CN117200265B - Marine electro-hydrogen system capacity planning method considering uncertainty fault - Google Patents
Marine electro-hydrogen system capacity planning method considering uncertainty fault Download PDFInfo
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- 239000001257 hydrogen Substances 0.000 title claims abstract description 178
- 229910052739 hydrogen Inorganic materials 0.000 title claims abstract description 178
- 238000000034 method Methods 0.000 title claims abstract description 79
- UFHFLCQGNIYNRP-UHFFFAOYSA-N Hydrogen Chemical compound [H][H] UFHFLCQGNIYNRP-UHFFFAOYSA-N 0.000 claims abstract description 129
- 239000000446 fuel Substances 0.000 claims abstract description 119
- 230000005540 biological transmission Effects 0.000 claims abstract description 50
- 230000009977 dual effect Effects 0.000 claims abstract description 46
- 238000003860 storage Methods 0.000 claims description 33
- 238000012423 maintenance Methods 0.000 claims description 12
- 238000004519 manufacturing process Methods 0.000 claims description 10
- 239000013598 vector Substances 0.000 claims description 9
- 238000005457 optimization Methods 0.000 claims description 7
- 238000010248 power generation Methods 0.000 claims description 7
- 239000003513 alkali Substances 0.000 claims description 6
- QVGXLLKOCUKJST-UHFFFAOYSA-N atomic oxygen Chemical compound [O] QVGXLLKOCUKJST-UHFFFAOYSA-N 0.000 claims description 6
- 238000006243 chemical reaction Methods 0.000 claims description 6
- 230000005611 electricity Effects 0.000 claims description 6
- 239000007789 gas Substances 0.000 claims description 6
- 239000001301 oxygen Substances 0.000 claims description 6
- 229910052760 oxygen Inorganic materials 0.000 claims description 6
- 101100001674 Emericella variicolor andI gene Proteins 0.000 claims description 3
- 230000020411 cell activation Effects 0.000 claims description 3
- 125000004435 hydrogen atom Chemical group [H]* 0.000 claims description 3
- 239000012528 membrane Substances 0.000 claims description 3
- 238000003672 processing method Methods 0.000 claims description 3
- 230000002441 reversible effect Effects 0.000 claims description 3
- 238000010586 diagram Methods 0.000 description 4
- 230000009286 beneficial effect Effects 0.000 description 3
- 238000010521 absorption reaction Methods 0.000 description 1
- 238000010835 comparative analysis Methods 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000004146 energy storage Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
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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
Technical Field
The invention relates to the field of capacity planning, in particular to a method for planning the capacity of an offshore electro-hydrogen system by considering uncertainty faults.
Background
Clean energy gradually dominates at the power generation end, wherein wind power generation is one of the main forms of new energy power generation. As the offshore wind power resources are sufficient, the planning capacity of the offshore wind turbine is continuously increased and gradually develops towards the middle and open sea. However, wind power has uncertainty and fluctuation, so that the wind power output at different wind speeds is very different, and the phenomenon of wind abandoning or load abandoning can be caused, so that the stability of the power grid is influenced.
At present, as hydrogen production and hydrogen energy storage technologies are mature continuously, the feasibility of the hydrogen energy system in power supply guarantee is realized, and the system converts surplus wind power into hydrogen through an electrolytic tank and stores the hydrogen into a hydrogen storage tank. The hydrogen can be supplied to hydrogen load, and can be converted into electric energy through a fuel cell when the wind power output is insufficient so as to ensure power supply. The system can effectively improve the wind power absorption capacity and the power supply guarantee capacity. However, offshore electro-hydrogen systems still have the following problems: the capacity planning is carried out without considering whether the system can reliably supply power or not after the equipment fails, and the consumption is realized.
Disclosure of Invention
Technical problems: the invention provides a capacity planning method of an offshore electro-hydrogen system considering uncertainty faults, which mainly relates to capacity planning of the offshore electro-hydrogen system considering equipment faults and considers the uncertainty of faulty equipment.
The technical scheme is as follows: in order to solve the technical problems, the invention provides a capacity planning method of an offshore electro-hydrogen system considering uncertainty faults, which comprises the following steps:
1, constructing an objective function of a capacity planning model of an offshore hydrogen system according to capacity planning of an electrolytic tank, a fuel cell, a hydrogen storage tank and a power transmission line in the hydrogen system and normal operation and fault operation of the hydrogen system;
2, establishing equipment fault models of the electrolytic tank, the fuel cell and the power transmission line;
3, constructing a fault uncertainty set of the offshore electro-hydrogen system based on the equipment fault models of the electrolytic tank, the fuel cell and the power transmission line, which are established in the step 2;
4, obtaining constraint conditions of the capacity planning model of the offshore hydrogen system according to the objective function and the equipment fault model;
5, taking the objective function in the step 1, the equipment fault model of the electrolytic tank, the fuel cell and the power transmission line in the step 2, the fault uncertainty set of the offshore hydrogen system in the step 3 and the constraint condition in the step 4 as a capacity planning model of the offshore hydrogen system, and writing out a linearization form of the model;
6 writing a dual form based on the linearization form of the capacity planning model of the offshore hydrogen system proposed in the step 5;
And 7, solving the capacity planning model by using a nested column constraint generation algorithm based on the capacity planning model of the offshore hydrogen system in the step 5 and the linearization form and the dual form in the step 6, and carrying out capacity planning on the model according to a solving result.
Further, the specific process of step 1 is as follows:
An objective function of a capacity planning model of the offshore hydrogen system is constructed, and the form of the objective function is as follows:
Where u f represents the uncertainty variable vector for all component states; u represents the uncertainty set of the component state; s e represents the uncertainty variable vectors for all scene states; s sce represents a set of uncertainty of the scene state; r is the discount rate; m is the operational life; p ELmax、PFCmax、Vhmax、Ptrans is the planning capacity of the electrolytic tank, the fuel cell, the hydrogen storage tank and the power transmission line respectively; l is the sea cable length; e k is a correlation coefficient planned for each device, k=1, 2,..5, where k=1 represents an electrolyzer, k=2 represents a fuel cell, k=3 represents a hydrogen storage tank, k=4 represents a power line, and k=5 represents an infrastructure; e HVDC1 and e HVDC2 are fixed coefficients for converter station planning and coefficients related to the power line capacity, respectively; r e1、Rh1、Re2 is the output quantity generated by supplying power to an upper-layer power grid, and the output quantity generated by supplying hydrogen and the output quantity generated by supplying power to a load respectively; c com、Cwloss、Closs respectively represents maintenance cost required by the operation of the electro-hydrogen system, penalty caused by wind power which is not consumed and penalty caused by load loss power;
the specific expression of part of the parameters in the objective function is as follows:
In the formula, s represents a scene of system operation, and the output of the wind turbine generator is different in different scenes; the operation of all scenes under s epsilon omega nor is defined as the normal operation of the electro-hydrogen system, and the operation of all scenes under s epsilon omega xtm is defined as the fault operation of the electro-hydrogen system; omega nor is all scenes in which the electro-hydrogen system is operating normally; omega xtm is all scenes of fault operation of the electro-hydrogen system; t represents the running time, and T is the total running time number; k e1,t、Kh、Ke2 is related parameters for supplying power to an upper power grid, and related parameters for supplying hydrogen and related parameters for supplying power to loads; mu loss is the power transmission consumption coefficient; p net,s,t is the power delivered to the upper grid; v hsell,s,t is the amount of hydrogen output to the hydrogen load; p wload,s,t is used for supplying load power for wind power; p FC1,s,t is the power supplied by the fuel cell to the load; 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 electrolytic cell related to 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 fuel cell consumed hydrogen volume; v EL,s,t represents the hydrogen production volume of the electrolytic cell at the time t; p loss,s,t and c loss are penalty coefficients of no-load power and no-load respectively; p wloss,s,t represents the wind power which is not consumed when the scene is s and the moment is t; c wloss is penalty coefficient of wind power which is not consumed; pi 1～π6 is the corresponding dual variable of each formula.
Further, the specific process of step 2 is as follows:
(201) The method comprises the steps of establishing a device fault model of the fuel cell, wherein the device fault model comprises a relation between current and voltage in the fuel cell, a relation between hydrogen consumption and electricity generation of the fuel cell and a fuel cell operation constraint, and the device fault model is specifically expressed as follows:
μFC,s,t·PFC min≤PFC,s,t≤μFC,s,t·PFC max
wherein U fc,s,t and I fc,s,t represent the operating voltage and current of the fuel cell, respectively; correlation coefficient of fuel cell electromotive force τ 1、τ2、τ3、τ4; t fc is the fuel cell operating temperature; And/> The partial pressures of a hydrogen interface and an oxygen interface of the fuel cell are respectively; ζ i is an empirical coefficient, i=1, 2, 4; /(I)Oxygen concentration at the cathode gas level; j fc max is the maximum current density of the fuel cell; a fc represents the fuel cell activation area; b is a constant coefficient; r m is equivalent membrane impedance; r c is the equivalent contact resistance of the film; p' FC,s,t and P FC,s,t are the ideal output power and the actual output power of the fuel cell, respectively; k f is a unit conversion coefficient; f is Faraday constant; /(I)Represents the state in which the fuel cell is in the scene s, q=1, 2,..5; /(I)The working efficiency of the fuel cell under different running states is shown; p FC min is the minimum value of the fuel cell output power; mu FC,s,t is the start-stop state of the fuel cell,Respectively representing the states of four components of the fuel cell;
(202) The method comprises the steps of establishing an equipment fault model of the electrolytic cell comprising the relation between electricity consumption and hydrogen production of the electrolytic cell, the relation between operating power and current of the electrolytic cell and the operation constraint of the electrolytic cell, wherein the equipment fault model is specifically expressed as follows:
wherein I el,s,t represents the operating current of the electrolytic cell; t el 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 electrolyzer; And/> Respectively representing the ohmic resistance of the alkali liquor under normal operation and the ohmic resistance and the thermal coefficient of the alkali liquor under derated operation; /(I)Fitting the obtained electrode overvoltage coefficient; η f is the Faraday efficiency; p EL,s,t represents the power consumption of the electrolytic tank at the time t; /(I)Representing the power consumption of the electrolytic cell under different operating conditions, z=1, 2,3; p EL min represents the minimum value of the cell power consumption; /(I)Indicating the operating state of the electrolyzer; mu EL,s,t represents the start-stop state of the electrolytic cell; /(I)Respectively representing the states of two components of the electrolytic cell;
(203) Equipment fault model of power transmission line
When the transmission line does not fail, the power required to be transmitted to the upper power grid cannot exceed the capacity of the upper power grid; when the power transmission line fails, the electro-hydrogen system is not connected with the upper power grid any more, the power transmitted to the upper power grid is 0, and the capacity constraint of the power transmission line considering the failure is as follows:
0≤Pnet,s,t≤υjtrans,s·Ptrans
Wherein jtrans represents a faulty component in the power line; v jtrans,s represents the state of the component jtrans in the transmission line under the scene s, v jtrans,s =1 represents the normal operation of the component, and v jtrans,s =0 represents the failure of the component.
Further, the specific process of step 3 is as follows:
constructing a fault uncertainty set of the offshore electro-hydrogen system, limiting the number of component faults in each fault scene and the total number of times that each component breaks down all the year round, and limiting the number of fault scenes in all the scenes:
uf＝[ujel;ujfc;ujtrans]
Wherein omega s is an operation scene set; jel, jfc represent components of the electrolyzer and the fuel cell, respectively, that fail; n el,nfc,ntrans represents the number of components in the electrolytic cell, fuel cell and power line; lambda jel,s represents the condition of the component jel in the electrolytic cell in the field s, lambda jel,s =1 represents the normal operation of the component, and lambda jel,s =0 represents the failure of the component; ζ jfc,s represents the state of the component jfc in the fuel cell under the condition s, ζ jfc,s =1 represents the normal operation of the component, and ζ jfc,s =0 represents the failure of the component; let the number of scenes s in omega xtm be N s;Nxtm as the upper limit of the component faults in the fault scene, and N sce as the upper limit of the total number of faults of the component in one year; u jel,ujfc,ujtrans is the variable vector form of lambda jel,s、ζjfc,s and v jtrans,s respectively; s sce,s denotes the state of scene s.
Further, the specific process of step 4 is as follows:
establishing constraint conditions of a capacity planning model of the offshore electro-hydrogen system considering uncertainty faults:
(401) Power balance constraint:
Wherein P load,s,t is the load power; p w,s,t and P wnet,s,t respectively represent the power generation amount of the wind power at the moment t and the power of the wind power transmitted to an upper grid; The method comprises the steps of (1) setting a pair variable corresponding to each formula in power balance constraint;
(402) Hydrogen storage tank restraint:
Wherein V h,s,t is the gas capacity in the hydrogen storage tank; v hload,s,t is hydrogen load demand; v h0 and V hT are the hydrogen volumes of the hydrogen storage tanks at the beginning and end periods; Is a dual variable corresponding to each formula in the constraint of the hydrogen storage tank.
Further, the specific process of step 5 is as follows:
the capacity planning model of the offshore hydrogen system is a nonlinear mixed integer planning problem, wherein equipment fault models of an electrolytic tank, a fuel cell and a power transmission line comprise nonlinear variables, and a linearization form of the capacity planning model of the offshore hydrogen system is written by adopting a linear fitting and linearization processing method;
(501) The linearization of the plant failure model of the electrolyzer is as follows:
Wherein bigM is a constant; n el is the number of electrolytic cells; N el and/> The result of the multiplication; /(I)N el andThe result of the multiplication; /(I)ForA result of multiplication with mu EL,s,t; /(I)ForA result of multiplication with mu EL,s,t; i el min and I el max are respectively the minimum operating current and the maximum operating current of the electrolytic cell; /(I)AndRespectively representing the products of I el,s,t and N el of the electrolytic tank under different running states; /(I)AndRespectively expressAnd/>, after linear fittingAndThe associated coefficients; /(I)AndRespectively expressAnd/>, after linear fittingAndThe associated coefficients; /(I)And (3) withThe method is characterized in that the method is a dual variable corresponding to each formula in a linearization form of an equipment fault model of the electrolytic tank;
(502) The linearization of the device failure model of the fuel cell is as follows:
PFC max＝(kfc1·Ifc max+kfc2)·Nfc
Wherein k fc1 and k fc2 represent P FC,s,t, respectively, and INfc s,t after linear fitting The associated coefficients; 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 a minimum operating current and a maximum operating current of the fuel cell, respectively; v' FC,s,t represents the hydrogen volume consumed by the fuel cell under ideal conditions; /(I)Represents mu FC,s,t andIs a product of (2); /(I)RepresentationProduct with N fc; /(I)RepresentationProduct with V' FC,s,t; /(I)RepresentationProduct with V' FC,s,t; /(I)RepresentationProduct with V' FC,s,t; /(I)The method is characterized in that the method is a dual variable corresponding to each formula in a linearization form of an equipment fault model of the fuel cell;
(503) The linearization of the equipment failure model of the transmission line is as follows:
In the method, in the process of the invention, Represents the product of P trans and v jtrans,s; /(I)AndIs a dual variable corresponding to each formula in the linearization form of the equipment fault model of the transmission line.
Further, the specific process of step 6 is as follows:
(601) The part of the capacity planning model, which is not affected by u f and s e, is defined as a planning stage, and the form of the objective function of the capacity planning model of the offshore hydrogen system is as follows:
(602) The capacity planning method is a two-stage robust optimization problem and comprises an upper model and a lower model, wherein the upper model is defined as an outer layer main problem, the lower model is defined as an outer layer sub-problem, and the outer layer main problem is as follows:
RESULTMP≤(Re1+Rh1+Re2-Ccom-Cwloss-Closs)
Wherein RESULT MP is an auxiliary variable of the outer layer main problem and acts as relaxation of the outer layer sub-problem objective function; the constraints of the outer main problems comprise equipment fault models of an electrolytic tank, a fuel cell and a power transmission line, power balance constraints and hydrogen storage tank constraints;
(603) The form of the lower model is as follows:
the constraint of the lower model comprises linearization forms of equipment fault models of an electrolytic tank, a fuel cell and a power transmission line, power balance constraint, hydrogen storage tank constraint and a fault uncertainty set of an offshore electric hydrogen system, the lower model is a min-max problem, the problem is converted into a dual form based on a strong dual theory for solving, the dual form of the lower model is defined as an inner layer main problem, and the dual form is as follows:
π1≥1
π2≥1
π3≥1
π4≥-1
π5≥-1π6≥-1
Wherein RESULT SP-MP is an auxiliary variable to the primary problem of the inner layer, due to the dual form Mu EL,s,t、μFC,s,t andAre integer variables, the dual problem cannot be solved, and initial values/> are respectively given to the variables AndThe new dual form is as follows:
Linearizing the new dual form, solving and determining a fault scene set to obtain a new lower model form, and defining the new lower model form as an inner layer sub-problem:
RESULTSP-SP＝max(Re1+Rh1+Re2-Ccom-Cwloss-Closs)
Wherein RESULT SP-SP is an auxiliary variable to the inner layer sub-problem.
In step 7, a nested column constraint generating algorithm is adopted to solve the capacity planning model, and the specific steps of the nested column constraint generating algorithm are as follows:
(1) Let the initial lower bound OTL down = - ≡of the upper layer model, the initial upper bound OTL up = -infinity, the initial iteration number num OTL =1 of the upper layer model, the convergence gap of the upper layer iteration is delta OTL; an initial lower bound INL down = - +_infinity, an initial upper bound INL up = infinity, an initial iteration number num INL =1 of the lower model, and a convergence gap of the lower iteration is delta INL;
(2) Giving an initial fault scene, merging the initial fault scene into a scene uncertainty set, solving an outer layer main problem to obtain a capacity planning scheme of each device, and updating the upper bound of an upper model by using an OTL up＝min{OTLup,RESULTMP;
(3) Inputting a capacity planning result obtained by an upper layer model into an inner layer main problem, setting a group of preset initial values for integer variables in the inner layer main problem, merging the initial values into an integer variable scene set, solving the inner layer main problem, determining the lower boundary of a lower layer model by utilizing INL down＝max{INLdown,RESULTSP-MP, and carrying the capacity planning result and a fault scene solved by the inner layer main problem into an inner layer sub-problem to solve the inner layer sub-problem to obtain an upper boundary INL up＝min{INLup,RESULTSP-SP of the lower layer model;
(4) Judging whether the lower model is converged or not according to the |INL up-INLdown|≤δINL, if the condition is met, obtaining an optimal solution of the lower model and taking the optimal solution as a lower bound OTL down of the upper model, and performing the process (5); if not, num INL＝numINL +1 is merged into the integer variable scene set, new variables and constraints are generated, and the process returns to the process (3);
(5) Judging whether the upper model is converged according to the |OTL up-OTLdown|≤δOTL, if the condition is not met, num OTL＝numOTL +1, merging the fault scene solved by the lower model into a scene uncertainty set, adding new variables and constraints, and returning to the process (2); if yes, obtaining an optimal solution of the upper model, and performing a process (6);
(6) And outputting a capacity planning result, and ending the solving.
The beneficial effects are that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
The invention applies the hydrogen energy equipment to the offshore wind power system, can store surplus wind power in the form of hydrogen energy, can ensure power supply through the fuel cell when the wind power output is insufficient, is beneficial to solving the problem caused by large fluctuation of the wind power output, and improves the power supply guarantee capability. The invention considers uncertainty fault in capacity planning, so that the load loss can be reduced as much as possible when the fault occurs in the system, and the power supply reliability is further improved. According to the invention, uncertain faults of equipment are considered in capacity planning, so that the load loss caused by equipment faults is reduced, and the power supply reliability is improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of an offshore electro-hydrogen system;
FIG. 3 is a fault scenario 1 load diagram;
FIG. 4 is a fault scenario 2 load diagram;
fig. 5 is a fault scenario 3 load diagram.
Detailed Description
As shown in fig. 1, the present invention proposes a capacity planning method of an offshore hydrogen system considering an uncertainty fault, the method comprising the steps of:
1, constructing an objective function of a capacity planning model of an offshore hydrogen system according to capacity planning of an electrolytic tank, a fuel cell, a hydrogen storage tank and a power transmission line in the hydrogen system and normal operation and fault operation of the hydrogen system;
2, establishing equipment fault models of the electrolytic tank, the fuel cell and the power transmission line;
3, constructing a fault uncertainty set of the offshore electro-hydrogen system based on the equipment fault models of the electrolytic tank, the fuel cell and the power transmission line, which are established in the step 2;
4, obtaining constraint conditions of the capacity planning model of the offshore hydrogen system according to the objective function and the equipment fault model;
5, taking the objective function in the step 1, the equipment fault model of the electrolytic tank, the fuel cell and the power transmission line in the step 2, the fault uncertainty set of the offshore hydrogen system in the step 3 and the constraint condition in the step 4 as a capacity planning model of the offshore hydrogen system, and writing out a linearization form of the model;
6 writing a dual form based on the linearization form of the capacity planning model of the offshore hydrogen system proposed in the step 5;
And 7, solving the capacity planning model by using a nested column constraint generation algorithm based on the capacity planning model of the offshore hydrogen system in the step 5 and the linearization form and the dual form in the step 6, and carrying out capacity planning on the model according to a solving result.
Further, the specific process of step 1 is as follows:
An objective function of a capacity planning model of the offshore hydrogen system is constructed, and the form of the objective function is as follows:
Where u f represents the uncertainty variable vector for all component states; u represents the uncertainty set of the component state; s e represents the uncertainty variable vectors for all scene states; s sce represents a set of uncertainty of the scene state; r is the discount rate; m is the operational life; p ELmax、PFCmax、Vhmax、Ptrans is the planning capacity of the electrolytic tank, the fuel cell, the hydrogen storage tank and the power transmission line respectively; l is the sea cable length; e k is a correlation coefficient planned for each device, k=1, 2,..5, where k=1 represents an electrolyzer, k=2 represents a fuel cell, k=3 represents a hydrogen storage tank, k=4 represents a power line, and k=5 represents an infrastructure; e HVDC1 and e HVDC2 are fixed coefficients for converter station planning and coefficients related to the power line capacity, respectively; r e1、Rh1、Re2 is the output quantity generated by supplying power to an upper-layer power grid, and the output quantity generated by supplying hydrogen and the output quantity generated by supplying power to a load respectively; c com、Cwloss、Closs respectively represents maintenance cost required by the operation of the electro-hydrogen system, penalty caused by wind power which is not consumed and penalty caused by load loss power;
the specific expression of part of the parameters in the objective function is as follows:
In the formula, s represents a scene of system operation, and the output of the wind turbine generator is different in different scenes; the operation of all scenes under s epsilon omega nor is defined as the normal operation of the electro-hydrogen system, and the operation of all scenes under s epsilon omega xtm is defined as the fault operation of the electro-hydrogen system; omega nor is all scenes in which the electro-hydrogen system is operating normally; omega xtm is all scenes of fault operation of the electro-hydrogen system; t represents the running time, and T is the total running time number; k e1,t、Kh、Ke2 is related parameters for supplying power to an upper power grid, and related parameters for supplying hydrogen and related parameters for supplying power to loads; mu loss is the power transmission consumption coefficient; p net,s,t is the power delivered to the upper grid; v hsell,s,t is the amount of hydrogen output to the hydrogen load; p wload,s,t is used for supplying load power for wind power; p FC1,s,t is the power supplied by the fuel cell to the load; 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 electrolytic cell related to 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 fuel cell consumed hydrogen volume; v EL,s,t represents the hydrogen production volume of the electrolytic cell at the time t; p loss,s,t and c loss are penalty coefficients of no-load power and no-load respectively; p wloss,s,t represents the wind power which is not consumed when the scene is s and the moment is t; c wloss is penalty coefficient of wind power which is not consumed; pi 1～π6 is the corresponding dual variable of each formula.
Further, the specific process of step 2 is as follows:
(201) The method comprises the steps of establishing a device fault model of the fuel cell, wherein the device fault model comprises a relation between current and voltage in the fuel cell, a relation between hydrogen consumption and electricity generation of the fuel cell and a fuel cell operation constraint, and the device fault model is specifically expressed as follows:
P′FC,s,t＝2·kf·F·Ufc,s,t·VFC,s,t
μFC,s,t·PFC min≤PFC,s,t≤μFC,s,t·PFC max
Wherein U fc,s,t and I fc,s,t represent the operating voltage and current of the fuel cell, respectively; correlation coefficient of fuel cell electromotive force τ 1、τ2、τ3、τ4; t fc is the fuel cell operating temperature; And/> The partial pressures of a hydrogen interface and an oxygen interface of the fuel cell are respectively; ζ i is an empirical coefficient, i=1, 2, 4; /(I)Oxygen concentration at the cathode gas level; j fc max is the maximum current density of the fuel cell; a fc represents the fuel cell activation area; b is a constant coefficient; r m is equivalent membrane impedance; r c is the equivalent contact resistance of the film; p' FC,s,t and P FC,s,t are the ideal output power and the actual output power of the fuel cell, respectively; k f is a unit conversion coefficient; f is Faraday constant; /(I)Represents the state in which the fuel cell is in the scene s, q=1, 2,..5; /(I)The working efficiency of the fuel cell under different running states is shown; p FC min is the minimum value of the fuel cell output power; mu FC,s,t is the start-stop state of the fuel cell,Respectively representing the states of four components of the fuel cell;
(202) The method comprises the steps of establishing an equipment fault model of the electrolytic cell comprising the relation between electricity consumption and hydrogen production of the electrolytic cell, the relation between operating power and current of the electrolytic cell and the operation constraint of the electrolytic cell, wherein the equipment fault model is specifically expressed as follows:
wherein I el,s,t represents the operating current of the electrolytic cell; t el 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 electrolyzer; And/> Respectively representing the ohmic resistance of the alkali liquor under normal operation and the ohmic resistance and the thermal coefficient of the alkali liquor under derated operation; /(I)Fitting the obtained electrode overvoltage coefficient; η f is the Faraday efficiency; p EL,s,t represents the power consumption of the electrolytic tank at the time t; /(I)Representing the power consumption of the electrolytic cell under different operating conditions, z=1, 2,3; p EL min represents the minimum value of the cell power consumption; /(I)Indicating the operating state of the electrolyzer; mu EL,s,t represents the start-stop state of the electrolytic cell; /(I)Respectively representing the states of two components of the electrolytic cell;
(203) Equipment fault model of power transmission line
When the transmission line does not fail, the power required to be transmitted to the upper power grid cannot exceed the capacity of the upper power grid; when the power transmission line fails, the electro-hydrogen system is not connected with the upper power grid any more, the power transmitted to the upper power grid is 0, and the capacity constraint of the power transmission line considering the failure is as follows:
0≤Pnet,s,t≤υjtrans,s·Ptrans
Wherein jtrans represents a faulty component in the power line; v jtrans,s represents the state of the component jtrans in the transmission line under the scene s, v jtrans,s =1 represents the normal operation of the component, and v jtrans,s =0 represents the failure of the component.
Further, the specific process of step 3 is as follows:
constructing a fault uncertainty set of the offshore electro-hydrogen system, limiting the number of component faults in each fault scene and the total number of times that each component breaks down all the year round, and limiting the number of fault scenes in all the scenes:
uf＝[ujel;ujfc;ujtrans]
Wherein omega s is an operation scene set; jel, jfc represent components of the electrolyzer and the fuel cell, respectively, that fail; n el,nfc,ntrans represents the number of components in the electrolytic cell, fuel cell and power line; lambda jel,s represents the condition of the component jel in the electrolytic cell in the field s, lambda jel,s =1 represents the normal operation of the component, and lambda jel,s =0 represents the failure of the component; ζ jfc,s represents the state of the component jfc in the fuel cell under the condition s, ζ jfc,s =1 represents the normal operation of the component, and ζ jfc,s =0 represents the failure of the component; let the number of scenes s in omega xtm be N s;Nxtm as the upper limit of the component faults in the fault scene, and N sce as the upper limit of the total number of faults of the component in one year; u jel,ujfc,ujtrans is the variable vector form of lambda jel,s、ζjfc,s and v jtrans,s respectively; s sce,s denotes the state of scene s.
Further, the specific process of step 4 is as follows:
establishing constraint conditions of a capacity planning model of the offshore electro-hydrogen system considering uncertainty faults:
(401) Power balance constraint:
Wherein P load,s,t is the load power; p w,s,t and P wnet,s,t respectively represent the power generation amount of the wind power at the moment t and the power of the wind power transmitted to an upper grid; The method comprises the steps of (1) setting a pair variable corresponding to each formula in power balance constraint;
(402) Hydrogen storage tank restraint:
Wherein V h,s,t is the gas capacity in the hydrogen storage tank; v hload,s,t is hydrogen load demand; v h0 and V hT are the hydrogen volumes of the hydrogen storage tanks at the beginning and end periods; Is a dual variable corresponding to each formula in the constraint of the hydrogen storage tank.
Further, the specific process of step 5 is as follows:
the capacity planning model of the offshore hydrogen system is a nonlinear mixed integer planning problem, wherein equipment fault models of an electrolytic tank, a fuel cell and a power transmission line comprise nonlinear variables, and a linearization form of the capacity planning model of the offshore hydrogen system is written by adopting a linear fitting and linearization processing method;
(501) The linearization of the plant failure model of the electrolyzer is as follows:
Wherein bigM is a constant; n el is the number of electrolytic cells; N el and/> The result of the multiplication; /(I)Is N el andThe result of the multiplication; /(I)ForA result of multiplication with mu EL,s,t; /(I)ForA result of multiplication with mu EL,s,t; i el min and I el max are respectively the minimum operating current and the maximum operating current of the electrolytic cell; /(I)AndRespectively representing the products of I el,s,t and N el of the electrolytic tank under different running states; /(I)AndRespectively expressAnd/>, after linear fittingAndThe associated coefficients; /(I)AndRespectively expressAnd/>, after linear fittingAndThe associated coefficients; /(I)AndThe method is characterized in that the method is a dual variable corresponding to each formula in a linearization form of an equipment fault model of the electrolytic tank;
(502) The linearization of the device failure model of the fuel cell is as follows:
PFC max＝(kfc1·Ifc max+kfc2)·Nfc
Wherein k fc1 and k fc2 represent P FC,s,t, respectively, and INfc s,t after linear fitting The associated coefficients; 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 a minimum operating current and a maximum operating current of the fuel cell, respectively; v' FC,s,t represents the hydrogen volume consumed by the fuel cell under ideal conditions; /(I)Represents mu FC,s,t andIs a product of (2); /(I)RepresentationProduct with N fc; /(I)RepresentationProduct with V' FC,s,t; /(I)RepresentationProduct with V' FC,s,t; /(I)RepresentationProduct with V' FC,s,t; /(I)The method is characterized in that the method is a dual variable corresponding to each formula in a linearization form of an equipment fault model of the fuel cell;
(503) The linearization of the equipment failure model of the transmission line is as follows:
In the method, in the process of the invention, Represents the product of P trans and v jtrans,s; /(I)AndIs a dual variable corresponding to each formula in the linearization form of the equipment fault model of the transmission line.
Further, the specific process of step 6 is as follows:
(601) The part of the capacity planning model, which is not affected by u f and s e, is defined as a planning stage, and the form of the objective function of the capacity planning model of the offshore hydrogen system is as follows:
(602) The capacity planning method is a two-stage robust optimization problem and comprises an upper model and a lower model, wherein the upper model is defined as an outer layer main problem, the lower model is defined as an outer layer sub-problem, and the outer layer main problem is as follows:
RESULTMP≤(Re1+Rh1+Re2-Ccom-Cwloss-Closs)
Wherein RESULT MP is an auxiliary variable of the outer layer main problem and acts as relaxation of the outer layer sub-problem objective function; the constraints of the outer main problems comprise equipment fault models of an electrolytic tank, a fuel cell and a power transmission line, power balance constraints and hydrogen storage tank constraints;
(603) The form of the lower model is as follows:
the constraint of the lower model comprises linearization forms of equipment fault models of an electrolytic tank, a fuel cell and a power transmission line, power balance constraint, hydrogen storage tank constraint and a fault uncertainty set of an offshore electric hydrogen system, the lower model is a min-max problem, the problem is converted into a dual form based on a strong dual theory for solving, the dual form of the lower model is defined as an inner layer main problem, and the dual form is as follows:
π1≥1
π2≥1
π3≥1
π4≥-1
π5≥-1
π6≥-1
Wherein RESULT SP-MP is an auxiliary variable to the primary problem of the inner layer, due to the dual form Mu EL,s,t、μFC,s,t andAre integer variables, the dual problem cannot be solved, and initial values/> are respectively given to the variables AndThe new dual form is as follows:
Linearizing the new dual form, solving and determining a fault scene set to obtain a new lower model form, and defining the new lower model form as an inner layer sub-problem:
RESULTSP-SP＝max(Re1+Rh1+Re2-Ccom-Cwloss-Closs)
Wherein RESULT SP-SP is an auxiliary variable to the inner layer sub-problem.
In step 7, a nested column constraint generating algorithm is adopted to solve the capacity planning model, and the specific steps of the nested column constraint generating algorithm are as follows:
(1) Let the initial lower bound OTL down = - ≡of the upper layer model, the initial upper bound OTL up = -infinity, the initial iteration number num OTL =1 of the upper layer model, the convergence gap of the upper layer iteration is delta OTL; an initial lower bound INL down = - +_infinity, an initial upper bound INL up = infinity, an initial iteration number num INL =1 of the lower model, and a convergence gap of the lower iteration is delta INL;
(2) Giving an initial fault scene, merging the initial fault scene into a scene uncertainty set, solving an outer layer main problem to obtain a capacity planning scheme of each device, and updating the upper bound of an upper model by using an OTL up＝min{OTLup,RESULTMP;
(3) Inputting a capacity planning result obtained by an upper layer model into an inner layer main problem, setting a group of preset initial values for integer variables in the inner layer main problem, merging the initial values into an integer variable scene set, solving the inner layer main problem, determining the lower boundary of a lower layer model by utilizing INL down＝max{INLdown,RESULTSP-MP, and carrying the capacity planning result and a fault scene solved by the inner layer main problem into an inner layer sub-problem to solve the inner layer sub-problem to obtain an upper boundary INL up＝min{INLup,RESULTSP-SP of the lower layer model;
(4) Judging whether the lower model is converged or not according to the |INL up-INLdown|≤δINL, if the condition is met, obtaining an optimal solution of the lower model and taking the optimal solution as a lower bound OTL down of the upper model, and performing the process (5); if not, num INL＝numINL +1 is merged into the integer variable scene set, new variables and constraints are generated, and the process returns to the process (3);
(5) Judging whether the upper model is converged according to the |OTL up-OTLdown|≤δOTL, if the condition is not met, num OTL＝numOTL +1, merging the fault scene solved by the lower model into a scene uncertainty set, adding new variables and constraints, and returning to the process (2); if yes, obtaining an optimal solution of the upper model, and performing a process (6);
(6) And outputting a capacity planning result, and ending the solving.
A typical structure of an established offshore electro-hydrogen system is shown in fig. 2. The system comprises a wind turbine generator, an electrolytic tank, a fuel cell, a hydrogen storage tank, an upper power grid and a hydrogen load.
Taking hours as a time scale, enabling N xtm and N sce to be 1, enabling the value of N s to be 3, and obtaining a capacity planning result of the offshore wind power-system hydrogen energy system according to the established model, wherein the result is shown in a table 1, and the load loss during fault is shown in a table 2.
Table 1 comparison of capacities before and after optimal configuration
Table 2 comparison of scheduling results before and after capacity optimization
The obtained result shows that after the uncertain faults are considered in capacity planning, the dead load during the faults is obviously reduced compared with that before optimization, and the power supply guarantee capability of the offshore hydrogen system can be effectively improved when the uncertain faults are considered. And the wind abandoning rate is less than 0.3% under normal conditions before and after the optimization, which indicates that the wind power absorbing capacity of the system is not affected by adopting the optimization method.
Fig. 3 to 5 show operation conditions under three fault scenarios determined by the present invention, wherein (a) in fig. 3, 4 and 5 show operation conditions of the electro-hydrogen system when the present invention is not adopted, and (b) in fig. 3, 4 and 5 show operation conditions of the electro-hydrogen system after the present invention is adopted. As can be seen from comparative analysis, after the invention is adopted, the load loss of the system is obviously reduced when the electro-hydrogen system fails to operate, and the output of the fuel cell is increased to a certain extent compared with that of the fuel cell without adopting the invention. The capacity of the fuel cell and the hydrogen storage tank is improved, so that more power is provided for the electro-hydrogen system to operate in a fault mode, the load loss is reduced, and the feasibility of considering uncertainty faults in capacity planning is proved.
In terms of planning capacity of each device, after the method is adopted, the capacities of an electrolytic tank and a power transmission line connected with an upper power grid are not obviously changed, and the capacities of a fuel cell and a hydrogen storage tank are increased, because wind power is less in severe fault scenes, at the moment, wind power cannot independently complete the task of guaranteeing power supply, the fuel cell is required to supply power to the part with power deficiency, and if the fuel cell fails, the power generation capacity of the fuel cell is reduced, and the requirement of complete power supply cannot be met, so that the capacity can be properly increased during planning. In addition, insufficient wind power results in a hydrogen storage tank incapable of obtaining additional hydrogen sources, and more available hydrogen can be ensured only by improving the capacity of the hydrogen storage tank when faults occur.
Claims (4)
1. A method for planning capacity of an offshore electro-hydrogen system taking into account uncertainty faults, the method comprising the steps of:
(1) According to capacity planning of an electrolytic tank, a fuel cell, a hydrogen storage tank and a power transmission line in the electro-hydrogen system, and normal operation and fault operation of the electro-hydrogen system, constructing an objective function of a capacity planning model of the offshore electro-hydrogen system;
(2) Establishing equipment fault models of the electrolytic tank, the fuel cell and the power transmission line;
(3) Constructing a fault uncertainty set of the offshore electro-hydrogen system based on the equipment fault models of the electrolytic tank, the fuel cell and the power transmission line established in the step (2);
(4) Obtaining constraint conditions of a capacity planning model of the offshore hydrogen system according to the objective function and the equipment fault model;
(5) Taking the objective function in the step (1), the equipment fault model of the electrolytic tank, the fuel cell and the power transmission line in the step (2), the fault uncertainty set of the offshore hydrogen system in the step (3) and the constraint condition in the step (4) as a capacity planning model of the offshore hydrogen system, and writing out a linearization form of the capacity planning model;
(6) Writing a dual form based on the linearization form of the capacity planning model of the offshore hydrogen system proposed in the step (5);
(7) Solving the capacity planning model by using a nested column constraint generation algorithm based on the capacity planning model of the offshore hydrogen system in the step (5) and the linearization form thereof and the dual form in the step (6), and planning the capacity of the model according to the solving result;
the specific process of the step (1) is as follows:
An objective function of a capacity planning model of the offshore hydrogen system is constructed, and the form of the objective function is as follows:
Where u f represents the uncertainty variable vector for all component states; u represents the uncertainty set of the component state; s e represents the uncertainty variable vectors for all scene states; s sce represents a set of uncertainty of the scene state; r is the discount rate; m is the operational life; p ELmax、PFCmax、Vhmax、Ptrans is the planning capacity of the electrolytic tank, the fuel cell, the hydrogen storage tank and the power transmission line respectively; l is the sea cable length; e k is a correlation coefficient planned for each device, k=1, 2, …,5, where k=1 denotes an electrolyzer, k=2 denotes a fuel cell, k=3 denotes a hydrogen storage tank, k=4 denotes a power line, and k=5 denotes an infrastructure; e HVDC1 and e HVDC2 are fixed coefficients for converter station planning and coefficients related to the power line capacity, respectively; r e1、Rh1、Re2 is the output quantity generated by supplying power to an upper-layer power grid, and the output quantity generated by supplying hydrogen and the output quantity generated by supplying power to a load respectively; c com、Cwloss、Closs respectively represents maintenance cost required by the operation of the electro-hydrogen system, penalty caused by wind power which is not consumed and penalty caused by load loss power;
the specific expression of part of the parameters in the objective function is as follows:
In the formula, s represents a scene of system operation, and the output of the wind turbine generator is different in different scenes; the operation of all scenes under s epsilon omega nor is defined as the normal operation of the electro-hydrogen system, and the operation of all scenes under s epsilon omega xtm is defined as the fault operation of the electro-hydrogen system; omega nor is all scenes in which the electro-hydrogen system is operating normally; omega xtm is all scenes of fault operation of the electro-hydrogen system; t represents the running time, and T is the total running time number; k e1,t、Kh、Ke2 is related parameters for supplying power to an upper power grid, and related parameters for supplying hydrogen and related parameters for supplying power to loads; mu loss is the power transmission consumption coefficient; p net,s,t is the power delivered to the upper grid; v hsell,s,t is the amount of hydrogen output to the hydrogen load; p wload,s,t is used for supplying load power for wind power; p FC1,s,t is the power supplied by the fuel cell to the load; 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 electrolytic cell related to 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 fuel cell consumed hydrogen volume; v EL,s,t represents the hydrogen production volume of the electrolytic cell at the time t; p loss,s,t and c loss are penalty coefficients of no-load power and no-load respectively; p wloss,s,t represents the wind power which is not consumed when the scene is s and the moment is t; c wloss is penalty coefficient of wind power which is not consumed; pi 1:π6 is a dual variable corresponding to each formula;
The specific process of the step (2) is as follows:
(201) The method comprises the steps of establishing a device fault model of the fuel cell, wherein the device fault model comprises a relation between current and voltage in the fuel cell, a relation between hydrogen consumption and electricity generation of the fuel cell and a fuel cell operation constraint, and the device fault model is specifically expressed as follows:
PF'C,s,t＝2·kf·F·Ufc,s,t·VFC,s,t
μFC,s,t·PFCmin≤PFC,s,t≤μFC,s,t·PFCmax
Wherein U fc,s,t and I fc,s,t represent the operating voltage and current of the fuel cell, respectively; correlation coefficient of fuel cell electromotive force τ 1、τ2、τ3、τ4; t fc is the fuel cell operating temperature; And/> The partial pressures of a hydrogen interface and an oxygen interface of the fuel cell are respectively; ζ i is an empirical factor, i=1, 2, …,4; /(I)Oxygen concentration at the cathode gas level; j fcmax is the maximum current density of the fuel cell; a fc represents the fuel cell activation area; b is a constant coefficient; r m is equivalent membrane impedance; r c is the equivalent contact resistance of the film; p F'C,s,t and P FC,s,t are the ideal output power and the actual output power of the fuel cell, respectively; k f is a unit conversion coefficient; f is Faraday constant; /(I)Representing the state of the fuel cell in the scene s, q=1, 2, …,5; /(I)The working efficiency of the fuel cell under different running states is shown; p FCmin is the minimum value of the fuel cell output power; mu FC,s,t is the start-stop state of the fuel cell,Respectively representing the states of four components of the fuel cell;
(202) The method comprises the steps of establishing an equipment fault model of the electrolytic cell comprising the relation between electricity consumption and hydrogen production of the electrolytic cell, the relation between operating power and current of the electrolytic cell and the operation constraint of the electrolytic cell, wherein the equipment fault model is specifically expressed as follows:
wherein I el,s,t represents the operating current of the electrolytic cell; t el 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 electrolyzer; And/> Respectively representing the ohmic resistance of the alkali liquor under normal operation and the ohmic resistance and the thermal coefficient of the alkali liquor under derated operation; /(I)Fitting the obtained electrode overvoltage coefficient; η f is the Faraday efficiency; p EL,s,t represents the power consumption of the electrolytic tank at the time t; /(I)Representing the power consumption of the electrolytic cell under different operating conditions, z=1, 2,3; p ELmin represents the minimum value of the cell power consumption; /(I)Indicating the operating state of the electrolyzer; mu EL,s,t represents the start-stop state of the electrolytic cell; /(I)Respectively representing the states of two components of the electrolytic cell;
(203) Equipment fault model of power transmission line
When the transmission line does not fail, the power required to be transmitted to the upper power grid cannot exceed the capacity of the upper power grid; when the power transmission line fails, the electro-hydrogen system is not connected with the upper power grid any more, the power transmitted to the upper power grid is 0, and the capacity constraint of the power transmission line considering the failure is as follows:
0≤Pnet,s,t≤υjtrans,s·Ptrans
Wherein jtrans represents a faulty component in the power line; v jtrans,s represents the state of the component jtrans in the transmission line under the scene s, v jtrans,s =1 represents the normal operation of the component, and v jtrans,s =0 represents the failure of the component;
The specific process of the step 3 is as follows:
constructing a fault uncertainty set of the offshore electro-hydrogen system, limiting the number of component faults in each fault scene and the total number of times that each component breaks down all the year round, and limiting the number of fault scenes in all the scenes:
uf＝[ujel;ujfc;ujtrans]
Wherein omega s is an operation scene set; jel, jfc represent components of the electrolyzer and the fuel cell, respectively, that fail; n el,nfc,ntrans represents the number of components in the electrolytic cell, fuel cell and power line; lambda jel,s represents the condition of the component jel in the electrolytic cell in the field s, lambda jel,s =1 represents the normal operation of the component, and lambda jel,s =0 represents the failure of the component; ζ jfc,s represents the state of the component jfc in the fuel cell under the condition s, ζ jfc,s =1 represents the normal operation of the component, and ζ jfc,s =0 represents the failure of the component; let the number of scenes s in omega xtm be N s;Nxtm as the upper limit of the component faults in the fault scene, and N sce as the upper limit of the total number of faults of the component in one year; u jel,ujfc,ujtrans is the variable vector form of lambda jel,s、ζjfc,s and v jtrans,s respectively; s sce,s denotes the state of scene s;
The specific process of the step 4 is as follows:
establishing constraint conditions of a capacity planning model of the offshore electro-hydrogen system considering uncertainty faults:
(401) Power balance constraint:
Wherein P load,s,t is the load power; p w,s,t and P wnet,s,t respectively represent the power generation amount of the wind power at the moment t and the power of the wind power transmitted to an upper grid; The method comprises the steps of (1) setting a pair variable corresponding to each formula in power balance constraint;
(402) Hydrogen storage tank restraint:
Wherein V h,s,t is the gas capacity in the hydrogen storage tank; v hload,s,t is hydrogen load demand; v h0 and V hT are the hydrogen volumes of the hydrogen storage tanks at the beginning and end periods; Is a dual variable corresponding to each formula in the constraint of the hydrogen storage tank.
2. The method for planning capacity of an offshore hydrogen system with uncertainty fault in mind of claim 1, wherein the specific process of step 5 is as follows:
The capacity planning model of the offshore hydrogen system is a nonlinear mixed integer planning problem, wherein equipment fault models of an electrolytic tank, a fuel cell and a power transmission line comprise nonlinear variables, and a linear fitting and linearization processing method is adopted to obtain a linearization form of the capacity planning model of the offshore hydrogen system;
(501) The linearization of the plant failure model of the electrolyzer is as follows:
Wherein bigM is a constant; n el is the number of electrolytic cells; N el and/> The result of the multiplication; /(I)N el andThe result of the multiplication; /(I)ForA result of multiplication with mu EL,s,t; /(I)Is the result of multiplication of κ EL,n2,s by μ EL,s,t; i elmin and I elmax are respectively the minimum operating current and the maximum operating current of the electrolytic cell; /(I)AndRespectively representing the products of I el,s,t and N el of the electrolytic tank under different running states; /(I)AndRespectively expressAnd/>, after linear fittingAndThe associated coefficients; And/> Respectively expressAnd/>, after linear fittingAndThe associated coefficients; /(I)AndThe method is characterized in that the method is a dual variable corresponding to each formula in a linearization form of an equipment fault model of the electrolytic tank;
(502) The linearization of the device failure model of the fuel cell is as follows:
Wherein k fc1 and k fc2 represent P FC,s,t, respectively, and INfc s,t after linear fitting The associated coefficients; 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 a minimum operating current and a maximum operating current of the fuel cell, respectively; v' FC,s,t represents the hydrogen volume consumed by the fuel cell under ideal conditions; /(I)Represents μ FC,s,t andIs a product of (2); /(I)RepresentationProduct with N fc; /(I)Represents the product of ζ jfc4,s and V' FC,s,t; /(I)RepresentationProduct with V' FC,s,t; Representation/> Product with V' FC,s,t; /(I)The method is characterized in that the method is a dual variable corresponding to each formula in a linearization form of an equipment fault model of the fuel cell;
(503) The linearization of the equipment failure model of the transmission line is as follows:
In the method, in the process of the invention, Represents the product of P trans and v jtrans,s; /(I)AndIs a dual variable corresponding to each formula in the linearization form of the equipment fault model of the transmission line.
3. The method for planning capacity of an offshore hydrogen system with uncertainty fault in mind of claim 2, wherein the specific process of step 6 is as follows:
(601) The part of the capacity planning model, which is not affected by u f and s e, is defined as a planning stage, and the form of the objective function of the capacity planning model of the offshore hydrogen system is as follows:
(602) The capacity planning method is a two-stage robust optimization problem and comprises an upper model and a lower model, wherein the upper model is defined as an outer layer main problem, the lower model is defined as an outer layer sub-problem, and the outer layer main problem is as follows:
RESULTMP≤(Re1+Rh1+Re2-Ccom-Cwloss-Closs)
Wherein RESULT MP is an auxiliary variable of the outer layer main problem and acts as relaxation of the outer layer sub-problem objective function; the constraints of the outer main problems comprise equipment fault models of an electrolytic tank, a fuel cell and a power transmission line, power balance constraints and hydrogen storage tank constraints;
(603) The form of the lower model is as follows:
the constraint of the lower model comprises linearization forms of equipment fault models of an electrolytic tank, a fuel cell and a power transmission line, power balance constraint, hydrogen storage tank constraint and a fault uncertainty set of an offshore electric hydrogen system, the lower model is a min-max problem, the problem is converted into a dual form based on a strong dual theory for solving, the dual form of the lower model is defined as an inner layer main problem, and the dual form is as follows:
Wherein RESULT SP-MP is an auxiliary variable to the primary problem of the inner layer, due to the dual form Mu EL,s,t、μFC,s,t andAre integer variables, the dual problem cannot be solved, and initial values/> are respectively given to the variables And (3) withThe new dual form is as follows:
Linearizing the new dual form, solving and determining a fault scene set to obtain a new lower model form, and defining the new lower model form as an inner layer sub-problem:
RESULTSP-SP＝max(Re1+Rh1+Re2-Ccom-Cwloss-Closs)
Wherein RESULT SP-SP is an auxiliary variable to the inner layer sub-problem.
4. The method for planning capacity of an offshore hydrogen system with uncertainty fault being considered as claimed in claim 3, wherein in step 7, a nested column constraint generating algorithm is adopted to solve a capacity planning model, and the specific steps of the nested column constraint generating algorithm are as follows:
(1) Let the initial lower bound OTL down = - ≡of the upper layer model, the initial upper bound OTL up = -infinity, the initial iteration number num OTL =1 of the upper layer model, the convergence gap of the upper layer iteration is delta OTL; an initial lower bound INL down = - +_infinity, an initial upper bound INL up = infinity, an initial iteration number num INL =1 of the lower model, and a convergence gap of the lower iteration is delta INL;
(2) Giving an initial fault scene, merging the initial fault scene into a scene uncertainty set, solving an outer layer main problem to obtain a capacity planning scheme of each device, and updating the upper bound of an upper model by using an OTL up＝min{OTLup,RESULTMP;
(3) Inputting a capacity planning result obtained by an upper layer model into an inner layer main problem, setting a group of preset initial values for integer variables in the inner layer main problem, merging the initial values into an integer variable scene set, solving the inner layer main problem, determining the lower boundary of a lower layer model by utilizing INL down＝max{INLdown,RESULTSP-MP, and carrying the capacity planning result and a fault scene solved by the inner layer main problem into an inner layer sub-problem to solve the inner layer sub-problem to obtain an upper boundary INL up＝min{INLup,RESULTSP-SP of the lower layer model;
(4) Judging whether the lower model is converged or not according to the |INL up-INLdown|≤δINL, if the condition is met, obtaining an optimal solution of the lower model and taking the optimal solution as a lower bound OTL down of the upper model, and performing the process (5); if not, num INL＝numINL +1 is merged into the integer variable scene set, new variables and constraints are generated, and the process returns to the process (3);
(5) Judging whether the upper model is converged according to the |OTL up-OTLdown|≤δOTL, if the condition is not met, num OTL＝numOTL +1, merging the fault scene solved by the lower model into a scene uncertainty set, adding new variables and constraints, and returning to the process (2); if yes, obtaining an optimal solution of the upper model, and performing a process (6);
(6) And outputting a capacity planning result, and ending the solving.
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