**5. Results**

Simulations were completed to determine the steady-state optimal control method's performance compared to the current control strategies in place in the UBO, using Equation (18) as the objective function. An additional simulation was completed to demonstrate the current control method's ability to track LOP optimal (PMV = −0.25) zone temperature setpoints. By using LOP optimal temperature setpoints, a more direct performance difference can be determined between the current control method and the proposed steady-state optimal control method. Lastly, a simulation showcasing the proposed optimal control method's ability to prioritize certain zones over other zones was completed.

#### *5.1. UBO Simulation with Current Building Controls*

The current control method was simulated on the UBO building under two operational cases: (1) with the building operator defined zone temperature setpoints (23 °C); and (2) with LOP optimal zone temperature setpoints (the air temperature at which PMV = −0.25). The numerical results of the first case are used as a baseline to compare against, while this section details the performance of the second case. Figure 10 shows one day of the zone temperatures for the UBO building using the current control method and PMV optimal temperature setpoints. The outdoor air temperature (dashed line) is included in the plot for reference.

The current control method with demand calculations and local PID control shows the ability to track the LOP setpoints fairly accurately. Worth noting is that beginning around 2 pm, Zone 1's temperature starts to drift upwards away from the optimal temperature. This is due to Zone 1's damper being fully open combined with the fact that the AHU fan has reached its power limit and the discharge air temperature is not decreasing fast enough to provide the additional required cooling. Figure 11 shows the system's end static pressure (dashed green line) and the total air flow (solid blue line) in the AHU. Shortly after 1 PM, the end static pressure begins to decrease as the total air flow continues to increase. This is the point where the AHU fan has reached its maximum power capabilities. As the zone dampers continue to open, there is less obstruction to the passage of air, decreasing the pressure and increasing the flow.

Figure 12 shows the chilled water flow and discharge air temperature of the AHU. The discharge air temperature gradually decreases throughout the day (dashed green line), responding to the increase in cooling demand. As the temperature drops, more chilled water is required to cool the air, displayed by the increase in the mass flow rate of the chilled water (solid blue line).

**Figure 10.** Zone and outdoor air temperatures for the UBO using the currently implemented methods with PMV optimal temperature setpoints. None of the rooms violated the prescribed PMV thresholds.

**Figure 11.** Total air flow and end static pressure in the AHU for the UBO using the currently implemented control methods with PMV optimal temperature setpoints.

**Figure 12.** Chilled water flow and discharge air temperature for the UBO using the currently implemented control methods with PMV optimal temperature setpoints.

## *5.2. Steady-State Optimal Control Simulation*

The proposed steady-state optimal control method was simulated on the UBO building with the user-defined temperature setpoints equal to the PMV optimal temperature. All the zone temperatures can be seen in Figure 13. Compared to Figure 10, the zone temperatures appear to vary slightly more through out the day. This is not because the zones temperatures are not optimal, but because of the range of PMV (−0.5 to 0) for zero loss of productivity. This range of PMV's allows the optimization a band in the individual zone temperatures while minimizing the utility cost of the chilled water and electricity and leveraging the coupling that exists between zones.

Figure 14 shows the end static pressure and the total air flow through the AHU. Comparing to the current control method simulation, the air flows follow relatively similar paths, with the pressure in the steady-state method simulation taking a higher value but remaining more constant throughout the day. Figure 15 shows a lower discharge air temperature for the steady-state case. While this results in increased flow rates of the chilled water, the cost may not necessarily be higher as the return chilled water temperature may be lower, meaning the chiller has to cool the water over a smaller difference in temperatures. This lower discharge air temperature helps the steady-state optimal control method to achieve more reduction in the cost of lost productivity due to discomfort, enabling lower temperatures in the zones.

**Figure 13.** Zone and outdoor air temperatures for the UBO using the steady-state control method with PMV optimal temperature setpoints. None of the rooms violated the prescribed PMV thresholds.

**Figure 14.** Total air flow and end static pressure in the AHU for the UBO using the steady-state control method with PMV optimal temperature setpoints.

**Figure 15.** Chilled water flow and discharge air temperature for the UBO using the steady-state control method with PMV optimal temperature setpoints.

#### *5.3. Very Important Person Simulation*

To demonstrate one of the proposed steady-state algorithms capabilities, a simulation in which the comfort conditions of one zone was valued significantly more over the other zones in the building was completed. This can occur in the situation where there is a very important person (VIP) that requires comfortable conditions to be maintained, or in the case where other rooms are less important to maintain at a specific comfort level and can be warmer to reduce utility usage. In this simulation, Zone 5 was chosen as the VIP zone. Figure 16 shows all of the zone temperatures. The other zones are higher in temperature throughout the day, while Zone 5 is maintained at a lower temperature. Several zone temperatures can be seen rising above the 0 PMV threshold after 1 PM, when the cooling demand for the day is the greatest. This departure from the optimal LOP range between −0.5 and 0 PMV is due to the optimization balancing the cost of discomfort in the zones with the cost of the utilities.

Figure 17 provides further insight into the maintaining of comfort in Zone 5. The zone temperature is shown with the solid blue line and two thresholds are displayed: (1) the dashed red represents the 0 PMV threshold; and (2) the dashed green represents the −0.5 PMV threshold. After the building is initially occupied, the zone temperature is maintained between the two thresholds resulting in zero loss of productivity for Zone 5.

**Figure 16.** Zone and outdoor air temperatures for the UBO using the steady-state optimal control method with a VIP zone.

**Figure 17.** Zone and outdoor air temperatures for the UBO using the steady-state optimal control method with a VIP zone.
