Components Interaction

Figure 2.20: Rescheduling scheme.

Algorithm 1 The steps of the rescheduling algorithm initialize MPC constraints with P_app

event ← False ▷no event is triggered For k=₁to N_slot do

MPC actuating the heating system at k

if P OWmrg(k)< P OW_hvac(k) _AND Tin(k)< T_d(k) then P OW_av(k)←0

event ← True

P OWapp(k)← C1(event,P OWav(k)₎

else if P OW_mrg(k)> P OW_hvac(k) _ANDT_in(k)< T_d(k) then event ← False

end if

MPC constraints update end for

scheduling query to provide the missing information to run until the end of the prediction horizon. For these scenarios, no modifications to the energy constraints are needed.

Figure 2.21: Rescheduling event when MPC’s horizon exceeds the scheduling horizon.

2.5.1 Rescheduling Events Scenarios

The simulation of the two components interacting with each other is analyzed in this subsec-tion. The MPC strategy is initialized based on the appliances’ optimal schedule from Schedul-ing Scenario 1. The desired temperature in this scenario is constant along the scheduling horizon the same way as in ITC scenario (i.e., T_d=_24°C).

Consider the results obtained in Simulation 1, illustrated in Fig. 2.9. When the remaining power margin after scheduling is insufficient, reaching the desired temperature becomes impossible. Therefore, a rescheduling event is triggered by C2 to relax the energy constraints.

Figure 2.22 shows the indoor temperature before the rescheduling event (old T_in) with insufficient power margin (old P OW_mrg). A rescheduling event is triggered when conditions are met (green solid line). C1 reschedules the appliances accordingly and resets the MPC’s input constraints, hence the power margin changes and a new one can be shown in Fig. 2.22 as (newP OW_mrg). The MPC then resumes the control so that T_in approaches the setpoint.

The new schedule is defined in the new scheduling horizon starting from the time when the trigger event occurred until the end of 24 hours, and it is illustrated in Fig. 2.23.

Since rescheduling eliminates the temperature error, one may see no practical usage for the inconvenience-based algorithm if rescheduling is possible. However, the power margin may still not be guaranteed to be sufficient for the time after rescheduling since it may not bring significant effects. For example, the ToU tariff is low at the same time when the rescheduling is triggered, and the optimal scheduler assigns multiple appliances operation for that time. The following simulation scenario illustrates such a case.

From Fig. 2.24 (top), it can be seen that the indoor temperature at one point is not in the thermal comfort level bounded byT_minandT_max. This is due to the insufficient power margin

Figure 2.22: Indoor temperature without (top) and with(third) the rescheduling with the corresponding power margin remaining from the first component without (second) and with (bottom) the rescheduling.

Figure 2.23: Appliances schedule in the new schedule horizon with the assigned ToU tariff.

to actuate the heating system. In this case, the rescheduling event is automatically triggered based on the conditions in the rescheduling Algorithm 1. Hence, the energy constraints are modified to accommodate the heating system consumption. However, the power margin resulting after the rescheduling is still relatively narrow to drive and maintain the indoor temperature in the thermal comfort level specified by the consumer. The power stored in the EV’s battery is also available for the heating system actuation to at least enter the thermal comfort (k= [_76,85,86]_{) range.}

Figure 2.24: Indoor temperature without (top) and with (third) the rescheduling with the corresponding power margin remaining from the first component without (second) and with (bottom) the rescheduling.

For this scenario, the inconvenience-based strategy must be implemented to compensate the consumer since the MPC fails to reach the desired thermal comfort range. Hence, Table 2.9 presents the results of the inconvenience-based algorithm before and after triggering the rescheduling event. It is clear that the inconvenience factor decreases when the appliances are rescheduled. However, the rescheduling does not fully eliminate the temperature error;

therefore, compensation is still necessary.

Table 2.9: Results of inconvenience factor without and with the implementation of the inconvenience-based algorithm.

Rescheduling

Inconvenience

factor Compensation (wrt to total heating costs)

without 130.36 23%

with 106.48 20%

2.5.2 The Plant Model Mismatch Analysis

For this example, we consider the situation where the MPC’s prediction horizon exceeded the scheduling horizon and there is no more energy information available. To study the efficiency of the MPC strategy, we apply modifications on the plant where we consider that one window in the household is suddenly opened. Such plant mismatch is considered as unmeasured disturbance by the MPC component.

The rescheduling event is triggered by the end of the scheduling horizon to request further energy information. Different exterior temperature is considered for the next scheduling horizon as well. The new schedule is assumed to have similar power distribution of the scheduled appliances as the previous scheduling horizon. The desired temperature remains similar T_d. Figure. 2.25 illustrates the indoor temperature of this scenario. The MPC succeeded in reaching the consumer’s thermal comfort; however, due to the open window, the heat starts to flow quicker through it by convection. Hence, more energy is required to actuate the heating system to maintain thermal comfort inside the household. It is also noted from Fig. 2.25 (top) that the indoor temperature Tin is not always inside the comfort range, which could be explained by the insufficient power margin resulting from C1. Therefore, a rescheduling event is again triggered to correct the measured temperature error. The bottom figure of Fig. 2.25 illustrates the indoor temperature after the rescheduling, where the resulting T_in is maintained inside the thermal range after the rescheduling is triggered, and the inconvenience factor is kept minimum.

The total power distribution of the household before and after the rescheduling is pre-sented in Fig. 2.26. As shown in the figure, the new total power distribution after reschedul-ing, including the heating system’s consumed power, does not violate the energy constraints while most of the appliances are operating in low-price periods.

This study demonstrates the proposed framework’s ability to adapt to different changes since it guarantees the consumer’s comfort with low complexity. Precisely, the efficiency of the MPC strategy in handling unmeasured disturbances without violating the control objectives.