How to coordinate the power resources based on the cheapest cost using optimization based problem in matlab.

Hi all,

I am working on optimization of several resources and using problem based optimization method. so I have this constraints

prob.Constraints.resourcebalance= Pgrid + Pbattery + Pwind + Psolar == Pload;

every of these resources have a cost. What I want is that how to coordinate these resouces based on the cheapest cost. for example, we calculate the cost for each of the resources(costpower grid, costbattery, costwind, costsolar) and after that it turns out that the costsolar has the cheapest cost, so I want to coordiante these power resources from cheapest to expensive.

I can explain more. for example the cheapest is costsolar, then costbattery, then, costwind, then finally costpower grid. According to the previous sorts of cost, how to coordinate the power resources (I should first Psolar, then Pbattery, then Pwind and finally Pgrid. How to coordinate the power resources based on the cheapest cost using optimiation based problem in matlab. Thanks in advance.

Answer 1

[MULI]

Hi Hossam,

I understand that you are required to generate power based on the cost of different sources available. The below steps will help you in implementing this.

• Firstly, define decision variables for the power outputs of each resource.
• Define constraints, including the resource balance constraint i.e source generation must be equal to load.
• Define the objective function to minimize the total cost based on the costs of each resource.
• Set up the optimization problem with the defined decision variables, constraints, and objective function and solve it

Below is the MATLAB code which implements these steps:

% Define costs and maximum power values for each resource 

costs = [0.2, 0.4, 0.6, 1]; % Costs of solar, battery, wind, grid power ($/kWh) 

max_power = [50, 30, 40, 60]; % Maximum power output for each resource (kWh) 

% Define total load 

P_load = 100; % Define your total load here 

% Define optimization problem 

prob = optimproblem; 

% Define decision variables 

P = optimvar('P', 4, 'LowerBound', 0, 'UpperBound', max_power); 

% Define constraints 

resource_balance_constraint = sum(P) == P_load; 

% Define objective function to minimize total cost 

total_cost = costs * P; 

prob.Objective = total_cost; 

% Add constraints to the problem 

prob.Constraints.resource_balance = resource_balance_constraint; 

% Solve the optimization problem 

[sol, fval, exitflag, output] = solve(prob); 

% Display solution 

disp(['Optimal power output for solar: ', num2str(sol.P(1))]); 

disp(['Optimal power output for battery: ', num2str(sol.P(2))]); 

disp(['Optimal power output for wind: ', num2str(sol.P(3))]); 

disp(['Optimal power output for grid: ', num2str(sol.P(4))]); 

disp(['Total cost: ', num2str(fval)]);

This code will find the optimal power outputs for each resource while ensuring that the total cost is minimized, following the order of cheapest cost from solar to grid.

For more information on the functions used such as ‘optimproblem’ ‘optimvar’ and ‘solve’ you may refer these documentation links

https://www.mathworks.com/help/releases/R2020a/optim/ug/optimproblem.html

https://www.mathworks.com/help/releases/R2020a/optim/ug/optimvar.html

https://www.mathworks.com/help/releases/R2020a/optim/ug/optim.problemdef.optimizationproblem.solve.html

Hope this answers your query!