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
- Publication number
- CN117200265B CN117200265B CN202310939867.2A CN202310939867A CN117200265B CN 117200265 B CN117200265 B CN 117200265B CN 202310939867 A CN202310939867 A CN 202310939867A CN 117200265 B CN117200265 B CN 117200265B
- Authority
- CN
- China
- Prior art keywords
- model
- fuel cell
- hydrogen
- capacity planning
- power
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Landscapes
- Fuel Cell (AREA)
Abstract
Description
技术领域Technical Field
本发明涉及容量规划领域,尤其涉及一种考虑不确定性故障的海上电氢系统容量规划方法。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.
背景技术Background Art
清洁能源逐步在发电端占据主导地位,其中,风力发电是新能源发电的主要形式之一。由于海上的风力资源较为充足,海上风电机组的规划容量正不断增加,并且逐步向中远海发展。但是,由于风电具有不确定性和波动性,不同风速下风电的出力差异很大,可能会导致出现弃风或者弃负荷的现象,对电网的稳定性产生影响。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.
目前,由于制氢、氢储能技术不断成熟,氢能系统应用于供电保障具有了可行性,该系统通过电解槽将富余的风电转换为氢气并存于储氢罐中。氢气可以提供给氢负荷,也可以在风电出力不足时通过燃料电池将其转化为电能以保障供电。该系统可以有效的提升风电消纳能力以及供电保障能力。但是,海上电氢系统仍存在以下问题:在进行容量规划时未考虑设备发生故障后系统是否能够可靠供电以及实现消纳。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.
发明内容Summary of the invention
技术问题:本发明提出了一种考虑不确定性故障的海上电氢系统容量规划方法,本发明提出的方法重点涉及了考虑设备故障的海上电氢系统的容量规划,并考虑了故障设备的不确定性。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.
技术方案:为了解决上述技术问题,本发明提出一种考虑不确定性故障的海上电氢系统容量规划方法,该方法包括以下步骤: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根据电氢系统中电解槽、燃料电池、储氢罐与输电线的容量规划以及电氢系统正常运行与故障运行,构建海上电氢系统容量规划模型的目标函数;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建立电解槽、燃料电池与输电线的设备故障模型;2. Establish equipment failure models for electrolyzers, fuel cells, and transmission lines;
3基于步骤2中所建立的电解槽、燃料电池与输电线的设备故障模型,构建海上电氢系统的故障不确定集合;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根据所述的目标函数与设备故障模型得出海上电氢系统容量规划模型的约束条件;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将步骤1中的目标函数,步骤2中的电解槽、燃料电池与输电线的设备故障模型,步骤3中的海上电氢系统的故障不确定集合与步骤4中的约束条件作为海上电氢系统容量规划模型,并写出其线性化形式;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基于步骤5中提出的海上电氢系统容量规划模型的线性化形式,写出对偶形式;6 Based on the linearized form of the offshore electric-hydrogen system capacity planning model proposed in step 5, write the dual form;
7基于步骤5中海上电氢系统容量规划模型及其线性化形式与步骤6中的对偶形式,使用嵌套列约束生成算法对容量规划模型进行求解,根据求解结果对该模型进行容量规划。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.
进一步的,步骤1的具体过程如下:Furthermore, the specific process of step 1 is as follows:
构建海上电氢系统容量规划模型的目标函数,目标函数的形式如下:The objective function of the offshore electric hydrogen system capacity planning model is constructed. The objective function is in the following form:
式中,uf表示所有组件状态的不确定性变量向量;U表示组件状态的不确定性集合;se表示所有场景状态的不确定性变量向量;Ssce表示场景状态的不确定性集合;r为折现率;m为运行年限;PELmax、PFCmax、Vhmax、Ptrans分别为电解槽、燃料电池、储氢罐与输电线的规划容量;L为海缆长度;ek为各设备规划的相关系数,k=1,2,...,5,其中,k=1表示电解槽、k=2表示燃料电池、k=3表示储氢罐、k=4表示输电线、k=5表示基础设施;eHVDC1与eHVDC2分别为换流站规划的固定系数和与输电线容量相关的系数;Re1、Rh1、Re2分别为向上层电网供电产生的输出量,供氢产生的输出量与向负荷供电产生的输出量;Ccom、Cwloss、Closs分别表示电氢系统运行所需要的维护成本,未被消纳的风电功率导致的惩罚,失负荷功率导致的惩罚;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;
目标函数中部分参数的具体表达式如下:The specific expressions of some parameters in the objective function are as follows:
式中,s表示系统运行的场景,不同场景下风电机组的出力不同;将s∈Ωnor下的所有场景的运行定义为电氢系统正常运行,将s∈Ωxtm下的所有场景的运行定义为电氢系统故障运行;Ωnor为电氢系统正常运行的所有场景;Ωxtm为电氢系统故障运行的所有场景;t表示运行时刻,T为运行的总时刻数;Ke1,t、Kh、Ke2分别为向上层电网供电的相关参数,供氢相关参数与向负荷供电的相关参数;μloss为输电消耗系数;Pnet,s,t为输送至上层电网的功率;Vhsell,s,t为输出给氢负荷的氢气量;Pwload,s,t为风电供给负荷功率;PFC1,s,t为燃料电池供应给负荷的功率;Qk为各设备的运维系数,k=1,2,...,5;Qh1为电解槽与制氢量相关的运维系数;Qh2为燃料电池与耗氢量相关的运维系数;VFC,s,t为燃料电池消耗氢气体积;VEL,s,t表示t时刻下电解槽的产氢体积;Ploss,s,t与closs分别为失负荷功率与失负荷的惩罚系数;Pwloss,s,t表示场景为s、时刻为t时未被消纳的风电功率;cwloss为未被消纳风电功率的惩罚系数;π1~π6为各公式对应的对偶变量。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.
进一步,步骤2的具体过程如下:Further, the specific process of step 2 is as follows:
(201)建立包括了燃料电池内电流与电压关系,燃料电池耗氢与产电关系以及燃料电池运行约束的燃料电池的设备故障模型,具体表述如下:(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:
μFC,s,t·PFC min≤PFC,s,t≤μFC,s,t·PFC max μ FC,s,t ·P FC min ≤P FC,s,t ≤μ FC,s,t ·P FC max
式中,Ufc,s,t与Ifc,s,t分别表示燃料电池的运行电压与电流;τ1、τ2、τ3、τ4燃料电池电动势的相关系数;Tfc为燃料电池运行温度;与分别为燃料电池氢界面与氧界面分压;ξi为经验系数,i=1,2,...,4;为阴极气液面的氧气浓度;Jfc max为燃料电池最大电流密度;Afc表示燃料电池活化面积;B为常系数;Rm为等效膜阻抗;Rc为膜的等效接触电阻;P′FC,s,t和PFC,s,t分别为燃料电池的理想输出功率与实际输出功率;kf为单位转换系数;F为法拉第常数;表示燃料电池在场景s下所处的状态,q=1,2,...,5;为燃料电池在不同运行状态下的工作效率;PFC min为燃料电池输出功率的最小值;μFC,s,t为燃料电池的启停状态,分别表示燃料电池四个组件的状态;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)建立包括了电解槽的耗电与产氢关系,电解槽运行功率与电流关系和电解槽运行约束的电解槽的设备故障模型,具体表述如下:(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:
式中,Iel,s,t表示电解槽的运行电流;Tel为电解槽运行温度;Ael为电解槽的有效反应面积;Urev为电解槽的可逆电压;和分别表示正常运行下碱液的欧姆电阻,降额运行下碱液的欧姆电阻和碱液的热阻系数;为拟合得到的电极过电压系数;ηf为法拉第效率;PEL,s,t表示t时刻下电解槽的耗电功率;表示不同运行状态下电解槽的耗电功率,z=1,2,3;PEL min表示电解槽耗电功率的最小值;表示电解槽的运行状态;μEL,s,t表示电解槽的启停状态;分别表示电解槽两个组件的状态;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)输电线的设备故障模型(203) Equipment Failure Model of Transmission Line
当输电线未发生故障时,要求向上层电网输送的功率不能超过其容量;当输电线发生故障时,电氢系统将不再与上层电网连接,向上层电网输送的功率为0,考虑故障的输电线容量约束如下: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≤Pnet,s,t≤υjtrans,s·Ptrans 0≤P net,s,t ≤υ jtrans,s ·P trans
式中,jtrans表示输电线中发生故障的组件;υjtrans,s表示输电线中组件jtrans在场景s下的状态,υjtrans,s=1表示组件正常运行,υjtrans,s=0则表示组件发生故障。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.
进一步的,步骤3的具体过程如下:Furthermore, the specific process of step 3 is as follows:
构建海上电氢系统的故障不确定集合,对每一故障场景中的组件故障数与每一组件全年发生故障的总次数做出限制,并对所有场景中故障场景数量进行限制: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:
uf=[ujel;ujfc;ujtrans]u f = [u jel ; u jfc ; u jtrans ]
式中,Ωs为运行场景集合;jel,jfc分别表示电解槽与燃料电池中发生故障的组件;nel,nfc,ntrans分别表示电解槽,燃料电池与输电线中的组件个数;λjel,s表示电解槽中组件jel在场景s下的状态,λjel,s=1表示组件正常运行,λjel,s=0则表示组件发生故障;ζjfc,s表示燃料电池中组件jfc在场景s下的状态,ζjfc,s=1表示组件正常运行,ζjfc,s=0则表示组件发生故障;令Ωxtm中场景s的个数为Ns;Nxtm为故障场景中的组件故障上限,Nsce为组件一年内的故障总次数上限;ujel,ujfc,ujtrans分别为λjel,s、ζjfc,s与υjtrans,s的变量向量形式;ssce,s表示场景s的状态。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.
进一步的,步骤4的具体过程如下:Furthermore, the specific process of step 4 is as follows:
建立考虑不确定性故障的海上电氢系统容量规划模型的约束条件:Establish constraints for the offshore electric-hydrogen system capacity planning model considering uncertain faults:
(401)功率平衡约束:(401) Power balance constraint:
式中,Pload,s,t为负荷功率;Pw,s,t和Pwnet,s,t分别表示t时刻风力发电量与风电输送给上层电网的功率;为功率平衡约束中各公式对应的对偶变量;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)储氢罐约束:(402) Hydrogen storage tank constraints:
式中,Vh,s,t为储氢罐内的气体容量;Vhload,s,t为氢负荷需求;Vh0和VhT为初、末时段储氢罐的氢气体积;为储氢罐约束中各公式对应的对偶变量。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.
进一步的,步骤5的具体过程如下:Furthermore, the specific process of step 5 is as follows:
上述的海上电氢系统容量规划模型为非线性混合整数规划问题,其中,电解槽、燃料电池与输电线的设备故障模型包含了非线性变量,采用线性拟合与线性化处理方法写出海上电氢系统容量规划模型的线性化形式;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)电解槽的设备故障模型的线性化形式如下:(501) The linearized form of the equipment failure model of the electrolytic cell is as follows:
式中,bigM为一个常数;Nel为电解槽数量;为Nel与相乘的结果;为Nel与相乘的结果;为与μEL,s,t相乘的结果;为与μEL,s,t相乘的结果;Iel min与Iel max分别为电解槽的最小运行电流与最大运行电流;与分别表示电解槽在不同运行状态下Iel,s,t与Nel的乘积;与分别表示在线性拟合后与和相关的系数;与分别表示在线性拟合后与和相关的系数;与为电解槽的设备故障模型的线性化形式中各公式对应的对偶变量;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)燃料电池的设备故障模型的线性化形式如下:(502) The linearized form of the fuel cell equipment failure model is as follows:
PFC max=(kfc1·Ifc max+kfc2)·Nfc P FC max =(k fc1 ·I fc max +k fc2 )·N fc
式中,kfc1与kfc2分别表示PFC,s,t在线性拟合后与INfcs,t和相关的系数;Nfc表示燃料电池数量;INfcs,t表示Ifc,s,t与Nfc的乘积;Ifcmin与Ifcmax分别表示燃料电池最小运行电流与最大运行电流;V′FC,s,t表示理想状态下燃料电池消耗的氢气体积;表示μFC,s,t与的乘积;表示与Nfc的乘积;表示与V′FC,s,t的乘积;表示与V′FC,s,t的乘积;表示与V′FC,s,t的乘积;为燃料电池的设备故障模型的线性化形式中各公式对应的对偶变量;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)输电线的设备故障模型的线性化形式如下:(503) The linearized form of the equipment failure model of the transmission line is as follows:
式中,表示Ptrans与υjtrans,s的乘积;与为输电线的设备故障模型的线性化形式中各公式对应的对偶变量。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.
进一步的,步骤6的具体过程如下:Furthermore, the specific process of step 6 is as follows:
(601)将容量规划模型中不受uf与se影响的部分定义为规划阶段,海上电氢系统容量规划模型目标函数的形式如下:(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)该容量规划方法为两阶段鲁棒优化问题,包括了上层模型与下层模型,将上层模型定义为外层主问题,下层模型定义为外层子问题,其中外层主问题如下所示:(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:
RESULTMP≤(Re1+Rh1+Re2-Ccom-Cwloss-Closs)RESULT MP ≤(R e1 +R h1 +R e2 -C com -C wloss -C loss )
式中,RESULTMP为外层主问题的辅助变量,其作用是对外层子问题目标函数的松弛;外层主问题的约束包括了电解槽、燃料电池与输电线的设备故障模型,功率平衡约束与储氢罐约束;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)下层模型的形式如下:(603) The lower model is in the following form:
下层模型的约束包括了电解槽、燃料电池与输电线的设备故障模型的线性化形式,功率平衡约束、储氢罐约束与海上电氢系统的故障不确定集合,下层模型为min-max问题,为进行求解,基于强对偶理论将该问题转化为对偶形式,将下层模型的对偶形式定义为内层主问题,对偶形式如下: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:
π1≥1π 1 ≥1
π2≥1π 2 ≥1
π3≥1π 3 ≥1
π4≥-1π 4 ≥ -1
π5≥-1π6≥-1π 5 ≥ -1π 6 ≥ -1
式中,RESULTSP-MP为内层主问题的辅助变量,由于对偶形式中的μEL,s,t、μFC,s,t与都为整数变量,对偶问题无法求解,对于这些变量分别给定初值 与新的对偶形式如下: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:
将新的对偶形式做线性化处理,在进行求解后确定故障场景集合,得到新的下层模型的形式,并定义为内层子问题: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:
RESULTSP-SP=max(Re1+Rh1+Re2-Ccom-Cwloss-Closs)RESULT SP-SP =max(R e1 +R h1 +R e2 -C com -C wloss -C loss )
式中,RESULTSP-SP为内层子问题的辅助变量。Where RESULT SP-SP is the auxiliary variable of the inner subproblem.
进一步的,步骤7中,采用嵌套列约束生成算法对容量规划模型进行求解,嵌套列约束生成算法的具体步骤如下: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)令上层模型的初始下界OTLdown=-∞,初始上界OTLup=∞,上层模型的初始迭代次数numOTL=1,上层迭代的收敛间隙为δOTL;下层模型的初始下界INLdown=-∞,初始上界INLup=∞,下层模型的初始迭代次数numINL=1,下层迭代的收敛间隙为δINL;(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)给定初始的故障场景,合并入场景不确定集中,并求解外层主问题,得到各个设备的容量规划方案,用OTLup=min{OTLup,RESULTMP}更新上层模型的上界;(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)将上层模型所得的容量规划结果输入至内层主问题中,并给内层主问题中的整数变量设置一组预设的初值,将其合并入整数变量场景集合中,对内层主问题进行求解,利用INLdown=max{INLdown,RESULTSP-MP}确定下层模型的下界,将容量规划结果与内层主问题求解出的故障场景带入到内层子问题中进行求解,得到下层模型的上界INLup=min{INLup,RESULTSP-SP};(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)依据|INLup-INLdown|≤δINL判断下层模型是否收敛,若满足条件,则得出下层模型的最优解并作为上层模型的下界OTLdown,进行过程(5);若不满足,则numINL=numINL+1,将内层子问题求出的整数变量合并入整数变量场景集合中,并生成新的变量与约束,返回至过程(3);(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)依据|OTLup-OTLdown|≤δOTL,判断上层模型是否收敛,若不满足条件,则numOTL=numOTL+1,将下层模型所求解出的故障场景合并入场景不确定集中,增加新的变量与约束,返回至过程(2);若满足,则得出上层模型的最优解,进行过程(6);(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)输出容量规划结果,求解结束。(6) Output the capacity planning results and the solution is completed.
有益效果:与现有技术相比,本发明的技术方案具有以下有益技术效果:Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:
该发明将氢能设备应用于海上风电系统中,可将富余的风电以氢能形式储存,并在风电出力不足时可以通过燃料电池保障供电,有利于解决由风电出力波动大所导致的问题,并提升了供电保障能力。该发明在容量规划时考虑了不确定性故障,使得系统中发生故障时能够尽可能的减少失负荷量,进一步提升了供电可靠性。本发明在进行容量规划时考虑了设备的不确定故障,减小了因设备故障而导致的失负荷,提升了供电可靠性。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.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为本发明的方法流程图;Fig. 1 is a flow chart of the method of the present invention;
图2为海上电氢系统结构示意图;Figure 2 is a schematic diagram of the structure of an offshore electric hydrogen system;
图3为故障场景1负荷图;Figure 3 is a load diagram for fault scenario 1;
图4为故障场景2负荷图;Figure 4 is a load diagram for fault scenario 2;
图5为故障场景3负荷图。Figure 5 is the load diagram for fault scenario 3.
具体实施方式DETAILED DESCRIPTION
如图1所示,本发明提出一种考虑不确定性故障的海上电氢系统容量规划方法,该方法包括以下步骤: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根据电氢系统中电解槽、燃料电池、储氢罐与输电线的容量规划以及电氢系统正常运行与故障运行,构建海上电氢系统容量规划模型的目标函数;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建立电解槽、燃料电池与输电线的设备故障模型;2. Establish equipment failure models for electrolyzers, fuel cells, and transmission lines;
3基于步骤2中所建立的电解槽、燃料电池与输电线的设备故障模型,构建海上电氢系统的故障不确定集合;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根据所述的目标函数与设备故障模型得出海上电氢系统容量规划模型的约束条件;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将步骤1中的目标函数,步骤2中的电解槽、燃料电池与输电线的设备故障模型,步骤3中的海上电氢系统的故障不确定集合与步骤4中的约束条件作为海上电氢系统容量规划模型,并写出其线性化形式;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基于步骤5中提出的海上电氢系统容量规划模型的线性化形式,写出对偶形式;6 Based on the linearized form of the offshore electric-hydrogen system capacity planning model proposed in step 5, write the dual form;
7基于步骤5中海上电氢系统容量规划模型及其线性化形式与步骤6中的对偶形式,使用嵌套列约束生成算法对容量规划模型进行求解,根据求解结果对该模型进行容量规划。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.
进一步的,步骤1的具体过程如下:Furthermore, the specific process of step 1 is as follows:
构建海上电氢系统容量规划模型的目标函数,目标函数的形式如下:The objective function of the offshore electric hydrogen system capacity planning model is constructed. The objective function is in the following form:
式中,uf表示所有组件状态的不确定性变量向量;U表示组件状态的不确定性集合;se表示所有场景状态的不确定性变量向量;Ssce表示场景状态的不确定性集合;r为折现率;m为运行年限;PELmax、PFCmax、Vhmax、Ptrans分别为电解槽、燃料电池、储氢罐与输电线的规划容量;L为海缆长度;ek为各设备规划的相关系数,k=1,2,...,5,其中,k=1表示电解槽、k=2表示燃料电池、k=3表示储氢罐、k=4表示输电线、k=5表示基础设施;eHVDC1与eHVDC2分别为换流站规划的固定系数和与输电线容量相关的系数;Re1、Rh1、Re2分别为向上层电网供电产生的输出量,供氢产生的输出量与向负荷供电产生的输出量;Ccom、Cwloss、Closs分别表示电氢系统运行所需要的维护成本,未被消纳的风电功率导致的惩罚,失负荷功率导致的惩罚;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;
目标函数中部分参数的具体表达式如下:The specific expressions of some parameters in the objective function are as follows:
式中,s表示系统运行的场景,不同场景下风电机组的出力不同;将s∈Ωnor下的所有场景的运行定义为电氢系统正常运行,将s∈Ωxtm下的所有场景的运行定义为电氢系统故障运行;Ωnor为电氢系统正常运行的所有场景;Ωxtm为电氢系统故障运行的所有场景;t表示运行时刻,T为运行的总时刻数;Ke1,t、Kh、Ke2分别为向上层电网供电的相关参数,供氢相关参数与向负荷供电的相关参数;μloss为输电消耗系数;Pnet,s,t为输送至上层电网的功率;Vhsell,s,t为输出给氢负荷的氢气量;Pwload,s,t为风电供给负荷功率;PFC1,s,t为燃料电池供应给负荷的功率;Qk为各设备的运维系数,k=1,2,...,5;Qh1为电解槽与制氢量相关的运维系数;Qh2为燃料电池与耗氢量相关的运维系数;VFC,s,t为燃料电池消耗氢气体积;VEL,s,t表示t时刻下电解槽的产氢体积;Ploss,s,t与closs分别为失负荷功率与失负荷的惩罚系数;Pwloss,s,t表示场景为s、时刻为t时未被消纳的风电功率;cwloss为未被消纳风电功率的惩罚系数;π1~π6为各公式对应的对偶变量。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.
进一步,步骤2的具体过程如下:Further, the specific process of step 2 is as follows:
(201)建立包括了燃料电池内电流与电压关系,燃料电池耗氢与产电关系以及燃料电池运行约束的燃料电池的设备故障模型,具体表述如下:(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·kf·F·Ufc,s,t·VFC,s,t P′ FC,s,t =2·k f ·F·U fc,s,t ·V FC,s,t
μFC,s,t·PFC min≤PFC,s,t≤μFC,s,t·PFC max μ FC,s,t ·P FC min ≤P FC,s,t ≤μ FC,s,t ·P FC max
式中,Ufc,s,t与Ifc,s,t分别表示燃料电池的运行电压与电流;τ1、τ2、τ3、τ4燃料电池电动势的相关系数;Tfc为燃料电池运行温度;与分别为燃料电池氢界面与氧界面分压;ξi为经验系数,i=1,2,...,4;为阴极气液面的氧气浓度;Jfc max为燃料电池最大电流密度;Afc表示燃料电池活化面积;B为常系数;Rm为等效膜阻抗;Rc为膜的等效接触电阻;P′FC,s,t和PFC,s,t分别为燃料电池的理想输出功率与实际输出功率;kf为单位转换系数;F为法拉第常数;表示燃料电池在场景s下所处的状态,q=1,2,...,5;为燃料电池在不同运行状态下的工作效率;PFC min为燃料电池输出功率的最小值;μFC,s,t为燃料电池的启停状态,分别表示燃料电池四个组件的状态;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)建立包括了电解槽的耗电与产氢关系,电解槽运行功率与电流关系和电解槽运行约束的电解槽的设备故障模型,具体表述如下:(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:
式中,Iel,s,t表示电解槽的运行电流;Tel为电解槽运行温度;Ael为电解槽的有效反应面积;Urev为电解槽的可逆电压;和分别表示正常运行下碱液的欧姆电阻,降额运行下碱液的欧姆电阻和碱液的热阻系数;为拟合得到的电极过电压系数;ηf为法拉第效率;PEL,s,t表示t时刻下电解槽的耗电功率;表示不同运行状态下电解槽的耗电功率,z=1,2,3;PEL min表示电解槽耗电功率的最小值;表示电解槽的运行状态;μEL,s,t表示电解槽的启停状态;分别表示电解槽两个组件的状态;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)输电线的设备故障模型(203) Equipment Failure Model of Transmission Line
当输电线未发生故障时,要求向上层电网输送的功率不能超过其容量;当输电线发生故障时,电氢系统将不再与上层电网连接,向上层电网输送的功率为0,考虑故障的输电线容量约束如下: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≤Pnet,s,t≤υjtrans,s·Ptrans 0≤P net,s,t ≤υ jtrans,s ·P trans
式中,jtrans表示输电线中发生故障的组件;υjtrans,s表示输电线中组件jtrans在场景s下的状态,υjtrans,s=1表示组件正常运行,υjtrans,s=0则表示组件发生故障。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.
进一步的,步骤3的具体过程如下:Furthermore, the specific process of step 3 is as follows:
构建海上电氢系统的故障不确定集合,对每一故障场景中的组件故障数与每一组件全年发生故障的总次数做出限制,并对所有场景中故障场景数量进行限制: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:
uf=[ujel;ujfc;ujtrans]u f = [u jel ; u jfc ; u jtrans ]
式中,Ωs为运行场景集合;jel,jfc分别表示电解槽与燃料电池中发生故障的组件;nel,nfc,ntrans分别表示电解槽,燃料电池与输电线中的组件个数;λjel,s表示电解槽中组件jel在场景s下的状态,λjel,s=1表示组件正常运行,λjel,s=0则表示组件发生故障;ζjfc,s表示燃料电池中组件jfc在场景s下的状态,ζjfc,s=1表示组件正常运行,ζjfc,s=0则表示组件发生故障;令Ωxtm中场景s的个数为Ns;Nxtm为故障场景中的组件故障上限,Nsce为组件一年内的故障总次数上限;ujel,ujfc,ujtrans分别为λjel,s、ζjfc,s与υjtrans,s的变量向量形式;ssce,s表示场景s的状态。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.
进一步的,步骤4的具体过程如下:Furthermore, the specific process of step 4 is as follows:
建立考虑不确定性故障的海上电氢系统容量规划模型的约束条件:Establish constraints for the offshore electric-hydrogen system capacity planning model considering uncertain faults:
(401)功率平衡约束:(401) Power balance constraint:
式中,Pload,s,t为负荷功率;Pw,s,t和Pwnet,s,t分别表示t时刻风力发电量与风电输送给上层电网的功率;为功率平衡约束中各公式对应的对偶变量;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)储氢罐约束:(402) Hydrogen storage tank constraints:
式中,Vh,s,t为储氢罐内的气体容量;Vhload,s,t为氢负荷需求;Vh0和VhT为初、末时段储氢罐的氢气体积;为储氢罐约束中各公式对应的对偶变量。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.
进一步的,步骤5的具体过程如下:Furthermore, the specific process of step 5 is as follows:
上述的海上电氢系统容量规划模型为非线性混合整数规划问题,其中,电解槽、燃料电池与输电线的设备故障模型包含了非线性变量,采用线性拟合与线性化处理方法写出海上电氢系统容量规划模型的线性化形式;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)电解槽的设备故障模型的线性化形式如下:(501) The linearized form of the equipment failure model of the electrolytic cell is as follows:
式中,bigM为一个常数;Nel为电解槽数量;为Nel与相乘的结果;为Nel与相乘的结果;为与μEL,s,t相乘的结果;为与μEL,s,t相乘的结果;Iel min与Iel max分别为电解槽的最小运行电流与最大运行电流;与分别表示电解槽在不同运行状态下Iel,s,t与Nel的乘积;与分别表示在线性拟合后与和相关的系数;与分别表示在线性拟合后与和相关的系数;与为电解槽的设备故障模型的线性化形式中各公式对应的对偶变量;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)燃料电池的设备故障模型的线性化形式如下:(502) The linearized form of the fuel cell equipment failure model is as follows:
PFC max=(kfc1·Ifc max+kfc2)·Nfc P FC max =(k fc1 ·I fc max +k fc2 )·N fc
式中,kfc1与kfc2分别表示PFC,s,t在线性拟合后与INfcs,t和相关的系数;Nfc表示燃料电池数量;INfcs,t表示Ifc,s,t与Nfc的乘积;Ifc min与Ifc max分别表示燃料电池最小运行电流与最大运行电流;V′FC,s,t表示理想状态下燃料电池消耗的氢气体积;表示μFC,s,t与的乘积;表示与Nfc的乘积;表示与V′FC,s,t的乘积;表示与V′FC,s,t的乘积;表示与V′FC,s,t的乘积;为燃料电池的设备故障模型的线性化形式中各公式对应的对偶变量;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)输电线的设备故障模型的线性化形式如下:(503) The linearized form of the equipment failure model of the transmission line is as follows:
式中,表示Ptrans与υjtrans,s的乘积;与为输电线的设备故障模型的线性化形式中各公式对应的对偶变量。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.
进一步的,步骤6的具体过程如下:Furthermore, the specific process of step 6 is as follows:
(601)将容量规划模型中不受uf与se影响的部分定义为规划阶段,海上电氢系统容量规划模型目标函数的形式如下:(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)该容量规划方法为两阶段鲁棒优化问题,包括了上层模型与下层模型,将上层模型定义为外层主问题,下层模型定义为外层子问题,其中外层主问题如下所示:(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:
RESULTMP≤(Re1+Rh1+Re2-Ccom-Cwloss-Closs)RESULT MP ≤(R e1 +R h1 +R e2 -C com -C wloss -C loss )
式中,RESULTMP为外层主问题的辅助变量,其作用是对外层子问题目标函数的松弛;外层主问题的约束包括了电解槽、燃料电池与输电线的设备故障模型,功率平衡约束与储氢罐约束;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)下层模型的形式如下:(603) The lower model is in the following form:
下层模型的约束包括了电解槽、燃料电池与输电线的设备故障模型的线性化形式,功率平衡约束、储氢罐约束与海上电氢系统的故障不确定集合,下层模型为min-max问题,为进行求解,基于强对偶理论将该问题转化为对偶形式,将下层模型的对偶形式定义为内层主问题,对偶形式如下: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:
π1≥1π 1 ≥1
π2≥1π 2 ≥1
π3≥1π 3 ≥1
π4≥-1π 4 ≥ -1
π5≥-1π 5 ≥ -1
π6≥-1π 6 ≥ -1
式中,RESULTSP-MP为内层主问题的辅助变量,由于对偶形式中的μEL,s,t、μFC,s,t与都为整数变量,对偶问题无法求解,对于这些变量分别给定初值 与新的对偶形式如下: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:
将新的对偶形式做线性化处理,在进行求解后确定故障场景集合,得到新的下层模型的形式,并定义为内层子问题: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:
RESULTSP-SP=max(Re1+Rh1+Re2-Ccom-Cwloss-Closs)RESULT SP-SP =max(R e1 +R h1 +R e2 -C com -C wloss -C loss )
式中,RESULTSP-SP为内层子问题的辅助变量。Where RESULT SP-SP is the auxiliary variable of the inner subproblem.
进一步的,步骤7中,采用嵌套列约束生成算法对容量规划模型进行求解,嵌套列约束生成算法的具体步骤如下: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)令上层模型的初始下界OTLdown=-∞,初始上界OTLup=∞,上层模型的初始迭代次数numOTL=1,上层迭代的收敛间隙为δOTL;下层模型的初始下界INLdown=-∞,初始上界INLup=∞,下层模型的初始迭代次数numINL=1,下层迭代的收敛间隙为δINL;(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)给定初始的故障场景,合并入场景不确定集中,并求解外层主问题,得到各个设备的容量规划方案,用OTLup=min{OTLup,RESULTMP}更新上层模型的上界;(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)将上层模型所得的容量规划结果输入至内层主问题中,并给内层主问题中的整数变量设置一组预设的初值,将其合并入整数变量场景集合中,对内层主问题进行求解,利用INLdown=max{INLdown,RESULTSP-MP}确定下层模型的下界,将容量规划结果与内层主问题求解出的故障场景带入到内层子问题中进行求解,得到下层模型的上界INLup=min{INLup,RESULTSP-SP};(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)依据|INLup-INLdown|≤δINL判断下层模型是否收敛,若满足条件,则得出下层模型的最优解并作为上层模型的下界OTLdown,进行过程(5);若不满足,则numINL=numINL+1,将内层子问题求出的整数变量合并入整数变量场景集合中,并生成新的变量与约束,返回至过程(3);(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)依据|OTLup-OTLdown|≤δOTL,判断上层模型是否收敛,若不满足条件,则numOTL=numOTL+1,将下层模型所求解出的故障场景合并入场景不确定集中,增加新的变量与约束,返回至过程(2);若满足,则得出上层模型的最优解,进行过程(6);(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)输出容量规划结果,求解结束。(6) Output the capacity planning results and the solution is completed.
所建立的海上电氢系统的典型结构如图2所示。该系统包括了风电机组,电解槽,燃料电池,储氢罐,上层电网,氢负荷。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.
以小时为时间尺度,令Nxtm与Nsce都为1,Ns的值为3,根据所建立的模型获得海上风电-系统氢能系统的容量规划结果,结果如表1所示,故障时的失负荷量如表2所示。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.
表1优化配置前与优化配置后的容量对比Table 1 Capacity comparison before and after optimization configuration
表2容量优化前后调度结果对比Table 2 Comparison of scheduling results before and after capacity optimization
所得结果表明,在容量规划时考虑不确定故障后,故障期间的失负荷相较于优化前有明显的降低,证明了在考虑不确定故障可以有效提升海上电氢系统的供电保障能力。而在优化前后正常情况下的弃风率都小于0.3%,说明采取优化方法并不会影响系统的风电消纳能力。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.
图3~图5为本发明所确定的三个故障场景下的运行情况,其中,图3、图4、图5中的(a)都为未采用本发明时的电氢系统运行情况,图3、图4、图5中的(b)都为采用本发明以后的电氢系统运行情况。通过对比分析可知,在采用本发明后,电氢系统故障运行时系统的失负荷量明显减少,而燃料电池的出力相较于未采取本发明时有一定幅度的增加。这是由于燃料电池与储氢罐容量的提升,为电氢系统在故障运行提供了更多的电力,从而降低了失负荷,证明了在容量规划时考虑不确定性故障具有可行性。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.
从各设备的规划容量方面,在采取该方法后,电解槽和与上层电网连接的输电线容量并没有发生明显变化,而增加了燃料电池与储氢罐的容量,这是因为在恶劣的故障场景中风电出力较少,此时风电无法单独完成保障供电的任务,需要燃料电池对电力缺失的部分进行供电,若此时燃料电池发生故障,其发电能力下降,可能无法达到完全供电的要求,因此在规划时会适当加大容量。此外,风电不足导致储氢罐无法获得额外的氢气来源,只能通过提升自身容量以保证故障发生时能有更多可用的氢气。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)
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202310939867.2A CN117200265B (en) | 2023-07-27 | 2023-07-27 | Marine electro-hydrogen system capacity planning method considering uncertainty fault |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202310939867.2A CN117200265B (en) | 2023-07-27 | 2023-07-27 | Marine electro-hydrogen system capacity planning method considering uncertainty fault |
Publications (2)
Publication Number | Publication Date |
---|---|
CN117200265A CN117200265A (en) | 2023-12-08 |
CN117200265B true CN117200265B (en) | 2024-05-28 |
Family
ID=89002448
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202310939867.2A Active CN117200265B (en) | 2023-07-27 | 2023-07-27 | Marine electro-hydrogen system capacity planning method considering uncertainty fault |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN117200265B (en) |
Families Citing this family (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN118485319B (en) * | 2024-07-11 | 2024-11-12 | 南京苏逸实业有限公司 | Robust planning method, device, electronic device and medium for electric-hydrogen integrated energy system |
Citations (7)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN108183512A (en) * | 2018-02-23 | 2018-06-19 | 南方电网科学研究院有限责任公司 | Reliability assessment method for power system accessed with new energy |
CN110909920A (en) * | 2019-11-07 | 2020-03-24 | 国网山东省电力公司经济技术研究院 | Power transmission network capacity planning optimization method and system considering multiple fault scenes |
CN111144620A (en) * | 2019-12-06 | 2020-05-12 | 东南大学 | An electric hydrogen integrated energy system considering seasonal hydrogen storage and its robust planning method |
CN113363964A (en) * | 2021-05-26 | 2021-09-07 | 国网天津市电力公司 | Power distribution network distributed energy storage planning method and device considering important load power supply |
CN115936265A (en) * | 2023-02-24 | 2023-04-07 | 华东交通大学 | Robust planning method for electric hydrogen energy system considering electric hydrogen coupling |
CN115940282A (en) * | 2022-07-15 | 2023-04-07 | 大连理工大学 | A capacity optimization configuration method for wind power hydrogen production energy storage system considering the constraint of hydrogen doping ratio |
WO2023134254A1 (en) * | 2022-01-11 | 2023-07-20 | 云南电网有限责任公司电力科学研究院 | Equipment model selection method for energy interconnection system |
Family Cites Families (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20210288493A1 (en) * | 2020-03-12 | 2021-09-16 | ComAp a.s. | Optimization of power generation from power sources using fault prediction based on intelligently tuned machine learning power management |
CN113393054B (en) * | 2021-07-05 | 2023-11-24 | 华北电力大学 | Optimal scheduling method and optimal scheduling system for wind-storage combined system |
-
2023
- 2023-07-27 CN CN202310939867.2A patent/CN117200265B/en active Active
Patent Citations (7)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN108183512A (en) * | 2018-02-23 | 2018-06-19 | 南方电网科学研究院有限责任公司 | Reliability assessment method for power system accessed with new energy |
CN110909920A (en) * | 2019-11-07 | 2020-03-24 | 国网山东省电力公司经济技术研究院 | Power transmission network capacity planning optimization method and system considering multiple fault scenes |
CN111144620A (en) * | 2019-12-06 | 2020-05-12 | 东南大学 | An electric hydrogen integrated energy system considering seasonal hydrogen storage and its robust planning method |
CN113363964A (en) * | 2021-05-26 | 2021-09-07 | 国网天津市电力公司 | Power distribution network distributed energy storage planning method and device considering important load power supply |
WO2023134254A1 (en) * | 2022-01-11 | 2023-07-20 | 云南电网有限责任公司电力科学研究院 | Equipment model selection method for energy interconnection system |
CN115940282A (en) * | 2022-07-15 | 2023-04-07 | 大连理工大学 | A capacity optimization configuration method for wind power hydrogen production energy storage system considering the constraint of hydrogen doping ratio |
CN115936265A (en) * | 2023-02-24 | 2023-04-07 | 华东交通大学 | Robust planning method for electric hydrogen energy system considering electric hydrogen coupling |
Non-Patent Citations (8)
Title |
---|
Distributionally Robust Co-Optimization of Energy and Reserve for Combined Distribution Networks of Power and District Heating;Yizhou Zhou等;IEEE TRANSACTIONS ON POWER SYSTEMS;20200531;第35卷(第3期);全文 * |
Investment equilibrium of an integrated multi-stakeholder electricity-gas-hydrogen system;Pan, GS (Pan, Guangsheng)等;RENEWABLE & SUSTAINABLE ENERGY REVIEWS;20210929;第150卷;全文 * |
Optimal Planning for Electricity-Hydrogen Integrated Energy System Considering Power to Hydrogen and Heat and Seasonal Storage;Guangsheng Pan;IEEE TRANSACTIONS ON SUSTAINABLE ENERGY;20201031;第11卷(第4期);全文 * |
区域综合能源系统的储能容量配置研究;郭志星;中国优秀硕士论文全文数据库;20220315;第2022卷(第3期);全文 * |
双碳目标下低碳综合能源系统规划关键技术及挑战;张沈习;电力系统自动化;20220425;第46卷(第8期);全文 * |
电力―天然气耦合系统建模与规划运行研究综述;乔铮;郭庆来;孙宏斌;;全球能源互联网;20200125(01);全文 * |
考虑暂态稳定性的网储多目标双层优化;方朝雄;吴晓升;江岳文;;电力建设;20200630(07);全文 * |
考虑热电综合利用的光伏储氢独立供能系统容量优化配置;熊宇峰;司杨;郑天文;陈来军;梅生伟;;中国电力;20201005(10);全文 * |
Also Published As
Publication number | Publication date |
---|---|
CN117200265A (en) | 2023-12-08 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
Xing et al. | Modeling and operation of the power-to-gas system for renewables integration: a review | |
Li et al. | Modeling and simulation of hydrogen energy storage system for power-to-gas and gas-to-power systems | |
CN109741110B (en) | A combined optimization modeling method for wind and hydrogen systems based on chance-constrained programming | |
US20200266468A1 (en) | Fuel cell control system | |
CN117200265B (en) | Marine electro-hydrogen system capacity planning method considering uncertainty fault | |
CN107046298A (en) | A kind of hydroenergy storage station capacity collocation method of the power system containing wind-powered electricity generation | |
CN116780646A (en) | Power system resource optimization scheduling method considering flexibility and terminal | |
CN117748453A (en) | Electric-hydrogen coupling system optimization operation method considering operation characteristics of electrolytic tank | |
CN114676897A (en) | Optimal scheduling method for comprehensive energy system of park containing CHP-P2G-hydrogen energy | |
CN117713228A (en) | A multi-energy coordination and optimization method and system for wind, solar and hydrogen energy storage systems | |
CN116562563A (en) | Power system optimization operation method based on minimum inertia demand evaluation | |
Wu et al. | Coordinated control algorithm of hydrogen production-battery based hybrid energy storage system for suppressing fluctuation of PV power | |
CN112332461A (en) | A multi-energy microgrid cluster control method based on a two-stage robust model | |
CN116070501A (en) | Reliability evaluation method for electric hydrogen energy system based on hydrogen energy equipment multi-state model | |
CN115907157A (en) | Site selection and volume fixing optimization method and terminal for adjustable resource joint planning | |
CN113949098B (en) | Island type hybrid micro-grid system reliability assessment method considering FCV | |
CN117060491B (en) | Operation optimization methods, systems, media and equipment of wind and solar hybrid energy storage systems | |
CN118569561A (en) | Energy base dispatching method and terminal based on distributed robust optimization method | |
CN117200270A (en) | An electrolysis hydrogen production system capacity optimization configuration method and related devices | |
CN117977710A (en) | Operation optimization control method and system for megawatt light-storage-hydrogen combined power generation system | |
CN117353318A (en) | Electric-hydrogen coupling system unit combination method for flexible excavation of electric hydrogen production | |
CN116227830A (en) | Virtual power plant optimization scheduling method containing CSP-P2G-CCUS | |
CN115378032A (en) | Electricity-hydrogen coordinated operation method of hydrogen-containing energy storage incremental power distribution network | |
JP7665253B1 (en) | Method and system for selecting equipment combinations in hydrogen energy full chain | |
Ma et al. | Optimal Configuration of Pumped-Hydrogen Coupling Energy Storage System for Island Microgrid |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PB01 | Publication | ||
PB01 | Publication | ||
SE01 | Entry into force of request for substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
GR01 | Patent grant | ||
GR01 | Patent grant |