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Verification of a VRF heat pump computer model in EnergyPlus.

INTRODUCTION

The motivation of this study was to verify the EnergyPlus VRF heat pump computer model using manufacturer's performance data. The US building sector energy consumption amount to 41% of the total primary energy use (US Department of Energy 2010). Availability of a nonproprietary building energy simulation tool is crucial in transforming the building energy sector into a sustainable industry. The Department of Energy (DOE) has been providing funding for maintaining and developing computer models for emerging HVAC technologies. Variable refrigerant flow (VRF) systems fall under the emerging technologies category (Geotzler at al. 2004; Geotzler 2007; Afify 2008). The VRF HVAC technologies are modular design, split, direct-expansion (DX) systems with multiple indoor units of various configuration connected to up to three outdoor units in a single refrigerant piping circuit. The refrigerant flow is controlled using a variable-speed compressor driven by a variable-frequency inverter or a combination of variable- and constant-speed compressors, and an electronic expansion valve installed for each indoor unit. VRF technologies have become attractive due to their high efficiency at part-load operation, capability of providing cooling and heating simultaneously when run in heat-recovery mode, and individual indoor unit control (Geotzler at al. 2004; Aynur et al. 2009; Aynur 2010; Li and Wu 2010).

Although VRF systems have been available in the market for more than two decades (Dyer 2006), VRF modeling capabilities in nonproprietary building and energy simulation tools have been lagging (Geotzler 2007). Researchers in China and Japan have developed a VRF heat pump system model and incorporated it into unofficial version of the EnergyPlus engine (Zhou et al. 2007, 2008; Li and Wu 2010; Li et al. 2010). A VRF heat pump computer model has been implemented in EnergyPlus and was first released in Version 7.0 in December, 2011 (US Department of Energy).

The objective of this paper is to verify the equation-fit EnergyPlus VRF heat pump model predicted system capacity and electric power against that of published manufacturer's performance data at full- and part-load operation over a wide range of indoor and outdoor air conditions. This paper describes the model, presents verification methodology, and discusses the results.

VRF-SYSTEM MODEL

The EnergyPlus VRF heat pump model is a semi-empirical steady-state model represented by several equation-fit performance curves of the indoor and outdoor coils generated from manufacturer's performance data. The indoor and outdoor coil entering air temperatures and part-load ratio (PLR) are the independent variables of the model; for each combination of indoor and outdoor coil entering air temperatures and PLR, these performance curves modify the rated performance values, which are user inputs to the model. These independent (1) variables may vary for heating and cooling modes of operation. The VRF-system model illustrated in Figure 1 describes the indoor and outdoor coils inputs and outputs relationships.

Indoor Coil Model

The indoor coil model is an extension of the DX coil model that exists in EnergyPlus (Raustad 2013). The indoor coil capacity at various indoor and outdoor air temperatures is determined using the rated capacity and capacity-modifying biquadratic or cubic curves for temperature and a cubic or quadratic capacity modifying curve for Flow Fraction (2). The general formulation of the equations used to predict the cooling and heating capacities of an indoor coil is given by:

[Q.sub.Full,j] = [Q.sub.Rated] x [CAPFT.sub.ID,j]([T.sub.ID], [T.sub.OD]) x [CAPFF.sub.ID,j](EF) (1)

[Q.sub.L,j] = [Q.sub.Full,j] x [PLR.sub.j] (2)

[PLR.sub.j] = MIN(1.0, [Q.sub.L,j]/[Q.sub.Full,j]) (3)

[FIGURE 1 OMITTED]

The load met by the system is the sum of the capacity delivered by each of the indoor coils connected to a single outdoor unit and is limited by the maximum available system or outdoor unit capacity.

[Q.sub.L] = [summation over j] [Q.sub.L,j] (4)

Outdoor Unit Model

The outdoor unit component model is simply the VRF-system model and predicts the system capacity and electric power. The independent variables of the outdoor unit model are the average of the indoor coil entering air temperature, and outdoor coil entering air temperature. Depending on the Combination Ratio, (3) the available capacity of all indoor coils connected to a single outdoor unit may exceed the system or outdoor unit capacity. Thus the delivered system capacity at a given system PLR and design Combination Ratio is limited using a capacity operating ratio (CAPOR) curve generated from manufacturer's performance data. The capacity operating ratio is the capacity correction factor when the system is overloaded. The system capacity using the outdoor coil model is given by:

[Q.sub.Full] = [Q.sub.Rated] x [CAPFT.sub.OD] ([[bar.T].sub.ID], [T.sub.OD]) (5)

[Q.sub.Actual] = [Q.sub.Full] x [PLR.sub.sys] (6)

[PLR.sub.sys] = [Q.sub.L]/[Q.sub.Full] (7)

CAPOR = CAPFPLR ([PLR.sub.sys]) (8)

[PLR.sub.sys] = MIN ([PLR.sub.sys], CAPOR) (9)

The VRF-system electric power includes the compressor power, the outdoor coil fan power, and associated parasitic electric power. The system heating or cooling electric power is given by Equation 11.

[P.sub.Full] = ([Q.sub.Rated]/[COP.sub.Rated]). (10)

[CAPFT.sub.OD] ([[bar.T].sub.ID], [T.sub.OD]) x [EIRFT.sub.OD] ([[bar.T].sub.ID], [T.sub.OD]) (10)

[P.sub.Actual] = [P.sub.Full] x PFPLR([PLR.sub.sys]) x RTF (11)

MANUFACTURER'S DATA

The first step in model verification is generation of performance curves or performance tables that represent the manufacturer's data over its entire operation range as accurately as possible. VRF manufacturers commonly publish performance data that allows establishing the following functional relationships: (1) full-load capacity and electric power as a function of indoor and outdoor coil entering air temperatures as independent variables and (2) the system capacity and electric power as a function of PLR up to 1.0 and exceeding when the system is overloaded and the combination ratio is greater than 1.0. The system capacity and electric power modifier curves for temperature and PLR are equation fitted to dual curves, one for low and one for high operating ranges (Raustad 2012). A cubic boundary temperature curve fitted to average indoor coil entering air temperature allows us to discern the operating point of the dual range CAPFT and EIRFT curves. For this model verification, publicly available, normalized graphical performance data is used. The various performance curves required by the EnergyPlus VRF-system model and the coefficients of the curves generated using generalized least-squares regression technique are presented in tabular form in the Appendix. The rated performance parameters of the model used for this verification are provided in Table 1.

VERIFICATION METHODOLOGY

This paper provides verification results of the system capacity and system electric power; the verification compares predicted capacity and electric power against that of manufacturer's performance data at full- and part-load conditions. The comparison was made between the EnergyPlus VRF model output, digitized manufacturer's performance data, and spreadsheet calculations. The EnergyPlus Output is the capacity and electric power report variables of the EnergyPlus VRF heat pump model at full-load condition (4) normalized using Equations 12 and 13 for various combinations of indoor and outdoor coil entering air temperatures.

[bar.Q] = [Q.sub.Full]/[Q.sub.Rated] (12)

[bar.P] = [P.sub.Full]/[P.sub.Rated] (13)

Furthermore, the EnergyPlus outputs were also checked against spreadsheet calculations for code verification. The system-normalized capacity and electric power for the spreadsheet calculation at full load were determined by rearranging Equations 5 and 10 for the same set of indoor and outdoor coil entering air temperatures as EnergyPlus outputs and are given by Equations 14 and 15:

[bar.Q] = [CAPFT.sub.OD] ([[bar.T].sub.ID], [T.sub.OD]) (14)

[bar.P] = [CAPFT.sub.OD] ([[bar.T].sub.ID], [T.sub.OD]) x [EIRFT.sub.OD] ([[bar.T].sub.ID], [T.sub.OD]) (15)

The CAPFT, energy input ratio (EIR), and Boundary TFT curves-input temperatures that correspond to the EnergyPlus output were exported for use in the spreadsheet calculation. The spreadsheet calculation is solely meant for the source-code verification. The VRF heat pump model code was debugged and corrected line-by-line until the EnergyPlus output and the spreadsheet calculation matched exactly. Thus, the EnergyPlus model output is expected to be accurate within the margin of error of the curve fit performance curves. The margin of error for the capacity and electric power biquadratic curves is provided in Table A1 and Table A2 in the Appendix.

To verify the part-load performance of the model, the system capacity, and electric power at any given indoor and outdoor coil entering air temperatures, PLR, and RTF of 1.0, were determined using Equations 16 and 17, respectively, and compared with that of manufacturer's performance data.

[Q.sub.Actual] = [Q.sub.Rated] x [CAPFT.sub.OD]([[bar.T].sub.ID], [T.sub.OD]) x [PLR.sub.sys] (16)

[P.sub.Actual] = [P.sub.Rated] x [CAPFT.sub.OD] ([[bar.T].sub.ID], [T.sub.OD]). (17)

[EIRFT.sub.OD] ([[bar.T].sub.ID], [T.sub.OD]) x PFPLR([PLR.sub.sys])

BUILDING AND TEST CONDITIONS

The VRF heat pump model performance was evaluated in a lightweight, single-story, commercial building with five conditioned zones and a plenum zone. The building has four perimeter zones and one interior zone. Each zone is served by a single, indoor terminal unit and has its own thermostat. The building description, construction, thermostat settings, internal gain, and infiltration levels are given in Table 2, Table 3, and Table 4, respectively. The model was simulated using Chicago TMY3 weather in heating season and Miami TMY3 weather in cooling season. Besides the internal gains given in Table 3, various levels of heating and cooling plug loads were used such that the system operates above the minimum operating PLR for the different thermostat setpoints examined under the wide range of heating and cooling outdoor conditions.

RESULTS AND DISCUSSION

The VRF heat pump computer model results are presented for heating-only and cooling-only operation modes. In full load, the verification compared the predicted normalized system capacity and electric power to that of a manufacturer's data for a set of constant indoor coil entering air temperature and a range of outdoor conditions. In part-load operation the verification compared the predicted system capacity and electric power of the model to that of manufacturer data at different part-load ratio for a set of constant indoor and outdoor coil entering air temperature pairs. A zone thermostat controller maintains the indoor air temperature at the desired test condition.

Heating Full-Load Performance

Figure 2 shows the results for the heating mode system normalized heating capacity of the EnergyPlus output and the corresponding manufacturer data for a set of constant indoor coil entering air average dry-bulb temperature and outdoor air wet-bulb temperature. The energy plus output shows good match to the manufacturer data. Since the VRF heat pump model is tested within the range of the validity of the performance curves, the model accuracy is bound by the margin of errors of the system-normalized heating-capacity performance curves given in Table A1 in the appendix. The normalized heating capacity curves over and under prediction error margins were 0.98% and-0.94%, respectively.

Figure 3 shows the results for the heating mode EnergyPlus output and the manufacturers data normalized heating electric power for a wide range of outdoor air wet-bulb temperature and a set of constant indoor coil entering air average dry-bulb temperatures. The full-load predicted normalized heating electric power closely matches the manufacturer data and is bound by the margin of errors of the heating electric power equation-fit performance curves given in Table A1. The predicted normalized heating electric power prediction error margins were 3.97% and -3.41%. The predicted, normalized electric power is the product of the capacity (CAPFT) and EIR (EIRFT) modifying curves; hence, the prediction error is proportional to the CAPFT and EIRFT biquadratic curves error. The relatively higher deviation in the predicted heating electric power is attributed to the high error in EIR curve.

Heating Part-Load Performance

Figure 4 and Figure 5 show the results for the heating capacities delivered and electric power, respectively, as a function of PLR for a set of constant indoor and outdoor coil entering air temperatures pair. The system heating capacities plot labeled as "Rated" is determined using Equation 6 with CAPFT and EIRFT values set to 1.0 and matches the manufacturer data exactly for the entire range of PLR. The predicted heating capacity at 21.1[degrees]C (70.0[degrees]F) indoor air dry-bulb and 6.1[degrees]C (43.0[degrees]F) outdoor air wet-bulb temperatures pair, which is the rated test condition, is slightly off from the manufacturer's rated capacity trend due to inherent errors associated with regression techniques. In this case, the maximum percent error observed for heating capacity is -0.90% and it is within the CAPFT biquadratic curve equation-fit prediction error margin provided in Table A1 in the appendix. For similar reason, the predicted heating electric power at 21.1[degrees]C (70.0[degrees]F) dry-bulb and 6.1[degrees]C (43.0[degrees]F) wet-bulb temperature pair deviates from the rated value by as high as -2.90% and it is within the electric power prediction error margins of 3.97% and -3.41%. The system performance for the off-rated operating conditions follows the trend of the rated system performance but is offset by a factor depending on the coil entering air temperatures. This factor is constant for a given indoor and outdoor coil entering air temperatures pair, hence the predicted capacity and electric power for each temperature pair strictly follows the rated performance trend for the entire PLR range. One of the distinct features of a VRF-system built-in control algorithm is the ability to modulate capacity by varying the expansion valve opening and the compressor speed depending on the indoor and outdoor air conditions. The capacity and electric power draw labeled 26.7[degrees]C DB/15.0[degrees]C WB in Figure 4 and Figure 5, respectively, depicts such phenomena for a range of part-load operating condition.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Cooling Full-Load Performance

In cooling-mode simulation it is almost impossible to maintain the indoor coil entering air wet-bulb temperature constant under varying indoor and outdoor conditions. However, attempts have been made to limit the variation of the indoor coil entering air wet-bulb temperature using different techniques. The range of variations of indoor coil entering air average wet-bulb temperatures during the full-load cooling-mode simulation are shown in Table 5. For cooling-mode verification, output results that are near or at the desired indoor wet-bulb temperatures only were mined from several simulation run results.

Figure 6 shows the results for cooling-mode predicted normalized cooling capacity and the corresponding manufacturer data at full-load condition. It can be inferred from these results that the EnergyPlus VRF model full-load cooling capacity prediction is in good agreement with manufacturer's performance data. The EnergyPlus output in cooling-only operating mode is expected to be bound by the error margins of system-normalized, cooling-capacity performance curves given in Table A2, except for the variability of the indoor coil entering air average wet-bulb temperature. The normalized cooling capacity biquadratic curve prediction error margins were 1.10% and-1.34%.

Figure 7 shows the results of cooling mode predicted normalized electric power and the corresponding manufacturer data at full load. The cooling electric power performance curves over- and underprediction error margins were 0.87% and -0.85%, respectively. It can be deduced that the EnergyPlus VRF heat pump model represents the full-load cooling electric power manufacturer's performance data very well and deviations observed were within the margin of error of the equation-fit performance curves.

Cooling Part-Load Performance

Figure 8 and Figure 9 show the results for cooling mode predicted and the manufacturer's cooling capacity and electric power over a wide range of part-load ratios at rated and off-rated conditions for a set of constant indoor and outdoor coil entering air temperature pairs. The rated cooling capacities plot labeled as "Rated" at various PLR is calculated with CAPFT curve set to 1.0, per Equation 16, and hence it is a perfect match with that of the manufacturer data for the entire range. The predicted cooling capacity for nominal coil entering temperature pairs of 19.4[degrees]C/35.0[degrees]C (67.0[degrees]F/95.0[degrees]F), which is the rated condition for cooling mode, shows a good match to the manufacturer data over the entire PLR range. However, in cooling mode, unlike heating the nominal indoor coil entering air average wet-bulb temperature, could not be maintained constant; instead it varied in the range from 19.21[degrees]C (66.6[degrees]F) to 20.47[degrees]C (68.9[degrees]F) with a mean value of 19.61[degrees]C (67.3[degrees]F) as shown in Table 6. As the result of this indoor coil entering air wet-bulb temperature variation, the predicted cooling capacities were not aligned as well as in the heating-only mode verification; the predicted cooling capacities deviation compared to the manufacturer data ranges from 0.15% to 3.87% with a mean value of 1.34%. This deviation is not within the cooling CAPFT biquadratic curve over- and underprediction error margins of 1.10%, and -1.34%, respectively. The main reason is that the EnergyPlus output and the manufacturer data were not compared at exactly the same indoor coil entering air wet-bulb temperature due to the variability of the latter. Correcting the predicted cooling capacity to the rated coil entering air temperature of 19.4[degrees]C/35.0[degrees]C (67.0[degrees]F/95.0[degrees]F) brings down the prediction error in the range 0.64%-0.72% with a mean value of 0.70%, which is within the CAPFT curve error margin given in Table A2. The cooling capacities at off-rated conditions follow the performance trend of the rated condition over the entire PLR range and they are off-set from the rated value by a factor of the cooling capacity modifying curve value. The value of this cooling capacity modifier (CAPFT) curve at off-rated condition depends on the indoor coil entering air average wet-bulb temperature and the latter has been slightly varying as explained earlier; as the result of this variation, the predicted cooling capacity showed slight scattering.

Figure 9 shows the results for predicted cooling electric power for a set of constant indoor and outdoor coil entering air temperatures pairs and various PLR. Similar to the predicted cooling capacities plots, the cooling electric power at off-rated condition did not align perfectly to that of the rated condition. Again, this problem was due to variation of indoor coil entering air average wet-bulb temperature. For similar reason, the predicted cooling electric power nominal coil entering temperature pair of 19.4[degrees]C/35.0[degrees]C (67.0[degrees]F/95.0[degrees]F), which is the rated condition, deviates from the rated values in the range from 0.59% to 1.85% with a mean deviation of 1.01%; hence the latter is outside the over- and underprediction error margins of 0.87% and -0.85%, respectively, provided in Table A2. Correcting the predicted cooling electric power from the nominal indoor coil entering air condition to the rated test condition using the CAPFT and EIRFT modifying curve brings down the prediction error in the range 0.73%-0.79% with a mean value of 0.78% which is within the margin of error of the electric power prediction. Had the indoor coil entering conditions been constant, the predicted values at the off-rated condition would have been aligned perfectly to the manufacturer's rated performance trend.

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

CONCLUSION

Verification of the EnergyPlus VRF heat pump model in cooling-only and heating-only modes of operation has been presented. The VRF heat pump computer model is an equation fit model based on curves generated from manufacturer's performance data. These curves modify the user input rated capacity and electric power for off-rated operation performance prediction. In addition to the biquadratic curves for temperature correction, the indoor coil model uses a cubic or quadratic curve for flow fraction. The VRF-system model, which is based on the outdoor coil performance, uses dual range CAPFT biquadratic capacity modifier curves for temperature, dual range CAPFT and EIRFT biquadratic electric power modifier curves for temperature, and dual range PFPLR cubic or quadratic electric power modifier curves for part-load ratio. The EnergyPlus VRF heat pump computer model performance verification results can be summarized as follows:

* The heating capacity is predicted within the maximum prediction error limits of -0.94% and 0.98%. The heating electric power is predicted within the prediction error margins of -3.31% and 3.97%. The heating performance was investigated for an indoor condition range of 15[degrees]C to 27[degrees]C (59[degrees]F to 80.6[degrees]F) dry-bulb temperature and an outdoor condition range of -20[degrees]C to 15[degrees]C (-4.0[degrees]F to 59[degrees]F) wet-bulb temperature.

* The cooling capacity is predicted within the maximum prediction error limits of -1.34% and 1.10%. The cooling electric power is predicted within the under- and over-prediction error margins of -0.85% and 0.87%, respectively. The cooling performance was investigated for an indoor condition range of 16[degrees]C to 24[degrees]C (60.8[degrees]F to 75.2[degrees]F) wet-bulb temperature and an outdoor condition range of -4[degrees]C to 43[degrees]C (24.8[degrees]F to 109.4[degrees]F) dry-bulb temperature.

* The VRF-system part-load performance also shows good match to the manufacturer's data as depicted in Figure 4 and Figure 5 for heating, and Figure 8 and Figure 9 for cooling.

In general, the VRF heat pump computer model can predict the capacity and electric power of the manufacturer's performance data within the accuracy limits of the capacity and electric power modifying biquadratic curves; hence the EnergyPlus VRF model is as good as the accuracy of the various equation-fit performance curves generated from the manufacturer's performance data. The verification results, therefore, demonstrate that the VRF system can be represented with a black box type model, and can predict with an accuracy range similar to packaged and split system HVAC computer models that are commonly found in energy simulation programs.

NOMENCLATURE

CAPFF = quadratic or cubic capacity modifying curve as a function of flow fraction, (--)

CAPFT = biquadratic or cubic capacity modifying curve as a function of temperature, (--)

CAPOR = the system capacity operating ratio, (--)

CAPFPLR = system capacity modifying curve as a function of PLR, (--)

COP = heating or cooling coefficient of performance, (--)

EIRFT = biquadratic EIR modifying curves as a function of temperature, (--)

FF = ratio of actual to rated air mass flow rate through an indoor coil, (--)

MIN = function that returns the smaller of the two arguments

PFPLR = electric power modifying curve as a function of PLR, (--)

PLR = heating or cooling part-load ratio, (--)

RTF = system runtime fraction, (--)

P = system heating or cooling electric power, (W)

Q = heating or cooling load delivered or capacity, (W)

[bar.Q] = normalized full-load system heating or cooling capacity delivered, (--)

[bar.P] = normalized full-load system heating or cooling electric power, (--)

T = coil entering air dry-bulb or wet-bulb temperature, ([degrees]C, [degrees]F)

[bar.T] = average of indoor coil entering air dry-bulb or wet-bulb temperature, ([degrees]C, [degrees]F)

V = supply air volume flow rate, ([m.sup.3]/s, cfm)

m = supply air mass flow rate, (kg/s, lbm/h)

N = number of indoor coils connected to a single outdoor unit, (--)

Subscripts

ID = indoor coil or indoor coil entering air condition

OD = outdoor coil or outdoor air condition

j = the [j.sup.th] indoor coil

Rated = rated test condition

Full = full-load capacity of an indoor coil or outdoor unit

Actual = actual load or electric power at a given PLR and coil entering temperatures

L = heating or cooling load delivered by cooling or heating coil

Sys = the VRF system or outdoor unit

p = predicted data point

M = manufacturers data point

DB = dry-bulb temperature

WB = wet-bulb temperature

APPENDIX

The various performance curves used in the EnergyPlus VRF model verification were generated from publicly available manufacturer's performance data map. These performance curves were generated using generalized least-squares regression techniques and the coefficients are provided in tabular formats. The statistical error parameters that describe the accuracy of the equation-fit performance curves prediction of the manufacturer's performance data are described as follows. The root-mean-squared error (RMSE) of performance variable [Y.sup.5] is calculated as follows:

RMSE = [square root of ([summation over k][([Y.sub.P] - [Y.sub.M]).sup.2.sub.k]/[summation over k]1)] (18)

The mean percent error (MPE) of a performance variable Y is determined as follows:

MPE = [1/[summation over k]1] [summation over k][([Y.sub.P] - [Y.sub.M]/[Y.sub.M]).sub.k] (19)

The RMSE and MPE of the normalized capacity and normalized energy input ratio curves prediction in heating and cooling modes of operation are given in Table A1 and Table A2, respectively.

The various performance curves used in the model are defined in brief next. The VRF system or outdoor unit performance is represented using load weighted average of indoor coil entering air wet bulb or dry bulb temperature. The average indoor coil entering air dry bulb or wet bulb temperature is calculated as follows:

[[bar.T].sub.ID] = [summation over k][T.sub.ID,j] x [Q.sub.L,j]/[summation over k][Q.sub.L,j] (20)

The CAPFT and EIRFT performance are represented by dual range curves. The quadratic or cubic boundary temperature curve that separates the low and high temperature operating ranges as function of the average indoor coil entering air temperatures is given by Equation 24.

Boundary TFT = [a.sub.1] + [a.sub.2] x [[bar.T].sub.ID] + [a.sub.3] * [[bar.T].sup.2.sub.ID] + [a.sub.4] * [[bar.T].sup.3.sub.ID] (21)

The normalized heating and cooling capacity data points for indoor and outdoor coils as a function of indoor and outdoor coil entering air temperatures are determined from Equation 25:

CAPFT = Q([T.sub.ID], [T.sub.OD])/[Q.sub.Rated] (22)

The normalized capacity biquadratic curves for an indoor coil and an outdoor coil as a function of temperatures are given by

[CAPFT.sub.ID] = [a.sub.1] + [a.sub.2] x [T.sub.ID] + [a.sub.3] x [T.sup.2.sub.ID] + [a.sub.4] x [T.sub.OD] + [a.sub.5] + [T.sup.2.sub.OD] + [a.sub.6] x [T.sub.ID] x [T.sub.OD] (23)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

The indoor coil capacity modifier as a function of mass flow fraction (CAPFF) is determined from the ratio of the capacity at a given mass flow rate and the capacity at the rated mass flow rate all determined at the rated indoor and outdoor temperatures and is given by:

CAPFF = Q([m.sub.actual])/[Q.sub.rated] (25)

The capacity modifying quadratic or cubic curve as a function of mass flow fraction (CAPFF) is given by:

CAPFF = [a.sub.1] + [a.sub.2] x FF + [a.sub.3] x [FF.sup.2] + [a.sub.4] x [FF.sup.3] (26)

The normalized energy input ratio (EIR) of the system as a function of temperature is defined as follows:

[EIRFT.sub.OD] = [P([[bar.T].sub.ID], [T.sub.OD])/[P.sub.rated]]/[Q([[bar.T].sub.ID], [T.sub.OD])/[Q.sub.rated]] (27)

The normalized energy input ratio biquadratic curve as a function of average indoor coil entering air temperature and outdoor coil entering air temperature (EIRFT) is given by:

[EIRFT.sub.OD] = [a.sub.1] + [a.sub.2] x [[bar.T].sub.ID] + [a.sub.3] x [[bar.T]..sup.2.sub.ID] + [a.sub.4] x [T.sub.OD] + [a.sub.5] x [[bar.T].sup.2.sub.OD] + [a.sub.6] x [[bar.T].sub.ID] x [[bar.T].sub.OD] (28)

The VRF system or outdoor unit electric power modifying performance curve as a function of part-load ratio (PFPLR) is defined as follows:

PFPLR = [P([PLR.sub.sys])/[P.sub.rated]] (29)

The electric power modifying quadratic or cubic curve as a function of part-load ratio is given by:

PFPLR = [a.sub.1] + [a.sub.2] x [PLR.sub.sys] + [a.sub.3] x [PLR.sub.Sys] + [a.sub.4] x [PLR.sup.3.sub.sys] (30)

Coefficients of the various performance curves of the VRF system used in this model verification are given in Table A3 to Table A7.
Table A1. Error of Normalized Heating Capacity, EIR and Electric
Power Curves

Parameter           Maximum          Maximum        MPE, %      RMSE
                Underprediction   Overprediction
                   Error, %          Error, %

Normalized           -0.94             0.98        -0.00059   0.003865
  Capacity
Normalized           -3.59             3.88        0.00590    0.015816
  EIR
Normalized           -3.41             3.97        0.00644    0.014566
  Power
Number of                                                        70
  data points

Table A2. Error of Normalized Cooling Capacity, EIR and Electric
Power Curves

Parameter           Maximum          Maximum       MPE, %     RMSE
                Underprediction   Overprediction
                   Error, %          Error, %

Normalized           -1.34             1.10        0.0018   0.002863
  Capacity
Normalized           -1.67             1.60        0.0003   0.006017
  EIR
Normalized           -0.85             0.87        0.0005   0.003028
  Power
Number of                                                      78
  data points

Table A3. Normalized System Heating Capacity and EIR as a Function
of Temperature

Biquadratic curves: CAPFT and EIRFT

CurveValue = [a.sub.1] + [a.sub.2] x [X.sub.1] + [a.sub.3] x
[X.sup.2.sub.1] + [a.sub.4] x [X.sub.2] + [a.sub.5] x [X.sup.2.sub.2]
+ [a.sub.6] x [X.sub.1] x [X.sub.2]

Operation       Coefficients         CAPFT               EIRFT
Mode

                 [a.sub.1]       1.0135124245         0.904731281
                 [a.sub.2]       -0.0024806523       -0.015842414
                 [a.sub.3]       -0.0001391084        0.001161224
Heating Low      [a.sub.4]       0.0268121406        -0.013278606
  Temperature    [a.sub.5]       0.0000024790         0.000875833
  Range          [a.sub.6]       -0.0003501383       -0.000128018
                 [R.sub.2]          0.9999              0.9969
                 [a.sub.1]       1.1689057116        0.9047312805
                 [a.sub.2]       0.0264062374        -0.0158424143
                 [a.sub.3]       -0.0016559645       0.0011612241
                 [a.sub.4]       0.0019214090        -0.0132786064
Heating High     [a.sub.5]       0.0000043803        0.0008758335
  Temperature    [a.sub.6]       -0.0000752045       -0.0001280178
  Range          [R.sub.2]          0.9994              0.9975
                 [X.sub.1]     [[bar.T].sub.ID],   [[bar.T].sub.ID],
                                      DB                  DB
                 [X.sub.2]      [T.sub.OD], WB      [T.sub.OD], WB

Table A4. Normalized System Cooling Capacity and EIR as
a Function of Temperature

Biquadratic curves: CAPFT and EIRFT CurveValue = [a.sup.1] +
[a.sup.2] * [X.sub.1] + [a.sup.3] * [X.sup.1.sub.2] +[a.sup.4] *
[X.sub.2] + [a.sup.5] * [X.sup.2.sub.2] + [a.sup.6] *
[X.sub.1] * [X.sub.2]

Operation Mode   Coefficients          CAPFT

                  [a.sub.1]         0.5639351498
                  [a.sub.2]         0.0192294354
                  [a.sub.3]         0.0005320223
Cooling Low       [a.sub.4]         0.0000034026
Temperature       [a.sub.5]        -0.0000001439
Range             [a.sub.6]        -0.0000001261
                  [R.sup.2]            0.9999
                  [a.sub.1]         0.6573824973
                  [a.sub.2]         0.0245369112
                  [a.sub.3]         0.0004441080
                  [a.sub.4]        -0.0018018536
Cooling High      [a.sub.5]         0.0000023363
Temperature       [a.sub.6]        -0.0003433687
Range             [R.sup.2]            0.9991
                  [X.sub.1]     [[bar.T].sub.ID], DB
                  [X.sub.2]        [T.sub.OD], WB

Operation Mode          EIRFT

                     0.9698394689
                    -0.0214090898
                     0.0001446160
Cooling Low          0.0055987679
Temperature          0.0000004999
Range               -0.0001376554
                        0.9986
                     0.1807447089
                     0.0161024978
                    -0.0003378681
                     0.0239640178
Cooling High         0.0001754871
Temperature         -0.0006169919
Range                   0.9985
                 [[bar.T].sub.ID], DB
                    [T.sub.OD], WB

Table A5. Boundary Temperature Curves as a Function of
Indoor Coil Entering Air Temperature

Cubic or quadratic curves: BoundaryTFT

CurveValue = [a.sub.1] + [a.sub.2] * [X.sub.1] + [a.sub.3]
* [X.sup.1.sub.2] + [a.sub.4] * [X.sup.3.sub.1]

Operation Mode   Coefficients       BoundaryTFT

                  [a.sub.1]         25.73473775
                  [a.sub.2]         -0.03150043
Cooling           [a.sub.3]         -0.01416595
                  [a.sub.4]              0
                  [X.sub.1]     [[bar.T].sub.ID], WB
                  [R.sup.2]            1.0000
                  [a.sub.1]         -6.631900953
                  [a.sub.2]         2.905991692
Heating           [a.sub.3]         -0.109267888
                  [a.sub.4]         -0.000110430
                  [X.sub.1]     [[bar.T].sub.ID], DB
                  [R.sup.2]            1.0000

Table A6. Electric Power Modifier Curve as a
Function Part-Load Ratio

Cubic or quadratic curves: PFPLR or EIRFPLR

CurveValue = [a.sub.1] + [a.sub.2] * [X.sub.1] + [a.sub.3] *
[X.sup.2.sub.1] + [a.sub.4] * [X.sup.3.sub.1]

Operation Mode   Coefficients   PFPLR (PLR [less   PFPLR (PLR > 1.0)
                                 than or equal
                                    to] 1.0)

                  [a.sub.1]        0.4628123              1.0
                  [a.sub.2]        -1.0402406             0.0
Cooling           [a.sub.3]        2.1749100              0.0
                  [a.sub.4]        -0.5974817              0
                  [X.sub.1]           PLR                 PLR
                  [R.sup.2]          1.0000             1.0000
                  [a.sub.1]        0.1400093           2.4294355
                  [a.sub.2]        0.6415002          -2.2358870
Heating           [a.sub.3]        0.1339047           0.8064516
                  [a.sub.4]        0.0845859               0
                  [X.sub.1]           PLR                 PLR
                  [R.sup.2]          1.0000             1.0000

Table 7. Capacity Operating Ratio Curve as a Function
Part-Load Ratio

Cubic or quadratic curves: CAPFPLR

CurveValue = [a.sub.1] + [a.sub.2] x [X.sub.1] + [a.sub.3]
x [X.sup.2.sub.1] + [a.sub.4] x [X.sup.3.sub.1]

Operation   Coefficients      CAPFPLR        CAPFPLR
Mode                        (PLR [less     (PLR > 1.0)
                           than or equal
                             to] 1.0)

Cooling      [a.sub.1]          1.0         0.618055
             [a.sub.2]          0.0         0.381945
             [a.sub.3]          0.0            0.0
             [a.sub.4]          0.0            0.0
             [X.sub.1]          PLR            PLR
             [R.sup.2]        1.0000         1.0000

Heating      [a.sub.1]          1.0          0.96034
             [a.sub.2]          0.0          0.03966
             [a.sub.3]          0.0            0.0
             [a.sub.4]          0.0            0.0
             [X.sub.1]          PLR            PLR
             [R.sup.2]        1.0000         1.0000


ACKNOWLEDGMENTS

This material is based upon work supported by the Department of Energy under Award Numbers DE EE0003848.

Disclaimer: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

REFERENCES

Afify, R. 2008. Designing of VRF system. ASHRAE Journal 50(6):52-5.

Aynur, T.N., Y. Hwang, and R. Radermacher. 2009. Simulation comparison of VAV and VRF air conditioning systems in an existing building for the cooling season. Energy and Buildings 41:1143-50.

Aynur, T.N. 2010. Variable refrigerant flow systems: A review. Energy and Buildings 42:1106-12.

Dyer, Mark. June 2006. Approaching 20 years of VRF in the UK. Modern Building Services. http://www.modbs.co.uk/news/fullstory.php/aid/2127/ Approaching_20_years_of_VRF_in_the_UK.html.

Goetzler, W., K.W. Roth, and J. Brodrick. 2004. Variable Flow and Volume Refrigerant System. ASHRAE Journal 46(1):164-5.

Goetzler, W. 2007. Variable refrigerant flow system. ASHRAE Journal 49(4):24-31.

Li, Y.M., and J.Y. Wu. 2010. Energy simulation and analysis of the heat recovery variable refrigerant flow system in winter. Energy and Buildings 42:1093-1099.

Li, Y.M., J.Y. Wu, and S. Shiochi. 2010. Experimental validation of the simulation module of the water-cooled variable refrigerant flow system under cooling operation. Applied Energy 87:1513-1521.

Raustad, R. 2012. Creating performance curves for variable refrigerant flow heat pumps in EnergyPlus. Report: FSEC-CR-1910-12. Florida Solar Energy Center. March, 2012.

Raustad, R. 2013. A variable refrigerant flow heat pump computer model in EnergyPlus. ASHRAE Transactions 119(1):299-308.

USA Mitsubishi Electric Corporation (MEC). 2009. R2-Series, City Multi Outdoor Units.

US Department of Energy. 2010. Buildings Energy Data Book, Chapter 1: Buildings Sector. Washington, DC: U.S. Department of Energy. http://buildingsdatabook.eren.doe.gov/ChapterIntro1.aspx?1.

US Department of Energy. 2011. EnergyPlus Engineering Reference--The Reference to EnergyPlus Calculations, Version 7.0. Washington, DC: U. S. Department of Energy.

Zhou, Y.P., J.Y. Wu, R.Z. Wang, and S. Shiochi. 2007. Energy simulation in the variable refrigerant flow air-conditioning system under cooling conditions. Energy and Buildings 39:212-220.

Zhou, Y.P., J.Y. Wu, R.Z. Wang, S. Shiochi, and Y.M. Li. 2008. Simulation and experimental validation of the variable-refrigerant-volume (VRV) air-conditioning system in EnergyPlus. Energy and Buildings 40:1041-1047.

(1.) For heating, the independent variables are the indoor coil entering air dry-bulb temperature and the outdoor coil entering air wet-bulb or dry-bulb temperature depending users choice. For cooling, the independent variables are indoor coil entering air wet-bulb temperature and the outdoor coil entering outdoor air dry-bulb temperature. The system or outdoor coil model uses the average of all interconnected indoor coil entering air temperature.

(2.) Flow Fraction is the ratio of actual supply air mass flow rate to the rated supply air mass flow rate through an indoor coil.

(3.) Combination Ratio is the ratio of the sum of the design capacities of the all indoor coils connected to a single outdoor unit to the design capacity of the outdoor coil.

(4.) Full-load condition refers to the condition when the VRF system is operating at full capacity, i.e., when the PLR and RTF are 1.0 for any given indoor and outdoor coil entering air temperatures.

(5.) Performance variable Y can be either of the normalized capacity (CAPFT), normalized energy input ratio (EIRFT) and normalized electric power (CAPFT times EIRFT).

Bereket Nigusse, PhD

Associate Member ASHRAE

Richard Raustad

Bereket Nigusse is a research engineer and Richard Raustad is a senior research engineer at the Florida Solar Energy Center, University of Central Florida, Cocoa, Florida.
Table 1. System-Rated Performance Data of a VRF Heat
Pump Model

System Parameters                        Description

Rated heating capacity, kW (kBtu/hr)    35.20 (120.0)
Rated heating COP, --(BtuW-hr)          3.55 (12.11)
Rated cooling capacity, W (kBtu/hr)     31.7 (108.0)
Rated cooling COP, --(Btu/W-hr)         3.25 (11.09)

Table 2. Building Design Information

Items or Components                        Description

Test Weather                       TMY3: Chicago, Illinois, and
                                           Miami, Florida
Conditioned                    463.6 [m.sup.2] (4990.1 [ft.sup.2])
  Floor Area
Windows:        Area            60.9 [m.sup.2] (655.5 [ft.sup.2])
                Glazing type       double pane clear glass with
                                    air gap conductance 2.72 W/
                                     [m.sup.2] x K (15.45 Btu/
                                   [ft.sup.2] x hr x [degrees]F),
                                            SHGC = 0.764
Zones                                 Six zones: 1 plenum, 4
                                     perimeters and 1 interior
                                               zone.
Thermostat      Heating           15[degrees]C, 21.1[degrees]C,
  Set Points:                      25[degrees]C, and 27[degrees]C
                                    (59[degrees]F, 70[degrees]F,
                                         77[degrees]F, and
                                          80.6[degrees]F)
                Cooling            16[degrees]C, 18[degrees]C,
                                   20[degrees]C, 22[degrees]C and
                                   24[degrees]C (60.8[degrees]F,
                                   64.4[degrees]F, 68[degrees]F,
                                        and 75.2[degrees]F)
Outdoor         Heating           -20[degrees]C to 15[degrees]C
  Condition:                       (-4[degrees]F to 59[degrees]F)
                Cooling            -4[degrees]C to 43[degrees]C
                                         (24.8[degrees]F to
                                          109.4[degrees]F)

Table 3. Levels of Internal Heat Gains

Zones      Floor Area,     People (#)     Lighting,
            [m.sup.2]                    W/[m.sup.2]
          ([ft.sup.2])                  (W/[ft.sup.2])

Zone 1   99.16 (1067.5)        11        16.15 (1.5)
Zone 2    42.73 (459.9)        5
Zone 3   96.48 (1038.5)        11
Zone 4    42.73 (459.9)        5
Zone 5   182.49 (1964.3)       60

Zones      Electric        Infiltration,
           Equipment     [m.sup.3]/s (cfm)
         (W/[m.sup.2])

Zone 1    10.76 (1.0)    0.016700 (35.39)
Zone 2                   0.007170 (15.19)
Zone 3                   0.016700 (35.39)
Zone 4                   0.007170 (15.19)
Zone 5                   0.031089 (65.87)

Table 4. Construction Thermophysical Properties

Layers               Thickness      Conductivity W/m x K
(outer to inner)      mm (in)          (Btu x in/hr x
                                       [ft.sup.2] F)

Roof

RG01                12.7 (0.50)         1.442 (10.0)
BR01                 9.5 (0.40)         0.162 (1.10)
IN46                76.2 (3.00)         0.023 (0.20)
WD01                19.1 (0.75)         0.115 (0.80)

Ceiling

CP01, R = 0.6523 [m.sup.2] x K/W (R = 3.704 hr x [ft.sup.2] x F/Btu)

External Wall

WD01                19.1 (0.75)         0.115 (0.80)
PW03                12.7 (0.50)         0.115 (0.80)
IN02                90.1 (3.55)         0.043 (0.30)

GP01                12.7 (0.50)         0.160 (1.10)

Internal Wall

GP02                0.0159 (0.63)       0.160 (1.10)

Air Gap, R = 0.157 [m.sup.2] x KW (R = 0.89 hr
  x [ft.sup.2] x F/Btu)

GP01                0.0159 (0.63)       0.160 (1.10)

Floor

CC03                0.1016 (4.0)        1.310 (9.10)
CP02, R = 0.367 [m.sup.2] x K/W (R = 2.08 hr x [ft.sup.2] x F/Btu)

Layers             Density kg/[m.sup.3]      Specific heat
(outer to inner)       ([lb.sub.m]/            kJ/kg x K
                       [ft.sup.3])        (Btu/[lb.sub.m] x F)

Roof

RG01                   881.0 (55.0)           1.674 (0.40)
BR01                  1121.0 (70.0)           1.464 (0.35)
IN46                     24.0 (1.5)           1.590 (0.38)
WD01                   513.0 (32.0)           1.381 (0.33)

Ceiling

CP01, R = 0.6523 [m.sup.2] x K/W (R = 3.704 hr x [ft.sup.2] x F/Btu)

External Wall

WD01                   513.0 (32.0)           1.381 (0.33)
PW03                   545.0 (34.0)           1.213 (0.29)
IN02                    10.0 (0.60)           0.837 (0.20)

GP01                   801.0 (50.0)           0.837 (0.20)

Internal Wall

GP02                   801.0 (50.0)           0.837 (0.20)

Air Gap, R = 0.157 [m.sup.2] x KW (R = 0.89 hr
  x [ft.sup.2] x F/Btu)

GP01                   801.0 (50.0)           0.837 (0.20)

Floor

CC03                  2243.0 (140.0)          0.837 (0.20)
CP02, R = 0.367 [m.sup.2] x K/W (R = 2.08 hr x [ft.sup.2] x F/Btu)

Table 5. Variations of Indoor Coil Entering Air Wet-Bulb
Temperature at Full Load

Nominal [[bar.T].sub.ID], WB,          Minimum,
[degrees]C ([degrees]F)'        [degrees]C ([degrees]F)

16.0 (60.8)                          15.98 (60.76)
18.0 (64.4)                          17.98 (64.36)
20.0 (68.0)                          19.95 (67.91)
22.0 (71.6)                          21.95 (71.51)
24.0 (75.2)                          23.95 (75.11)

Nominal [[bar.T].sub.ID], WB,          Maximum,
[degrees]C ([degrees]F)'        [degrees]C ([degrees]F)

16.0 (60.8)                          16.03 (64.85)
18.0 (64.4)                          18.03 (64.45)
20.0 (68.0)                          20.02 (68.04)
22.0 (71.6)                          22.03 (71.65)
24.0 (75.2)                          24.03 (75.25)

Nominal [[bar.T].sub.ID], WB,          Average,
[degrees]C ([degrees]F)'        [degrees]C ([degrees]F)

16.0 (60.8)                          16.01 (60.82)
18.0 (64.4)                          18.00 (64.04)
20.0 (68.0)                          20.00 (68.00)
22.0 (71.6)                          22.00 (71.60)
24.0 (75.2)                          24.00 (75.20)

Table 6. Variations of Indoor Coil Entering Air
Wet-Bulb Temperature at Part Load

Nominal [[bar.T].sub.ID,WB]/          Minimum,
[T.sub.OD,DB], [degrees]C      [degrees]C ([degrees]F)
([degrees]F)

19.4/35.0 (67.0/95.0)          19.21/35.0 (66.6/95.0)
24.0/35.0 (75.2/95.0)          23.38/35.0 (74.1/95.0)
19.4/43.0 (67.0/109.4)         19.07/43.0 (66.3/109.4)
24.0/43.0 (75.2/109.4)         23.68/43.0 (74.6/109.4)

Nominal [[bar.T].sub.ID,WB]/          Maximum,
[T.sub.OD,DB], [degrees]C      [degrees]C ([degrees]F)
([degrees]F)

19.4/35.0 (67.0/95.0)          20.47/35.0 (68.9/95.0)
24.0/35.0 (75.2/95.0)          24.89/35.0 (76.8/95.0)
19.4/43.0 (67.0/109.4)         20.63/43.0 (69.1/109.4)
24.0/43.0 (75.2/109.4)         25.21/43.0 (77.4/109.4)

Nominal [[bar.T].sub.ID,WB]/          Average,
[T.sub.OD,DB], [degrees]C      [degrees]C ([degrees]F)
([degrees]F)

19.4/35.0 (67.0/95.0)          19.61/35.0 (67.3/95.0)
24.0/35.0 (75.2/95.0)          23.96/35.0 (75.1/95.0)
19.4/43.0 (67.0/109.4)         19.62/43.0 (67.3/109.4)
24.0/43.0 (75.2/109.4)         24.45/43.0 (76.0/109.4)
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Date:Jul 1, 2013
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