The bypass valve opening level calculated by the weather data of August 23, 2016 is compared to the real opening level, as shown in Fig. 16. NRMSE is 0.127 meaning that the model has a fitness of 87.3%. Fig. 17 demonstrates the discrepancy between the calculated value Yp and the real value Yr, all the blue point are clustered around the line: Yr = Yp. From these two figures, it can be seen that the model accuracy is satisfied. The comparison does not include the transition process because the transition process after chillers re-start is not modeled in this study.

4.2. Control simulation

Before incorporating the MPC strategy in an online experiment, it was tested under simulation environment. The objective of the simulation study was to examine the closed loop performance. Usually, when MPC is applied online, the control object outputs are measured by the sensors and then fed back to the controller. For simulation purpose,

Fig. 14. The control structure of this study.

Fig. 16. Comparison of the calculated and real value.

Fig. 17. Bypass valve opening level prediction error.

the controlled object in Fig. 15 is replaced by the model same as the prediction model. Although the prediction model is different from the real system, MPC can still overcome the small model mismatch, since MPC algorithm includes a feedback alignment.

The weather prediction only have the maximum and minimum outdoor temperatures for the next day, and the solar radiation has no prediction. Outdoor temperature forecast can be replaced by sinusoidal curve [41]. Solar radiation prediction can be obtained by Eq. (18) [42]:

Where Ih is total horizontal radiation, I0 is solar constant and the value is 1353 W/m2, h is solar elevation angel, CC is cloud cover and the value is 0,1, …10, θn and θn−3 are the temperatures at some moment and 3 h ago, ϕ is relative humidity, and C0…C5 and k are constants given in Table 1. Fig. 18 demonstrates the simulation result from test data obtained in August 24, 2016. Since the transition process after chillers re-start is not studied, the control is implemented when system reaches a steady state.

5. Conclusion and future work

Buildings are usually approximated as linear systems, and there is a tradeoff between the model accuracy and the control performance. If a control strategy can well compensate model error, the model can be simplified to a low order model, vice versa. In the real practice, the error caused by the approximation of a high-order system to a loworder system is allowable, and the approximation can greatly simplify the analysis of modeling. This study proposes a new modeling method for a medium-sized commercial building. A MPC strategy with feedforward control structure is developed to increase the supply chilled water temperature.

In the proposed modeling framework, the inputs are pided into two categories as manipulated variable and random variable to analyze their effects on the system by different methods. Step response method and PSD method are used respectively for system modeling under these two categories of variables. Step response method is more applicable in the real practice due to its simplicity and easy to implement. PSD method belongs to data driven methods, and its accuracy depends on the richness of the data. Given the proposed method, higher model accuracy is achieved and modeling complex is lowered through being applied in a medium sized commercial building in China.

The test bypass valve in chiller plant was controlled through the proposed MPC strategy. Energy saving can be achieved by the proposed MPC strategy.

We expect to further improve the accuracy of this bypass valve control model by including more random variables such as occupancy and electricity rate. It is worth studying that how much of these variables that will be added to improve the accuracy of the model, and then improve the control performance.

Acknowledgements

The research work presented in this paper is financially supported by Beijing Municipal Education Commission science and technology program