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I am currently working on a project where I am modelling a set of combined heat and power production units (CHP).

I am using linear programming to do this for now.

The main idea is to minimize the overall production cost. In order to that one must consider the taxation on the fuel type used. The general idea is that heat produced with fossil fuels will have a tax on it and power produced with green energy will have a subsidy on it.

In order to calculate this I could do the following:

    FossilShare = FossilFuel / TotalFuel
    FossilHeat = FossilShare * Q
    GreenPower = (1-FossilShare) * P

Where P and Q are the heat and power produced. Then my taxation cost function would be as following:

    Cost = FossilHeat * Tax - GreenPower * subsidy

The problem, however, is that this is not linear. I cannot think of a way to linearise this and I cannot think of another way of doing it, because I need to calculate the portion of heat produced with fossil fuel and the portion of power produced with green energy.

Any help or suggestions would be much appreciated.

Thanks in advance

M. Frank

M.frank
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  • Difficult to answer as we don't know which quantities are decision variables or parameters. If really nonlinear, there are many good NLP (nonlinear programming) solvers readily available. – Erwin Kalvelagen Apr 28 '16 at 10:31
  • I do not see why that is necessary, but if you must know, I am taking the convex combination of the extreme operating points for a unit, such that my decision variables are the alphas used to express the convex combination. What you see there is only a mix of parameters (Tax and subsidy) and variables (FossilFuel, TotalFuel, FossilShare, GreenPower, cost, P and Q) – M.frank Apr 28 '16 at 12:29
  • The power plant is using a mixed fuel, some biomass (green) and some fossil fuel and I need to calculate the share of the heat produced with fossil fuel and the share of power produced with green fuel. Hence the fractions above. That is by definition not linear. So can you think of another way of expressing this, which is linear? – M.frank Apr 28 '16 at 12:29
  • If everything is endogenous then indeed there are nonlinearities. So either use a piecewise linear formulation or a real NLP solver. – Erwin Kalvelagen Apr 28 '16 at 13:26

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