These authors contributed equally to this work.
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).
This paper presents a study based on real plant data collected from chiller plants at the University of Texas at Austin. It highlights the advantages of operating the cooling processes based on an optimal strategy. A multicomponent model is developed for the entire cooling process network. The model is used to formulate and solve a multiperiod optimal chiller loading problem, posed as a mixedinteger nonlinear programming (MINLP) problem. The results showed that an average energy savings of 8.57% could be achieved using optimal chiller loading as compared to the historical energy consumption data from the plant. The scope of the optimization problem was expanded by including a chilled water thermal storage in the cooling system. The effect of optimal thermal energy storage operation on the net electric power consumption by the cooling system was studied. The results include a hypothetical scenario where the campus purchases electricity at wholesale market prices and an optimal hourbyhour operating strategy is computed to use the thermal energy storage tank.
As global energy demand rises and climate change concerns grow ever larger, the importance of using energy more efficiently continues to increase. One method of improving energy efficiency of a complex process is to create an accurate system model, and then use optimization algorithms to determine more efficient operating strategies for the system. This is especially true of building systems, which consume nearly 40% of the primary energy in the United States [
Depending on a building’s heating ventilation and air conditioning (HVAC) system, a building may require heating and cooling year round. In the summer, air may be cooled to lower than required room temperatures in order to remove humidity, and then reheated to bring it back up to the desired temperature. In the winter, thermal zones in the middle of large buildings require cooling because they are not exposed to ambient conditions, thus, the thermal needs are driven by the internal gains of the zone. Chillers are generally used to meet building cooling needs, and boilers are often used to provide heating.
Steadystate chiller models have been used extensively for a variety of chiller types and sizes. Chiller models can be based on firstprinciples [
Simple linear regression model
Biquadratic regression model
Multivariate polynomial regression model
Simpler multivariate polynomial regression model
DOE2 model
Modified DOE2 model
GordonNg universal model (based on the evaporator inlet water temperature)
GordonNg universal model (based on the evaporator outlet water temperature) *
Modified GordonNg universal model
GordonNg simplified model
Lee simplified model
* This model is used in the current work.
All necessary equations for each model are included in Lee
Chiller models have been used to determine the best operation conditions of a chiller. For example, Ng
Chillers can be used in conjunction with thermal energy storage (TES) to further improve system efficiency and reduce costs. Thermal energy storage is the storage of thermal energy (hot or cold) in some medium. Hot storage is used in applications such as district heating systems, where warm water is stored in large tanks, or in a concentrating solar power system, where solar energy is stored in the form of molten salts or synthetic oils. Cold storage is most commonly used for cooling buildings or district cooling networks where the cooling energy is stored as chilled water or ice. Thermal storage has been identified as a costeffective way to reduce required thermal or electric equipment capacities (such as chillers or turbines) [
Nomenclature.
Symbol  Description  Units 

Total cooling demand for 
kW  
Amount of stored thermal energy at 
kWh  
Maximum capacity of the TES tank  kWh  
Lower bound on the cooling load on 
kW  
Power consumed by the auxiliary equipment at 
kW  
Total power consumed by 
kW  
Electric power consumption of the 
kW  
Maximum charging/discharging rate of TES tank  kW  

Condenser water inlet temperature at 
K 

Chilled water outlet temperature  K 
Upper bound on the cooling load on 
kW  
Cooling load on 
kW  
Condenser heat exchanger coefficient of the 
W K^{−1}  
Evaporator heat exchanger coefficient of the 
W K^{−1}  
Internal condenser heat loss rate in the 
kW  
Internal evaporator heat loss rate in the 
kW  
Realtime market rate of electric energy at 
$/kWh  
Binary variable representing on or off status of 
Dimensionless  
Coefficient of performance of the 
Dimensionless  
Dry bulb temperature at 
K  
Number of cooling stations  Dimensionless  
Total number of chillers upto the 
Dimensionless  

Total number of chillers  Dimensionless 
Number of hours in the optimization horizon  Dimensionless  
Relative humidity at 
Dimensionless  
Wet bulb temperature at 
K  
Total cooling load at 
kW  
Penalty coefficient  $/kW  
Pdata  Actual power consumed by the cooling system operation in a day  MWh 
Popt  Estimated power consumption by the cooling system operation in a day for the cooling load profile resulted from solving optimization  MWh 
Modeling and optimizing a system that has both a large number of chillers or boilers and TES leads to complex optimization problems with binary or integer variables. For example, Tveit
In this paper the cooling system of a large campus is modeled and optimal chilling loads are determined. As the modeling is based on real data, the optimal results are able to be benchmarked against an actual operating strategy in order to accurately assess the potential of the optimization scheme. The optimization formulation includes a penalty term to account for the cost of switching chillers on and off. Additionally, this paper is unique in that it also considers the benefits of using a thermal energy storage system to perform optimal load shifting in a wholesale electricity market using actual wholesale market prices. All the symbols used in this paper are defined in
The University of Texas at Austin (UT Austin) has its own independent cogeneration based power plant (see
Simplified schematic of the Hal C. Weaver power plant complex at the University of Texas at Austin.
About a third of the power generated by the power plant is used by the cooling system; primarily by chillers, cooling towers, and pumps. UT Austin has a large district cooling network to meet the cooling demands of the entire campus. The cooling system includes three chiller plants (also called cooling stations) and a four million gallon (15,100 m^{3}) chilled water thermal energy storage tank. This tank has a storage capacity of 39,000 tonhr (494 GJ). The tank can be filled with chilled water during the night and then discharged during the day when demand for cooling is highest. This cooling system serves over 160 buildings with approximately 17 million square feet (1.6 million m^{2}) of space. The three active cooling stations are numbered as Station 3, Station 5, and Station 6 (Stations 1, 2, and 4 have either been decommissioned or are not currently in use). Each station includes three centrifugal chillers, a set of cooling towers, condenser water pumps, and chilled water pumps. Station 6 has variable frequency drives installed on all equipment. The chillers in any Station X are named as X.1, X.2, and X.3.
A multicomponent model of the cooling system has been developed with the purpose of determining an expression for the power consumed by the cooling system in terms of several independent variables. These variables include the individual chiller loads, the ambient weather conditions and the chilled water temperature set point. The individual chiller loads are the decision variables in the optimal chiller loading (OCL) problem, as defined in the next section. The chilled water temperature set point (
Chillers are responsible for providing chilled water to the 160 campus buildings. Hence they account for about 60% to 70% of the total cooling station power consumption. The UT Austin chiller plant, like most largescale cooling systems, consists of several centrifugal electric chillers. Power consumption (
Coefficient of performance (
Data from nine chillers were individually fitted to the above models.
Error analysis for centrifugal chiller modeling.
Chiller Number  Range of absolute error (%)  Mean % absolute error 

3.1  0–6.18  1.41 
3.2  0–9.70  1.36 
3.3  0–30.08  2.25 
5.1  0–7.11  1.61 
5.2  0–6.5  0.99 
5.3  0–13.71  1.19 
6.1  0–23.02  1.34 
6.2  0–31.22  0.93 
6.3  0–3.17  0.64 
Electric power consumed by chiller 6.1 in the month of September–Model
Auxiliaries include the components of a chilling station other than chillers,
By minimizing the sum of the squared error, the models show good agreement between the model’s predicted values and the data obtained from the plant (
Total power consumed by the auxiliary equipment in the cooling station 6–Model
The total power consumption by a cooling station as a function of the cooling load distribution and ambient weather conditions is obtained by adding Equations (1) and (2):
Error analysis for auxiliary component modeling.
Station Number  Range of absolute error (%)  Mean absolute error (%) 

3  0–40.81  9.96 
5  0–20.31  2.17 
6  0–23.67  6.98 
Total  0–26.48  5.85 
The existing strategy for operating two out of the three chiller plants at UT Austin (plant 3 and plant 5), which do not have motors with variable speed drives, is based on heuristics and operators’ discretion drives, and hence may be suboptimal. Chiller plant 6 has variable speed drives (VSD) installed on all its equipment and the decisions regarding its chiller loads are based on equal marginal performance principal (EMPP) [
It is proposed in this paper that independent optimization problems solved at regular intervals with wisely chosen initial conditions and satisfying constraints should give better results for all chiller plants, as compared to the current operating strategy. The optimal chiller loading problem is formulated in two ways, as described in detail in the following subsections. First, it is solved as hourly independent steady state optimization problems where the cooling system is considered without any thermal storage. Next, the thermal storage is included as part of the cooling system, and the time span of one optimization problem is expanded to 24 h in order to take advantage of the flexibility to shift cooling loads.
Optimal chiller loading is solved as a multiperiod static optimization problem. The objective of this problem is to minimize the total power consumed by the cooling system. This objective is achieved by optimizing the cooling load distribution among various chillers operating in parallel. There are two decision variables for each chiller—the individual chiller load and a binary variable defining the chiller state,
In Equation (4a),
For a system of M chillers, the total number of possible
The hessian of matrix H was verified to be positive definite for all possible cases. Hence, the optimization problem (Equation (4) with a fixed set of
Another goal of this research is to determine the advantage of using thermal energy storage (TES) with a large scale cooling system. Thermal storage is used to shift cooling load between different hours of the day. The extra chilled water generated during a given lowdemand hour is sent to the storage tank and is retrieved during a highdemand hour to satisfy the extra cooling demand. The use of TES gives flexibility to shift cooling load across time periods and, hence, to use the most efficient chillers more often and the least efficient chillers less often. The addition of storage also makes the optimization problem dynamic because the current state of the storage depends on previous states. Optimal operation of the cooling system with storage should lead to additional energy savings.
Apart from savings on energy cost, the use of TES may benefit the chiller plant operation by flattening the cooling load profile over a day. Typically the total cooling load is at a lower level during the night and increases after sunrise and when occupants arrive on campus. After reaching a peak load, it again decreases in the evening. Depending on the fluctuations in the ambient temperature and building occupancy, this cooling load profile sometimes undergoes many fluctuations during the day (
Hourly campus cooling load values (left axis) and ambient wetbulb temperature values (right axis) over 24 h period. This data is from 11 July 2012. It serves as an example for days with more than one maxima in the cooling load profile.
Therefore, optimization with thermal energy storage aims at two improvements in the energy efficiency by reducing the energy cost associated with (a) operating the chillers; and (b) frequent cold starts.
The optimization problem formulation for a time span over
An important thing to note is that the objective of this problem (Equation (6a)) is to minimize the total cost ($) of power. On the other hand, the objective of the optimization problem without storage (Equation (4a)) was to minimize the total power consumed (kWh) by the cooling system.
This optimization problem is solved in two stages [
This section discusses the optimization results from several different cases. The cooling process system optimization problem was solved for the duration of a year. The problem of optimization without storage was solved hourly while optimization with storage was solved daily.
Hourly static optimization problems were solved for a year for the cooling system without storage. The model’s predicted optimal power consumption values were compared against real data collected from the UT chiller plants. The results predict energy savings as high as 40% for a single time step which is of one hour. The average energy savings over 8784 h of a year is predicted to be 8.57%. In an absolute sense, the static optimal chiller loading could save about 8.1 GWh (~$486,000) over the year in 2012. In the current operation, the cooling loads for six out of nine chillers (Stations 3 and 5) are determined based on operators’ discretion and some heuristics that are easy to follow but not based on optimal operation. The cooling loads for chillers in Station 6 are determined based on a gradient based control strategy [
With the objective of adding more degrees of freedom to the optimization, thermal energy storage was included in the system for the next study. Assuming
Cooling load distribution among 24 h (Day 1) from different optimization conditions.
Cooling load distribution among 24 h (Day 2) from different optimization conditions.
Comparison of power consumption values from plant data, static optimization and dynamic optimization.
It can be observed from
However, an interesting observation is made from the above results (
Effect of optimal chiller loading (OCL) with thermal energy storage on the frequency of cold starts.
Cooling load profile  Number of chiller turning on/off events in 24 h  Total power consumption in 24 h (MWh) 

Plant data  4  356.45 
OCL Without storage  4  342.34 
OCL With storage, α = 0  5  341.99 
OCL With storage, α = 0.1  1  342.81 
OCL With storage, α = 0.5  0  344.51 
Comparison of the variations in the total number of operating chillers under different cooling load profiles.
This section evaluates the advantages of using thermal storage in a scenario where electricity prices vary hourly. Realtime market prices from the Austin Load Zone in the Electricity Reliability Council of Texas (ERCOT) market, from 2012, were used for the analysis of optimization results. Such a variable cost scenario highlights the advantage of using thermal energy storage. The market price data (
Variation in the hourly realtime prices in the ERCOT wholesale market over the year 2012, in Austin, TX, USA.
For the purpose of studying the effect of using TES in the case of time varying prices, the value of α was assumed to be zero while solving the optimization problem with storage. Possible savings from using TES in this case were simulated for 366 days of the year 2012 by solving 366 optimization problems. The daily optimal cost (with TES) is compared with the daily estimated cost (without TES) based on real hourly cooling load values and the variable price of electricity from ERCOT. The days with large variation in the electricity price demonstrate large savings in the cost of cooling. The percentage savings in the cooling cost for an hour are predicted to be up to 42.2% with a mean of 13.45%. In an absolute sense, it translates to a sum total of $400,000 saved over a year for a large system such as UT Austin.
Comparison of the cooling cost in case of time varying electricity prices—With TES (α = 0)
In the current paper, the optimization of a large scale cooling system was performed using various MINLP formulations. The optimization results were compared against the hourly real plant data from UT Austin chiller plants spanning over one year. Multiperiod static optimal chiller loading yielded energy savings up to 40% for a time period (one hour). Assuming a constant electricity cost of 6 cents/kWh, annual savings of $486,000 were estimated for the year 2012. Hence, optimal chiller loading emerges as an effective way to reduce electrical energy consumption. As the cooling system at UT Austin consumes over 30% of the annual total power generation, efficient operation of cooling system will reduce the load on power generation equipment.
Addition of thermal energy storage to the cooling system provides additional flexibility in its operation. A multiperiod optimization problem over a larger time horizon (24 h) was solved to study the effect of using TES on power consumption and operational stability. The results in this case did not translate to significant energy savings. Moreover, the objective function did not include the heat losses associated with the use of TES. Therefore in a real situation, the energy savings from using TES are expected to be somewhat lower. However, for a hypothetical scenario of time varying electricity prices, shifting of cooling load with the help of TES predicted economic savings up to 42.2% for a day.
The optimal operation of cooling system with TES was also shown to have a significant positive impact on the chiller plant operations in terms of the frequency of cold starts. Due to the added flexibility to adjust the cooling load profile, the cooling system with TES was able to generate a less fluctuating operating strategy with the help of the proposed optimization routine. It was shown that the number of occurrences of turning a chiller on or off over a period of 24 h can be reduced from 4 to 0 by using thermal storage. It is expected to even further reduce the energy losses that occur during the transient phase of a chiller operation. Additionally, with a smoother cooling operation, the equipment wear is also expected to be reduced.
The findings from the current study suggest that optimal chiller loading is an effective energy saving operating strategy for large scale cooling systems with multiple chillers sharing a common cooling load. The installation and operation of thermal energy storage (TES) is marginally beneficial to save energy costs where the cost of electricity is constant with time. On the other hand, the use of TES can minimize the fluctuations in cooling load profile. In situations where time varying electricity prices are used, TES is shown to be quite useful in reducing electricity bills. The current study can be further extended in many ways. The choice of time horizon of the optimization problem with TES can have a significant impact on improving the cooling operation. The starting point of one optimization cycle was assumed to be midnight in the current study, assuming an empty TES tank at that time. Different starting points also need to be considered in order to expand the proposed study. For systems like UT Austin, shifting of cooling loads with the help of TES can also shift loads on the power generation equipment. Variable efficiency curves of turbines suggest another possible optimization problem to minimize the total natural gas consumption by the power plant.
The authors thank The Department of Utilities and Energy Management at UT Austin for providing the chiller data needed to perform the study. Apart from the data, the facility manager Ryan Thompson and the operators were also helpful and supportive in providing insight into the power plant operation.
The authors declare no conflict of interest.