Date of Completion
mixed-integer, nonlinear, optimization
Krishna R. Pattipati
Field of Study
Doctor of Philosophy
Chiller plants provide cooling to buildings. Efficiency and reliability are two key concerns of plant owners, in this thesis, topics beginning with efficiency optimization, evolving with minimum up/down times and uncertainties considered, and expanding to efficiency and reliability joint optimization are studied. Efficiency optimization is challenging: Supply temperatures are critical in improving chiller efficiency, while chiller power consumption is a highly nonlinear function of the temperatures; In addition, the problem is combinatorial in the presence of mixed-integers. In this work, a formulation with supply temperatures considered as decision variables is established based on static empirical models. To efficiently solve the problem for near-optimal solutions, a recently developed decomposition and coordination approach is combined with Sequential Quadratic Programming (SQP). Complexity and nonlinearity of a subproblem (e.g., chiller subproblem) are much reduced as compared with the original problem. To explore potential energy savings and complexity increase, considering that chiller minimum up/down times are relatively long among a plant but short as compared with the time interval, efficiency optimization with chiller minimum up/down time constraints is studied in the second topic. Since on/off statues of active chillers depend on not only current load but also previous chiller statues, chiller subproblem is dynamic. To overcome this new challenge, stage-wise costs without MUDT are established. Then possible state transitions are developed based on MUDT before Dynamic Programming (DP) or local search is used. To improve robustness of our method, uncertainties are considered in the third topic. A reasonable simplified formulation is established where all the uncertainties in chillers considered and cooling towers are simplified by using expected values of water uncertainties out of chillers. The number of constraints could be very large considering the combination of uncertainties. To overcome this difficulty, interval arithmetic is used. The results for energy savings, however, may reduce plant reliability. In the last topic, efficiency and reliability joint optimization is thus studied and a dynamic reliability model is adopted. To be compatible for different plants, a hybrid performance model based on the first topic with the empirical chiller model replaced by a Deep Neural Network (DNN) model is used. Different from efficiency, reliability has a long time scale in terms of years, making it difficult to optimize efficiency and reliability simultaneously. To address this issue, Taylor series expansion is used where reliability change as a function of operations is generated. With common decision variables, chiller reliability and power consumption are grouped together. To efficiently solve the problem, our decomposition and coordination-based method is combined with DP with rollout, where the plant is decomposed into a simplified dynamic chiller subproblem and three simple static subproblems. Gradients needed are approximated by using finite difference without requiring explicit equations.
Zhang, Danxu, "Mixed-Integer Nonlinear Optimization for Efficient and Reliable Chiller Plants" (2019). Doctoral Dissertations. 2299.