the initial upper bound INL _up = ∞, the initial number of iterations of the lower model num _INL = 1, and the convergence gap of the lower iteration be δ _INL ;

(2) Given an initial fault scenario, merge it into the scenario uncertainty set, solve the outer main problem, obtain the capacity planning solution for each device, and use OTL _up = min{OTL _up ,RESULT _MP } to update the upper bound of the upper model;

(3) Input the capacity planning results obtained from the upper model into the inner main problem, set a set of preset initial values for the integer variables in the inner main problem, merge them into the set of integer variable scenarios, solve the inner main problem, use INL _down = max{INL _down ,RESULT _SP-MP } to determine the lower bound of the lower model, bring the capacity planning results and the fault scenarios solved by the inner main problem into the inner sub-problem for solution, and obtain the upper bound of the lower model INL _up = min{INL _up ,RESULT _SP-SP };

(4) Determine whether the lower model converges based on |INL _up -INL _down |≤δ _INL. If the condition is met, the optimal solution of the lower model is obtained and used as the lower bound OTL _down of the upper model, and process (5) is performed; if not, num _INL = num _INL + 1, the integer variables obtained from the inner subproblem are merged into the integer variable scenario set, and new variables and constraints are generated, and the process is returned to process (3);

(5) According to |OTL _up -OTL _down |≤δ _OTL , determine whether the upper model has converged. If the condition is not met, num _OTL = num _OTL + 1, merge the fault scenarios solved by the lower model into the scenario uncertainty set, add new variables and constraints, and return to process (2); if the condition is met, obtain the optimal solution of the upper model and proceed to process (6);

(6) Output the capacity planning results and the solution is completed.

The typical structure of the established offshore electric hydrogen system is shown in Figure 2. The system includes wind turbines, electrolyzers, fuel cells, hydrogen storage tanks, upper power grids, and hydrogen loads.

Taking hours as the time scale, let N _xtm and N _sce be 1, and the value of N _s be 3. According to the established model, the capacity planning results of the offshore wind power-system hydrogen energy system are obtained. The results are shown in Table 1, and the load loss during the fault is shown in Table 2.

Table 1 Capacity comparison before and after optimization configuration

Table 2 Comparison of scheduling results before and after capacity optimization

The results show that after considering uncertain faults in capacity planning, the load loss during the fault period is significantly reduced compared with before optimization, proving that considering uncertain faults can effectively improve the power supply guarantee capability of the offshore hydrogen power system. The wind abandonment rate under normal circumstances before and after optimization is less than 0.3%, indicating that the optimization method does not affect the system's wind power absorption capacity.

Figures 3 to 5 show the operating conditions under the three fault scenarios determined by the present invention, among which (a) in Figures 3, 4 and 5 are the operating conditions of the electric hydrogen system when the present invention is not adopted, and (b) in Figures 3, 4 and 5 are the operating conditions of the electric hydrogen system after the present invention is adopted. Through comparative analysis, it can be seen that after adopting the present invention, the load loss of the system is significantly reduced when the electric hydrogen system fails to operate, and the output of the fuel cell has a certain increase compared to when the present invention is not adopted. This is because the increase in the capacity of the fuel cell and the hydrogen storage tank provides more electricity for the electric hydrogen system during fault operation, thereby reducing the load loss, proving the feasibility of considering uncertain faults in capacity planning.

In terms of the planned capacity of each device, after adopting this method, the capacity of the electrolyzer and the transmission line connected to the upper power grid did not change significantly, but the capacity of the fuel cell and hydrogen storage tank increased. This is because in severe fault scenarios, the wind power output is low. At this time, wind power cannot complete the task of ensuring power supply alone, and fuel cells are needed to supply power to the missing part of the power. If the fuel cell fails at this time, its power generation capacity will decrease and it may not be able to meet the requirements of full power supply. Therefore, the capacity will be appropriately increased during planning. In addition, the lack of wind power makes it impossible for the hydrogen storage tank to obtain additional hydrogen sources, and it can only increase its own capacity to ensure that there is more available hydrogen when a fault occurs.

Claims (4)

1. A method for capacity planning of an offshore electric hydrogen system considering uncertain faults, characterized in that the method comprises the following steps: (1) Based on the capacity planning of electrolyzers, fuel cells, hydrogen storage tanks and transmission lines in the electric-hydrogen system and the normal operation and fault operation of the electric-hydrogen system, the objective function of the offshore electric-hydrogen system capacity planning model is constructed; (2) Establish equipment failure models for electrolyzers, fuel cells, and transmission lines; (3) constructing a fault uncertainty set of the offshore hydrogen power system based on the equipment failure models of the electrolyzer, fuel cell and transmission line established in step (2); (4) deriving constraints of the offshore electric hydrogen system capacity planning model based on the objective function and the equipment failure model; (5) The objective function in step (1), the equipment failure models of the electrolyzer, fuel cell and transmission line in step (2), the failure uncertainty set of the offshore electric hydrogen system in step (3) and the constraints in step (4) are used as the offshore electric hydrogen system capacity planning model, and their linearized form is written; (6) Based on the linearized form of the offshore electric-hydrogen system capacity planning model proposed in step (5), write the dual form; (7) Based on the offshore electric-hydrogen system capacity planning model in step (5) and its linearized form and the dual form in step (6), the capacity planning model is solved using a nested column constraint generation algorithm, and capacity planning is performed on the model according to the solution result; The specific process of step (1) is as follows: The objective function of the offshore electric hydrogen system capacity planning model is constructed. The objective function is in the following form: where _uf represents the uncertainty variable vector of all component states; U represents the uncertainty set of component states; s _e represents the uncertainty variable vector of all scenario states; S _sce represents the uncertainty set of scenario states; r is the discount rate; m is the operating life; P _ELmax , P _FCmax , V _hmax , and P _trans are the planned capacities of electrolyzer, fuel cell, hydrogen storage tank, and transmission line, respectively; L is the length of the submarine cable; e _k is the correlation coefficient of each equipment planning, k = 1, 2, …, 5, where k = 1 represents electrolyzer, k = 2 represents fuel cell, k = 3 represents hydrogen storage tank, k = 4 represents transmission line, and k = 5 represents infrastructure; e _HVDC1 and e _HVDC2 are the fixed coefficients of converter station planning and the coefficient related to the transmission line capacity, respectively; _Re1 , R _h1 , and _Re2 are the output generated by supplying power to the upper grid, the output generated by supplying hydrogen, and the output generated by supplying power to the load, respectively; C _com , C _wloss , and C _loss represents the maintenance cost required for the operation of the electric hydrogen system, the penalty caused by the unabsorbed wind power, and the penalty caused by the lost load power; The specific expressions of some parameters in the objective function are as follows: Wherein, s represents the scenario of system operation, and the output of wind turbines is different in different scenarios; the operation of all scenarios under s∈Ω _nor is defined as the normal operation of the electric hydrogen system, and the operation of all scenarios under s∈Ω _xtm is defined as the fault operation of the electric hydrogen system; Ω _nor is all scenarios of the normal operation of the electric hydrogen system; Ω _xtm is all scenarios of the fault operation of the electric hydrogen system; t represents the operation time, and T is the total number of operation times; _Ke1,t , _Kh , and _Ke2 are the relevant parameters for power supply to the upper power grid, the relevant parameters for hydrogen supply, and the relevant parameters for power supply to the load, respectively; μ _loss is the transmission consumption coefficient; P _net,s,t is the power transmitted to the upper power grid; V _hsell,s,t is the amount of hydrogen output to the hydrogen load; P _wload,s,t is the power supplied to the load by wind power; P _FC1,s,t is the power supplied to the load by the fuel cell; Q _k is the operation and maintenance coefficient of each device, k=1,2,…,5; Q _h1 is the operation and maintenance coefficient of the electrolyzer related to the hydrogen production; Q _h2 is the operation and maintenance coefficient of the fuel cell related to the hydrogen consumption; V _FC,s,t is the volume of hydrogen consumed by the fuel cell; V _EL,s,t is the volume of hydrogen produced by the electrolyzer at time t; P _loss,s,t and c _loss are the load loss power and the penalty coefficient of load loss respectively; P _wloss,s,t is the wind power that is not absorbed when the scene is s and the time is t; c _wloss is the penalty coefficient of the wind power that is not absorbed; π ¹ :π ⁶ are the dual variables corresponding to each formula; The specific process of step (2) is as follows: (201) A fuel cell equipment failure model is established, which includes the relationship between the current and voltage in the fuel cell, the relationship between the hydrogen consumption and electricity production of the fuel cell, and the fuel cell operation constraints. The specific expression is as follows: P _F ' _C,s,t ＝2·k _f ·F·U _fc,s,t ·V _FC,s,t μ _FC,s,t ·P _FCmin ≤P _FC,s,t ≤μ _FC,s,t ·P _FCmax Wherein, U _fc,s,t and I _fc,s,t represent the operating voltage and current of the fuel cell respectively; τ ₁ , τ ₂ , τ ₃ , τ ₄ are the correlation coefficients of the electromotive force of the fuel cell; T _fc is the operating temperature of the fuel cell; and are the partial pressures of the hydrogen interface and oxygen interface of the fuel cell respectively; ξ _i is the empirical coefficient, i = 1, 2, …, 4; is the oxygen concentration at the cathode gas-liquid surface; J _fcmax is the maximum current density of the fuel cell; A _fc represents the active area of the fuel cell; B is a constant coefficient; R _m is the equivalent membrane impedance; R _c is the equivalent contact resistance of the membrane; P _F ' _C,s,t and P _FC,s,t are the ideal output power and actual output power of the fuel cell respectively; k _f is the unit conversion coefficient; F is the Faraday constant; represents the state of the fuel cell in scenario s, q = 1, 2, …, 5; is the working efficiency of the fuel cell under different operating conditions; P _FCmin is the minimum output power of the fuel cell; μ _FC,s,t is the start and stop state of the fuel cell, Respectively represent the status of the four components of the fuel cell; (202) An electrolytic cell equipment failure model is established, which includes the relationship between the electrolytic cell's power consumption and hydrogen production, the relationship between the electrolytic cell's operating power and current, and the electrolytic cell's operating constraints. The specific expression is as follows: Where, I _el,s,t represents the operating current of the electrolytic cell; _Tel is the operating temperature of the electrolytic cell; A _el is the effective reaction area of the electrolytic cell; U _rev is the reversible voltage of the electrolytic cell; and They represent the ohmic resistance of the alkali solution under normal operation, the ohmic resistance of the alkali solution under derating operation, and the thermal resistance coefficient of the alkali solution respectively; is the electrode overvoltage coefficient obtained by fitting; η _f is the Faraday efficiency; P _EL,s,t represents the power consumption of the electrolytic cell at time t; Indicates the power consumption of the electrolytic cell under different operating conditions, z = 1, 2, 3; P _ELmin indicates the minimum power consumption of the electrolytic cell; Indicates the operating status of the electrolytic cell; μ _EL,s,t indicates the start and stop status of the electrolytic cell; Respectively represent the status of the two components of the electrolyzer; (203) Equipment Failure Model of Transmission Line When the transmission line is not faulty, the power transmitted to the upper grid must not exceed its capacity. When the transmission line fails, the electric hydrogen system will no longer be connected to the upper grid, and the power transmitted to the upper grid is 0. The capacity constraints of the transmission line considering the fault are as follows: 0≤P _net,s,t ≤υ _jtrans,s ·P _trans Wherein, jtrans represents the faulty component in the transmission line; υ _jtrans,s represents the state of the component jtrans in the transmission line under scenario s, υ _jtrans,s = 1 indicates that the component operates normally, and υ _jtrans,s = 0 indicates that the component fails; The specific process of step 3 is as follows: Construct an uncertain set of faults for the offshore electric hydrogen system, set limits on the number of component failures in each fault scenario and the total number of failures of each component throughout the year, and set limits on the number of fault scenarios in all scenarios: u _f = [u _jel ; u _jfc ; u _jtrans ] Wherein, Ω _s is a set of operating scenarios; jel, jfc represent the faulty components in the electrolyzer and fuel cell, respectively; n _el , n _fc , n _trans represent the number of components in the electrolyzer, fuel cell and transmission line, respectively; λ _jel,s represents the state of component jel in the electrolyzer under scenario s, λ _jel,s = 1 represents the normal operation of the component, and λ _jel,s = 0 represents the component failure; ζ _jfc,s represents the state of component jfc in the fuel cell under scenario s, ζ _jfc,s = 1 represents the normal operation of the component, and ζ _jfc,s = 0 represents the component failure; let the number of scenarios s in Ω _xtm be N _s ; N _xtm is the upper limit of component failure in the fault scenario, and N _sce is the upper limit of the total number of component failures within one year; u _jel , u _jfc , u _jtrans are the variable vector forms of λ _jel,s , ζ _jfc,s and υ _jtrans,s, respectively; s _sce,s represents the state of scenario s; The specific process of step 4 is as follows: Establish constraints for the offshore electric-hydrogen system capacity planning model considering uncertain faults: (401) Power balance constraint: Where P _load,s,t is the load power; P _w,s,t and P _wnet,s,t represent the wind power generation and the power transmitted to the upper grid at time t respectively; It is the dual variable corresponding to each formula in the power balance constraint; (402) Hydrogen storage tank constraints: Where V _h,s,t is the gas capacity in the hydrogen storage tank; V _hload,s,t is the hydrogen load demand; V _h0 and V _hT are the hydrogen volumes in the hydrogen storage tank at the beginning and end of the period; It is the dual variable corresponding to each formula in the hydrogen storage tank constraint. 2. According to the method for capacity planning of an offshore electric hydrogen system considering uncertain faults in claim 1, the specific process of step 5 is as follows: The above-mentioned offshore electric hydrogen system capacity planning model is a nonlinear mixed integer programming problem, in which the equipment failure models of the electrolyzer, fuel cell and transmission line contain nonlinear variables. The linear form of the offshore electric hydrogen system capacity planning model is obtained by using linear fitting and linearization processing methods; (501) The linearized form of the equipment failure model of the electrolytic cell is as follows: Where bigM is a constant; N _el is the number of electrolytic cells; For N _el and The result of multiplication; For N _el and The result of multiplication; for The result of multiplication with μ _EL,s,t ; is the product of κ _EL,n2,s and μ _EL,s,t ; I _elmin and I _elmax are the minimum operating current and maximum operating current of the electrolytic cell respectively; and They represent the product of I _el,s,t and N _el under different operating conditions of the electrolytic cell; and Respectively After linear fitting with and The coefficient of correlation; and Respectively After linear fitting with and The coefficient of correlation; and is the dual variable corresponding to each formula in the linearized form of the equipment failure model of the electrolyzer; (502) The linearized form of the fuel cell equipment failure model is as follows: Where _kfc1 and _kfc2 represent the linear relationship between _PFC,s,t and INfc _s,t after linear fitting. The relevant coefficient; N _fc represents the number of fuel cells; INfc _s,t represents the product of I _fc,s,t and N _fc ; I _fcmin and I _fcmax represent the minimum operating current and maximum operating current of the fuel cell respectively; V′ _FC,s,t represents the volume of hydrogen consumed by the fuel cell under ideal conditions; represents μ _FC,s,t and The product of express The product of _Nfc ; represents the product of ζ _jfc4,s and V′ _FC,s,t ; express The product of V′ _FC,s,t ; express The product of V′ _FC,s,t ; is the dual variable corresponding to each formula in the linearized form of the equipment failure model of the fuel cell; (503) The linearized form of the equipment failure model of the transmission line is as follows: In the formula, represents the product of P _trans and υ _jtrans,s ; and It is the dual variable corresponding to each formula in the linearized form of the equipment failure model of the transmission line. 3. According to the method for capacity planning of an offshore electric hydrogen system considering uncertain faults in claim 2, the specific process of step 6 is as follows: (601) The part of the capacity planning model that is not affected by u _f and s _e is defined as the planning stage. The objective function of the offshore electric hydrogen system capacity planning model is as follows: (602) The capacity planning method is a two-stage robust optimization problem, including an upper model and a lower model. The upper model is defined as an outer main problem, and the lower model is defined as an outer sub-problem. The outer main problem is as follows: RESULT _MP ≤(R _e1 +R _h1 +R _e2 -C _com -C _wloss -C _loss ) Where, RESULT _MP is the auxiliary variable of the outer main problem, which is used to relax the objective function of the outer sub-problem; the constraints of the outer main problem include the equipment failure model of the electrolyzer, fuel cell and transmission line, power balance constraint and hydrogen storage tank constraint; (603) The lower model is in the following form: The constraints of the lower model include the linearized form of the equipment failure model of the electrolyzer, fuel cell and transmission line, the power balance constraint, the hydrogen storage tank constraint and the fault uncertainty set of the offshore hydrogen system. The lower model is a min-max problem. In order to solve it, the problem is transformed into a dual form based on the strong duality theory. The dual form of the lower model is defined as the inner master problem. The dual form is as follows: In the formula, RESULT _SP-MP is the auxiliary variable of the inner master problem. μ _EL,s,t 、μ _FC,s,t and All are integer variables, and the dual problem cannot be solved. For these variables, the initial values are given and The new dual form is as follows: The new dual form is linearized, and after solving it, the set of fault scenarios is determined to obtain the form of the new lower-level model, which is defined as the inner-level sub-problem: RESULT _SP-SP =max(R _e1 +R _h1 +R _e2 -C _com -C _wloss -C _loss ) Where RESULT _SP-SP is the auxiliary variable of the inner subproblem. 4. According to the method for capacity planning of an offshore electric hydrogen system considering uncertain faults in claim 3, it is characterized in that in step 7, a nested column constraint generation algorithm is used to solve the capacity planning model, and the specific steps of the nested column constraint generation algorithm are as follows: (1) Let the initial lower bound of the upper model OTL _down = -∞, the initial upper bound OTL _up = ∞, the initial number of iterations of the upper model num _OTL = 1, and the convergence gap of the upper iteration be δ _OTL ; let the initial lower bound of the lower model INL _down = -∞, the initial upper bound INL _up = ∞, the initial number of iterations of the lower model num _INL = 1, and the convergence gap of the lower iteration be δ _INL ; (2) Given an initial fault scenario, merge it into the scenario uncertainty set, solve the outer main problem, obtain the capacity planning solution for each device, and use OTL _up = min{OTL _up ,RESULT _MP } to update the upper bound of the upper model; (3) Input the capacity planning results obtained from the upper model into the inner main problem, set a set of preset initial values for the integer variables in the inner main problem, merge them into the set of integer variable scenarios, solve the inner main problem, use INL _down = max{INL _down ,RESULT _SP-MP } to determine the lower bound of the lower model, bring the capacity planning results and the fault scenarios solved by the inner main problem into the inner sub-problem for solution, and obtain the upper bound of the lower model INL _up = min{INL _up ,RESULT _SP-SP }; (4) Determine whether the lower model converges based on |INL _up -INL _down |≤δ _INL. If the condition is met, the optimal solution of the lower model is obtained and used as the lower bound OTL _down of the upper model, and process (5) is performed; if not, num _INL = num _INL + 1, the integer variables obtained from the inner subproblem are merged into the integer variable scenario set, and new variables and constraints are generated, and the process is returned to process (3); (5) According to |OTL _up -OTL _down |≤δ _OTL , determine whether the upper model has converged. If the condition is not met, num _OTL = num _OTL + 1, merge the fault scenarios solved by the lower model into the scenario uncertainty set, add new variables and constraints, and return to process (2); if the condition is met, obtain the optimal solution of the upper model and proceed to process (6); (6) Output the capacity planning results and the solution is completed.