Fig. 1
Power gradient energy correction. The figure shows the set values Pset, elec for an exemplary run of a CHP unit. The graph PCHP, output displays the reaction of the CHP unit to the given set values, under the assumption that it behaves linearly. The red triangles illustrate the Term A in equation 8. Term A aims to approximate the area between the graphs of Pset, elec and PCHP, output. The hatched area is equal to Pstart − up in term B of equation 8. Time step 4: In t = 4 a turn-off process is illustrated. Term A slightly underestimates the electrical energy. Time step 3: In t = 3 a decrease in power production is shown. In this particular case, term A slightly overestimates the electrical energy, still produced by the CHP unit because of its inertia. Time step 2: Between time step t = 2 and t = 1 there is no change in power. Term A in equation 8 is zero. Time step 1: In t = 1 a start-up process is illustrated. Again, term A is displayed as a red triangle. Because this is a start-up case, δstart − up1 is equal to one and term B is non-zero. The hatched area is equal to term B, which is determined by Pstart − up. Pstart − up can be chosen, so that the hatched area fits the remaining error. In that way, the error between PCHP, output and Pavailable is minimal for the majority of the CHP start-ups