134 lines
3.8 KiB
Matlab
134 lines
3.8 KiB
Matlab
%% battery.m
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%%
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%% Battery maths
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close all;clear all;clc;
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% Flags
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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INTEGER_CELLS = true;
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P_OUT_INCLUDES_P_IN = true; % subtract power in from power out
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% assumes that battery and generation coupled for connection to P out
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% Parameters
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%% 18650 Cell
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cell_voltage = 3.6; % V
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cell_capacity = 2850; % mAh
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cell_dis_c = 1; % 1/h
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cell_charge_c = 0.5; % 1/h
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cell_weight = 48; % g
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cell_dia = 18.4; % mm
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cell_height = 65; % mm
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cell_price = 6; % £
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cell_emb_c = 117.5; % kgCO2eq/kWh
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cell_rec_emb_c = 15; % kgCO2eq/kWh
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%%%%%%% P IN
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%V_IN = 450; % V
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%I_IN = 10; % A
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% above ignored if P_IN defined
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MAX_P_IN = 8e6; % W, max power from fuel cells
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P_IN_LOAD = 0.8; % most efficient load percent
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P_IN = MAX_P_IN * P_IN_LOAD; % W
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%%%%%%% P OUT
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V_OUT = 450; % V
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I_OUT = 10; % A
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% above ignored if P_OUT defined
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PROP_P_OUT = 8e6; % W, propulsion max output power
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HOTEL_P_OUT = 3e4; % W, hotel average power usage
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P_OUT = PROP_P_OUT + HOTEL_P_OUT; % W
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%%%%%%% unit conversions
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cell_capacity = 1e-3 * cell_capacity; % mAh to Ah
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cell_dia = 1e-3 * cell_dia; % mm to m
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cell_height = 1e-3 * cell_height; % mm to m
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cell_weight = 1e-3 * cell_weight; % g to kg
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% Series/Parallel
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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if exist('P_OUT') % SOLVE FOR CELLS USING POWER
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if P_OUT_INCLUDES_P_IN
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solvable_power = P_OUT - P_IN;
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else
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solvable_power = P_OUT;
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end
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total_cells = solvable_power / (cell_voltage * cell_dis_c * cell_capacity);
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series_length = sqrt(total_cells);
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parallel_length = series_length;
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if INTEGER_CELLS
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series_length = ceil(series_length);
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parallel_length = ceil(parallel_length);
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total_cells = series_length * parallel_length;
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end
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voltage_out = series_length * cell_voltage;
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current_out = parallel_length * cell_dis_c * cell_capacity;
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else % SOLVE FOR CELLS USING VOLTAGE AND CURRENT
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series_length = V_OUT / cell_voltage;
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% c-rate = current / capacity
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required_capacity = I_OUT / cell_dis_c;
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parallel_length = required_capacity / cell_capacity;
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if INTEGER_CELLS
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series_length = ceil(series_length);
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parallel_length = ceil(parallel_length);
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end
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total_cells = series_length * parallel_length;
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voltage_out = V_OUT;
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current_out = I_OUT;
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end
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max_power_out = voltage_out * current_out; % W
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total_capacity = parallel_length * cell_capacity; % Ah
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total_capacity_Wh = total_capacity * voltage_out; % Wh
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% Physical Space
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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cell_volume = (pi * (cell_dia/2)^2) * cell_height; % m^3
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total_volume = cell_volume * total_cells; % m^3
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total_weight = cell_weight * total_cells; % kg
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% Output
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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fprintf('%d cells arranged %d x %d cells\n', total_cells, series_length, parallel_length);
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fprintf('%.2f m3, weighs %.2f kg\n', total_volume, total_weight);
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fprintf('£%.2fM\n\n', total_cells * cell_price / 1e6);
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fprintf('%.2f Ah, %.2f MWh, \n', total_capacity, total_capacity_Wh / 1e6);
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fprintf('%.2f V, %.2f A for %.2f MW\n', voltage_out, current_out, max_power_out / 1e6);
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if P_OUT_INCLUDES_P_IN
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fprintf('Totals to %.2f MW including %.2f MW of coupled input power\n', P_OUT / 1e6, P_IN / 1e6);
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end
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fprintf('%.2ft (CO2e)\n', ((total_capacity_Wh / 1e3) * cell_emb_c) / 1e3);
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fprintf('%.2ft (CO2e) for recycling\n', ((total_capacity_Wh / 1e3) * cell_rec_emb_c) / 1e3);
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