How can I plot the graph with the highest, lowest and middle values?

num_simulations = 10000;

%Common parameters
Discount_Rate_min = 0.06;       % assume 6-8%
Discount_Rate_max = 0.08;
Discount_Rate_values = unifrnd(Discount_Rate_min, Discount_Rate_max, [num_simulations, 1]);

Lifetime = 20;    % years

Electricity_Cost_mean = 0.255;   %EUR/kWh
Electricity_Cost_std = 0.04;
Electricity_Cost_values = normrnd(Electricity_Cost_mean, Electricity_Cost_std, [num_simulations,1]);
Electricity_Cost_values(Electricity_Cost_values < 0.02) = 0.02;
Electricity_Cost_values(Electricity_Cost_values > 0.9) = 0.9;

% Define the 3-sigma range
lower_E = Electricity_Cost_mean - 3 * Electricity_Cost_std;
upper_E = Electricity_Cost_mean + 3 * Electricity_Cost_std;
mean_E = Electricity_Cost_mean;

FLH_min = 1000;       
FLH_max = 8760;
FLH = unifrnd(FLH_min, FLH_max, [num_simulations, 1]);

LHV = 33.33;    %kWh/kgH2

%SOEC parameters
CAPEX_System_SOEC_mean = 4200;     %$/kW
CAPEX_System_SOEC_std = 500;
CAPEX_System_SOEC_values = normrnd(CAPEX_System_SOEC_mean, CAPEX_System_SOEC_std, [num_simulations,1]);
CAPEX_System_SOEC_values(CAPEX_System_SOEC_values < 2800) = 2800;
CAPEX_System_SOEC_values(CAPEX_System_SOEC_values > 5600) = 5600;

CAPEX_Stack_SOEC_values = 0.5*CAPEX_System_SOEC_values;    % 50% of CAPEX system 

CAPEX_SOEC_values = (CAPEX_System_SOEC_values + CAPEX_Stack_SOEC_values);

OPEX_SOEC_values = 3;   % 3% of CAPEX/a

System_Efficiency_SOEC_mean = 0.775;
System_Efficiency_SOEC_std = 0.05;
System_Efficiency_SOEC_values = normrnd(System_Efficiency_SOEC_mean, System_Efficiency_SOEC_std, [num_simulations,1]);
System_Efficiency_SOEC_values(System_Efficiency_SOEC_values < 0.74) = 0.74;
System_Efficiency_SOEC_values(System_Efficiency_SOEC_values > 0.81) = 0.81;

%PEM parameters
CAPEX_System_PEM_mean = 1450;      %$/kW
CAPEX_System_PEM_std = 50;
CAPEX_System_PEM_values = normrnd(CAPEX_System_PEM_mean, CAPEX_System_PEM_std, [num_simulations,1]);
CAPEX_System_PEM_values(CAPEX_System_PEM_values < 1100) = 1100;
CAPEX_System_PEM_values(CAPEX_System_PEM_values > 1800) = 1800;

CAPEX_Stack_PEM_values = 0.35*CAPEX_System_PEM_values;    % 35% of CAPEX system

CAPEX_PEM_values = (CAPEX_System_PEM_values + CAPEX_Stack_PEM_values);

OPEX_PEM_values = 3;

System_Efficiency_PEM_mean = 0.58;
System_Efficiency_PEM_std = 0.01;
System_Efficiency_PEM_values = normrnd(System_Efficiency_PEM_mean, System_Efficiency_PEM_std, [num_simulations,1]);
System_Efficiency_PEM_values(System_Efficiency_PEM_values < 0.56) = 0.56;
System_Efficiency_PEM_values(System_Efficiency_PEM_values > 0.6) = 0.6;

%AEC parameters
CAPEX_System_AEC_mean = 950;     % $/kW
CAPEX_System_AEC_std = 50;
CAPEX_System_AEC_values = normrnd(CAPEX_System_AEC_mean, CAPEX_System_AEC_std, [num_simulations,1]);
CAPEX_System_AEC_values(CAPEX_System_AEC_values < 500) = 500;
CAPEX_System_AEC_values(CAPEX_System_AEC_values > 1400) = 1400;

CAPEX_Stack_AEC_values = 0.35*CAPEX_System_AEC_values;     % 35% of CAPEX system

CAPEX_AEC_values = (CAPEX_System_AEC_values + CAPEX_Stack_AEC_values);

OPEX_AEC_values = 3;

System_Efficiency_AEC_mean = 0.665;
System_Efficiency_AEC_std = 0.05;
System_Efficiency_AEC_values = normrnd(System_Efficiency_AEC_mean, System_Efficiency_AEC_std, [num_simulations,1]);
System_Efficiency_AEC_values(System_Efficiency_AEC_values < 0.63) = 0.63;
System_Efficiency_AEC_values(System_Efficiency_AEC_values > 0.7) = 0.7;

% Calculate SOEC LCOH values
term1_S = LHV ./ (System_Efficiency_SOEC_values);
term2_S = Discount_Rate_values .* (1 + Discount_Rate_values).^Lifetime;
term3_S = (OPEX_SOEC_values / 100);
term4_S = CAPEX_SOEC_values ./ FLH;
Lower_LCOH_SOEC = term1_S .* ((term2_S ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_S) .* term4_S + lower_E);
Upper_LCOH_SOEC = term1_S .* ((term2_S ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_S) .* term4_S + upper_E);
Mean_LCOH_SOEC = term1_S .* ((term2_S ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_S) .* term4_S + mean_E);

% Calculate PEM LCOH values
term1_P = LHV ./ (System_Efficiency_PEM_values);
term2_P = Discount_Rate_values .* (1 + Discount_Rate_values).^Lifetime;
term3_P = (OPEX_PEM_values / 100);
term4_P = CAPEX_PEM_values ./ FLH;
Lower_LCOH_PEM = term1_P .* ((term2_P ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_P) .* term4_P + lower_E);
Upper_LCOH_PEM = term1_P .* ((term2_P ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_P) .* term4_P + upper_E);
Mean_LCOH_PEM = term1_P .* ((term2_P ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_P) .* term4_P + mean_E);

% Calculate AEC LCOH values
term1_A = LHV ./ (System_Efficiency_AEC_values);
term2_A = Discount_Rate_values .* (1 + Discount_Rate_values).^Lifetime;
term3_A = (OPEX_AEC_values / 100);
term4_A = CAPEX_AEC_values ./ FLH;
Lower_LCOH_AEC = term1_A .* ((term2_A ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_A) .* term4_A + lower_E);
Upper_LCOH_AEC = term1_A .* ((term2_A ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_A) .* term4_A + upper_E);
Mean_LCOH_AEC = term1_A .* ((term2_A ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_A) .* term4_A + mean_E);

% Calculate average values for mean LCOH
Avg_Lower_LCOH_SOEC = mean(Lower_LCOH_SOEC, 2);
Avg_Upper_LCOH_SOEC = mean(Upper_LCOH_SOEC, 2);
Avg_Mean_LCOH_SOEC = mean(Mean_LCOH_SOEC, 2);

Avg_Lower_LCOH_PEM = mean(Lower_LCOH_PEM, 2);
Avg_Upper_LCOH_PEM = mean(Upper_LCOH_PEM, 2);
Avg_Mean_LCOH_PEM = mean(Mean_LCOH_PEM, 2);

Avg_Lower_LCOH_AEC = mean(Lower_LCOH_AEC, 2);
Avg_Upper_LCOH_AEC = mean(Upper_LCOH_AEC, 2);
Avg_Mean_LCOH_AEC = mean(Mean_LCOH_AEC, 2);

% Plot the graph for lower, upper, and mean LCOH of SOEC, PEM, and AEC
figure;

% Plot SOEC
plot(FLH, Lower_LCOH_SOEC, 'b-', 'LineWidth', 1.5);
hold on;
plot(FLH, Upper_LCOH_SOEC, 'b-', 'LineWidth', 1.5);
plot(FLH, Mean_LCOH_SOEC, 'b--', 'LineWidth', 1.5);

% Plot PEM
plot(FLH, Lower_LCOH_PEM, 'g-', 'LineWidth', 1.5);
plot(FLH, Upper_LCOH_PEM, 'g-', 'LineWidth', 1.5);
plot(FLH, Mean_LCOH_PEM, 'g--', 'LineWidth', 1.5);

% Plot AEC
plot(FLH, Lower_LCOH_AEC, 'm-', 'LineWidth', 1.5);
plot(FLH, Upper_LCOH_AEC, 'm-', 'LineWidth', 1.5);
plot(FLH, Mean_LCOH_AEC, 'm--', 'LineWidth', 1.5);

xlabel('FLH');
ylabel('LCOH');
title('LCOH vs FLH for SOEC, PEM, and AEC');
legend('Lower SOEC', 'Upper SOEC', 'Mean SOEC', 'Lower PEM', 'Upper PEM', 'Mean PEM', 'Lower AEC', 'Upper AEC', 'Mean AEC');
grid on;
hold off;

This result is below;

How can I plot the line graph with the highest value of Upper, the lowest value of Lower, and mean value of Mean?

Image is like this;

[Star Strider]

Related post — How to change the graph type

Answer 1

[Torsten]

Add the lines

[FLH,I] = sort(FLH);

Lower_LCOH_SOEC = Lower_LCOH_SOEC(I);
Upper_LCOH_SOEC = Upper_LCOH_SOEC(I);
Mean_LCOH_SOEC = Mean_LCOH_SOEC(I);

Lower_LCOH_PEM = Lower_LCOH_PEM(I);
Upper_LCOH_PEM = Upper_LCOH_PEM(I);
Mean_LCOH_PEM = Mean_LCOH_PEM(I);

Lower_LCOH_AEC = Lower_LCOH_AEC(I);
Upper_LCOH_AEC = Upper_LCOH_AEC(I);
Mean_LCOH_AEC = Mean_LCOH_AEC(I);

for that FLH is ordered.

But I doubt that the data for the curves in the image were obtained in the same way as your Lower/Upper/Mean arrays.

[Minhee]

The graph is still like this.

Answer 2

[Aquatris]

do you know of functions min(), max() and mean()? Example

% generate random data
t = (0:0.01:10)';
x = exp(-.2*t).*(2+(2*rand(length(t),5)-1)*0.01); %  n x 5 data set

plot(t,x,'g',t,min(x,[],2),'r--',t,max(x,[],2),'b--',t,mean(x,2),'m--')
xlim([2 2.5])

Answer 3

[Torsten]

Yes, I corrected one mistake in your code, but I also wrote that I don't think that the curves in the image were produced the way you try to do it.

What are the curves in the image ? Probability density functions ?

I tried "movmean" and "cumtrapz" to average your values.

num_simulations = 1000000;
%Common parameters
Discount_Rate_min = 0.06;       % assume 6-8%
Discount_Rate_max = 0.08;
Discount_Rate_values = unifrnd(Discount_Rate_min, Discount_Rate_max, [num_simulations, 1]);
Lifetime = 20;    % years
Electricity_Cost_mean = 0.255;   %EUR/kWh
Electricity_Cost_std = 0.04;
Electricity_Cost_values = normrnd(Electricity_Cost_mean, Electricity_Cost_std, [num_simulations,1]);
Electricity_Cost_values(Electricity_Cost_values < 0.02) = 0.02;
Electricity_Cost_values(Electricity_Cost_values > 0.9) = 0.9;
% Define the 3-sigma range
lower_E = Electricity_Cost_mean - 3 * Electricity_Cost_std;
upper_E = Electricity_Cost_mean + 3 * Electricity_Cost_std;
mean_E = Electricity_Cost_mean;
FLH_min = 1000;       
FLH_max = 8760;
FLH = unifrnd(FLH_min, FLH_max, [num_simulations, 1]);
LHV = 33.33;    %kWh/kgH2
%SOEC parameters
CAPEX_System_SOEC_mean = 4200;     %$/kW
CAPEX_System_SOEC_std = 500;
CAPEX_System_SOEC_values = normrnd(CAPEX_System_SOEC_mean, CAPEX_System_SOEC_std, [num_simulations,1]);
CAPEX_System_SOEC_values(CAPEX_System_SOEC_values < 2800) = 2800;
CAPEX_System_SOEC_values(CAPEX_System_SOEC_values > 5600) = 5600;
CAPEX_Stack_SOEC_values = 0.5*CAPEX_System_SOEC_values;    % 50% of CAPEX system 
CAPEX_SOEC_values = (CAPEX_System_SOEC_values + CAPEX_Stack_SOEC_values);
OPEX_SOEC_values = 3;   % 3% of CAPEX/a
System_Efficiency_SOEC_mean = 0.775;
System_Efficiency_SOEC_std = 0.05;
System_Efficiency_SOEC_values = normrnd(System_Efficiency_SOEC_mean, System_Efficiency_SOEC_std, [num_simulations,1]);
System_Efficiency_SOEC_values(System_Efficiency_SOEC_values < 0.74) = 0.74;
System_Efficiency_SOEC_values(System_Efficiency_SOEC_values > 0.81) = 0.81;
%PEM parameters
CAPEX_System_PEM_mean = 1450;      %$/kW
CAPEX_System_PEM_std = 50;
CAPEX_System_PEM_values = normrnd(CAPEX_System_PEM_mean, CAPEX_System_PEM_std, [num_simulations,1]);
CAPEX_System_PEM_values(CAPEX_System_PEM_values < 1100) = 1100;
CAPEX_System_PEM_values(CAPEX_System_PEM_values > 1800) = 1800;
CAPEX_Stack_PEM_values = 0.35*CAPEX_System_PEM_values;    % 35% of CAPEX system
CAPEX_PEM_values = (CAPEX_System_PEM_values + CAPEX_Stack_PEM_values);
OPEX_PEM_values = 3;
System_Efficiency_PEM_mean = 0.58;
System_Efficiency_PEM_std = 0.01;
System_Efficiency_PEM_values = normrnd(System_Efficiency_PEM_mean, System_Efficiency_PEM_std, [num_simulations,1]);
System_Efficiency_PEM_values(System_Efficiency_PEM_values < 0.56) = 0.56;
System_Efficiency_PEM_values(System_Efficiency_PEM_values > 0.6) = 0.6;
%AEC parameters
CAPEX_System_AEC_mean = 950;     % $/kW
CAPEX_System_AEC_std = 50;
CAPEX_System_AEC_values = normrnd(CAPEX_System_AEC_mean, CAPEX_System_AEC_std, [num_simulations,1]);
CAPEX_System_AEC_values(CAPEX_System_AEC_values < 500) = 500;
CAPEX_System_AEC_values(CAPEX_System_AEC_values > 1400) = 1400;
CAPEX_Stack_AEC_values = 0.35*CAPEX_System_AEC_values;     % 35% of CAPEX system
CAPEX_AEC_values = (CAPEX_System_AEC_values + CAPEX_Stack_AEC_values);
OPEX_AEC_values = 3;
System_Efficiency_AEC_mean = 0.665;
System_Efficiency_AEC_std = 0.05;
System_Efficiency_AEC_values = normrnd(System_Efficiency_AEC_mean, System_Efficiency_AEC_std, [num_simulations,1]);
System_Efficiency_AEC_values(System_Efficiency_AEC_values < 0.63) = 0.63;
System_Efficiency_AEC_values(System_Efficiency_AEC_values > 0.7) = 0.7;
% Calculate SOEC LCOH values
term1_S = LHV ./ (System_Efficiency_SOEC_values);
term2_S = Discount_Rate_values .* (1 + Discount_Rate_values).^Lifetime;
term3_S = (OPEX_SOEC_values / 100);
term4_S = CAPEX_SOEC_values ./ FLH;
Lower_LCOH_SOEC = term1_S .* ((term2_S ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_S) .* term4_S + lower_E);
Upper_LCOH_SOEC = term1_S .* ((term2_S ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_S) .* term4_S + upper_E);
Mean_LCOH_SOEC = term1_S .* ((term2_S ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_S) .* term4_S + mean_E);
% Calculate PEM LCOH values
term1_P = LHV ./ (System_Efficiency_PEM_values);
term2_P = Discount_Rate_values .* (1 + Discount_Rate_values).^Lifetime;
term3_P = (OPEX_PEM_values / 100);
term4_P = CAPEX_PEM_values ./ FLH;
Lower_LCOH_PEM = term1_P .* ((term2_P ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_P) .* term4_P + lower_E);
Upper_LCOH_PEM = term1_P .* ((term2_P ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_P) .* term4_P + upper_E);
Mean_LCOH_PEM = term1_P .* ((term2_P ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_P) .* term4_P + mean_E);
% Calculate AEC LCOH values
term1_A = LHV ./ (System_Efficiency_AEC_values);
term2_A = Discount_Rate_values .* (1 + Discount_Rate_values).^Lifetime;
term3_A = (OPEX_AEC_values / 100);
term4_A = CAPEX_AEC_values ./ FLH;
Lower_LCOH_AEC = term1_A .* ((term2_A ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_A) .* term4_A + lower_E);
Upper_LCOH_AEC = term1_A .* ((term2_A ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_A) .* term4_A + upper_E);
Mean_LCOH_AEC = term1_A .* ((term2_A ./ ((1 + Discount_Rate_values).^Lifetime - 1) + term3_A) .* term4_A + mean_E);
% Calculate average values for mean LCOH
Avg_Lower_LCOH_SOEC = mean(Lower_LCOH_SOEC, 2);
Avg_Upper_LCOH_SOEC = mean(Upper_LCOH_SOEC, 2);
Avg_Mean_LCOH_SOEC = mean(Mean_LCOH_SOEC, 2);
Avg_Lower_LCOH_PEM = mean(Lower_LCOH_PEM, 2);
Avg_Upper_LCOH_PEM = mean(Upper_LCOH_PEM, 2);
Avg_Mean_LCOH_PEM = mean(Mean_LCOH_PEM, 2);
Avg_Lower_LCOH_AEC = mean(Lower_LCOH_AEC, 2);
Avg_Upper_LCOH_AEC = mean(Upper_LCOH_AEC, 2);
Avg_Mean_LCOH_AEC = mean(Mean_LCOH_AEC, 2);

[FLH,I] = sort(FLH);
Lower_LCOH_SOEC = Lower_LCOH_SOEC(I);
Upper_LCOH_SOEC = Upper_LCOH_SOEC(I);
Mean_LCOH_SOEC = Mean_LCOH_SOEC(I);
Lower_LCOH_PEM = Lower_LCOH_PEM(I);
Upper_LCOH_PEM = Upper_LCOH_PEM(I);
Mean_LCOH_PEM = Mean_LCOH_PEM(I);
Lower_LCOH_AEC = Lower_LCOH_AEC(I);
Upper_LCOH_AEC = Upper_LCOH_AEC(I);
Mean_LCOH_AEC = Mean_LCOH_AEC(I);

Lower_LCOH_SOEC_ct = cumtrapz(FLH,Lower_LCOH_SOEC)./(FLH-FLH(1));
Upper_LCOH_SOEC_ct = cumtrapz(FLH,Upper_LCOH_SOEC)./(FLH-FLH(1));
Mean_LCOH_SOEC_ct = cumtrapz(FLH,Mean_LCOH_SOEC)./(FLH-FLH(1));
Lower_LCOH_PEM_ct = cumtrapz(FLH,Lower_LCOH_PEM)./(FLH-FLH(1));
Upper_LCOH_PEM_ct = cumtrapz(FLH,Upper_LCOH_PEM)./(FLH-FLH(1));
Mean_LCOH_PEM_ct = cumtrapz(FLH,Mean_LCOH_PEM)./(FLH-FLH(1));
Lower_LCOH_AEC_ct = cumtrapz(FLH,Lower_LCOH_AEC)./(FLH-FLH(1));
Upper_LCOH_AEC_ct = cumtrapz(FLH,Upper_LCOH_AEC)./(FLH-FLH(1));
Mean_LCOH_AEC_ct = cumtrapz(FLH,Mean_LCOH_AEC)./(FLH-FLH(1));

N = 100;
Lower_LCOH_SOEC_mm = movmean(Lower_LCOH_SOEC,N);
Upper_LCOH_SOEC_mm = movmean(Upper_LCOH_SOEC,N);
Mean_LCOH_SOEC_mm = movmean(Mean_LCOH_SOEC,N);
Lower_LCOH_PEM_mm = movmean(Lower_LCOH_PEM,N);
Upper_LCOH_PEM_mm = movmean(Upper_LCOH_PEM,N);
Mean_LCOH_PEM_mm = movmean(Mean_LCOH_PEM,N);
Lower_LCOH_AEC_mm = movmean(Lower_LCOH_AEC,N);
Upper_LCOH_AEC_mm = movmean(Upper_LCOH_AEC,N);
Mean_LCOH_AEC_mm = movmean(Mean_LCOH_AEC,N);

% Plot the graph for lower, upper, and mean LCOH of SOEC, PEM, and AEC
figure(1);
% Plot SOEC
plot(FLH, Lower_LCOH_SOEC_ct, 'b-', 'LineWidth', 1.5);
hold on;
plot(FLH, Upper_LCOH_SOEC_ct, 'b-', 'LineWidth', 1.5);
plot(FLH, Mean_LCOH_SOEC_ct, 'b--', 'LineWidth', 1.5);
% Plot PEM
plot(FLH, Lower_LCOH_PEM_ct, 'g-', 'LineWidth', 1.5);
plot(FLH, Upper_LCOH_PEM_ct, 'g-', 'LineWidth', 1.5);
plot(FLH, Mean_LCOH_PEM_ct, 'g--', 'LineWidth', 1.5);
% Plot AEC
plot(FLH, Lower_LCOH_AEC_ct, 'm-', 'LineWidth', 1.5);
plot(FLH, Upper_LCOH_AEC_ct, 'm-', 'LineWidth', 1.5);
plot(FLH, Mean_LCOH_AEC_ct, 'm--', 'LineWidth', 1.5);
xlabel('FLH');
ylabel('LCOH');
title('LCOH vs FLH for SOEC, PEM, and AEC');
legend('Lower SOEC', 'Upper SOEC', 'Mean SOEC', 'Lower PEM', 'Upper PEM', 'Mean PEM', 'Lower AEC', 'Upper AEC', 'Mean AEC');
grid on;
hold off;

% Plot the graph for lower, upper, and mean LCOH of SOEC, PEM, and AEC
figure(2);
% Plot SOEC
plot(FLH, Lower_LCOH_SOEC_mm, 'b-', 'LineWidth', 1.5);
hold on;
plot(FLH, Upper_LCOH_SOEC_mm, 'b-', 'LineWidth', 1.5);
plot(FLH, Mean_LCOH_SOEC_mm, 'b--', 'LineWidth', 1.5);
% Plot PEM
plot(FLH, Lower_LCOH_PEM_mm, 'g-', 'LineWidth', 1.5);
plot(FLH, Upper_LCOH_PEM_mm, 'g-', 'LineWidth', 1.5);
plot(FLH, Mean_LCOH_PEM_mm, 'g--', 'LineWidth', 1.5);
% Plot AEC
plot(FLH, Lower_LCOH_AEC_mm, 'm-', 'LineWidth', 1.5);
plot(FLH, Upper_LCOH_AEC_mm, 'm-', 'LineWidth', 1.5);
plot(FLH, Mean_LCOH_AEC_mm, 'm--', 'LineWidth', 1.5);
xlabel('FLH');
ylabel('LCOH');
title('LCOH vs FLH for SOEC, PEM, and AEC');
legend('Lower SOEC', 'Upper SOEC', 'Mean SOEC', 'Lower PEM', 'Upper PEM', 'Mean PEM', 'Lower AEC', 'Upper AEC', 'Mean AEC');
grid on;
hold off;