Model Predictive Control of mixed solar and electric heating
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In this report we will model a heat system consisting of a heat storage tank and an application. The heat storage tank is supplied by a heating element and heated water from a solar collector. The main objective of the heat system is to mainatian a reference temperature in the application (a house). Weather forecasts will be used as weather data affecting the heat system. We will assume that the weather forecasts and the actual weather will be the same. The heat sytem will consist of simplified nonlinear differential equations and be controlled by a model predictive controller (mpc). The mpc controller will use a linearized model of the nonlinear process. The average predicted outside temperature from the weather forecasts will be used as nominal value for the same temperature in the linearized model in the mpc controller. The mpc controller will measure some disturbances to make more efficient control. The most imortant disturbance will be the temperature of the water coming out of the solar collector, that will flow into the heat storage. By measuring this temperature, the mpc controller can apply it to its predictor and make sure that the power of the heating element in the heat storage is reduced when solar collector heated water is available. This is to make sure that the heat storage has enough capacity to receive the heated water from the solar collector, while still maintaining a reasonable temperature in the heat storage. Simulation with different weighting of the inputs in the mpc controller will show that heating element power consumption is influenced by these weights.