# Energy Targeting Using Mathematical Programming Method

### Other Info

Document Category Engineering

## Energy Targeting Using Mathematical Programming Method

The algebraic method illustrated above can be generalized using optimization techniques.
Any mathematical programming “optimization” model can be written in the following
forms:

g(x) ≤ 0.0 is the set of r inequality constraints.

In general, the number of variables, n, will be greater than the number of equations, m, and the difference between (n-m) is commonly denoted as the number of degrees of freedom of the optimization problem. If we want to maximize a function this is equivalent to minimizing the negative of that function.

Now for the heating and cooling utilities minimization problem, let us go back to our
simple problem solved algebraically before using pinch technology and use FCP of the cold
streams of 19 and 2 kW/ºC respectively. The new problem can be easily solved using
mathematical programming model. We can write our objective function not only including
heating and cooling utilities loads but also including heating and cooling utilities costs;
formulate our model/constraints using the cascade approach; and then solving the
optimization problem using any commercial solver.

### Objective Function

Define the loads of heating and cooling utilities in each temperature interval and the surplus from each interval as we did before in the algebraic method through the development of temperature interval diagram, tables of exchangeable loads and un-balanced thermal cascade diagram.

The model equations are heat balance around each temperature interval in the thermal