# Method for estimating energy savings potential of chilled-water plant retro-commissioning.

INTRODUCTION

Retro-commissioning has been widely used for central chilled-water (ChW) plants to improve their performance. Some measures are very popular and effective, such as chW supply temperature reset, cooling tower (CT) approach temperature reset, secondary loop differential pressure (DP) reset, and condenser water (CW) flow rate reset. Accurately estimating the energy savings potential of each measure is crucial for the success of a retro-commissioning project. Generally, these measures interact with each other and the performance of chiller (CHLR) plant equipment is nonlinear, making it difficult to conduct an accurate savings potential estimation using simplified engineering calculations. At the same time, building a detailed plant model for each project is time consuming. Sometimes it is even impractical due to the lack of enough information or divergence of iterations. In response to this challenge, this paper introduces a method to estimate the savings potential of some popular measures by building a forward simulating model for a chiller plant without storage.

A chiller plant produces ChW and transports it to end users (such as air-handling units [AHUs]) through piping. Central ChW plants are widely employed because they have long been promoted as an energy-efficient and low-operating-cost means of rejecting heat from building air-conditioning systems to the atmosphere. A large portion of the power required to run a facility is consumed in the central chiller plant. However, the energy performance of most existing chiller plants is not very efficient. It was estimated that about 90% of water-cooled, centrifugal central plants operated in the 1.0 to 1.2 kW per ton (2.9 to 3.5 coefficient of performance [COP]) "needs improvement" range, while a highly efficient plant can reach 0.75 kW per ton (4.7 COP) (Erpelding 2006). All kinds of problems are to blame, such as the low delta-T syndrome (Kirsner 1995), low chiller part-load ratio (PLR, which equals chiller actual cooling load over design cooling capacity), significant mixing, valve and pump hunting, higher than needed pump pressure, etc. In addition, there are other reasons for a lack of plant optimization, such as equipment performance degrading with age, load changes (Taylor 2006), plant expansion in an unorganized manner, and energy cost fluctuations. Today, more and more people are aware of sustainability and the importance of saving energy. The fluctuating energy prices also make plant owners and operators try various ways to enhance the performance of chiller plants so as to reduce the energy costs.

Automatic control systems have been widely applied in chiller plants to achieve robust, effective, and efficient operation of the system on the basis of ensuring thermal comfort of occupants and satisfying indoor air quality. Generally, all the control methods used in heating, ventilating, and air-conditioning (HVAC) systems can be divided into supervisory control and relational control. Supervisory control, often named optimal control, seeks stable and efficient operation by systematically choosing properly controlled variable setpoints, such as flow, pressure, or temperature. These setpoints can be reset when uncontrolled variables (such as ambient air wet bulb [WB] temperature, dry bulb [DB] temperature, and building cooling load) are changed, and they are maintained by modulating control variables (speed of components) through proportional integral derivative (PID) controllers or sequencing. This method is easy to understand and is widely accepted in practice due to the simplicity and effectiveness. The fundamentals of supervisory control strategies have been comprehensively introduced in ASHRAE Handbook--HVAC Applications (2003) and are widely applied in practice. Most of these controls originated from the supervisory control methodology developed by Braun (1988). Relational control is determining continuous and discrete control variables directly according to uncontrollable variables or equipment power input, such as demand-based control (Hartman 2001) and load-based control (Yu and Chan 2008). It was claimed by the authors that these controls could realize tremendous energy savings.

The chiller plant models can be divided into component-based and system-based. The component-based model simulates plant performance by modeling each plant component individually. Sometimes, it takes too much effort to build a component-based model or the necessary data may not be available. An alternative way to simulate plant performance is to simulate the plant power with one function. This methodology was first advanced by Braun et al. (1989) when they developed a system-based optimization based on results from component-based optimization. The method involves correlating overall cooling plant power consumption using a quadratic function form. The inputs are uncontrolled variables and controlled continuous variables while the outputs are total cost. Separate cost functions are necessary for each operating mode. Minimizing this function leads to linear control laws for controlled continuous variables in terms of uncontrolled variables. The empirical coefficients of this function depend on the operating modes so that these constants must be determined for each feasible combination of discrete control modes. The determined controlled variables, such as ChW flow rate, will be maintained by modulating continuous control variables, such as valve open percentage and motor speed.

The system-based method has been adopted by Ahn and Mitchell (2001) to find the influence of the controlled variables on the total system and component power consumption. A quadratic linear regression equation for predicting the total cooling system power, in terms of the controlled and uncontrolled variables, was developed using simulated data collected under different values of controlled and uncontrolled variables. The trade-off among the components of power consumption resulted in the total system power use in that both simulated and predicted systems were minimized at lower supply air, higher ChW, and lower condenser-water temperature conditions. Bradford (1998) developed linear, neural network, and quadratic system-based models and a component-based model to predict the system energy consumption including demand side. It has been shown that the use of component-based models for either on-line or off-line optimal control is viable and robust.

Although the system-based plant model is much simpler than the component-based model, the objective function under each feasible combination of discrete control modes has to be generated, and considerable regression error as well as solution difficulty may exist. The component-based model is more accurate, but it takes a longer time to build the model for each project. Iterations are inevitable and convergence could be a problem. Some sophisticated algorithms are also required to optimize such a system.

The objective of this paper is to develop a method to estimate the savings potential of some popular measures by building a forward simulating model for a ChW plant without storage. Its application is illustrated with an example system to find the optimal reset schedule of the chiller ChW leaving temperature, CW flow rate, and CT approach temperature. The energy and billing cost savings potential of several energy conservation measures can also be estimated.

METHOD

A central ChW plant consists of cooling towers, CW pumps, chillers, and primary and secondary ChW pumps. Figure 1 shows the simplified general physical configuration of a primary-secondary loop ChW system. Most valves and fittings are omitted for simplicity purposes. All the variables shown in Figure 1 are setpoints that could be optimized by implementing reset schedules. In practice, these setpoints are maintained by adjusting the equipment speed or control valve position with a PID controller. Except for continuous controlled variables, discrete control variables will also need to be optimized, such as the sequencing of chillers, cooling towers, and pumps. The constraints on the equipment operations, such as maximum and minimum flow rates, limit the number of feasible combinations of control variables. For example, chillers have lower and upper limits on the evaporator flow rate. The number of chillers running simultaneously should ensure the actual evaporator flow be within this range. This limits the possible number of chillers staged on simultaneously.

[FIGURE 1 OMITTED]

Plant Power Modeling

The cooling system total power can be divided into plant power and non-plant power. The electricity consumed by ChW production is considered plant power while all other electricity consumptions (such as plant AHU fans, lighting, and plug loads) are non-plant power.

Figure 2 is a flow chart of the ChW plant power simulation model. All the variables on the left are the inputs, while the output is the plant total power. The plant model deter-mines the plant total power consumption in response to a set of external parameters and a set of plant parameters. The driving force of chiller plant operations is the ChW flow demanded by users on the secondary loop. This demand cannot be controlled by operators. For each given plant total ChW flow demand, the ChW plant model will export the total plant power under the given conditions. In this study, an equipment performance-oriented plant model is proposed to calculate the plant power under predefined conditions. This model is based on a wire-to-water (WTW) plant efficiency concept. The WTW efficiency of a pump was first introduced by Bernier and Bourret (1999). It was originally used to quantify the whole performance of a ChW plant. In this study, it is used to define the transportation efficiency of plant equipment except for secondary pumps (SPMPs). The power of SPMPs is determined by the secondary loop ChW flow rate, pumping system total efficiency, and pressure drop of the secondary distribution system including pipe friction and valve losses.

[FIGURE 2 OMITTED]

The system total power can be calculated from the following formula:

[P.sub.sys] = ([[zeta].sub.CT] + [[zeta].sub.CWP] + [[zeta].sub.CHLR] + [[zeta].sub.PPLR]) [Q.sub.Plant,ChW] + [P.sub.SPMP] + [P.sub.non_plant] (1)

Some regression formulas, together with energy conservation laws, are used to simulate the WTW efficiency of pumps and CTs. This forward plant model can be easily set up and used for plant energy simulation. Since it is based on basic physical definitions and conservation laws, it has an explicit physical meaning. Its application is not restricted by the equipment number and sequencing strategies. All calculations are explicit expressions and no iterations are required. One prerequisite is that the pumps are well sequenced and controlled so that the pump flow rate is within the normal operation range.

In most cases, the optimization target of a chiller plant operation is to minimize the operating cost within a billing period, such as a year. This target is achieved by implementing the optimal reset schedules of some controlled variables, such as ChW supply temperature, CW flow rate, and CT approach temperature. This is a nonlinear programming (NLP) problem and can be solved with the generalized reduced gradient (GRG) nonlinear solver. This method and specific implementation have been proven in use over many years as one of the most robust and reliable approaches to solve difficult NLP problems.

Chiller Modeling

This paper selected the Gordon-Ng model (Gordon and Ng 2000) to simulate chiller performance. This model is valid for vapor-compression chillers with variable condenser flow. It can apply to unitary and large chillers operating under steady-state variable condenser flow conditions. This model is strictly applicable to inlet guide vane capacity control (as opposed to cylinder unloading for reciprocating chillers or variable-speed drive [VSD] for centrifugal chillers) (Jiang and Reddy 2003). It is in the following form:

y = [c.sub.0] + [c.sub.1][x.sub.1] + [c.sub.2][x.sub.2] + [c.sub.3][x.sub.3] (2)

where

[x.sub.1] = [T.sub.cho]/[Q.sub.ChW], [x.sub.2] = ([T.sub.cdi] - [T.sub.cho])/([Q.sub.ChW][T.sub.cdi]), [x.sub.3] = ((1/COP) + 1)[Q.sub.ChW])/[T.sub.cdi],

and

y = ((1/COP) + 1)[Q.sub.ChW])/[T.sub.cdi]

where -1-(1/([V.sub.CW, per][[rho].sub.w][c.sub.pw])) (((1/COP) + 1)[Q.sub.ChW])/[T.sub.cdi]

[T.sub.cho] = (([T.sub.CHLR,ChW,S] - 32) * 5)/9 + 273.15,

[T.sub.cdi] = (([T.sub.CHLR,CW,S] - 32) * 5)/9 + 273.15,

[Q.sub.ChW] = (12,000[Q.sub.CHLR, per])/3412, COP = [Q.sub.ChW]/[P.sub.CHLR],

and

[V.sub.CW] = 0.00006309[V.sub.CHLR, CW, per]

The chiller WTW effciency (kW per ton) is:

[[xi].sub.CHLR] = [P.sub.CHLR]/([Q.sub.ChW] 3412/12,000)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

It is recognized that the actual chiller ChW flow is also limited by the upper and lower limits of evaporator ChW flow rate. The upper limit is intended to prevent erosion and the lower limit is to prevent freezing in the tubes.

Pump Modeling

The general calculation formula of the ChW pump power is:

[P.sub.pump] = (0.746V x H)/(3960[[eta].sub.all]) (4)

where [[eta].sub.all] is the overall efficiency including pumps, motors, and VSDs.

The total cooling transported by the water pump is approximately calculated by:

[Q.sub.ChW] = ([V.sub.ChW][DELTE][T.sub.ChW])/24 (5)

The pump WTW efficiency is:

[[xi].sub.pump] = [p.sub.pump]/[Q.sub.ChW] = (0.746v x H)/3960[[eta].sub.all] x (24/[V.sub.ChW][[DELTE]T.sub.ChW]) (6)

For primary pumps (PPMPs), V = [V.sub.ChW]. The WTW efficiency is:

[[xi].sub.PPMP] = 0.004521 [H.sub.PPMP]/ ([[eta].sub.PPMP][[DELTE]T.sub.ChW]) (7)

For condenser water pumps (CWPs), V = [N.sup.pump] * [V.sub.CW, per] * Consequently, the CW pump WTW efficiency is:

[[xi].sub.CWP] = 0.0001884 [H.sub.CWP]/[[eta].sub.CWP][Q.sub.ChW, per] (8)

For SPMPs, the pump power is:

[P.sub.SPMP] = (0.746[V.sub.LP_ChW] x 2.31 ([DP.sub/LP] + e[V.sub.LP_ChW.sup.2]))/3960[[eta].sub.SPMP] (9)

The head and efficiency of pumps can be simulated as functions of pump flow rate or be constant. Obviously, the energy consumption of SPMPs is subject to the loop-side operation and is not determined by plant operations.

Cooling Tower Modeling

The mass and heat transfer process in a cooling tower is fairly complicated. The effectiveness-NTU model is the most popular model in CT simulations, but iterations are required to obtain a converged solution (Braun 1989). To overcome this obstacle, a simple CT fan power model is proposed to calculate the tower WTW performance:

[[xi].sub.CT] = [P.sub.CT]/[Q.sub.ChW] = ([d.sub.1] + [d.sub.2]/ [[DELTA]T.sub.APP]) (1 + 0.2843[[xi].sub.CHLR] (10)

The actual CT approach temperature is obtained from the following formula:

[[DELTA]T.sub.APP] = [T.sub.CT, CW, R] - [T.sub.wb] (11)

The coefficients [d.sub.1] and [d.sub.2] are regressed from the trended data, and '[DELTA][T.sub.APP] = [T.sub.CT, CW, R] - [T.sub.wb] is maintained by sequencing the cooling towers or modulating fan speed.

Loop Delta-T

The loop ChW delta-T is subject to many factors, such as chiller ChW leaving temperature, cooling coil air leaving temperature, type of flow control valves, coil design parameters and degrading due to fouling, tertiary connection types, coil cooling load, air economizers, etc. Considering the difficulties in developing a physical model to simulate the loop delta-T, a linear model regressed from the trended data is used in this study.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

where [x.sub.i] are the variables that could be the dominant factors of the loop delta-T model, such as ChW supply temperature, loop total cooling load, ambient DB and WB temperatures, hour of the day, weekday or weekend, and month. The air system side parameters, such as coil air leaving temperature, total airflow rate, coil design delta-T, and sensible load ratio, are not included due to diversity or unpredictability.

The exact form of the regression model may vary for different projects. It could be necessary to build different models to accommodate air-conditioning system operation changes at different seasons. A constant delta-T can be used in a rough, first-order simulation.

APPLICATION

Example System Description

The example system investigated in this study is a central utility plant called Energy Plaza (EP) located in the Dallas-Fort Worth metropolitan area. The EP consists of six 5500 ton (19,343 kWt) constant-speed centrifugal chillers, called on-site manufactured (OM) chillers; one 90,000 ton * h (316,517 [kW.sub.t] * h) naturally stratified ChW storage tank; six 150 hp constant-speed primary pumps; four 450 hp variable-speed secondary pumps; eight 400 hp CW pumps; and eight 150 hp two-speed cooling towers. Figure 3 shows a schematic diagram of this ChW system. This study only deals with the ChW system operated without ChW thermal storage.

The monthly electricity billing cost consists of a meter charge, current month non-coincident peak (NCP) demand charge, four coincident peak (4CP) demand charge, and energy consumption charge. The total monthly electricity billing charge ([C.sub.Total]) is:

[FIGURE 3 OMITTED]

[C.sub.Total] = [C.sub.delivery_point = [R.sub.4CP][D.sub.4CP] + [R.sub.NCP][D,sub.NCP] + [R.sub.energy][E.sub.consumption] (13)

The rates [R.sub.4CP], [R.sub.NCP], and [R.sub.energy] for each month are subject to minor adjustments, and the rates from a selected one-year period are used in the simulation. The meter charge [C.sub.delivery_point] is constant for each month. All demand kilo-watts used have been adjusted to 95% power factor. The monthly average power factors during this period will be used in the power factor correction.

The 4CP demand kilowatt is the average of the plant's integrated 15 minute demands at the time of the monthly Electric Reliability Council of Texas (ERCOT) system 15 minute peak demand for the months of June, July, August, and September (called summer months) of the previous calendar year. The exact time will be announced by ERCOT. The plant's average 4CP demand will be updated January 1 of each calendar year and remain fixed throughout the calendar year. The NCP kilowatt applicable shall be the kilowatt supplied during the 15 minute period of maximum use during the billing month. The current month NCP demand kilowatt shall be the higher of the NCP kilowatt for the current billing month or 80% of the highest monthly NCP kilowatt established in the eleven months preceding the current billing month.

The ChW flow through the chiller evaporator is controlled by modulating flow control valves on the leaving side of the evaporator. The sequencing of the constant-speed PPMPs is dedicated to the corresponding chillers. The variable-frequency device speed of the SPMPs is modulated to maintain the average of differential pressures at the loop ends at a given setpoint. This setpoint is manually adjusted to be between 25 and 48 psid (172.4 and 330.9 kPa) all year round to ensure there are no hot complaints. The cooling tower staging control in place is to stage the number of fans and select high and low speeds of fans to minimize the chiller compressor plus CT fan electricity consumption.

System Modeling

System Power. The trended historical data are used for system modeling. The electricity consumed by OM chillers, CT fans, CW pumps, PPMPs, and SPMPs is considered plant ChW electricity load while all other electricity consumptions, such as EP air-conditioning, air compressors, lighting, and plug loads, are non-plant electricity loads.

To check the accuracy of the system model, the EP monthly utility bills are compared with the simulation results. A good match is found, although minor differences exist in several months. This could be attributed to imperfection of models, inaccurate parameter inputs, or operations different from actual situations. The present system power model can reasonably predict the monthly electricity consumption.

Loop-Side Modeling. The parameters and inputs for the thermal energy storage (TES) system loop side are shown in Table 1. The upper and lower limits of the loop end DP, as well as the loop flow rate change points, are subject to hydraulic requirements and operating experiences. If the loop total ChW flow rate is equal to or lower than 10,000 gallons per minute (gpm) (0.631 [m.sup.3]/s), the DP setpoint is 22.0 psid (151.7 kPa). If the rate is equal to or higher than 16,000 gpm (1.009 [m.sup.3]/s), the DP setpoint is 28.0 psid (193.1 kPa). The ChW secondary DP setpoint is reset linearly from 22 to 28 psi (151.7 to 193.1 kPa), when the secondary ChW flow is between 10,000 and 16,000 gpm (0.631 and 1.009 [m.sup.3]/s). A loop load factor is defined to test the savings when the actual load profile is different from the one used in the simulation.

A temperature rise exists between the loop supply temperature and the chiller ChW leaving temperature, which is due to pumping heat gain and piping heat losses. The trended data show that the temperature rise fluctuates between 0.0[degrees]F and 2.0[degrees]F (0[degrees]C and 1.1[degrees]C) most of time and the annual average temperature rise is 1.0[degrees]F (0.6[degrees]C).

When the loop end DP setpoints are determined, a loop hydraulic coefficient is required to calculate the differential pressure before and after the SPMPs. Three hydraulic coefficients are regressed from trended data corresponding to one, two, or three SPMPs running scenarios. The coefficients can be regressed from a plot of piping DP losses versus loop total flow rate.

Equation 14 is a linear regression model developed to simulate the loop delta-T as a function of ChW loop supply temperature ([x.sub.1]), loop total cooling load ([x.sub.2]), and ambient WB temperature ([x.sub.3]). A higher loop supply temperature, a lower WB temperature, and a lower loop total ChW load lead to a lower loop delta-T, which is consistent with the observations. An upper and a lower limit are defined to avoid unreasonable regression results when an extrapolation is applied. The system error of the loop delta-T can be used to check the effect of loop delta-T prediction deviations on the system total energy and costs.

[[DELTA]T.sub.LP] = [h.sub.0] + [h.sub.1][x.sub.1] + [h.sub.2][x.sub.2] + [h.sub.3][x.sub.3] (14)

Figure 4 is a comparison of the measured and predicted ChW supply and return temperatures. If the model accurately fits the data on which it was trained, this type of evaluation is referred to as internal predictive ability. The external predictive ability of a model is to use a portion of the available data set for model calibration, while the remaining data are used to evaluate the predictive accuracy. The root mean square errors (RMSEs) of the internal and external predictions are both 1.1[degrees]F (0.63[degrees]C). The coefficient of variations (CVs) of the internal and external predictions are 6.86% and 6.93%, respectively.

[FIGURE 4 OMITTED]

Plant-Side Modeling. Table 2 shows the main parameters and inputs for the plant side. The efficiencies of all pumps are assumed constant or determined from pump efficiency curves. The overall efficiency is a product of motor efficiency, shaft efficiency, and pump efficiency (and variable-frequency drive efficiency for SPMPs). The pump heads are determined from pump head curves. The primary side flow rate is controlled to be equal to the secondary side flow rate. It is assumed that all pumps are sequenced reasonably to ensure that the running pumps are operated around the design points.

The CT coefficients are obtained from the regression results of the historical data. The CT model fitting curve is shown in Figure 5. It should be noted that the coefficients obtained from the trended historical data are only applicable to the current cooling tower operation strategy. If a new CT operation strategy is used, the coefficients are subject to adjustment.

[FIGURE 5 OMITTED]

The coefficients of the Gordon-Ng chiller model are obtained by regressing with the trended historical data of the OM chillers. The rated CW flow rate is equal to the average of the trended data. In this study, the total available chiller number is limited to six. The chiller ChW leaving temperature default setpoint is 36[degrees]F (2.2[degrees]C). The ChW flow rate limits and CW entering temperature limits are based on the chiller design specifications. Figure 6 is a comparison between measured and predicted motor power using the Gordon-Ng model.

[FIGURE 6 OMITTED]

Non-Plant Power Modeling. The non-plant power is composed of two segments. When the ambient DB temper-ture is lower than 60[degrees]F (15.6[degrees]C), the non-plant power is 750 kW constant. Otherwise, a second-order polynomial is used to calculate the total non-plant power contributed by plant HVAC, glycol cooling systems, air compressors, etc. The coefficients are shown in Table 3, and Equation 15 shows the mathematical form of the regression model.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

Simulation and Results

The selected variables to be optimized are chiller ChW leaving temperature, CT approach temperature, and chiller CW flow rate. The default and upper and lower limits of each variable are shown in Table 4. Different default values are used to test their effects on the optimal solutions found by the solver. The monthly optimal setpoints, as well as the energy and utility billing cost savings, are shown in Table 5.

In the winter months, the loop cooling load and loop delta-T are both pretty low. Running chillers are lightly loaded most of time and the evaporator flow rate has reached the upper limit. A lower ChW leaving temperature is preferred to increase the loop delta-T, which benefits the part-load ratio (PLR) of the chiller. This may sound a little counterintuitive, as most plants will increase supply ChW temperature to improve chiller performance. When the efficiency improvement due to higher PLR dominates the degrading due to lower supply temperature, we will see improved overall chiller efficiency. This phenomenon has been observed for this project. However, it should be recognized that this is a case-by-case result and cannot be generalized to other systems. In the summer months when the loop cooling load is high, the chiller can still be loaded up to the optimal PLR; even the ChW supply temperature rises to 44[degrees]F. A higher ChW leaving temperature can improve the chiller efficiency. The optimal CT approach temperature is around 4.6[degrees]F (2.6[degrees]C) and the optimal chiller condenser water flow rate is 11,000 gpm (0.694 [m.sup.3]/s) all year round. Compared to the scenario with default setpoints, the optimal reset schedule can reduce electricity energy consumption by 2,559,426 kWh per year and reduce electricity billing costs by $261,387.00 (U.S.) per year or 3.3% of the baseline annual electricity costs.

As the change of each variable may place different impacts on the performance of each component, a single-variable sensitivity study is performed using August as an example. Table 6 shows the electricity consumption change if the setpoints are different from the default values. The percentage is the change of monthly kilowatt--hour consumption for each corresponding component. If the chiller ChW leaving temperature increases by 1.0[degrees]F to 36[degrees]F (0.6[degrees]C to 2.8[degrees]C), the monthly total electricity consumption of the plant reduces by 82,242 kWh. Particularly, the chiller electricity consumption reduces by 1.1% of the chiller monthly consumption due to a higher chiller efficiency. This is consistent with the rule of thumb that for each 1[degrees]F (0.6[degrees]C) increase in ChW temperature, constant-speed chiller efficiency increases 1.0% to 2.0%. The SPMPs consume 4.3% more of the monthly electricity usage due to a higher ChW flow rate as a result of a lower loop delta-T. The minor changes to cooling towers, condenser water pumps, and primary pumps are due to chiller staging change.

If the cooling tower approach decreases by 1.0[degrees]F (0.6[degrees]C), the chiller will consume 0.9% less electricity due to a lower CW entering temperature. However, the cooling tower fan will consume 12.2% more electricity as it needs to run harder to approach closer to the ambient WB temperature. As a result, chillers consume 78,075 kWh less and tower fans consume 63,705 kWh more. Overall, this measure can still save 23,414 kWh in August. This result is also consistent with the annual optimizations that the optimal approach is around 4.6[degrees]F (2.6[degrees]C).

If the chiller CW flow rate increases to 11,000 gpm (0.694 [m.sup.3]/s), the chiller efficiency is improved due to enhanced heat transfer in the condenser. The kilowatt--hour savings from chillers are 70,625 kWh. For this particular project, the CW pumps consume even less energy when the flow rate increases. This is associated with the particular performance curves of the selected CW pumps and may not be valid for other systems.

This model is also used to test the energy saving sensitivity of several energy conservation measures, such as reducing the loop end DP setpoint upper limit ([DP.sub.h]), the loop cooling demand, and the loop ChW supply temperature rise ([[DELTA]T.sub.s]). Table 7 shows the annual billing cost savings potential of each measure. It is estimated that, when the loop DP upper limit decreases by 2.0 psid (13.8 kPa), the annual electric usage of SPMPS can be reduced by 80,534 kWh or 3.7% of the SPMP power consumption. The utility cost decreases by $7487 per year or 0.1% of system annual total utility costs. If the cooling demand by the end users can be cut by 5%, the electric consumption can be saved by 3,467,316 kWh per year and the annual utility costs can be reduced by 4.9%. Generally, the temperature of the ChW reaching the end users is higher than that produced by the chiller. This could be due to piping heat losses, mixing, or pumping power. In the baseline case, the loop supply temperature rise is assumed to be 1.0[degrees]F (0.6[degrees]C). If the temperature rise can be reduced by half, 1,765,763 kWh can be saved each year and the annual utility costs savings is 2.0%. These results can be used to estimate the payback of each measure.

SUMMARY AND CONCLUSION

A chilled-water plant is a high-energy-density facility. However, the energy performance of most existing chilled-water plants is not very efficient. With volatile energy prices, improving the plant efficiency to save utility costs is an urgent task for chiller plant owners and operators. Some effective retro-commissioning measures have been widely adopted to reduce plant energy usage by 3% to 5%. Estimating the energy savings potential of these measures is crucial for the success of a retrocommissioning project.

Modeling and simulating is a popular method to optimize the plant operation and estimate the savings potential of various measures. The system-based model is simple but not accurate, while the component-based model is accurate but complicated. This paper proposes a forward plant model based on a wire-to-water efficiency concept. The wire-to-water efficiency of each type of equipment is calculated with selected models or equations. This is a nonlinear programming problem and can be solved with the generalized reduced gradient nonlinear solver. This forward plant model can be easily set up and used for plant energy simulation. Its application is not restricted by the equipment number or sequencing strategies. All calculations are explicit expressions and no iterations are required. It is also easy to implement this model for different systems. The coefficients of each equipment model as well as the upper and lower limits should be updated to reflect the performance of targeted systems.

The application of this method is illustrated with an example system. The chilled-water system is modeled and three variables are selected for optimization. Compared to the base-line, 3.3% of the annual total utility costs are saved by implementing the new reset schedules of the controlled variables. A single-variable sensitivity study shows that the reset of each variable can affect the energy consumption of several types of equipment. The saving potentials of reducing loop end dew-point setpoint upper limit, loop cooling demand, and loop chilled-water supply temperature rise are also analyzed and presented.

NOMENCLATURE

C = cost, $

[C.sub.p] = water heat capacity, kJ/kg * K (Btu/lbm * [degrees]F)

d = cooling tower model coefficients

e = loop hydraulic performance coefficient

g = non-plant power model coefficients

h = loop delta-T model coefficient

H = water head, ft (m)

N = number

P = power, kW

Q = cooling load, ton (kW)

R = electricity energy or demand rate, $/kWh or $/kW

T = temperature, [degrees]F ([degrees]C)

V = flow rate, gpm ([m.sup.3]/s)

x = independent variables

[DELTA]T = temperature difference, [degrees]F ([degrees]C)

Greek Symbols

[eta] = efficiency

[xi] = wire-to-water efficiency, kW/ton

[rho] = density, kg/[m.sup.3]

Subscripts

App = approach

cdi = condenser water inlet

cho= chilled-water outlet

d = demand

db = dry bulb

e = energy

Lp = loop

max = maximum

min = minimum

mtr = motor

R = return

S = supply

sys = system

sp = setpoint

t = thermal

wb = wet bulb

REFERENCES

Ahn, B.C., and J.W. Mitchell. 2001. Optimal control development for chilled-water plants using a quadratic representation. Energy and Buildings 33(4):371-78.

ASHRAE. 2003. ASHRAE Handbook--HVAC Applications, Chapter 41. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers.

Bernier, M.A., and B.Bourret. 1999. Pumping energy and variable frequency drives. ASHRAE Journal 41(12):37-40.

Bradford, J.D. 1998. Optimal supervisory control of cooling plants without storage. PhD Dissertation, Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, CO.

Braun, J.E. 1988. Methodologies for the design and control of central cooling plants. PhD Dissertation, Department of Mechanical Engineering, University of Wisconsin--Madison, Madison, WI.

Braun, J.E. 1989. Effectiveness models for cooling towers and cooling coils. ASHRAE Transactions 96(2):164-74.

Braun, J.E., J.W. Mitchell, S.A. Klein, and W.A. Beckman. 1987. Performance and control characteristics of a large central cooling system. ASHRAE Transactions 93(1):1830-52.

Braun, J.E., S.A. Klein, J.W. Mitchell, and W.A. Beckman. 1989. Methodologies for optimal control to chilled-water systems without storage. ASHRAE Transactions 95(1):652-62.

Erpelding, B. 2006. Ultra efficient all-variable-speed chilled-water plants. Heating Piping Air Conditioning 78(3):35-43.

Gordon, J.M. and K.C. Ng. 2000. Cool Thermodynamics. Cambridge, UK: Cambridge International Science Publishing.

Hartman, T.B. 2001. Ultra-efficient cooling with demand-based control. HPAC Engineering 73(12):29-35.

Jiang, W., and T.A. Reddy. 2003. Re-evaluation of the Gordon-Ng performance models for water-cooled chillers. ASHRAE Transactions 109(2):272-87.

Kirsner, W. 1995. Troubleshooting chilled-water distribution problems at the NASA Johnson Space Center. Heating Piping Air Conditioning 67(2):51-59.

Taylor, S.T. 2006. chilled-water plant retrofit--A case study. ASHRAE Transactions 112(2):187-97.

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Zhiqin Zhang, PhD

William D. Turner, PhD, PE

Zhiqin Zhang is a senior project engineer at Nexant Inc., San Francisco, CA, and William D. Turner is a professor in the Department of Mechanical Engineering, Texas A&M University, College Station, TX.

Retro-commissioning has been widely used for central chilled-water (ChW) plants to improve their performance. Some measures are very popular and effective, such as chW supply temperature reset, cooling tower (CT) approach temperature reset, secondary loop differential pressure (DP) reset, and condenser water (CW) flow rate reset. Accurately estimating the energy savings potential of each measure is crucial for the success of a retro-commissioning project. Generally, these measures interact with each other and the performance of chiller (CHLR) plant equipment is nonlinear, making it difficult to conduct an accurate savings potential estimation using simplified engineering calculations. At the same time, building a detailed plant model for each project is time consuming. Sometimes it is even impractical due to the lack of enough information or divergence of iterations. In response to this challenge, this paper introduces a method to estimate the savings potential of some popular measures by building a forward simulating model for a chiller plant without storage.

A chiller plant produces ChW and transports it to end users (such as air-handling units [AHUs]) through piping. Central ChW plants are widely employed because they have long been promoted as an energy-efficient and low-operating-cost means of rejecting heat from building air-conditioning systems to the atmosphere. A large portion of the power required to run a facility is consumed in the central chiller plant. However, the energy performance of most existing chiller plants is not very efficient. It was estimated that about 90% of water-cooled, centrifugal central plants operated in the 1.0 to 1.2 kW per ton (2.9 to 3.5 coefficient of performance [COP]) "needs improvement" range, while a highly efficient plant can reach 0.75 kW per ton (4.7 COP) (Erpelding 2006). All kinds of problems are to blame, such as the low delta-T syndrome (Kirsner 1995), low chiller part-load ratio (PLR, which equals chiller actual cooling load over design cooling capacity), significant mixing, valve and pump hunting, higher than needed pump pressure, etc. In addition, there are other reasons for a lack of plant optimization, such as equipment performance degrading with age, load changes (Taylor 2006), plant expansion in an unorganized manner, and energy cost fluctuations. Today, more and more people are aware of sustainability and the importance of saving energy. The fluctuating energy prices also make plant owners and operators try various ways to enhance the performance of chiller plants so as to reduce the energy costs.

Automatic control systems have been widely applied in chiller plants to achieve robust, effective, and efficient operation of the system on the basis of ensuring thermal comfort of occupants and satisfying indoor air quality. Generally, all the control methods used in heating, ventilating, and air-conditioning (HVAC) systems can be divided into supervisory control and relational control. Supervisory control, often named optimal control, seeks stable and efficient operation by systematically choosing properly controlled variable setpoints, such as flow, pressure, or temperature. These setpoints can be reset when uncontrolled variables (such as ambient air wet bulb [WB] temperature, dry bulb [DB] temperature, and building cooling load) are changed, and they are maintained by modulating control variables (speed of components) through proportional integral derivative (PID) controllers or sequencing. This method is easy to understand and is widely accepted in practice due to the simplicity and effectiveness. The fundamentals of supervisory control strategies have been comprehensively introduced in ASHRAE Handbook--HVAC Applications (2003) and are widely applied in practice. Most of these controls originated from the supervisory control methodology developed by Braun (1988). Relational control is determining continuous and discrete control variables directly according to uncontrollable variables or equipment power input, such as demand-based control (Hartman 2001) and load-based control (Yu and Chan 2008). It was claimed by the authors that these controls could realize tremendous energy savings.

The chiller plant models can be divided into component-based and system-based. The component-based model simulates plant performance by modeling each plant component individually. Sometimes, it takes too much effort to build a component-based model or the necessary data may not be available. An alternative way to simulate plant performance is to simulate the plant power with one function. This methodology was first advanced by Braun et al. (1989) when they developed a system-based optimization based on results from component-based optimization. The method involves correlating overall cooling plant power consumption using a quadratic function form. The inputs are uncontrolled variables and controlled continuous variables while the outputs are total cost. Separate cost functions are necessary for each operating mode. Minimizing this function leads to linear control laws for controlled continuous variables in terms of uncontrolled variables. The empirical coefficients of this function depend on the operating modes so that these constants must be determined for each feasible combination of discrete control modes. The determined controlled variables, such as ChW flow rate, will be maintained by modulating continuous control variables, such as valve open percentage and motor speed.

The system-based method has been adopted by Ahn and Mitchell (2001) to find the influence of the controlled variables on the total system and component power consumption. A quadratic linear regression equation for predicting the total cooling system power, in terms of the controlled and uncontrolled variables, was developed using simulated data collected under different values of controlled and uncontrolled variables. The trade-off among the components of power consumption resulted in the total system power use in that both simulated and predicted systems were minimized at lower supply air, higher ChW, and lower condenser-water temperature conditions. Bradford (1998) developed linear, neural network, and quadratic system-based models and a component-based model to predict the system energy consumption including demand side. It has been shown that the use of component-based models for either on-line or off-line optimal control is viable and robust.

Although the system-based plant model is much simpler than the component-based model, the objective function under each feasible combination of discrete control modes has to be generated, and considerable regression error as well as solution difficulty may exist. The component-based model is more accurate, but it takes a longer time to build the model for each project. Iterations are inevitable and convergence could be a problem. Some sophisticated algorithms are also required to optimize such a system.

The objective of this paper is to develop a method to estimate the savings potential of some popular measures by building a forward simulating model for a ChW plant without storage. Its application is illustrated with an example system to find the optimal reset schedule of the chiller ChW leaving temperature, CW flow rate, and CT approach temperature. The energy and billing cost savings potential of several energy conservation measures can also be estimated.

METHOD

A central ChW plant consists of cooling towers, CW pumps, chillers, and primary and secondary ChW pumps. Figure 1 shows the simplified general physical configuration of a primary-secondary loop ChW system. Most valves and fittings are omitted for simplicity purposes. All the variables shown in Figure 1 are setpoints that could be optimized by implementing reset schedules. In practice, these setpoints are maintained by adjusting the equipment speed or control valve position with a PID controller. Except for continuous controlled variables, discrete control variables will also need to be optimized, such as the sequencing of chillers, cooling towers, and pumps. The constraints on the equipment operations, such as maximum and minimum flow rates, limit the number of feasible combinations of control variables. For example, chillers have lower and upper limits on the evaporator flow rate. The number of chillers running simultaneously should ensure the actual evaporator flow be within this range. This limits the possible number of chillers staged on simultaneously.

[FIGURE 1 OMITTED]

Plant Power Modeling

The cooling system total power can be divided into plant power and non-plant power. The electricity consumed by ChW production is considered plant power while all other electricity consumptions (such as plant AHU fans, lighting, and plug loads) are non-plant power.

Figure 2 is a flow chart of the ChW plant power simulation model. All the variables on the left are the inputs, while the output is the plant total power. The plant model deter-mines the plant total power consumption in response to a set of external parameters and a set of plant parameters. The driving force of chiller plant operations is the ChW flow demanded by users on the secondary loop. This demand cannot be controlled by operators. For each given plant total ChW flow demand, the ChW plant model will export the total plant power under the given conditions. In this study, an equipment performance-oriented plant model is proposed to calculate the plant power under predefined conditions. This model is based on a wire-to-water (WTW) plant efficiency concept. The WTW efficiency of a pump was first introduced by Bernier and Bourret (1999). It was originally used to quantify the whole performance of a ChW plant. In this study, it is used to define the transportation efficiency of plant equipment except for secondary pumps (SPMPs). The power of SPMPs is determined by the secondary loop ChW flow rate, pumping system total efficiency, and pressure drop of the secondary distribution system including pipe friction and valve losses.

[FIGURE 2 OMITTED]

The system total power can be calculated from the following formula:

[P.sub.sys] = ([[zeta].sub.CT] + [[zeta].sub.CWP] + [[zeta].sub.CHLR] + [[zeta].sub.PPLR]) [Q.sub.Plant,ChW] + [P.sub.SPMP] + [P.sub.non_plant] (1)

Some regression formulas, together with energy conservation laws, are used to simulate the WTW efficiency of pumps and CTs. This forward plant model can be easily set up and used for plant energy simulation. Since it is based on basic physical definitions and conservation laws, it has an explicit physical meaning. Its application is not restricted by the equipment number and sequencing strategies. All calculations are explicit expressions and no iterations are required. One prerequisite is that the pumps are well sequenced and controlled so that the pump flow rate is within the normal operation range.

In most cases, the optimization target of a chiller plant operation is to minimize the operating cost within a billing period, such as a year. This target is achieved by implementing the optimal reset schedules of some controlled variables, such as ChW supply temperature, CW flow rate, and CT approach temperature. This is a nonlinear programming (NLP) problem and can be solved with the generalized reduced gradient (GRG) nonlinear solver. This method and specific implementation have been proven in use over many years as one of the most robust and reliable approaches to solve difficult NLP problems.

Chiller Modeling

This paper selected the Gordon-Ng model (Gordon and Ng 2000) to simulate chiller performance. This model is valid for vapor-compression chillers with variable condenser flow. It can apply to unitary and large chillers operating under steady-state variable condenser flow conditions. This model is strictly applicable to inlet guide vane capacity control (as opposed to cylinder unloading for reciprocating chillers or variable-speed drive [VSD] for centrifugal chillers) (Jiang and Reddy 2003). It is in the following form:

y = [c.sub.0] + [c.sub.1][x.sub.1] + [c.sub.2][x.sub.2] + [c.sub.3][x.sub.3] (2)

where

[x.sub.1] = [T.sub.cho]/[Q.sub.ChW], [x.sub.2] = ([T.sub.cdi] - [T.sub.cho])/([Q.sub.ChW][T.sub.cdi]), [x.sub.3] = ((1/COP) + 1)[Q.sub.ChW])/[T.sub.cdi],

and

y = ((1/COP) + 1)[Q.sub.ChW])/[T.sub.cdi]

where -1-(1/([V.sub.CW, per][[rho].sub.w][c.sub.pw])) (((1/COP) + 1)[Q.sub.ChW])/[T.sub.cdi]

[T.sub.cho] = (([T.sub.CHLR,ChW,S] - 32) * 5)/9 + 273.15,

[T.sub.cdi] = (([T.sub.CHLR,CW,S] - 32) * 5)/9 + 273.15,

[Q.sub.ChW] = (12,000[Q.sub.CHLR, per])/3412, COP = [Q.sub.ChW]/[P.sub.CHLR],

and

[V.sub.CW] = 0.00006309[V.sub.CHLR, CW, per]

The chiller WTW effciency (kW per ton) is:

[[xi].sub.CHLR] = [P.sub.CHLR]/([Q.sub.ChW] 3412/12,000)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

It is recognized that the actual chiller ChW flow is also limited by the upper and lower limits of evaporator ChW flow rate. The upper limit is intended to prevent erosion and the lower limit is to prevent freezing in the tubes.

Pump Modeling

The general calculation formula of the ChW pump power is:

[P.sub.pump] = (0.746V x H)/(3960[[eta].sub.all]) (4)

where [[eta].sub.all] is the overall efficiency including pumps, motors, and VSDs.

The total cooling transported by the water pump is approximately calculated by:

[Q.sub.ChW] = ([V.sub.ChW][DELTE][T.sub.ChW])/24 (5)

The pump WTW efficiency is:

[[xi].sub.pump] = [p.sub.pump]/[Q.sub.ChW] = (0.746v x H)/3960[[eta].sub.all] x (24/[V.sub.ChW][[DELTE]T.sub.ChW]) (6)

For primary pumps (PPMPs), V = [V.sub.ChW]. The WTW efficiency is:

[[xi].sub.PPMP] = 0.004521 [H.sub.PPMP]/ ([[eta].sub.PPMP][[DELTE]T.sub.ChW]) (7)

For condenser water pumps (CWPs), V = [N.sup.pump] * [V.sub.CW, per] * Consequently, the CW pump WTW efficiency is:

[[xi].sub.CWP] = 0.0001884 [H.sub.CWP]/[[eta].sub.CWP][Q.sub.ChW, per] (8)

For SPMPs, the pump power is:

[P.sub.SPMP] = (0.746[V.sub.LP_ChW] x 2.31 ([DP.sub/LP] + e[V.sub.LP_ChW.sup.2]))/3960[[eta].sub.SPMP] (9)

The head and efficiency of pumps can be simulated as functions of pump flow rate or be constant. Obviously, the energy consumption of SPMPs is subject to the loop-side operation and is not determined by plant operations.

Cooling Tower Modeling

The mass and heat transfer process in a cooling tower is fairly complicated. The effectiveness-NTU model is the most popular model in CT simulations, but iterations are required to obtain a converged solution (Braun 1989). To overcome this obstacle, a simple CT fan power model is proposed to calculate the tower WTW performance:

[[xi].sub.CT] = [P.sub.CT]/[Q.sub.ChW] = ([d.sub.1] + [d.sub.2]/ [[DELTA]T.sub.APP]) (1 + 0.2843[[xi].sub.CHLR] (10)

The actual CT approach temperature is obtained from the following formula:

[[DELTA]T.sub.APP] = [T.sub.CT, CW, R] - [T.sub.wb] (11)

The coefficients [d.sub.1] and [d.sub.2] are regressed from the trended data, and '[DELTA][T.sub.APP] = [T.sub.CT, CW, R] - [T.sub.wb] is maintained by sequencing the cooling towers or modulating fan speed.

Loop Delta-T

The loop ChW delta-T is subject to many factors, such as chiller ChW leaving temperature, cooling coil air leaving temperature, type of flow control valves, coil design parameters and degrading due to fouling, tertiary connection types, coil cooling load, air economizers, etc. Considering the difficulties in developing a physical model to simulate the loop delta-T, a linear model regressed from the trended data is used in this study.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

where [x.sub.i] are the variables that could be the dominant factors of the loop delta-T model, such as ChW supply temperature, loop total cooling load, ambient DB and WB temperatures, hour of the day, weekday or weekend, and month. The air system side parameters, such as coil air leaving temperature, total airflow rate, coil design delta-T, and sensible load ratio, are not included due to diversity or unpredictability.

The exact form of the regression model may vary for different projects. It could be necessary to build different models to accommodate air-conditioning system operation changes at different seasons. A constant delta-T can be used in a rough, first-order simulation.

APPLICATION

Example System Description

The example system investigated in this study is a central utility plant called Energy Plaza (EP) located in the Dallas-Fort Worth metropolitan area. The EP consists of six 5500 ton (19,343 kWt) constant-speed centrifugal chillers, called on-site manufactured (OM) chillers; one 90,000 ton * h (316,517 [kW.sub.t] * h) naturally stratified ChW storage tank; six 150 hp constant-speed primary pumps; four 450 hp variable-speed secondary pumps; eight 400 hp CW pumps; and eight 150 hp two-speed cooling towers. Figure 3 shows a schematic diagram of this ChW system. This study only deals with the ChW system operated without ChW thermal storage.

The monthly electricity billing cost consists of a meter charge, current month non-coincident peak (NCP) demand charge, four coincident peak (4CP) demand charge, and energy consumption charge. The total monthly electricity billing charge ([C.sub.Total]) is:

[FIGURE 3 OMITTED]

[C.sub.Total] = [C.sub.delivery_point = [R.sub.4CP][D.sub.4CP] + [R.sub.NCP][D,sub.NCP] + [R.sub.energy][E.sub.consumption] (13)

The rates [R.sub.4CP], [R.sub.NCP], and [R.sub.energy] for each month are subject to minor adjustments, and the rates from a selected one-year period are used in the simulation. The meter charge [C.sub.delivery_point] is constant for each month. All demand kilo-watts used have been adjusted to 95% power factor. The monthly average power factors during this period will be used in the power factor correction.

The 4CP demand kilowatt is the average of the plant's integrated 15 minute demands at the time of the monthly Electric Reliability Council of Texas (ERCOT) system 15 minute peak demand for the months of June, July, August, and September (called summer months) of the previous calendar year. The exact time will be announced by ERCOT. The plant's average 4CP demand will be updated January 1 of each calendar year and remain fixed throughout the calendar year. The NCP kilowatt applicable shall be the kilowatt supplied during the 15 minute period of maximum use during the billing month. The current month NCP demand kilowatt shall be the higher of the NCP kilowatt for the current billing month or 80% of the highest monthly NCP kilowatt established in the eleven months preceding the current billing month.

The ChW flow through the chiller evaporator is controlled by modulating flow control valves on the leaving side of the evaporator. The sequencing of the constant-speed PPMPs is dedicated to the corresponding chillers. The variable-frequency device speed of the SPMPs is modulated to maintain the average of differential pressures at the loop ends at a given setpoint. This setpoint is manually adjusted to be between 25 and 48 psid (172.4 and 330.9 kPa) all year round to ensure there are no hot complaints. The cooling tower staging control in place is to stage the number of fans and select high and low speeds of fans to minimize the chiller compressor plus CT fan electricity consumption.

System Modeling

System Power. The trended historical data are used for system modeling. The electricity consumed by OM chillers, CT fans, CW pumps, PPMPs, and SPMPs is considered plant ChW electricity load while all other electricity consumptions, such as EP air-conditioning, air compressors, lighting, and plug loads, are non-plant electricity loads.

To check the accuracy of the system model, the EP monthly utility bills are compared with the simulation results. A good match is found, although minor differences exist in several months. This could be attributed to imperfection of models, inaccurate parameter inputs, or operations different from actual situations. The present system power model can reasonably predict the monthly electricity consumption.

Loop-Side Modeling. The parameters and inputs for the thermal energy storage (TES) system loop side are shown in Table 1. The upper and lower limits of the loop end DP, as well as the loop flow rate change points, are subject to hydraulic requirements and operating experiences. If the loop total ChW flow rate is equal to or lower than 10,000 gallons per minute (gpm) (0.631 [m.sup.3]/s), the DP setpoint is 22.0 psid (151.7 kPa). If the rate is equal to or higher than 16,000 gpm (1.009 [m.sup.3]/s), the DP setpoint is 28.0 psid (193.1 kPa). The ChW secondary DP setpoint is reset linearly from 22 to 28 psi (151.7 to 193.1 kPa), when the secondary ChW flow is between 10,000 and 16,000 gpm (0.631 and 1.009 [m.sup.3]/s). A loop load factor is defined to test the savings when the actual load profile is different from the one used in the simulation.

Table 1. Parameters of TES System Loop Side LP end DP upper [DP.sub.h] 28.0 psid setpoint LP end DP lower [DP.sub.l] 22.0 psid setpoint LP end DP upper shift [V.sub.upper] 16,000 gpm flow Loop (LP) LP end DP lower shift [V.sub.lower] 10,000 gpm Hydraulic flow LP hydraulic [e.sub.1] 1.00E-07 coefficient 1 LP hydraulic [e.sub.2] 5.00E-08 coefficient 2 LP hydraulic [e.sub.3] 3.00E-08 coefficient 3 LP supply temperature [DELTA][T.sub.s] 1.0 rise Delta[degrees]F LP DT coefficient 0 [h.sub.1] 32.1898 LP DT coefficient 1 [h.sub.2] -0.5439 ([Q.sub.Lp,ChW,S]) Loop LP DT coefficient 2 [h.sub.3] 6.86E-05 Delta-T ([Q.sub.Lp,ChW]) (LP DT) LP DT coefficient 3 [h.sub.4] 6.34E-02 ([T.aub.wb]) LP max DT [DELTA][T.sub.Lp,max] 22.0 Delta[degrees]F LP min DT [DELTA][T.sub.Lp,min] 12.0 Delta[degrees]F LP end DP upper 1.009 kPa setpoint LP end DP lower 151.7 kPa setpoint LP end DP upper shift 3634 flow [m.sup.3]/s Loop (LP) LP end DP lower shift 0.631 Hydraulic flow [m.sup.3]/s LP hydraulic 1.0E-07 coefficient 1 LP hydraulic 5.0E-08 coefficient 2 LP hydraulic 3.0E-08 coefficient 3 LP supply temperature 0.6 rise Delta[degrees]C LP DT coefficient 0 32.1898 LP DT coefficient 1 -0.5439 ([Q.sub.Lp,ChW,S]) Loop LP DT coefficient 2 6.86E-05 Delta-T ([Q.sub.Lp,ChW]) (LP DT) LP DT coefficient 3 6.34E-02 ([T.aub.wb]) LP max DT 12.2 Delta[degrees]C LP min DT 6.7 Delta[degrees]C

A temperature rise exists between the loop supply temperature and the chiller ChW leaving temperature, which is due to pumping heat gain and piping heat losses. The trended data show that the temperature rise fluctuates between 0.0[degrees]F and 2.0[degrees]F (0[degrees]C and 1.1[degrees]C) most of time and the annual average temperature rise is 1.0[degrees]F (0.6[degrees]C).

When the loop end DP setpoints are determined, a loop hydraulic coefficient is required to calculate the differential pressure before and after the SPMPs. Three hydraulic coefficients are regressed from trended data corresponding to one, two, or three SPMPs running scenarios. The coefficients can be regressed from a plot of piping DP losses versus loop total flow rate.

Equation 14 is a linear regression model developed to simulate the loop delta-T as a function of ChW loop supply temperature ([x.sub.1]), loop total cooling load ([x.sub.2]), and ambient WB temperature ([x.sub.3]). A higher loop supply temperature, a lower WB temperature, and a lower loop total ChW load lead to a lower loop delta-T, which is consistent with the observations. An upper and a lower limit are defined to avoid unreasonable regression results when an extrapolation is applied. The system error of the loop delta-T can be used to check the effect of loop delta-T prediction deviations on the system total energy and costs.

[[DELTA]T.sub.LP] = [h.sub.0] + [h.sub.1][x.sub.1] + [h.sub.2][x.sub.2] + [h.sub.3][x.sub.3] (14)

Figure 4 is a comparison of the measured and predicted ChW supply and return temperatures. If the model accurately fits the data on which it was trained, this type of evaluation is referred to as internal predictive ability. The external predictive ability of a model is to use a portion of the available data set for model calibration, while the remaining data are used to evaluate the predictive accuracy. The root mean square errors (RMSEs) of the internal and external predictions are both 1.1[degrees]F (0.63[degrees]C). The coefficient of variations (CVs) of the internal and external predictions are 6.86% and 6.93%, respectively.

[FIGURE 4 OMITTED]

Plant-Side Modeling. Table 2 shows the main parameters and inputs for the plant side. The efficiencies of all pumps are assumed constant or determined from pump efficiency curves. The overall efficiency is a product of motor efficiency, shaft efficiency, and pump efficiency (and variable-frequency drive efficiency for SPMPs). The pump heads are determined from pump head curves. The primary side flow rate is controlled to be equal to the secondary side flow rate. It is assumed that all pumps are sequenced reasonably to ensure that the running pumps are operated around the design points.

Table 2. Parameters of ChW System Plant Side SPMP SPMP overall [[eta].sub.spmp] 75% efficiency SPMP design [V.sub.spmp] 8,000 gpm flow rate PPMP PPMP overall [[eta].sub.ppmp] 80% efficiency PPMP head [H.sub.ppmp] 80 ft CHLR [c.sub.0] -2.81E-01 coefficient 0 CHLR [c.sub.1] 1.02E+01 coefficient 1 CHLR [c.sub.2] 1.74E+03 coefficient 2 CHLR [c.sub.3] 2.71E-03 coefficient 3 CHLR [V.sub.cw] 10,300 gpm condenser water flow CHLR ChW leaving [T.sub.ChW,S] 36[degrees]F temperature CHLR ChW low [V.sub.chw,min] 4,000 gpm limit CHLR ChW [V.sub.chw,max] 7,400 gpm high limit Motor max [P.sub.mtr,max] 3,933 kW power input Max CW [T.sub.CW,max] 83.0[degrees]F entering temperature Min CW [T.sub.CW,min] 60.0[degrees]F entering temperature CT [d.sub.1] 0.01 coefficient 1 CT CT [d.sub.2] 0.16 coefficient 2 Approach [DELTA][T.sub.App,sp] 6.0[degrees]F default setpoint CWP Pump head [H.sub.cwp] 92 ft Pump overall [[eta].sub.cwp] 82% efficiency SPMP SPMP overall 75% efficiency SPMP design 0.505 flow rate [m.sup.3]/s PPMP PPMP overall 80% efficiency PPMP head 239.1 kPa CHLR -2.81E-01 coefficient 0 CHLR 1.02E+01 coefficient 1 CHLR 1.74E+03 coefficient 2 CHLR 2.71E-03 coefficient 3 CHLR 0.650 condenser [m.sup.3]/s water flow CHLR ChW leaving 2.2[degrees]C temperature CHLR ChW low 0.252 limit [m.sup.3]/s CHLR ChW 0.467 high limit [m.sup.3]/s Motor max 3,933 kW power input Max CW 28.3[degrees]C entering temperature Min CW 15.6[degrees]C entering temperature CT 0.01 coefficient 1 CT CT 0.16 coefficient 2 Approach 3.3 default Delta[degrees]C setpoint CWP Pump head 275.0 kPa Pump overall 82% efficiency

The CT coefficients are obtained from the regression results of the historical data. The CT model fitting curve is shown in Figure 5. It should be noted that the coefficients obtained from the trended historical data are only applicable to the current cooling tower operation strategy. If a new CT operation strategy is used, the coefficients are subject to adjustment.

[FIGURE 5 OMITTED]

The coefficients of the Gordon-Ng chiller model are obtained by regressing with the trended historical data of the OM chillers. The rated CW flow rate is equal to the average of the trended data. In this study, the total available chiller number is limited to six. The chiller ChW leaving temperature default setpoint is 36[degrees]F (2.2[degrees]C). The ChW flow rate limits and CW entering temperature limits are based on the chiller design specifications. Figure 6 is a comparison between measured and predicted motor power using the Gordon-Ng model.

[FIGURE 6 OMITTED]

Non-Plant Power Modeling. The non-plant power is composed of two segments. When the ambient DB temper-ture is lower than 60[degrees]F (15.6[degrees]C), the non-plant power is 750 kW constant. Otherwise, a second-order polynomial is used to calculate the total non-plant power contributed by plant HVAC, glycol cooling systems, air compressors, etc. The coefficients are shown in Table 3, and Equation 15 shows the mathematical form of the regression model.

Table 3. Parameters of Non-Plant Power Coefficient 1 [g.sub.1] 1266.3 1266.3 Non- Coefficient 2 [g.sub.2] -4.4327 -4.4327 Plant Power Coefficient 3 [g.sub.3] 0.1983 0.1983 Winter shift [T.sub.wb,shift] 60[degrees]F 15.6 DB [degrees]C Winter base [p.sub. w,base] 750 kW 750 kW power

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

Simulation and Results

The selected variables to be optimized are chiller ChW leaving temperature, CT approach temperature, and chiller CW flow rate. The default and upper and lower limits of each variable are shown in Table 4. Different default values are used to test their effects on the optimal solutions found by the solver. The monthly optimal setpoints, as well as the energy and utility billing cost savings, are shown in Table 5.

Table 4. Plant Optimization Controlled Variables Variable Unit Default Lower Limit Upper Limit Value [T.sub.ChW,S] [degrees]F 36 36 44 [degrees]C 2.2 2.2 6.7 [[DELTA]T.sub.App] [degrees]F 6 3 10 [degrees]C 3.3 1.7 5.6 [V.sub.cw] gpm 10,300 11,000 [m.sup.3]/s 0.650 0.568 0.694 Table 5. Monthly Results of Plant Optimization Month [T.sub.ChW,S] [[DELTA]T.sub.App] [degrees] F [degrees] C [degrees] F [degrees] C 1 36.0 2.2 4.6 2.6 2 36.0 2.2 4.6 2.6 3 39.8 4.3 4.6 2.6 4 40.2 4.6 4.6 2.6 5 39.8 4.3 4.6 2.6 6 42.3 5.7 4.6 2.6 7 42.9 6.1 4.6 2.6 8 44.0 6.7 4.7 2.6 9 42.0 5.6 4.6 2.6 10 41.0 5.0 4.6 2.6 11 37.0 2.8 4.6 2.6 12 36.0 2.2 4.6 2.6 Total Month [V.sub.cw] Energy Billing Cost Savings Savings Cost Percentage Savings gpm [m.sup.3]/s kWh $ 1 11,000 0.694 27,093 $6912 1.9% 2 11,000 0.694 30,229 $7159 1.9% 3 11,000 0.694 138,451 $16,132 2.8% 4 11,000 0.694 136,701 $15,563 2.8% 5 11,000 0.694 233,601 $23,172 3.1% 6 11,000 0.694 377,957 $34,289 3.9% 7 11,000 0.694 399,130 $36,903 3.9% 8 11,000 0.694 567,537 $51,490 4.9% 9 11,000 0.694 354,537 $32,368 3.8% 10 11,000 0.694 214,461 $21,568 3.2% 11 11,000 0.694 47,094 $8483 1.7% 12 11,000 0.694 32,634 $7347 1.9% Total 2,559,426 $261,387 3.3%

In the winter months, the loop cooling load and loop delta-T are both pretty low. Running chillers are lightly loaded most of time and the evaporator flow rate has reached the upper limit. A lower ChW leaving temperature is preferred to increase the loop delta-T, which benefits the part-load ratio (PLR) of the chiller. This may sound a little counterintuitive, as most plants will increase supply ChW temperature to improve chiller performance. When the efficiency improvement due to higher PLR dominates the degrading due to lower supply temperature, we will see improved overall chiller efficiency. This phenomenon has been observed for this project. However, it should be recognized that this is a case-by-case result and cannot be generalized to other systems. In the summer months when the loop cooling load is high, the chiller can still be loaded up to the optimal PLR; even the ChW supply temperature rises to 44[degrees]F. A higher ChW leaving temperature can improve the chiller efficiency. The optimal CT approach temperature is around 4.6[degrees]F (2.6[degrees]C) and the optimal chiller condenser water flow rate is 11,000 gpm (0.694 [m.sup.3]/s) all year round. Compared to the scenario with default setpoints, the optimal reset schedule can reduce electricity energy consumption by 2,559,426 kWh per year and reduce electricity billing costs by $261,387.00 (U.S.) per year or 3.3% of the baseline annual electricity costs.

As the change of each variable may place different impacts on the performance of each component, a single-variable sensitivity study is performed using August as an example. Table 6 shows the electricity consumption change if the setpoints are different from the default values. The percentage is the change of monthly kilowatt--hour consumption for each corresponding component. If the chiller ChW leaving temperature increases by 1.0[degrees]F to 36[degrees]F (0.6[degrees]C to 2.8[degrees]C), the monthly total electricity consumption of the plant reduces by 82,242 kWh. Particularly, the chiller electricity consumption reduces by 1.1% of the chiller monthly consumption due to a higher chiller efficiency. This is consistent with the rule of thumb that for each 1[degrees]F (0.6[degrees]C) increase in ChW temperature, constant-speed chiller efficiency increases 1.0% to 2.0%. The SPMPs consume 4.3% more of the monthly electricity usage due to a higher ChW flow rate as a result of a lower loop delta-T. The minor changes to cooling towers, condenser water pumps, and primary pumps are due to chiller staging change.

Table 6. Results of Single-Variable Sensitivity Study kWh Usage [T.sub.chw] [T.sub.App] = [V.sub.cw] = Change =37.0 5.0 [degrees] 11,000 gpm [degrees] F F (2.8 (0.694 (2.8 [degrees] C) [m.sup.3]/s) [degrees] C) CHLR 1.1% -88,228 -0.9% -78,075 -0.9% CT -0.1% -284 12.2% 63,705 -0.1% CWP -1.0% -6596 -1.0% -6596 -2.8% PPMP -0.3% -1028 -0.8% -2449 -0.8% SPMP 4.3% 13,894 0% 0 0% Total -82,242 -23,414 (kWh) kWh Usage Change CHLR -70,625 CT -755 CWP -19,564 PPMP -2449 SPMP 0 Total -93,393 (kWh)

If the cooling tower approach decreases by 1.0[degrees]F (0.6[degrees]C), the chiller will consume 0.9% less electricity due to a lower CW entering temperature. However, the cooling tower fan will consume 12.2% more electricity as it needs to run harder to approach closer to the ambient WB temperature. As a result, chillers consume 78,075 kWh less and tower fans consume 63,705 kWh more. Overall, this measure can still save 23,414 kWh in August. This result is also consistent with the annual optimizations that the optimal approach is around 4.6[degrees]F (2.6[degrees]C).

If the chiller CW flow rate increases to 11,000 gpm (0.694 [m.sup.3]/s), the chiller efficiency is improved due to enhanced heat transfer in the condenser. The kilowatt--hour savings from chillers are 70,625 kWh. For this particular project, the CW pumps consume even less energy when the flow rate increases. This is associated with the particular performance curves of the selected CW pumps and may not be valid for other systems.

This model is also used to test the energy saving sensitivity of several energy conservation measures, such as reducing the loop end DP setpoint upper limit ([DP.sub.h]), the loop cooling demand, and the loop ChW supply temperature rise ([[DELTA]T.sub.s]). Table 7 shows the annual billing cost savings potential of each measure. It is estimated that, when the loop DP upper limit decreases by 2.0 psid (13.8 kPa), the annual electric usage of SPMPS can be reduced by 80,534 kWh or 3.7% of the SPMP power consumption. The utility cost decreases by $7487 per year or 0.1% of system annual total utility costs. If the cooling demand by the end users can be cut by 5%, the electric consumption can be saved by 3,467,316 kWh per year and the annual utility costs can be reduced by 4.9%. Generally, the temperature of the ChW reaching the end users is higher than that produced by the chiller. This could be due to piping heat losses, mixing, or pumping power. In the baseline case, the loop supply temperature rise is assumed to be 1.0[degrees]F (0.6[degrees]C). If the temperature rise can be reduced by half, 1,765,763 kWh can be saved each year and the annual utility costs savings is 2.0%. These results can be used to estimate the payback of each measure.

Table 7. Billing Cost Savings Estimation of Energy Conservation Measures Variable Unit Default Lower Savings, Savings, $ Value Value kWh [DP.sub.h] psid 28 26 kPa 193.1 179.3 80,534 $7487 [f.sub.Lp,cooling] -- 1.00 0.95 3,467,316 $302,236 [degrees]F 1.0 0.5 [DELTA][T.sub.s] [degrees]C 0.6 0.3 1,765,763 $156,382 Variable Unit Savings, % [DP.sub.h] psid kPa 3.7% [f.sub.Lp,cooling] -- 4.9% [degrees]F [[DELTA]T.sub.s] [degrees]C 2.0%

SUMMARY AND CONCLUSION

A chilled-water plant is a high-energy-density facility. However, the energy performance of most existing chilled-water plants is not very efficient. With volatile energy prices, improving the plant efficiency to save utility costs is an urgent task for chiller plant owners and operators. Some effective retro-commissioning measures have been widely adopted to reduce plant energy usage by 3% to 5%. Estimating the energy savings potential of these measures is crucial for the success of a retrocommissioning project.

Modeling and simulating is a popular method to optimize the plant operation and estimate the savings potential of various measures. The system-based model is simple but not accurate, while the component-based model is accurate but complicated. This paper proposes a forward plant model based on a wire-to-water efficiency concept. The wire-to-water efficiency of each type of equipment is calculated with selected models or equations. This is a nonlinear programming problem and can be solved with the generalized reduced gradient nonlinear solver. This forward plant model can be easily set up and used for plant energy simulation. Its application is not restricted by the equipment number or sequencing strategies. All calculations are explicit expressions and no iterations are required. It is also easy to implement this model for different systems. The coefficients of each equipment model as well as the upper and lower limits should be updated to reflect the performance of targeted systems.

The application of this method is illustrated with an example system. The chilled-water system is modeled and three variables are selected for optimization. Compared to the base-line, 3.3% of the annual total utility costs are saved by implementing the new reset schedules of the controlled variables. A single-variable sensitivity study shows that the reset of each variable can affect the energy consumption of several types of equipment. The saving potentials of reducing loop end dew-point setpoint upper limit, loop cooling demand, and loop chilled-water supply temperature rise are also analyzed and presented.

NOMENCLATURE

C = cost, $

[C.sub.p] = water heat capacity, kJ/kg * K (Btu/lbm * [degrees]F)

d = cooling tower model coefficients

e = loop hydraulic performance coefficient

g = non-plant power model coefficients

h = loop delta-T model coefficient

H = water head, ft (m)

N = number

P = power, kW

Q = cooling load, ton (kW)

R = electricity energy or demand rate, $/kWh or $/kW

T = temperature, [degrees]F ([degrees]C)

V = flow rate, gpm ([m.sup.3]/s)

x = independent variables

[DELTA]T = temperature difference, [degrees]F ([degrees]C)

Greek Symbols

[eta] = efficiency

[xi] = wire-to-water efficiency, kW/ton

[rho] = density, kg/[m.sup.3]

Subscripts

App = approach

cdi = condenser water inlet

cho= chilled-water outlet

d = demand

db = dry bulb

e = energy

Lp = loop

max = maximum

min = minimum

mtr = motor

R = return

S = supply

sys = system

sp = setpoint

t = thermal

wb = wet bulb

REFERENCES

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Zhiqin Zhang, PhD

William D. Turner, PhD, PE

Zhiqin Zhang is a senior project engineer at Nexant Inc., San Francisco, CA, and William D. Turner is a professor in the Department of Mechanical Engineering, Texas A&M University, College Station, TX.

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Author: | Zhang, Zhiqin; Turner, William D. |
---|---|

Publication: | ASHRAE Transactions |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Jul 1, 2012 |

Words: | 7093 |

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