复现文献：LFO正极补锂

复现下文献，标题：How to design a zero-degradation battery by
compensating for loss of lithium inventory in LFP
cells with LFO additives
但是没有找到LFO的开路电压数据集，LFP直接调用了Prada2013参数集，也没有选择电压滞后简单做个仿真

importpybammimportnumpyasnpimportmatplotlib.pyplotasplt# 1. LFO找不到开路电压数据，开编sto_data=np.array([0.00,0.02,0.05,0.10,0.20,0.30,0.40,0.50,0.60,0.70,0.80,0.90,0.95,0.98,1.00])ocp_data=np.array([4.50,# sto=0.00: 充电截止，完全脱锂4.35,# sto=0.02: 极化迅速下降段4.15,# sto=0.054.05,# sto=0.10: 进入第二平台 (4.0V 附近)3.98,# sto=0.20: 维持第二平台3.92,# sto=0.30: 平台末端3.75,# sto=0.40: 两个平台之间的过渡段3.60,# sto=0.50: 逼近第一平台3.52,# sto=0.60: 进入第一平台 (3.5V 附近)3.49,# sto=0.70: 维持第一平台3.47,# sto=0.80: 平台末端3.42,# sto=0.90: 开始迅速掉电压3.20,# sto=0.952.80,# sto=0.982.50# sto=1.00: 放电状态，完全嵌锂])# 封装为接收 sto 变量的函数，匹配模型参数接口deflfo_ocp(sto):returnpybamm.Interpolant(sto_data,ocp_data,sto,name="LFO_OCP",interpolator="cubic")# 2. 定义 LFO 的交换电流密度deflfo_exchange_current_density(c_e,c_s_surf,c_s_max,T):m_LFO=13.86e-7returnm_LFO*pybamm.sqrt(c_e*c_s_surf*(c_s_max-c_s_surf))# ==============================================================================# 3. 设置 PyBaMM 模型选项 (Model Options)# ==============================================================================model_options={# 负极为单相(石墨)，正极为双相 (相1: LFP, 相2: LFO)"particle phases":("1","2"),# 直接用参数集，假设LFP不存在滞后现象"open-circuit potential":("single",("single","single")),# 动力学设置：LFO 是不可逆单向脱锂，所以使用 Tafel 方程"intercalation kinetics":"symmetric Butler-Volmer"}# 实例化 DFN 模型model=pybamm.lithium_ion.DFN(model_options)#打印所有的子模块名称#print(model.submodels.keys())# 2. 强行把 LFO (Secondary phase) 的动力学子模型替换为你查到的 ForwardTafel 类model.submodels['positive secondary interface']=pybamm.kinetics.ForwardTafel(model.param,domain="positive",reaction="lithium-ion main",options=model.options,phase="secondary")# 3. 手动完成模型构建model.update()# 4. 参数实例化与 LFO 属性重写 (Parameterization)param=pybamm.ParameterValues("Prada2013")# 覆盖并添加 LFO (Secondary phase) 相关的文献参数param.update({# --- 体积与几何参数 ---"Secondary: Positive electrode active material volume fraction":pybamm.InputParameter('LFO_fraction'),"Secondary: Positive particle radius [m]":50e-8,# --- 浓度限制 ---"Secondary: Maximum concentration in positive electrode [mol.m-3]":22806.0*5.1,"Secondary: Initial concentration in positive electrode [mol.m-3]":22806.0*5.0,# --- 固相扩散参数 ---"Secondary: Positive particle diffusivity [m2.s-1]":9.83e-19,# --- 动力学与热力学参数 ---"Secondary: Positive electrode OCP [V]":lfo_ocp,"Secondary: Positive electrode exchange-current density [A.m-2]":lfo_exchange_current_density,# 将 LFO (Secondary phase) 的传递系数设定为 1.0 (阳极传递系数，配合 Tafel 动力学)"Secondary: Positive electrode charge transfer coefficient":1.0,"Secondary: Positive electrode OCP entropic change [V.K-1]":3,},check_already_exists=False)print("复合正极模型(LFP-LFO)构建完成，等待 LFO OCP 数据输入。")experiment=pybamm.Experiment(["Charge at 0.5C until 4.2V"])sim=pybamm.Simulation(model,parameter_values=param,experiment=experiment)sim.solve(inputs={'LFO_fraction':0.04*0.374})''' sim.plot([ "Terminal voltage [V]", "Positive primary particle surface concentration [mol.m-3]", "Positive secondary particle surface concentration [mol.m-3]" ]) '''sol=sim.solution Q_DC=sol['Discharge capacity [A.h]'].entries Q_CC=-(Q_DC-Q_DC[0])V_cell=sol['Terminal voltage [V]'].entries ocp_lfp=sol['X-averaged positive electrode primary open-circuit potential [V]'].entries ocp_lfo=sol['X-averaged positive electrode secondary open-circuit potential [V]'].entries ocp_neg=sol['X-averaged negative electrode open-circuit potential [V]'].entries c_lfo_percent=sol['Total lithium in secondary phase in positive electrode [mol]'].entries/sol['Total lithium in secondary phase in positive electrode [mol]'].entries[0]fig,ax1=plt.subplots(1,1,figsize=(8,10))ax1.plot(Q_CC,V_cell,color='black',label='cell voltage')ax1.plot(Q_CC,ocp_lfp,color='blue',linestyle='--',label='ocp_lfp')ax1.plot(Q_CC,ocp_lfo,color='green',linestyle='-.',label='ocp_lfo')ax1.legend(loc='lower right',fontsize=10)ax1.set_ylim(2.2,4.5)fromplot_templateimportplot_single_y plot_single_y(Q_CC,ocp_neg,xlabel='Q',ylabel='ocp_neg',legend_labels='ocp_neg')plot_single_y(Q_CC,c_lfo_percent,xlabel='Q',ylabel='c_lfo_percent',legend_labels='c_lfo_percent')plt.show()