2.2. Building description

The test building is a medium-sized commercial building of a shopping mall in Sichuan province, China, located at 29°35′ north latitude, 103°43′ east longitude. The building has 31.4 m in height and 41,000 m2 with six-floor on the ground and two-floor basement. From outside layer to inside layer, the exposed walls are all made of granite, thermal insulation materials, gravel concrete, hollow brick, gravel concrete, and wall tile or lime. The exposed windows are all doubleglazing windows. Fig. 3 shows the external shape of the test building. Fig. 4 shows the building view in Google SketchUp™, in which the direction of the building can be clearly seen.

2.3. HVAC system description

The chiller plant has three centrifugal chillers with variable speed drivers for six floors above the ground and two screw chillers for two floors underground. In this study, only the six floors part above the ground will be studied, and the part is served by 28 air handling units (AHUs) and 22 fan coils (FCs). Each AHU has a controller that controls a valve to change chilled water flow according to return air temperature by using the PID control method. The return air temperature is set to 26 °C. Each FC controls chilled water flow by using ON/OFF control method according to the zone temperature directly. This study does not focus on the control of zone temperatures, for the control performance of AHUs and FCs, by and large, is perfect, which means that zone temperatures are controlled at about 26 °C. Although, the flow through a single FC is at an ON/OFF status which can be simplified as a discrete value, continuous value can also be obtained for the flow through the whole system due to the flow through 28 AHUs, that is continuous value, is much larger than 22 FCs and 22 FCs run at different time. The cooling rated capacity of each of the three centrifugal chillers is 2286 kW, and the consumption power of each is 437 kW. The chillers are parallel connected. Every day, the HVAC system works from 9:20 to 21:00. Usually there are two chillers running in July and August, and the rest of a chiller is for redundancy and maintenance in most time, unless in the very hot weather. The plant is shown in Fig. 5. Primary pump system is used for chiller plant which includes constant speed pumps. A bypass valve is used to balance the cooling capacity of the plant to the internal cooling load. The bypass valve is adjusted according to the chilled water differential pressure which is set at 0.12 MPa. The system was designed to be operated as 7 °C for the supply chilled water and 5 °C for the temperature difference between supply and return water.

3. Control system design

Firstly, as the three transfer functions which are related to the three inputs are determined, they are transformed to discrete form for subsequent use. Secondly, these transfer functions are converted into the form of state equations. Then the form of the cost function for MPC can be determined. The objective of this study is to minimize the opening level of the bypass valve. Therefore, the following cost function can be obtained.

where N is the prediction horizon, the symbol uk+ik denotes the variable u at time k+i predicted at time k, u is a vector of the control inputs within the prediction horizon N, that is the supply chilled water temperature as a scalar in this study, dk+i k are the random variables, outdoor temperature and solar radiation where the predicted value can be obtained from the local weather forecast station and it represents the feedforward control structure, yk+i k is the predicted output at time k, which is obtained by iteratively solving Eqs. (14) and (15) using the control inputs and random variables, umin and umax are set to 7 °C and 16 °C respectively.

As discussed in section 3.1, the smaller the bypass valve opening level is, the higher the supply chilled water temperature is, which means higher chiller efficiency. However, it means that the cooling capacity is less than the requirement of the building cooling load when the bypass valve is completely closed (i.e., the opening level is 0%). So the opening level set point w (k + i) is set to be 10% to avoid the fully closed bypass valve.