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Methodology for determining the optimal operating strategies for a chilled-water-storage system--part II: project application.

Introduction

In the Part I of this article, a general method is introduced to determine the optimal operating strategies for a chilled-water (ChW) storage system under a time-of-use (TOU) electricity rate structure. It combines a plant, thermal energy storage (TES) tank, and loop together to study the interactions among these three parts. This method is based on an investigation of multiple search paths performed month by month. Each operating strategy consists of a type of control strategy and the maximum number of chillers staged-on during the off-peak and on-peak periods, which is like demand limiting. For each month, a search is performed for all possible operating strategies, and the hourly profiles of the tank ChW level and system total power are simulated by a system model. For some operating strategies, the lowest tank water level is even lower than a predefined limit, and this is not allowed in operations. These strategies are removed from the list of possible strategies. An electricity rate model is run to calculate the monthly billing cost of each remaining operating strategy. The operating strategy with the lowest billing cost is selected as the optimal strategy for the current month. A plant optimization model with a generalized reduced gradient (GRG) nonlinear solver is followed for the selected optimal operating strategy to further improve the whole system performance.

The system model includes six sub-models. In the TES sub-model, the ChW volume is used to describe the tank inventory, and the ChW flow rate is selected to quantify the inventory change. The tank operating mode is controlled by modulating the plant total ChW flow rate. Based on a wire-to-water (WTW) efficiency concept, a plant model without iteration calculations is built to simulate the ChW plant power at each time step, and no iterations are involved. A regression model is selected to simulate the loop ChW supply and return temperature difference, which is critical for a ChW-storage system. Three control strategies are built into the control strategy sub-model: full storage, chiller priority, and storage priority. In addition, a nonplant power sub-model is required to simulate the power that is billed along with, but not covered in, the above models.

The application of this methodology is illustrated with a practical project. The purpose of the study is to optimize the operation of a ChW-storage tank and a ChW plant so as to reduce the utility billing costs of the system. Except for the introduction in the text, a nomenclature can be found at the end of the article for identification of abbreviations, Greek symbols, and subscripts.

ChW system

The system investigated in this study is a central utility plant called Energy Plaza (EP) serving an airport located in the Dallas-Fort Worth (DFW) metropolitan area. The EP consists of six 5500-ton (19,342 [kW.sub.t]) 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, five 1350-ton (4748 [kW.sub.t]) glycol-solution chillers, called pre-conditioned air (PCA) chillers, and eight two-speed cooling towers (CTs). This plant is designed with six 150-hp constant speed primary pumps (PPMPs) and four 450-hp variable-speed secondary pumps (SPMPs). The ChW produced in the EP is distributed to eight "vaults" beneath each terminal through underground piping in tunnels. The ChW is then branched off to the end users. Figure 1 shows a schematic diagram of this ChW system. This study only deals with the ChW system. The electricity consumed by the heating hot water system and glycol system are treated in the nonplant electricity part.

The EP condenser water (CW) system consists of eight identical CTs, each of which is equipped with a 150-hp two-speed fan and a 400-hp CW pump. These eight CTs are divided into two groups. Each group has four CTs located on one side of the EP, i.e., east and west, with a separate basin. The CW pumps are automatically staged-on or off to provide CW for all running OM and PCA chillers.

A naturally stratified, column-shaped ChW-storage tank is erected between the ChW PPMP suction-side header and the chiller discharge-side header. It is 138 ft (42.0 m) in diameter and 57 ft (17.4 m) in height. Since the TES tank was installed and is used as the "expansion tank," the existing expansion tank has been disabled. The top of the TES tank is open to the atmosphere, and the tank level is maintained at 54.3-54.9 ft (16.6-16.7 m). The design cooling storage capacity is 90,000 ton-h (316,517 [kW.sub.t]-h) when the ChW supply temperature is 36[degrees]F (2.2[degrees]C) and the return temperature is 60[degrees]F (15.6[degrees]C). However, in practice, the loop delta-T seasonally fluctuates between 10[degrees]F (5.6[degrees]C) and 20[degrees]F (11.1[degrees] C). The effective storage volume is around 5,400,000 gallons (20,441 [m.sup.3]).

The direct digital control system utilized on site is Emerson Process Management's Delta-V digital automation system. All the chillers, boilers, heat exchangers, CTs, TES tank, various pumps, and automatic control valves are monitored and controlled by this system. It also monitors and controls the ChW, steam, hot water, and PCA distribution systems in the tunnel and some of the air-handler units in the EP and the terminals.

[FIGURE 1 OMITTED]

Electricity rate structure

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

[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]. (1)

The rates [R.sub.4CP], [R.sub.NCP], and [R.sub.energy] for each month are subject to minor adjustments, and the rates from March 2007 to February 2008 are used in the simulation. The meter charge [C.sub.delivery-point] is constant for each month. All demand kWs used have been adjusted to 95% power factor. The monthly average power factors during this period will be used in the power factor correction.

4CP demand

The 4CP demand kW is the average of the plant's integrated 15-min demands at the time of the monthly Electric Reliability Council of Texas (ERCOT) system 15-min 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 effective on January 1 of each calendar year and remain fixed throughout the calendar year. It is impossible to precisely predict the time of the ERCOT system 15-min peak demand. There is no definition on the period of the 4CP demand. However, based on analyzing the historic 4CP events in the last nine years (ER COT 2009), it is found that the 4CP event always occurs between 3:30 p.m. and 5:00 p.m. on week days. Half-hour and 1-h allowances are made before and after this period to avoid hitting the 4CP peak time. Therefore, in this study, the highest kWs during 3:00 p.m. to 6:00 p.m. in the summer months are used to calculate the 4CP demand.

NCP demand

The NCP kW applicable will be the kW supplied during the 15-min period of maximum use during the billing month. The current month NCP demand kW will be the higher of the NCP kW for the current billing month or 80% of the highest monthly NCP kW established in the 11 months preceding the current billing month.

[FIGURE 2 OMITTED]

For this facility, every day--including weekends and holidays--is treated as a working day. The 4CP demand can be regarded as on-peak demand, while NCP demand is the all day demand. To reduce the energy charge, it is necessary to load chillers optimally to improve chiller efficiency. A lower CW entering temperature will save chiller power but consume more fan power. A higher chiller ChW leaving temperature (ChWLT) will save chiller power but consume more SPMP power. Sometimes, chillers cannot be optimally loaded due to lower delta-T as a result of high ChW loop supply temperature. Therefore, the selection of proper CT approach and chiller ChWLT is critical to minimize the total power of CT fans, chillers, and SPMPs. To reduce the demand charge, the demand kW from 3:00 p.m. to 6:00 p.m. should be kept as low as possible, while the system total power profile in each month should be maintained relatively level to decrease the maximum kW in that month.

Current system operation

At present, the chillers and TES tank are manually operated, and, at most, four OM chillers are allowed to run up to full load when EP operators are charging the TES tank. EP operators have been trying to charge and discharge the TES tank according to a predetermined schedule to minimize demand-related charges.

Figure 2 shows the electricity consumption daily profiles on four consecutive summer days. During the charging period, the maximal number of chillers running was four. From 6:00 p.m.-6:30 p.m., OM chillers were staged-on gradually to fully charge the tank and provide cooling to the loop side. One chiller was staged-off at around 6:30 a.m. The tank entered the match mode when the tank level reached a predetermined height. Around 3:00 p.m. or 3:30 p.m., all OM chillers were staged-off, and the TES tank took over the cooling load. The charged NCP demand exceeded 23,000 kW in the summer months. The power for each OM chiller and associated pumps and CTs is around 4400 kW at full load. When all OM chillers are off, the plant demand drops to around 3600 kW in the summer months, which is the baseline demand contributed by the PCA chillers, SPMPs, plant HVAC, lighting, boilers, etc.

On August 13, 2007, a 4CP peak demand of 16,904 kW was hit by the EP at 3:30 p.m., which led to a 3664-kW increase in the 4CP demand kW in 2008 compared with the 4CP demand in 2007. If the coincident peak in August was assumed to be 3800 kW, the 4CP demand kW in 2008 would be 3850 kW, which is 3276 kW lower than the current value of 7126 kW. If the annual average 4CP demand charge rate is US$2.00/kW, the plant would have paid $78,624 more in 2008 due to this high 4CP value.

The charging start time was determined by operators according to their experiences and judgment. No predefined operating strategy was followed for TES operations. When EP operators charged the TES tank overnight, they tended to fully load all four OM chillers, so they could fully charge the TES tank as quickly as possible. The operating strategy in the summer months is to minimize the EP monthly electricity billing cost by avoiding OM chillers running during 3:30 p.m. to 6:00 p.m. During other hours, the maximum number of chillers running is no larger than four to limit the plant NCP demand. The chiller ChWLT set-point is manually set at 36[degrees]F (2.2[degrees]C) and is fixed all year round to provide pre-cooling for the glycol system. A higher ChW supply temperature is acceptable for this ChW system. The problems with such operations are (1) it is possible to hit a high 4CP demand, (2) the NCP demand is high, (3) the chillers are loaded at various part load ratios (PLRs), and (4) the chiller ChWLT is lower than normal. These problems make the plant consume more electricity and pay more.

The ChW flow through the chiller evaporator is controlled by modulating flow control valves on the leaving side of the evaporator. The ChW flow rate set-point can be manually overridden, so the TES tank could be charged faster. The sequencing of the constant speed PPMPs is dedicated to the corresponding chillers. The variable-frequency device (VFD) speed of the SPMPs is modulated to maintain the average of differential pressures (DPs) at two loop ends in the tunnels at a given set-point. This set-point is manually adjusted to be between 25 psid and 48 psid (172 kPa and 331 kPa) all year round to ensure there are no hot complaints from terminals.

The CT staging control in place is a very complicated algorithm. The existing control intends to stage the number of fans and select high and low speed of fans to minimize the chiller compressor electricity consumption. Six stages are defined in the controllers. The CW pumps are automatically sequenced to provide CW for the OM chillers and the PCA chillers.

Validation of system modeling

System power

The trended historical data from March 1, 2007, to February 29, 2008, is used for system modeling and TES operating strategies simulations. The electricity consumed by OM chillers, CT fans, CW pumps, PPMPs, and SPMPs is considered as plant ChW electricity load, while all other electricity consumptions are nonplant electricity loads. According to trended historical data, 84.2% of EP total electricity consumption is contributed to the ChW system, 8.4% is consumed by the PCA system, and 7.4% is consumed by miscellaneous equipment, such as EP air-conditioning, air compressors, lighting, and plug loads. Therefore, the power consumed by the plant covers the majority of the total EP power consumption.

To check the accuracy of the system model, the EP monthly utility bills are compared with the simulation results of the full-storage scenario since the current tank control strategy is very close to full storage. A good match is found, although minor differences exist in several months. This could be attributed to the imperfection of models, inaccurate parameter inputs, or simulated 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 TES system loop side are shown in Table 1. The upper ([DP.sub.h]) and lower ([DP.sub.l]) 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) ([V.sub.lower]), the DP set-point 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) ([V.sub.upper]), the DP set-point is 28.0 psid (193.1 kPa). The ChW secondary DP set-point be reset linearly from 22 psi to 28 psi (151.7 kPa to 193.1 kPa) when the secondary ChW flow is between 10,000 GPM and 16,000 GPM (0.631 [m.sup.3]/s and 1.009 [m.sup.3]/s). A loop load factor ([f.sub.load]) is defined to test the reliability of operating strategies when the actual load profile is different from the one used in the simulation.

A temperature rise ([DELTA][T.sub.s]) exists between the loop supply temperature and the chiller ChWLT, which is due to tank heat losses, pumping heat gain, and piping heat losses. The trended data shows 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 the time, and the annual average temperature rise is 1.0[degrees]F (0.6[degrees]C). A linear regression model is generated with three input variables and four coefficients ([h.sub.0] through [h.sub.3]). To avoid unreasonable values, an upper limit ([DELTA][T.sub.Lp,max]) and a lower limit ([DELTA][T.sub.Lp,max]) are adopted.

When the tunnel end DP set-points are determined, a loop hydraulic coefficient is required to calculate the DP before and after the SPMPs. Three hydraulic coefficients (e1, e2, and e3) are regressed from trended data corresponding to one, two, or three SPMP running scenarios. The coefficients can be regressed from a plot of tunnel piping DP losses versus tunnel total flow rate.:

[H.sub.loss] = e[V.sup.2.sub.LP-ChW] (2)

Figure 3 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 1.13[degrees]F and 1.14[degrees]F (0.63[degrees]C and 0.63[degrees]C), respectively. The coefficients of variation (CVs) of the internal and external predictions are 6.86% and 6.93%, respectively.

Plant-side modeling

Table 2 shows the main parameters and inputs for the plant side. The efficiencies of all pumps are assumed to be constant and are determined from pump efficiency curves and design flow rates. The overall efficiency is a product of motor efficiency, shaft efficiency, and pump efficiency (and VFD efficiency for SPMPs). The pump heads are determined from pump head curves. It is assumed that all pumps are sequenced reasonably to ensure that the running pumps are operated around the design points.

CT model

The CT coefficients ([d.sub.1] and [d.sub.2]) are obtained from the regression results of the historical data. The CT model fitting curve is shown in Figure 4, and the WTW efficiency is shown in Equation 3. It should be noted that the coefficients obtained from the trended historical data are only applicable to the current CT operation strategy. If a new CT operation strategy is used, the coefficients are subject to adjustment. A physical CT model, such as an effectiveness number of transfer units (NTUs) model, is used to simulate the CT fan power under all operating conditions. Then, the simulation data are used to obtain the coefficients of the new CT model (Zhang 2010).

[[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]). (3)

Chiller model

The simulation can only be as accurate as the model. The accuracy of the model determines the reliability of the simulation results. OM chillers consume about 65% of the total electricity in the EP. The accuracy of the chiller model plays a critical role in system modeling. A physical model will lead to a high computational cost, and an empirical model or black-box model is not reliable out of the range of the training data. As a result, the semi-empirical Gordon-Ng model is selected to simulate the chiller performance (Gordon and Ng 2000).

[FIGURE 3 OMITTED]

The coefficients of the Gordon-Ng chiller model ([c.sub.0] through [c.sub.3]) are obtained by regressing with the trended historical data of the OM chillers. The rated CW flow rate ([V.sub.cw]) is equal to the average of the trended data. In this study, the total available chiller number ([N.sub.CHLR]) is limited to four. The chiller ChWLT default set-point ([T.sub.ChW,S]) is 36[degrees]F (2.2[degrees]C). The ChW flow rate limits ([V.sub.chw,min] and [V.sub.chw,max]) and CW entering temperature limits ([T.sub.CW,max] and [T.sub.CW,min]) are based on the chiller design specifications.

[FIGURE 4 OMITTED]

Figure 5 is a comparison between measured and predicted motor power using the Gordon-Ng model. statistical analysis shows that the RMSE of the internal predictions is 102.5 kW, and the CV is 2.96%. To test the external prediction performance of the calibrated OM chiller model, the trended data from March 2008 to January 2009 are selected, and a good match is also observed. The RMSE is 104.3 kW, and the CV is 3.14%. Specifically, the accuracy is obviously high--between 2500 kW and 3000 kW--which corresponds to the part load range of the OM chillers with the highest efficiency.

According to this model, a higher ChWLT, a lower CW entering temperature, and a higher CW flow rate lead to a lower kW per ton value. It is found that the optimal chiller PLR occurs at around 4400 ton (15,474 [kW.sub.t]) or 80% of chiller rated capacity.

In this study, a month-by-month plant optimization will be performed to optimize chiller ChWLT and CT approach set-point. They are assumed to be constant within each month and will be adjusted month by month.

Tank and nonplant power modeling

The tank parameters and nonplant power model are listed in Table 3. The tank water level lower ([x.sub.min]) and upper limits ([x.sub.max]) are set 0.2 and 1.0, respectively. They can be adjusted to accommodate a conservative or an aggressive operating strategy. The tank figure-of-merit (FOM) ([PHI]) is based on the statistic analysis of tank inventory change. Mild mixing is observed in this tank, and 0.95 is selected. A high limit for charging and discharging rate ([V.sub.tank,max] and [V.sub.tank,min]) is imposed to avoid intense turbulence around the dispensers.

The nonplant power is composed of two segments. When the ambient dry-bulb (DB) temperature is lower than 60[degrees]F (15.6[degrees]C)([T.sub.db,shift]), the nonplant power is 750 kW constant ([P.sub.base]). Otherwise, a second-order polynomial is used to calculate the total nonplant power contributed by plant HVAC, glycol production, air compressors, etc. Figure 6 shows the fitting curve of electricity consumption on non-ChW production, and Equation 4 shows the mathematical form of the regression model.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

[FIGURE 5 OMITTED]

Control strategies

Except for three conventional control strategies (full storage, chiller priority, and storage priority, as introduced in Part I of this article), a new control strategy is proposed in this study to make full use of the TES system. The purpose of this control strategy is (1) to level the plant load during the off-peak period, (2) to minimize the plant load during the on-peak period, and (3) to load chillers optimally as often as possible.

This strategy determines the number of chillers running and the ChW flow rate for each chiller in the next 24 h right before the end of the last on-peak period. To distinguish this new strategy from others, it is called the optimal control strategy. It is noted that "optimal" does not mean the globally best option but rather means the best among the options available. During the winter months when there is no definition for on-peak period in the utility rate structure, the high wet-bulb (WB) hours in a day can be artificially defined as the on-peak period, and the possibility of running chillers during this period should be reduced.

Figure 7 shows the algorithm of the new control strategy. Two subroutines are involved in the flowchart. "Planning model" provides the number profile of chillers running during the next cycle. "CHLR num" calculates the real on-stage chiller number as well as the ChW flow rate per chiller based on the actual plant ChW flow rate and chiller optimal and maximum flow rate.

[FIGURE 6 OMITTED]

Based on the loop total ChW flow demand in the next 24 h ([U.sub.Plant,ChW,Daily]), the planning model calculates the necessary running chiller numbers [N.sub.Low] and [N.sub.High] as well as the corresponding duration ([CT.sub.Low] and [CT.sub.High]). The daily average optimal chiller flow ([V.sub.CHLR,Opt,avg]) is used to calculate the sum of the running chiller numbers in each hour during the off-peak period ([N.sub.Tot]). The average number of the chillers running during the off-peak period is [N.sub.Avg]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

As a result, during the off-peak period, [N.sub.High] chillers will run for [CT.sub.High] hours, and then [N.sub.Low] chillers will run for [CT.sub.Low] hours. The function of the CHLR Num subroutine is to determine the actual on-stage chiller number and the ChW flow rate per chiller. The inputs are the plant total ChW flow rate and the chiller optimal or maximal cooling load. The maximal and minimal ChW flow rate in evaporators and the maximal numbers of chillers staged-on are taken into account in calculating the practical number of chillers staged-on.

Simulation and results

Simulation settings

Scenario design

There are six scenarios designed in the simulations, which are shown in Table 4. The first and second scenarios are the optimal control strategy proposed in this article, the next three are conventional strategies, and the last is the scenario without TES as the baseline. The plant optimization is only applied to the first scenario. The existing operation is very close to Scenario 3. The difference between Scenario 6 and Scenario 3 is due to TES application. The difference between Scenario 2 and Scenario 3 is due to TES optimization. The difference between Scenario 1 and Scenario 2 is due to plant optimization. Scenario 2 uses default values of chiller ChW leaving temperature set-point and CT approach temperature, while Scenario 1 adopts a plant optimization procedure to find the optimal values. The current rate structure will be applied for all scenarios. Since there is no special TES rate structure in Texas's deregulated electricity market, the same rate structure will be applied in calculating the baseline cost.

[FIGURE 7 OMITTED]

On-peak period definition

For each control strategy, an on-peak period and an off-peak period are defined for both the summer months and winter months. In the summer months, the on-peak period is defined as 3:00 p.m. to 6:00 p.m., and other hours are defined as the off-peak period. The on-peak period matches the 4CP demand period defined in the previous section. In the winter months, the on-peak period is defined as 2:00 p.m. to 5:00 p.m. when the ambient WB is high in a day. Running chillers during this period should be minimized, since the plant performance is low when the ambient WB temperature is high. However, if the gains by shifting cooling load from the high WB hours to the low WB hours are less than the losses through the tank heat losses and mixing effects, it is preferred to run chillers during the on-peak period.

4CP demand baseline

As the 4CP demand power is based on the metered data in the previous year, a baseline 4CP demand [D.sub.4CP,baseline] is determined for each control strategy by performing preliminary simulations for the summer months. The 4CP demand cost for the current month is calculated with the following formulas:

[C.sub.4CP] = [R.sub.4CP][D.sub.4CP,baseline] + [12R.sub.4CP] ([D.sub.4CP,current] - [D.sub.4CP,baseline])/4 for the summer months, (6)

[C.sub.4CP] = [R.sub.4CP][D.sub.4CP,baseline] for the winter months. (7)

These formulas indicate that in the summer months, if the current month 4CP demand is higher than the baseline demand, a quarter of the difference (the 4CP demand is the average of CP demands in the four summer months) will be charged for 12 months in the next year. In winter months, the 4CP demand charge is calculated with the baseline demand.

[FIGURE 8 OMITTED]

NCP demand ratchet

An 80% ratchet of the highest monthly NCP kW established in the 11 months preceding the current billing month is defined for the current month NCP demand. Historic data show that the peak NCP demand normally occurs in the summer months. In this study, a preliminary simulation is conducted for the summer months to establish the annual NCP demand for each control strategy. The NCP demand costs in each month can be calculated as follows:

[C.sub.NCP] = [R.sub.NCP]Max ([D.sub.NCP,current], 0.8 x [D.sub.NCP,peak]). (8)

Plant optimization

The plant variables to be optimized are chiller ChWLT and CT approach temperature set-point. The default values of 36[degrees]F (2.2[degrees]C) ChWLT and 6.0[degrees]F (3.3[degrees]C) CT approach are applied to all operating strategies during the search process. When the simulation is finished, a plant optimization is conducted to find the optimal set-points for Scenario 1. The upper and lower limits of the ChWLT are 44[degrees]F and 36[degrees]F (6.7[degrees]C and 2.2[degrees]C), respectively. The upper and lower limits of the CT approach temperature set-point are 10 delta [degrees]F and 2 delta [degrees]F (5.6 delta [degrees]C and 1.1 delta [degrees]C), respectively. The GRG algorithm in the Excel Solver tool is used to find the solution.

Simulation results

Scenario comparison

Figure 8 shows the monthly savings plots for different scenarios. The simulated monthly costs for each scenario are also shown in Table 5. It is obvious that the optimal control strategy outperforms others in each month. The optimal control strategy with plant optimization (Scenario 1) is the one with the lowest electricity billing cost for every month. The Scenario 2 has a higher saving percentage in each month than scenarios with conventional control strategies. If Scenario 6 is used as the baseline, the annual electricity total billing cost savings for full storage, chiller priority, and storage priority are 2.6%, 1.0%, and 2.6%, respectively. The annual savings due to implementing the TES tank are $199,185. There is no obvious difference in monthly billing costs between the full storage (Scenario 3) and storage priority (Scenario 5) because the tank is so large that it is not necessary to run chillers during the on-peak period in the summer months. For Scenario 2, the annual saving is 6.8%, which is 4.2% or $330,079 more than that of Scenario 3 (close to current operations). This could be regarded as the savings due to TES operation optimization. Compared to Scenario 3, Scenario 1 can reduce operating costs by 7.3% or $565,815 per year. Therefore, the annual savings due to plant optimization are $235,736. The analysis above shows that the savings due to TES and plant operation optimization can be very significant. Conventional control strategies could only reap part of the savings potential of a ChW storage tank.

The savings percentage of Scenario 1 is high in the winter months and low in the summer months. This can be explained by the larger difference of the chiller kW per ton for the optimal part loads and the extreme high or extreme low PLR when the chiller CW entering temperature is low. The savings for Scenario 4 are negligible because the demand savings are small. If the tank size is much smaller than the current size, the full-storage strategy may not be applicable, and the savings for Scenario 5 are close to that for Scenario 4. Further analysis shows that the demand cost savings for Scenario 1 cover 50% of total cost reduction. Without plant optimization, the ratio of demand cost savings rises to 69% in Scenario 2.

It is noted that the simulation can only be as accurate as the model. If the component model predicts different performance from the actual performance of the component, the simulated savings will be different from the achievable savings. For example, if the chillers are not constant speed but are equipped with variable-speed drives, higher cost savings can be obtained by staging-on more chillers and loading chillers at a lower PLR.

Results for Scenario 1

Tables 6 and 7 detail the simulation results of Scenario 1. The annual billing cost is $7,010,439, which is $765,000 less than that of the baseline. The billing cost savings consist of $384,395 per year from the energy costs reduction and $380,605 per year from the demand costs reduction. The highest monthly NCP demand in this year is 20,653 kW, and 4CP demand is 3,744 kW The annual electricity energy reduction is 4,830,190 kWh. However, the annual total cooling production increases 1,056,533 ton-h (3,715,671 [kW.sub.t]-h) due to tank heat losses and mixing effects.

In the summer months, no chiller is staged-on during the on-peak period for Scenario 1, and the maximum number of running chillers is four during the off-peak period. In the winter months, the maximum number of chillers running is two to four during the off-peak period. Sometimes, it is even more cost effective if chillers are running during the on-peak period. This is explained where the energy savings by reducing tank losses are higher than the energy savings due to improvements in the plant performance.

The optimal ChW supply temperature is 39 to 42[degrees]F (3.9 to 5.6 [degrees]C) from June to October, and it is 40 to 44[degrees]F (4.4 to 6.7[degrees]C) from November to May. This indicates that a higher ChW supply temperature is preferred in the winter months because the energy savings from chiller performance improvements outperform the pump energy increase due to a lower loop delta-T. The optimal CT approach set-point is 4.6 to 4.8 delta [degrees]F (2.6 to 2.7 delta [degrees]C) all year round, which is lower than the current set-point. This indicates that the energy savings from chiller performance improvements are more than the fan energy increase due to a lower CT CW leaving temperature (CWLT).

To help understand the plant operations under different strategies, Figure 9 shows the plant and loop ChW load profiles during three consecutive days in August. Figure 10 shows the plant total demand hourly profiles in the same three days. As expected, the load of the plant without TES closely follows the loop load, but it is a little higher because of loop supply temperature increases. When the tank is fully charged, the profile of the chiller-priority strategy almost overlaps the load profile because there is enough cooling capacity in the plant and the tank is in an idle mode. The profiles of the full storage and the storage priority match with each other because there is no need to run chillers during the on-peak period. These two strategies both charge the tank at the maximal capacity at the beginning of the off-peak period and then enter the idle mode before 6:00 a.m. The current operation profiles are also shown in Figures 9 and 10. The off-peak demand is close to that of chiller priority or storage priority, while there is a possibility to hit a high on-peak demand. Chillers are not optimally loaded during most of time.

Different from others, the optimal control strategy maintains a constant plant ChW production for a long time. One chiller is shed several hours before 3:00 p.m. to ensure the tank is fully charged right before 3:00p.m. During most hours, all chillers staged-on are loaded at part load with the highest efficiency. The off-peak demand for the optimal control strategy is around 4500 kW less than that for the full storage and the storage priority. The on-peak demand for the optimal control strategy is around 16,000 kW less than that for the chiller priority and the scenario without TES.

Sensitivity study

Considering that the practical conditions could be different from those assumed in the simulations, it is necessary to test the sensitivity of plant parameters on the monthly operating cost. Scenario 2 (optimal control strategy without plant optimization) is selected as an example, and a series of sensitivity studies are performed in August. Table 8 lists the selected parameters, the default values, and upper and lower limits of the fluctuation range. Five points are selected for each parameter.

The simulation and analysis results are shown in Figure 11. The most sensitive parameter is the chiller ChWLT. For a 1.0[degrees]F (0.6[degrees]C) increase in the chiller ChWLT, the monthly electricity billing cost decreases by 0.6%, or $6220. This includes both chiller efficiency improvement due to a higher chiller ChWLT and SPMP energy increases due to a lower loop delta-T. The next most important one is the FOM of the tank. A higher FOM leads to a lower monthly cost. For the normal range of 0.85 to 0.95, the corresponding change in monthly cost is 1.1%, or $10,816. This is followed by the CW flow rate per chiller. When the efficiency and pump head are assumed constant, a higher flow rate leads to a lower monthly cost.

[FIGURE 9 OMITTED]

The three parameters left have a positive correlation with the monthly electricity billing cost. If the loop supply temperature rise increases by 0.3[degrees]F (0.2[degrees]C) for any reason, such as bad tank wall insulation, the monthly electricity billing cost could increase by 1.3%, or $12,270. A higher loop end DP set-point will consume more SPMP power. If the loop DP set-point is reset from 32 psid to 28 psid (221 kPa to 193 kPa), the monthly billing cost savings are $3064. It is noted that an optimal CT approach set-point exists for this case, at around 5.0[degrees]F (2.8[degrees]C), which is consistent with the results of the system monthly simulation.

[FIGURE 10 OMITTED]

This study can also be used to estimate the savings potential for different plant retro-commissioning measures.

Application issues

The application of this methodology can be divided into two stages. The first stage is to determine optimal strategies by simulation. During this stage, the loop cooling load, weather conditions, and rate structures are assumed to be perfectly predicted. Perfect system knowledge is assumed, which means that the system in reality behaves exactly as modeled by a system model. The electricity billing costs under different operating strategies are simulated and compared. This method is a good option when it comes to making decisions on the long-term operating strategy or projecting the next year plant operating schedule and energy costs.

[FIGURE 11 OMITTED]

The secondary stage is implementation. Appropriate forecasting models are chosen to predict those inputs and a controller is designed to actualize the selected control strategy. For the following 24 h, the hourly profiles of cooling load, weather, nonplant power, and loop delta-T are predicted with corresponding models. The program will generate the operating number of chillers and optimal loading for the next 24 h. Chiller controllers will sequence chillers and load chillers optimally by modulating the ChW flow rate based on the actual loop return and supply ChW temperatures. To accommodate the uncertainties from predicting models, the designer can select a larger tank minimum level ratio, for example 0.3, to prevent prematurely depleting the tank. It is also possible to design several scenarios, from load underestimating to load overestimating, to test the robustness of the selected optimal operating strategy and compare the savings with possible risk.

Summary and conclusion

The system studied is a large-scale ChW system with a water-storage tank and an advanced control system. The methodology introduced in Part I is successfully applied in this system to optimize the operation of the TES and chiller plant. Historical profiles show that the current TES tank and plant operation can be improved further by avoiding running chillers during 4CP hours, leveling plant load during the non-4CP hours, and loading chillers optimally. Appropriate models are selected and calibrated for each component. Three conventional control strategies and one new control strategy are included in the control strategy sub-model. The utility rate structure is introduced and analyzed to define the off-peak and on-peak periods for the summer and winter months. Six scenarios are defined and simulated to study the electricity energy and cost savings potential due to TES application, TES optimization, and plant optimization. The baseline period of loop cooling loads and weather conditions is between March 2007 and February 2008. Following are some conclusions drawn based on the monthly comparison among the six scenarios.

(1) The methodology introduced in Part I is successfully applied in this project to find the optimal TES operation strategies and plant optimized parameters. The plant, TES tank, and loop are linked together according to the physical relationship among them. The new tank state equation can consistently describe the charging, idle, and discharging processes. The fluctuation of the loop return temperature justifies the implementation of a loop model. The forward plant model can simulate the plant power at a given cooling load instantly.

(2) The annual utility billing cost savings due to implementing a TES tank is $199,185 when a full-storage strategy is adopted. If an optimal TES operation strategy is used, it can result in additional savings of $330,079 per year. This strategy includes avoiding running chillers during the 3:00 p.m. to 6:00 p.m. time period in the summer months, optimally allocating cooling load to each chiller, and leveling the demand profile by optimally sequencing the chiller. If the suggested plant optimization measures are implemented, it may bring additional savings of $235,736 per year. These measures are resetting chiller ChWLT and CW entering temperature monthly.

(3) The plant optimization results show that a lower chiller ChWLT is preferred in the summer months, while a higher value is preferred in winter months. The optimized CT approach temperature is at around 4.7 delta [degrees]F (2.6 delta [degrees]C) all year round. The sensitivity study shows that the ChWLT is the most sensitive parameter for the monthly operating utility cost.

DOI: 10.1080/10789669.2011.564259

Nomenclature

4CP = four coincident peak

C = cost, $

CHLR = chiller

ChW = chilled water

ChWLT = chilled-water leaving temperature, [degrees]F ([degrees]C)

CT = cooling tower

CV = coefficient of variation

CW = condenser water

d = cooling tower model coefficients

DB = dry bulb

DP = differential pressure

e = loop hydraulic performance coefficient

EP = energy plaza

ERCOT = Electric Reliability Council of Texas

FOM = figure-of-merit

GPM = gallons per minute

GRG = generalized reduced gradient

h = loop delta-T model coefficient

H = water head, ft (m)

N = number

NCP = noncoincident peak

NTU = number of transfer units

OM = On-site manufactured

P = power, kW

PCA = pre-conditioned air

PLR = part-load ratio

PPMP = primary pump

Q = cooling load, ton

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

RMSE = root mean square error

SG = specific gravity of the fluid

SPMP = secondary pump

t = hour

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

TES = thermal energy storage

TOU = time-of-use

U = volume, gallon

V = flow rate, GPM

VFD = variable-frequency device

WB = wet bulb

WTW = wire-to-water

[chi] = tank ChW level ratio, or independent variables

[DELTA]t = time step, hour

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

db = dry bulb

e = energy

i = month

Init = initial

k = current hour

Lp = loop

max = maximum

min = minimum

mtr = motor

Opt = optimal

R = return

ref = reference

s = summer

S = supply

sp = set-point

sys = system

t = thermal

Tot = total

v = rate period

w = winter

wb = wet bulb

Greek symbols

[eta] = efficiency

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

[empty set] = figure-of-merit

Subscripts

App = approach

Avg = average

Cap = capacity

d = demand

References

ERCOT. 2009. 2001-2009 four coincident peak calculations. www.ercot.corn/mktinfo/data_agg/4cp/.

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

Zhang, Z. 2010. Methodology for determining the optimal operating strategies for a chilled water storage system. Ph.D. Dissertation, Department of Mechanical Engineering, Texas A&M University, College Station, TX.

Zhiqin Zhang, (1,2), * William D. Turner, (1) Qiang Chen, (2) Chen Xu, (3) and Song Deng (2)

(1) Department of Mechanical Engineering, Texas A&M University, College Station, TX 77943, USA

(2) Energy Systems Laboratory, Texas A&M University, 3581 TAMU, 214 Wisenbaker Engineering Research Center, Bizzel Street, College Station, TX77943-3581, USA

(3) VisionBEE, Austin, TX, USA

* Corresponding author e-mail: zhangzhiqin2010@gmail.com

Received September 20, 2010; accepted January 28, 2011

Zhiqin Zhang, is PhD Student and Research Assistant. William D. Turner, PhD, PE, is Professor. Qiang Chen, PE, Associate Member ASHRAE, is Research Engineer. Chen Xu, PE, Associate Member ASHRAE, is Project Manager. Song Deng, PE, Member ASHRAE, is Associate Director.
Table 1. Parameters of TES system loop side.

Loop hydraulic

 LP end DP upper set-point [DP.sub.h] 28.0

 LP end DP lower set-point [DP.sub.l] 22.0

 LP end DP upper shift flow [V.sub.upper] 16,000

 LP end DP lower shift flow [V.sub.lower] 10,000

 LP hydraulic coefficient 1 [e.sub.1] 1.0E-07

 LP hydraulic coefficient 2 [e.sub.2] 5.0E-08

 LP hydraulic coefficient 3 [e.sub.3] 3.0E-08

 LP load factor [f.sub.load] 1.00

Loop DT

 LP supply temperature rise [DELTA][T.sub.s] 1.0

 LP DT coefficient 0 [h.sub.0] 32.1898

 LP DT coefficient 1 [h.sub.1] -0.5439
 ([T.sub.LP,ChW,s])

 LP DT coefficient 2 [h.sub.2] 6.86E-05
 ([Q.sub.LP,ChW])

 LP DT coefficient 3 [h.sub.3] 6.34E-02
 ([T.sub.wb])

 LP max DT [DELTA][T.sub.Lp],max 22.0

 LP min DT [DELTA][T.sub.Lp],min 12.0

 LP DT system error [DELTA][T.sub.Lp],error 0.0

Loop hydraulic

 LP end DP upper set-point psid 1.009 kPa

 LP end DP lower set-point psid 151.7 kPa

 LP end DP upper shift flow GPM 3634 [m.sup.3]/s

 LP end DP lower shift flow GPM 0.631 [m.sup.3]/s

 LP hydraulic coefficient 1 1.0E-07

 LP hydraulic coefficient 2 5.0E-08

 LP hydraulic coefficient 3 3.0E-08

 LP load factor 1.00

Loop DT

 LP supply temperature rise Delta 0.6 Delta
 [degrees]F [degrees]C

 LP DT coefficient 0 32.1898

 LP DT coefficient 1 -0.5439
 ([T.sub.LP,ChW,s])

 LP DT coefficient 2 6.86E-05
 ([Q.sub.LP,ChW])

 LP DT coefficient 3 6.34E-02
 ([T.sub.wb])

 LP max DT Delta 12.2 Delta
 [degrees]F [degrees]C

 LP min DT Delta 6.7 Delta
 [degrees]F [degrees]C

 LP DT system error Delta 0.0 Delta
 [degrees]F [degrees]C

LP: Loop. DP: Differential pressure. DT: delta-T.

Table 2. Parameters of TES system plant side.

SPMP SPMP overall efficiency [[eta].sub.spmp] 75%
 SPMP design flow rate [V.sub.spmp] 8,000

PPMP PPMP overall efficiency [[eta].sub.ppmp] 80%
 PPMP head [H.sub.ppmp] 80

Chiller CHLR coefficient 0 [C.sub.0] -2.81E-01
 CHLR coefficient 1 [C.sub.1] 1.02E+01
 CHLR coefficient 2 [C.sub.2] 1.74E+03
 CHLR coefficient 3 [C.sub.3] 2.71E-03
 CHLR cond. water flow [V.sub.cw] 10,300
 Total CHLR number [N.sub.CHLR] 4
 ChWLT [T.sub.ChW,S] 36
 CHLR ChW low limit [V.sub.chw,min] 4000
 CHLR ChW high limit [V.sub.chw,max] 7400
 Motor max power input [P.sub.mtr,max] 3933
 Max CW enter temp [T.sub.CW,max] 83.0
 Min CW enter temp [T.sub.CW,min] 60.0

CT CT coefficient 1 [d.sub.1] 0.01
 CT coefficient 2 [d.sub.2] 0.16
 Approach set-point [DELTA][T.sub.app,sp] 6.0

CWP Pump head [H.sub.cwp] 92
 Pump overall efficiency [[eta].sub.cwp] 82%

SPMP 75% [m.sup.3]/s
 GPM 0.505

PPMP 80%
 ft 239.1 kPa

Chiller -2.81E-01
 1.02E+01
 1.74E+03
 2.71E-03
 GPM 0.650 [m.sup.3]/s
 4
 [degrees]F 2.2 [degrees]C
 GPM 0.252 [m.sup.3]/s
 GPM 0.467 [m.sup.3]/s
 kW 3,933 kW
 [degrees]F 28.3 [degrees]C
 [degrees]F 15.6 [degrees]C

CT 0.01
 0.16
 Delta [degrees]F 3.3 Delta [degrees]C

CWP ft 275.0 kPa
 82%

Table 3. Parameters of TES system tank and nonplant power.

TES Tank volume [U.sub.tank] 5,400,000
 Tank initial height [x.sub.initi] 0.20
 Tank ChW low limit [x.sub.min] 0.20
 Tank ChW high limit [x.sub.max] 1.00
 Tank charging high limit [V.sub.tank,max] 22,958
 Tank discharging high limit [V.sub.tank,min] -22,958
 Tank FOM [PHI] 0.95

Nonplant Coefficient 1 g1 1266.3
power Coefficient 2 g2 -4.4327
 Coefficient 3 g3 0.1983
 Shift DB [T.sub.db,shift] 60
 Base power [P.sub.base] 750

TES gal 20,441 [m.sup.3]
 0.20
 0.20
 1.00
 GPM 1.448 [m.sup.3]/s
 GPM -1.448 [m.sup.3]/s
 0.95

Nonplant 1266.3
power -4.4327
 0.1983
 [degrees]F 15.6 [degrees]C
 kW 750 kW

Table 4. Simulation scenario definition.

Scenario
no. Control strategy Plant optimization

1 Optimal Yes
2 Optimal No
3 Full storage No
4 Chiller priority No
5 Storage priority No
6 Without TES No

Table 5. Comparison of simulated monthly costs for DFW.

 Conventional
 Optimal control strategy control
 strategies
Scenario 1 2 3 4

Month Monthly Saving Optimal Full Chiller
priority bill, $ w/o plant storage priority
 optimal

Mar 507,562 -11.5% -8.1% -2.6% -1.5%
Apr 472,123 -12.7% -9.4% -3.0% -1.3%
May 678,620 -8.1% -5.4% -1.5% -0.5%
Jun 816,189 -6.1% -4.1% -0.6% -0.4%
Jul 858,703 -8.2% -4.6% -1.8% -1.2%
Aug 961,067 -6.6% -3.7% -1.1% 0.2%
Sept 774,267 -7.5% -4.3% -0.7% -0.4%
Oct 592,072 -10.5% -7.0% -3.1% -0.7%
Nov 416,077 -13.6% -10.3% -4.6% -1.8%
Dec 323,240 -15.7% -12.7% -6.5% -2.3%
Jan 297,200 -16.0% -13.6% -7.3% -2.5%
Feb 313,320 -15.8% -12.6% -6.6% -2.3%
Total 7,010,439 -9.8% -6.8% -2.6% -1.0%
Absolute -$765,000 $529,264 -$199,185 -$75,181 -$204,766
 saving

 Conventional Baseline
 control
 strategies
Scenario 5 6

Month Storage Monthly bill
priority priority without
 TES, $

Mar -2.8% 573,506
Apr -3.9% 540,835
May -1.5% 738,075
Jun -0.6% 869,079
Jul -1.8% 935,384
Aug -1.1% 1,029,173
Sept -0.7% 837,365
Oct -3.1% 661,379
Nov -4.6% 481,615
Dec -6.5% 383,306
Jan -7.3% 353,690
Feb -6.6% 372,033
Total -2.6% 7,775,439
Absolute
 saving

Table 6. Monthly results for optimal control strategy with plant
optimization (Scenario 1).

 Current
 On-peak Off-peak Charged Charged month
Month energy, kWh energy, kWh 4CP, kW NCP, kW 4CP, kW

3 210,513 5,207,181 3,744 16,523 2,908
4 193,983 4,987,660 3,744 16,523 3,135
5 559,494 7,251,778 3,744 16,523 15,912
6 257,960 9,164,301 3,744 20,449 3,584
7 280,923 9,679,940 3,744 20,266 3,745
8 303,185 10,926,673 3,744 20,653 4,006
9 265,707 8,654,059 3,744 19,895 3,642
10 241,315 6,376,364 3,744 19,309 3,638
11 185,397 4,311,455 3,744 16,523 3,060
12 224,638 3,079,563 3,744 16,764 16,764
1 115,851 2,867,172 3,744 16,523 2,858
2 196,780 2,991,516 3,744 16,523 9,695

Total 3,035,747 75,497,661 3,744

Diff. 8,886,173 -4,055,983

 Current On-peak ChW Off-peak ChW
 month production, production,
Month NCP, kW ton-h ton-h

3 13,082 6,343,352 0
4 14,552 6,195,198 0
5 16,379 8,007,623 427,326
6 20,449 9,817,257 0
7 20,266 10,452,526 0
8 20,653 11,588,419 0
9 19,895 9,446,183 0
10 19,309 7,416,188 0
11 13,601 5,303,138 0
12 16,764 3,986,745 149,818
1 10,425 3,630,117 0
2 9,695 3,796,718 85,416

Total 20,653 85,983,464 662,559

Diff. -12,526,689 11,470,155

Table 7. Monthly costs and operations for Scenario 1.

 Monthly
 electricity Demand Energy
Month billing cost, $ cost, $ cost, $ [N.sub.off]

3 507,562 65,224 442,338 3
4 472,123 65,224 406,899 3
5 678,620 65,224 613,396 3
6 816,189 76,287 739,902 4
7 858,703 76,506 782,197 4
8 961,067 79,220 881,847 4
9 774,267 73,825 700,443 4
10 592,072 72,405 519,666 4
11 416,077 62,952 353,124 3
12 323,240 63,771 259,469 3
1 297,200 62,952 234,248 2
2 313,320 62,952 $250,367 2

Total $7,010,439 $826,543 $6,183,896

Diff. $765,000 $380,605 $384,395

 [DELTA]T
 approach,
 ChWLT, [degrees] F delta [degrees]F
Month [N.sub.on] ([degrees]C) (delta [degrees]C)

3 0 43.5 (6.4) 4.6 (2.6)
4 0 42.8 (6.0) 4.7 (2.6)
5 3 40.3 (6.4) 4.8 (2.7)
6 0 39.3 (4.1) 4.7 (2.6)
7 0 42.0 (5.6) 4.7 (2.6)
8 0 40.7 (4.8) 4.8 (2.7)
9 0 41.1 (5.1) 4.8 (2.7)
10 0 42.2 (5.7) 4.6 (2.6)
11 0 43.0(6.1) 4.8 (2.7)
12 4 44.0 (6.7) 4.6 (2.6)
1 0 41.0(5.0) 4.6 (2.6)
2 2 43.3 (6.3) 4.6 (2.6)

Total

Diff.

Table 8. Parameter range of sensitivity study for DFW.

Variables Default Min Max Unit

Tank FOM 0.9 0.810 0.990 -
Chiller ChWLT 38.0 36.0 40.0 [degrees]F
 3.3 2.2 4.4 [degrees]C
[CT.sub.App,sp] 6.0 4.0 8.0 Delta [degrees]F
 3.3 2.2 4.4 Delta [degrees]C

CW flow 10,000 8,000 12,000 GPM
 0.631 0.505 0.757 [m.sup.3]/s
[LP.sub.DP,sp] 28 24 36 psid
 193.1 165.5 248.2 kPa
[LP.sub.ST,rise] 1.0 0.7 1.3 Delta [degrees]F
 0.6 0.4 0.7 Delta [degrees]C
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Date:Sep 1, 2011
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