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Optimal model-based control of chiller tower fan and cooling water pump.

INTRODUCTION

United Arab Emirates (UAE) has extreme hot and humid weather conditions for most of the year. During peak summer days, cooling systems consume 60-75% of electrical energy and cooling represents 40-55% of annual electricity consumption (Ali 2011; Friedrich 2013). For an oil and gas exporting country the fuel opportunity cost of using said fuels to generate electricity, plus amortization and other operational costs, is estimated to be 0.12USD/kWh (Husseini et al. 2008). In the UAE much of the cooling is delivered by central district cooling plants or roof top chillers. The objective of this work is to develop a chiller plant model whose parameters can be reliably estimated from operational data and show that, with such models, plant engineers can implement and maintain on-line optimal control of large cooling plants.

Heat pump and component models for chiller plants are extensively described in literature. Complex and computationally expensive models which require a large number of input variables are commonly used by manufactures for design purposes. Zakula et al (2011), Hiller (1976), Ellison et al (1979) and Rice (2006) describe comprehensive air- to-air Heat Pump Models (HPMs), where the reported error for respective quantities is within 5%. Because market competition makes producers reluctant to publish chiller design and performance parameters, researchers have developed simple component models derived from first principles or empirical relations. Braun et al (1987) developed a simple mechanistic model to predict performance of a chiller plant and compared the results with supervisory control and data acquisition (SCADA) values, under both constant and variable speed control. Van Houte et al (1994), Browne & Bansal (1998), Jin (2002), and Vera-Garcia et al (2010) also presented various simple component models, mostly based on physics and empirical relations. Armstrong et al (2009) presented a simple first principles model to optimize compressor and fan speeds for minimal total power given cooling rate, zone and ambient temperature. This work was further developed by Zakula et al (2011) by taking into account refrigerantside pressure drops, suction superheat, condenser sub-cooling and variable heat transfer coefficient. Of the foregoing only Braun et al (1987) and Browne & Bansal (1998) address centrifugal compressors. Additional centrifugal compressor modeling has been done by Popovic & Shapiro (1998), Braun (1988), Bendapudi et al (2005) and Wang et al (2000). The most detailed (short of CFD) impeller and diffuser models have been developed by Aungier (2000) to account for eleven major loss mechanisms in the compressor assembly. These models require detailed engineering dimensions of impeller, inlet guide vanes (IGVs) and diffuser geometry.

Use of variable- instead of fixed-speed compressors can save 28-35% according to Cohen et al (1974) and Qureshi (2013). These savings result from reduced condenser pressure and increased evaporator pressure at part load.

Although many chiller component models have been developed over the past four decades, there is still a need to put together first-principles component models whose parameters can be identified from measured performance of large district cooling plants. A model should efficiently simulate and optimize over a wide range of operating conditions, to estimate impact of variable speed controls and other retrofits and to implement and maintain energy-efficient control of a plant. In addition, the difficulty of dealing with two load-side variables (chilled water flow rate and return temperature), over which the plant operator may have no control, needs to be addressed.

DATA SOURCE

The measured values required for model training and analysis are evaporator and condenser pressures and water and refrigerant inlet and outlet temperatures; chilled water and cooling water flow rates; compressor input power and inlet vane position, and fan speed and power. Supervisory control and data acquisition (SCADA) data from chiller plant is sampled once per minute. Single samples of state at any given instant have a relatively high uncertainty arising from sensor and signal conditioning noise, short time transients and poor signal resolution. To address these problems values were averaged over ten minute successive intervals to reduce noise and signal resolution (discretization) problems. Records in extended periods with no value change (SCADA update failure) were eliminated as were periods of strong transients.

CHILLER MODEL FORMULATION

The chiller model consists of four component models within a main solver. Evaporator, condenser, compressor and cooling tower parameters are determined by regression using first principles models wherever possible. Refrigerant flow control is by an idealized isenthalpic throttling device. Power-law models for tower fan power versus speed, compressor motor loss fraction, and inverter losses are identified by regression.

Trial values are assumed for evaporator inlet enthalpy and compressor discharge pressure. Refrigerant mass flow rate, evaporator saturated pressure & temperature and chilled water supply are the outputs from the evaporator sub-model given cooling load, chilled water return temperature, mass flow rate of chilled water, degree of superheat and trial refrigerant inlet enthalpy. Refrigerant mass flow rate and pressure ratio are input to the compressor isentropic efficiency model, which returns compressor shaft power and discharge temperature. Transmission and miscellaneous losses are modeled as proportional to shaft power. Similarly, given the mass flow and inlet temperatures from both refrigerant and water side, the condenser model provides rejected heat rate, condenser pressure, enthalpy at condenser outlet and condenser water outlet temperature. The solver has converged when the calculated condenser pressure and liquid enthalpy at condenser outlet match latest trial values of pressure and enthalpy to a given tolerance.

Evaporator and Condenser Models

The (de)superheating and condenser subcooling sections are modeled by the crossflow effectiveness approximation:

[epsilon] = 1 - exp[[[[??].sub.max]/[[??].sub.min]][NTU.sup.0.22]{exp[[[-[[??].sub.max]/[[??].sub.min]][NTU.sup.0.78]]- 1}] (1)

where NTU = UA/[[??].sub.min] is the number of transfer units for the section in question and [[??].sub.min], [[??].sub.max] are the thermal capacitance rates with [[??].sub.min] usually found on the refrigerant side.

Two-phase sections are modeled by the single-stream heat-exchanger effectiveness relation with [[??].sub.min] on water side:

[epsilon] = (1 - [e.sup.-NTU]) (2)

The effective surface area, A, of the evaporator two-phase region was found to vary quadratically with refrigerant mass flow rate, probably as a result of changes in liquid level or droplets carried into the superheating section, according to:

A/[A.sub.0] = 1.095 - 0.0550[[??].sub.r] + 0.001356[[??].sup.2.sub.r] (3)

where [A.sub.0] is the nominal submerged water-side surface area. The condenser sub-cooling surface area is fixed by liquid level control while the de-superheating area varies and must be solved for a given condenser boundary condition (inlet temperatures and flow rates and condensing pressure). Relations between measured and predicted effectiveness, based on their respective refrigerant saturation temperatures and water side inlet & outlet temperatures, are shown for the evaporator and condenser in Figure 1.

Effectiveness is an approximate characterization of the condenser because its three sections (de-superheating, condensing and sub-cooling) all make substantial contributions to total heat transfer and the effective area and/or boundary conditions of each section vary depending on entering superheat and refrigerant flow rate. Also, although condensing dominates, the effectiveness-NTU relation is different for each section. In contrast to the variable chilled water flow rate, which results in wide range of evaporator effectiveness, the condenser water flow rate is almost constant resulting in a narrow range of condenser effectiveness. This situation will change, perhaps markedly, with variable cooling water flow control.

Compressor

The chiller under study uses a constant speed compressor that regulates capacity to maintain chilled water set point by varying inlet guide vane (IGV) position. Surge control is effected by an impeller discharge gate. The regions of normal (gate open) and active discharge gate operation are shown in Figure 2 for fourteen ranges of IGV position from 0 to 100%.

Discharge gate action is inferred from the ~2% drop in isentropic efficiency above a pressure ratio [P.sub.c]/[P.sub.e] threshold that is a function of IGV position. Discharge gate activity was rarely observed below 23% IGV in this particular instance of plant, load and climate. For 23-28% IGV the discharge gate becomes active at [P.sub.c]/[P.sub.e] ~2.6; for 28-54% IGV the discharge gate becomes active at [P.sub.c]/[P.sub.e] ~2.7; and for 54-82% IGV the discharge gate becomes active at [P.sub.c]/[P.sub.e] ~2.8. The conservative nature of surge control is evident in the 15-19% guide vane range where it is apparent that discharge gate control is keeping the gate active after pressure ratio has dropped to a point well below the surge region. We eliminate from the training set all observations for which the discharge gate is believed to be active. Isentropic efficiency measurements are susceptible to pressure and temperature error (Brasz 2010). The efficiencies shown in Figure 2 approach 100% rather more closely than expected. We revisit possible systematic bias in the isentropic efficiency measurement later in Other Losses section.

Isentropic efficiency, from evaporator to condenser, is given in terms of the refrigerant enthalpy [h.sub.in] evaluated at compressor inlet (evaporator outlet) and refrigerant enthalpy [h.sub.out] evaluated at diffuser outlet (condenser inlet) conditions by:

[[eta].sub.is] = [h([P.sub.c], [s.sub.in]) - [h.sub.in]]/[[h.sub.out] - [h.sub.in]] (4)

where h([P.sub.c], [s.sub. in]) is the discharge enthalpy that would result from reversible adiabatic compression.

Because several aerodynamic loss mechanisms are involved, die isentropic efficiency of centrifugal compressors is often modeled empirically. A bi-cubic function in pressure ratio, [P.sub.c]/[P.sub.e], and refrigerant flow rate [[??].sub.r], takes die following form:

f(xy) = [p.sub.00] + [p.sub.10]x + [p.sub.01]y + [p.sub.20][x.sup.2] + [p.sub.11]xy + [p.sub.02][y.sup.2] + [p.sub.30][x.sup.3] + [p.sub.21][x.sup.2]y + [p.sub.12]x[y.sup.2] + [p.sub.03][y.sup.3] (5)

where

x = [[??].sub.r] shifted by mean = 37.34 and scaled by standard deviation = 9.241 kg/s, and

y = [P.sub.c]/[P.sub.e] shifted by mean = 2.368 and scaled by standard deviation = 0.1454 (dimensionless).

As anticipated by Brasz (2010) a full bi-cubic results in physically unrealistic values of isentropic efficiency within the compressor envelope (and not far beyond the range of observation) in which slope and change in slope of the fitted surface seem to be implicated. A truncated bi-cubic eliminates this problem with almost no increase in residual norm (Table 1).

To model a variable speed compressor case we assume isentropic efficiency depends only on [P.sub.c]/[P.sub.e] and through a relationship approximated by evaluating die truncated bi-cubic at [[??].sub.r] = 55 kg/s as shown by die dotted profile in Figure 3.

Other Losses

Electrical power input is the sum of shaft work, mechanical and electrical losses, and other losses such as oil pumping:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

Motor losses are removed by a branch installed in parallel with the condenser cooling water ports and were measured by installing a flow meter and temperature sensors in the branch during May-July 2013. The relation between motor loss and input power is shown in Figure 4. A cubic with the physically meaningless constant term removed fits well.

The difference between net motor power and impeller shaft power represents mechanical and other losses. Percent bias errors resulting from errors in measurements used to identify the isentropic efficiency model and the motor loss model are also captured in this difference. The mechanical and other losses are found to be roughly proportional to and almost 25% of net motor power over the full range of input power.

Cooling Tower, CT Fan and CW Pump

In the existing plant we have a constant flow condenser cooling water pump hence we have performance data at constant flow. However for optimization purpose we require a variable flow model. For this purpose we used a simple constant efficiency cooling water pump model that accounts for frictional losses of turbulent flow, [DELTA][P.sub.f] = [C.sub.1][[??].sup.2] and for the static head above the tower basin [DELTA][P.sub.[DELTA]Z] is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

Pump efficiency is estimated from one time measurement of cooling water flow rate [[??].sub.0], static pressure drop across the pump [DELTA][P.sub.0] and power [[??].sub.0] using following equation

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

and friction loss parameter can be then estimated from

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

Tower effectiveness, defined as ratio of actual to maximum possible temperature rise, is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

NTU = [[C.sub.pa]/[C.sub.pw]][UA/[[??].sub.min]] is number of transfer units,

[C.sub.pa] = [[i.sub.a, out] - [i.sub.a, in]]/[[T.sub.wb, out] - [T.sub.wb, in]] is moist air equivalent thermal capacity,

[C.sub.pa] and [C.sub.p] are sensible heat capacities of air and water at constant pressure, and

UA is the conductance-area product for heat transfer from water to air, determined by nonlinear regression. The predicted effectiveness is plotted against measured effectiveness in Figure 5.

MODELED PERFORMANCE

Because the relation between capacity and refrigerant mass flow rate is almost a direct one, we can replace the three chilled water-side boundary conditions--chilled-water flow rate and supply and return temperatures--with the two refrigerant-side boundary conditions--capacity and evaporating temperature. The compressor, condenser, cooling tower, and cooling water loop can be treated as a single system with capacity, [Q.sub.e], evaporating temperature, [T.sub.e], and wet-bulb temperature, [T.sub.wb], as boundary conditions and cooling water flow rate, [V.sub.c], and tower fan speed, f as control variables. For plants in which the evaporating temperature is relatively constant, the boundary conditions can be further reduced, with little accuracy loss, so that performance can be mapped against capacity and external temperature lift given tower fan and cooling water pump speed. To illustrate this we use the plant model and solver to compute specific power, 1 /COP, at 80% tower fan speed and nominal cooling water flow rate versus capacity fraction and wet bulb temperature at four evaporating temperatures. The results, Figure 6, show that specific power is lowest when capacity fraction is maintained between 70% and 100%. Thus when operating at 70% plant load in hot humid weather, a four-chiller plant should be operated with all four chillers running at 70% rather than three chillers at 94%. Note that performance curves for different evaporating temperature but similar external lift are very similar. Figure 7 shows the performance in terms of capacity fraction and external temperature lift, [T.sub.wb] - [T.sub.e].

OPTIMAL CONTROL

The performance effects of condenser water flow rate and tower fan speed are not independent. Increasing condenser water flow increases the condenser effectiveness and reduces compressor work by reducing condensing temperature (lower condenser pressure is required to dissipate condenser load). However increasing flow rate increases the condenser pump power--an optimum flow rate exists for any given chiller operating point. Similar logic applies to the cooling tower airflow and fan speed and power. We utilize a grid optimization method to search for the best combination of condenser cooling water flow rate and tower airflow rate. The chiller model is called for every trial solution (fan speed and pump speed) presented by the grid search. The solver adjusts IGV (or compressor speed) to meet capacity at each trial solution.

To assess the value of optimal control we find the optimal control for every valid 10-minute record Dec-05 through Aug-27 2013. Figure 8 shows impact of optimal tower fan speed with fixed condenser pump speed (left) and of jointly optimal fan and pump speeds on the right. Energy consumption for each case is summarized, by component, in Table 2.

CONCLUSION

Chiller and cooling tower models were developed based on first principles and a few basic correlations. Parameters of the models were inferred from temperatures, pressures, flow rates and motor input power measured over a range of operating conditions. A clamp-on flow-meter was used to measure cooling water flow rates. All of the other variables were measured by existing sensors. Several innovations were made: use of [T.sub.e] as boundary condition to decouple the chiller from chilled water flow variations often beyond the operators control; an effective surface area relation was needed to model the co- current evaporator configuration; a method was developed to identify discharge gate status; and aerodynamic losses were treated separately from other compressor and motor losses.

Optimal control of existing variable-speed tower fans results in savings greater than 4% and a variable-speed cooling water pump will result in additional 0.8% savings in annual electrical use. Also it was found that a variable speed compressor results in almost 16% saving with optimal fan and cooling water pump operation. The work can be extended to include optimal condenser subcooling. A short-coming of typical plant instrumentation is absence of a refrigerant flow meter. The clamp-on sonic flow-meter is well suited to measuring liquid line flow upstream of the throttling valve where it should be used whenever possible to avoid error propagation. Since under normal plant operation, high pressure ratios were never observed, deliberate operation for a few hours with low cooling tower fan speed would be useful to obtain compressor performance data at [P.sub.c]/[P.sub.e] > 3 for a range of capacities.

NOMENCLATURE

A           = Area, [m.sup.2]
[??]        = Thermal Capacity Rate, kW/K
c           = Specific Heat, kJ/kg. K
h           = Enthalpy of Refrigerant, kJ/kg
i           = Enthalpy of moist air, kJ/kg
L           = Power Loss, kW
[??]        = Mass flow rate, kg/s
P           = Pressure, kPa
Q           = Heat Rate, kW
NTU         = Number of Transfer Units
S           = Entropy, kJ/kg-K
T           = Temperature, K
UA          = Overall Heat Transfer Coefficient, W/K
[??]        = Volumetric Flow Rate, [m.sup.3]/s
[??]        = Power, KW
[epsilon]   = Heat Exchanger Effectiveness
[eta]       = Efficiency

Subscripts

a           = Air
c           = Condenser/Condensing
CWR         = Condenser Water Return
CWS         = Condenser Water Supply
e           = Evaporator/Evaporating
in          = Inlet Condition
is          = Isentropic
max         = Maximum
min         = Minimum
out         = Outlet Condition
R           = Rated
r           = Refrigerant
t           = Total
w           = Water
wb          = Wet Bulb


ACKNOWLEDGMENTS

We thank National Central Cooling Co. (PJSC)--Tabreed and Masdar Institute of Science and Technology for supporting this research. Assistance and advice of Tabreed operations and engineering staff and especially Fredrick Lobo are gratefully acknowledged. MT Ali and Hanif Shaikh contributed to the instrumentation effort. The presentation was materially improved thanks to thoughtful reviewer comments.

REFERENCES

Ali, M.T., M.M. Mokhtar, M. Chiesa, P.R. Armstrong, (2011). A cooling change-point model of community-aggregate electrical load, Energy and Buildings, 43(1):28-37

Armstrong, P., W. Jiang, D.W. Winiarski, S. Katipamula, L.K. Norford, and R. Willingham. (2009). Efficient low-lift cooling with radiant distribution, thermal storage and variable-speed chiller controls--Part I: Component and subsystem models. HVAC&R Research, 15(2):367-401.

Aungier, R. H. (2000). Centrifugal Compressors: A Strategy for Aerodynamic Design and Analysis: ASME press New York.

Husseini, I.E., F. Walid, T.E. Sayed, and D. Zywietz (2008). A New Source of Power: The Potential for Renewable Energy in the MENA Region. Booz & Company.

Braun, J., Mitchell, J., Klein, S., & Beckman, W. (1987). Models for variable-speed centrifugal chillers. ASHRAE Transactions, 93, 1794-1813.

Brasz, J., (2010). 2010 A proposed centrifugal refrigeration compressor rating method, ICEC at Purdue.

Braun, J. E. (1988). Methodologies for the Design and Control of Central Cooling Plants: PhD Thesis, University of Wisconsin-Madison.

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Bendapudi, S., Braun, J. E., & Groll, E. A. (2005). Paper # 4754 Dynamic model of a centrifugal chiller system-model development, numerical study, and validation. ASHRAE Transactions 111(1), 132-148.

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Hiller, C.C. and L. Glicksman. (1977). Heat pump improvement using compressor flow modulation. ASHRAE Transactions, 83(2).

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Popovic, P., & Shapiro, H. N. (1998). Paper#4190. A modeling study of a centrifugal compressor. ASHRAE Transactions, 104(2), 121-135.

Qureshi, O.A. (2013), Optimal Control of District Cooling System with Variable Speed Plant & Distribution. MSME MSc Thesis MIST, Abu Dhabi UAE.

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Van Houte, U., & Van den Bulck, E. (1994). Modeling chiller performance using simultaneous equation-solving procedures. International Journal of Refrigeration, 17(3), 191-198.

Vera-Garcia, F., J. Garcia-Cascales, J. Gonzalvez-Macia, R. Cabello, R. Llopis, D. Sanchez & E. Torrella (2010). A simplified model for shell-and-tubes heat exchangers: Practical application. Applied Thermal Engineering, 30(10), 1231-1241.

Wang, S.-w., J. Wang, and J. Burnett (2000). Mechanistic model of centrifugal chillers for HVAC system dynamics simulation. Building Services Engineering Research and Technology, 21(2), 73-83.

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O.A. Qureshi,

Student Member ASHRAE

H.Javed,

Affiliate Member ASHRAE

A. Afshari, PhD

P.R. Armstrong, PhD

Member ASHRAE

All authors are from the Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates.

Table 1. Isentropic efficiency model: coefficients
and their estimated uncertainties.

Coefficient    Bi-cubic Full Form      Truncated Form

               VALUE        t-value    VALUE        t-value

p00            0.703300     111.05     0.703200     110.70
p10            0.053210     896.46     0.051610     866.92
p01            0.036230     11.57      0.036780     11.71
p20            -0.007780    -21.45     -0.008460    -23.23
p11            -0.000470    -0.98      0.000880     1.83
p02            -0.001220    -5.53      -0.001370    -6.16
p30            -0.000740    -2.02      0.001134     3.15
p21            0.003240     4.84       -0.001680    -2.50
p12            -0.003120    -6.04      --           --
p03            0.000149     1.05       --           --

               R-square: 0.981;        R-square: 0.9804;
               RMSE: 0.01125           RMSE: 0.01140

Table 2. Annual energy use in MWh and savings as
percentage of base case energy use

                                Compressor           Cooling Tower

                            Energy    (Saving)    Energy     (Saving)
                              MWh        (%)        MWh        (%)

Case 1: Base Case (Normal   3385.0       (-)       139.9       (-)
  Plant Operation)
Case 2: Vspd CT fan         3239.6     (4.29%)     131.5     (5.98%)
Case 3: Vspd CW Pump and    3279.1     (3.13%)     141.3     (-0.99%)
  CT fan
Case 4: Vspd Compressor,    2832.4    (16.32%)     156.4    (-11.77%)
  CW Pump and CT fan

                                 Pumping                Total

                            Energy    (Saving)    Energy    (Saving)
                              MWh        (%)        MWh        (%)

Case 1: Base Case (Normal   261.12       (-)      3786.0       (-)
  Plant Operation)
Case 2: Vspd CT fan         261.12     (0.00%)    3632.3     (4.06%)
Case 3: Vspd CW Pump and    183.08    (29.89%)    3603.5     (4.82%)
  CT fan
Case 4: Vspd Compressor,    200.02    (23.40%)    3188.8    (15.77%)
  CW Pump and CT fan
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Author:Qureshi, O.A.; Javed, H.; Afshari, A.; Armstrong, P.R.
Publication:ASHRAE Transactions
Article Type:Report
Date:Jul 1, 2014
Words:3863
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