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is taken as the reference time, in this paper this will be one day. As a reference for energy the total demanded energy is used. tref = tf (9) 0 Q ̇ref = Eref (10) tref flow rate: tf ̇ Qemdt Eref = From these quantities a reference value for heat flow rate can be determined as the average heat The energy price is nondimensionalized using the average energy price for heating the dwelling when no energy buffer is present. 1tf ̇ pref = t Qemp(t)dt (11) f0 In subsequent sections quantities divided by their reference quantity will be denoted with * as a superscript. 3. Results and discussion 3.1. Boundary conditions To determine the heat demand and emission system temperature a linear optimal control prob- lem similar to the one described in [17] was solved. The model consists of an RC-network with states for a single thermal zone, the emission system, internal walls and outer walls. Solar heat gains are added to the internal walls while internal gains are added directly to the thermal zone capacity. In this paper the internal heat gains are calculated from measurement data from [18]. The ambient temperature profile is calculated as a November design day in Belgian climate according to [19]. The total amount of energy supplied to the building is minimized while a minimum zone tem- perature of 20◦C is maintained. In the period from 23h in the evening to 16h in the afternoon the minimum temperature is decreased to 18◦C. The resulting optimal control problem is easily solved and the emission temperature Tem and heat demand Q ̇ em are extracted and given in Figure 3. Two price profiles were investigated, one corresponds to a general day night tariff as is common in Belgium (Figure 4(a)). The energy price reduction during off peak hours is 30%. The second pricing scheme is a time of use scheme where the price variation is determined by the variations of the nationwide energy use on a representative day according to [20] (Figure 4(b)). 3.2. Parameters of interest The parameters Q ̇max and C ̇max are both determined by the heat supply system. A maximum heater power of 6000 W was determined to be sufficient for a single family dwelling complying with Belgian regulations. The maximum heater capacity flow rate depends on it’s maximum power and was chosen to be 2100 W/K. The effectiveness of the emission system at the maximum capacity flow rate is assumed to be 0.6. As the hot zone of the storage receives energy from the heater it will be at the temperature of the heater outlet which is assumed constant at 35◦C. The temperature at the bottom of the 5PDF Image | Energy cost reduction by optimal control of ideal sensible thermal energy storage
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