Energy efficient hourly scheduling of multi-chiller systems using imperialistic competitive algorithm

Highlights

• ICA is used for solving optimal chiller loading problem and saving energy.

• Robustness and effectiveness of ICA is proved using simulations on three well-known test systems.

• ICA based optimization process is compared with recently published methods.

• ICA with fast convergence capability achieves better solutions in lower calculation time.

Abstract

The hour-ahead optimization of the multi-chiller systems is necessary in order to minimize their power consumption and save energy. In this paper, an imperialistic competitive algorithm based optimal chiller loading problem is solved to find the partial load ratio, cooling flux, and the electricity requirement of the chillers and minimize the energy consumption of the whole system. The proposed approach simulates the socio-political competition using the initial population composed of the colonies and imperialists. The empires with their relative colonies and imperialists compete with each other to collapse the weakest empire and dominate the most powerful one achieving the minimum power consumption. The cooling capacity of the chillers and balance constraint are satisfied in hourly economic dispatch process. The optimization problem is tested on three standard systems. The imperialistic competitive algorithm based optimal chiller loading method finds better operating points for chillers than those obtained by recently published strategies.

Introduction

In recent years, the economic operation of the power consumers such as air conditioning systems has become an important issue because of huge electricity utilization in summer, especially in subtropical zones [1]. Studies show that almost 30% of annual on-peak electrical demand is associated with multiple-chiller systems, which are employed for ventilation and cooling in large-scale commercial and industrial sectors [2]. In order to reduce the electricity consumption at peak-load hours, the optimal chiller loading (OCL) problem is solved in multi-chiller networks. The main objective of the OCL approach is to minimize the total electrical power consumed by the chillers at the 1-h study horizon. The value of the cooling flow produced by each chiller is selected as the decision variables. The cooling capacity of the chillers is handled in the hour-ahead economic dispatch problem using the partial load ratio (PLR). Then, the energy requirement of the chillers is calculated based on their PLRs.

In [3], a robust optimization algorithm is implemented to OCL problem to model the uncertainty of the building cooling load in a three-chiller microgrid. The daily electricity consumption of the chillers is minimized in three cases. A risk-neutral or deterministic optimization problem and two risk-averse or robust economic chiller dispatch strategies are studied under various budgets of uncertainty. It is demonstrated that the robust optimization technique with Γ% budget of uncertainty can find how the hourly refrigeration schedules of the chillers change when the actual cooling load is different from the forecasted one at Γ% of the whole study horizon. The opportunistic or risk-taker mode of the OCL program should also be intended using the information gap decision theory (IGDT) method [4] to gain higher energy savings from the under-estimated cooling demands. Authors of [5] revealed that the gradient method (GM) finds the better operating points for the chillers with less power consumptions than those determined by the Lagrangian optimization procedure in less calculation time. The simulated annealing (SA) algorithm, which is based on heating a material and then slowly cooling it to decrease defects, eliminates the limitations of the Lagrangian algorithm in solving the non-convex OCL problem [6,7]. Genetic algorithm (GA) [8,9], evolution strategy (ES) [10], differential evolution (DE) [11], particle swarm optimization (PSO) [12], differential cuckoo search algorithm (DCSA) [13], improved ripple be swarm optimization technique [14], augmented group search optimization method [15], and invasive weed optimization (IWO) [16] approach have been proposed by scholars to save more electricity in OCL process. According to [17,18], application of continuous Karnik–Mendel method (CEKM) combined fuzzy dynamic adaptation with type-2 fuzzy logic can reduce the computational cost of DE and GA based OCL strategy. Bernal et. al. [19] proved that the fuzzy logic can also be used for dynamic adjustment of the parameters in imperialist competitive algorithm (ICA) to solve the complex optimization problems, which should be incorporated in day-ahead economic chiller dispatch problem. In [20], branch-and-reduce optimization navigator (BARON) of generalized algebraic mathematical modeling system (GAMS) is used for minimization of energy consumption in conventional multi-chiller networks. It is demonstrated that BARON is able to produce more promising results than GA, PSO, SA and ES. Instead of minimizing the instant power consumption of the multiple-chiller air-conditioners based on real-time cooling load and ambient wet bulb temperature, sum of instant energy requirement and one-time-step-ahead future system power should be minimized according to both actual and forecasted building cooling demands [21]. Installation of a thermal energy storage tank, which is significantly less expensive than an industrial scale chiller unit, shifts a part of on-peak cooling demand to off-peak periods and causes a significant energy saving in summer. Yu and Chan [22] developed an optimal load sharing strategy for chillers to maximize their aggregated COP. They assumed that if there are two equally sized units, one should be partially loaded and another operated in full-load condition. Otherwise, if they are not equally sized, a chiller with larger refrigeration capacity should be fully loaded as another operate at part-load mode. It is shown that maximum aggregated COP is independent from ambient wet and condensing temperature. The probability density distribution function of the cooling load ratio could be defined by Parzen window density estimation method and used for modeling the building cooling demand variations [23]. Moreover, uncertainties associated with cooling demand and COPs of chillers could be quantified using the statistical distributions such as normal/triangular/uniform to select the optimum configuration of the multiple-chiller plants through the life-cycle analysis [24].

In the recently published works, the mathematical background of the hourly economic chiller dispatch problem is the same. The only difference between the reviewed works is the search algorithm and the best operating points (optimal values of decision variables such as on/off states, PLRs and refrigeration production) of the chiller units as well as their total power consumption (as the objective function) under the various cooling demand. Similarly, we combined the imperialistic competitive algorithm with the short-term optimal scheduling of the multiple-chiller systems to find better and more accurate PLRs/cooling generation/electricity consumption of the chillers in a way that their total electricity requirement at each operating time interval and given cooling load is less than those achieved by other algorithms. The contributions of the present work are presented as follows.

In this work, the ICA is applied to the OCL problem aiming to discover better solutions than those reported in recently published works. The total electrical power consumed by the chillers is minimized as the main objective function. The on/off status and PLR of the chillers are considered as the binary and random decision variables, respectively. Their cooling production and electricity consumption are considered as positive decision variables of mixed-integer non-linear programming problem. The refrigeration capacity limit and the cooling load-generation balance constraint are checked for each generated solution. If they are satisfied as well as the total power consumed by the chillers is minimum, the searching process is stopped; otherwise, a new scenario will be produced for the on/off states and PLRs of the units. Simulations are conducted on three well-known standard systems with three, four and six chiller units under different cooling loads. Numerical results associated with the PLRs and the total power utilized by the chillers are compared with those provided by other search algorithms such as SA [7], PSO [12], GA [8,9], ES [10], DE [11], DCSA [13], IWO [16]. It is revealed that the ICA based OCL strategy with fast convergence is more accurate and energy efficient than them. In other words, the ICA algorithm is able to find better values for the on/off states, PLRs, refrigeration production and electricity consumption of the chillers with less energy requirement of multi-chiller plants and lower calculation times than those obtained by SA, PSO, GA, ES, DE, DCSA and IWO.

The remainder of the present work is provided as follows: Section 2 models the hour-ahead economic dispatch of the conventional water-cooled multi-chiller plants. In Section 3, the imperialistic competitive algorithm is linked with the OCL problem. Three illustrative examples and discussions are presented in Section 4. Afterward, Section 5 concludes the paper.