Hybrid model predictive control for optimal energy management of a smart house

Optimal energy management of a small-size building via hybrid model predictive control

“…However, after about 45 hours and with a relatively low value of SoC, the controller decides to draw energy from the grid: this is probably due to a predicted violation of the lower bound on SoC in case the battery were used. In case of colder days, the controller would instead impose frequent changes in the value of u grid , as shown in the simulations in [26]. The distribution of the computation times needed to solve (20) is shown in the histogram in Fig.…”

“…The proposed MPC control law was first tested in simulation on the nominal model of the smart house, using real data for the time evolution of the disturbance vector d. Preliminary simulation results were presented in [26], in which u res was a binary signal, and the actual future evolution of d was used instead of the forecast in the MPC problem. In this work, the control system is tested on the actual experimental site, which also implies the use of weather forecast.…”

“…On the other hand, u res ∈ [0, 1] is a continuous variable representing the percentage of time in each sampling interval in which the resistor is powered (duty cycle): if u res = 0 the coil is off, if u res = 1 the coil is on full power, and all intermediate values are allowed. Although this variable is binary in nature, converting it to a continuous one by using a duty cycle simplifies the control problem as compared to the preliminary approach of [26]. In addition to pumps and resistor, the system behavior is influenced by the power P a drawn by the appliances, which include the control computer.…”

“…A preliminary version of the method proposed in this paper can be found in [26], where an early version of the described control strategy was presented, and tested only in simulation. k discrete time index J t,n total electricity cost from time t for n sampling instants The prototype smart house (Figs.…”

“…The following conditions, already formulated in [26], are assumed: (a) the discharge power capability of the battery pack is much greater than the maximum output power of the PV array (implying that the voltage of the DC bus is imposed by the state of charge of the battery pack); (b) the useful energy (i.e., total energy × depth of discharge) can be extracted from the battery pack in an interval of state of charge values for which the terminal voltage of the battery pack can be approximated as constant. Thus, the battery voltage can be approximated as constant for any rate of discharge if the state of charge does not become too low.…”