# Heat gain from power panelboards.

This paper is based on findings resulting from ASHRAE Research
Project RP-1395.

INTRODUCTION

The main goal of this paper is to create a model to predict heat gain from power panelboards for three phase balanced loads and 60 Hz so that HVAC equipment in industrial plants and buildings can be sized accordingly. McDonald and Hickok (1985) reported power losses for lighting panelboards but did not report any data for power panelboards. Rubin (1979) reported the same power losses for lighting and power panelboards based on the number of single pole circuit breakers as shown in Table 1.

In this paper, a panelboard classification is presented and a general description and construction details are given for those panelboard components that lead to environmental heat gain. The loss model of the power panelboard is based on the sum of partial power losses from circuit breakers, fusible switches, motor starters, and bus bars with enclosures. Information obtained from measurements, manufacturer literature, and published papers is used to create the power loss models of the electrical equipment that are used in power panelboards. Most of the component power loss data were reported in RP-1395 (White and Piesciorovsky 2010). In this study, the majority of power loss information was collected from manufacturer literature and electrical equipment designed from Underwriters Laboratories (UL) standards. The list and characteristics for all panelboard components are shown in Table 2.

A power panelboard heat gain example is presented for three phase balanced loads and 60 Hz. A hand and spreadsheet calculation is developed to estimate the heat gain rate for part loads. Although the results obtained from these two methods are the same, the spreadsheet is provided for convenience of use in repetitive calculations. In the example, the estimated heat gain rate is compared with results from Rubin (1979), showing that the presented power loss model has important advantages. The creation of the power panelboard loss model allows HVAC designers to predict heat gain rates in buildings and industrial plants, providing the correct HVAC sizing.

PANELBOARD CLASSIFICATION

The National Electrical Code (NEC) defines a panelboard as a "single panel or group of panel units designed for assembly in the form of a single panel, including buses, automatic overcurrent devices, and equipped with or without switches for the control of light, heat, or power circuits; designed to be placed in a cabinet or cutout box placed in or against a wall, partition, or other support; and accessible only from the front" (NEC 2008).

Panelboards are classified, according to their applications, as lighting or power panelboards. Lighting panelboards are used only in light control applications while power panel-boards are used not only in light but also in control heat or power circuits (motor applications). This paper concentrates on predicting heat gain rates from power panelboards that have current ratings higher than the lighting panelboards.

PARTIAL LOSSES FROM ELECTRICAL EQUIPMENT IN POWER PANELBOARDS

Circuit Breakers

The circuit breakers used in power panelboards have three-poles and are called molded case circuit breakers (MCCB). In power panelboard applications, these breakers are rated from 15 to 1200 amps at 600 VAC. MCCBs are designed and built according to UL 489-1996. In this paper, power loss data from thermal magnetic trip MCCBs were collected from manufacturer literature and measurements and compared with published information. The power loss model of MCCBs was based on collected measurements performed during RP-1395. A comparison of the tested MCCB power losses scaled to rated load with power loss data reported by McDonald and Hickok (1985) and two manufacturers is shown in Figure 1.

In Figure 1, the measured power losses were fitted with a linear regression curve that describes the power losses of the MCCBs at rated load. The curve fit [is

[p.sub.r] = 0.2658 [I.sub.br] (1)

where [I.sub.br] is the frame size or rated current of the breaker in amps and [P.sub.br] is the three phase breaker power loss at rated current in watts or Btu/h after multiplying Equation 1 by 3.412. On the other hand, the power loss of a breaker at any load is given by

[p.sub.breaker loss] = [((lf x I)/br).sup.2] x [p.sub.br] = [(lf x I).sup.2] x (0.2658/[I.subg.br]) (2)

where I is the breaker phase current in amps, lf is the load factor, [P.sub.breaker loss] is the breaker power loss in watts.

[FIGURE 1 OMITTED]

The load factor is the ratio of the average current, [I.sub.AVE], and the maximum current, [I.sub.H], flowing through the breaker. The load usually will vary in a cyclic manner during a period of time. The current flowing through the breaker is averaged so that over the same time span the average current adds the same amount of heat to the environment. The load factor, lf, is defined by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the product of lf and [I.sub.H] is the RMS current.

Low Voltage Fuses

Low-voltage fuses used in power panelboards are rated up to 600 VAC. Low voltage fuse power loss information was obtained from manufacturer literature for RK1 and J class fuses that are used widely in power panelboards in the United States. The J class fuses are rated from 15 to 600 amps and the RK1 class fuses are rated from 70 to 600 amps. According to Bene (1994), both classes of fuses have time delay characteristics to protect motor and transformers and non-delay (fast acting) characteristics to protect branch and feeder circuits. Table 3 shows the characteristics and applications of the RK1 and J class fuses.

RK1 and J class fuse power losses at rated current were collected from one manufacturer. Figure 2 shows the collected data for the RK1 and J fuses and the regression analysis that was performed on each fuse class. The power loss model for RK1 class fuses at rated load is

[p.pk1] = -4 x [10.sup.-5] x [I.sub.fr.sup.2] + 0.0160 x [I.sub.fr] (4)

and the power loss model for J class fuses at rated load is

[p.sub.J] = -10 x [I.sub.fr.sup.2] + 0.165 x [I.sub.fr] (5)

where [I.sub.fr] is the fuse current rating in amps, [P.sub.pki] is the power loss in watts for RK1 class fuses, and PJ is the power loss in watts for J class fuses. Note that Equations 4 and 5 provide the power loss at rated fuse current. The fuse power loss for part loads is given by

[p.sub.fuse loss] = [(if x I/[I.sub.fr]).sup.2] x [P.sub.fr] (6)

where [P.sub.fr] is provided by Equations 4 or 5 depending on the fuse class, I is the given current in amps, lf is the load factor of the load protected by the fuse, and [p.sub.fuse loss] is the fuse power loss in watts.

Low-Voltage Fusible Switches

Low-voltage fusible switches used in power panelboards are formed by a three-pole disconnect switch and three low-voltage fuses. The switch works as a disconnecting device and the fuses work as a protection device. The low-voltage switches are rated up to 600 VAC (UL 98-2004) and 690 VAC (IEC 60947-3-2008). The switches are always used with fuses that protect the main elements of the circuit such as cables, heaters, transformers, motors, and lighting from overloads and short circuits. In order to develop a model for these switches that are rated from 16 to 630 amps, data on power losses at rated load and balanced three phase operation were collected from three manufacturers. Figure 3 shows the collected data and the regression curve that was performed on the switches. The power loss model for low-voltage switches at rated load is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [I.sub.sr] is the rated switch current in amps and [p.sub.sr] is the three phase switch power loss at rated current in watts. The switch power loss at a given current is determined by

[p.sub.switch loss] = [(lf x I/[I.sub.sr]).sup.2] x [p.sub.sr] (8)

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

where [P.sub.switch loss] is the low-voltage switch power loss in watts (Btu/h), I is the given phase current flowing through the switch in amps, [I.sub.sr] is the switch current rating in amps, [P.sub.sr] is determined by Equation 7, and lf is the load factor applied to the load connected to the switch. Because each of the three phases of the switch are connected in series with a fuse, the power loss of the fusible-switch is

[P.sub.fusible switch loss] = [P.sub. switch loss] + 3 x [P.sub.fusible loss] (9)

where [P.sub.fusible switch loss] is the fusible-switch power loss in watts (Btu/h). Equation 9 is valid at balanced three phase loads and 60 Hz.

A comparison of Equation 9 using RK1 and J fuses is made with measured data collected from an online loss calculator found at http://pps2.com/b1/ndb/. The power loss calculator was developed by a manufacturer based on laboratory measurements made by the manufacturer. The power losses of the fusible switches are estimated using Equation 9 and with the constraint that the switches and fuses have the same current ratings. Figure 4 shows a comparison of the RK1 and J fusible switch power loss results from Equation 9 with the data from the calculator.

Engineers sometimes have to decide between breakers or fusible switches. Figure 4 shows the comparison of the power loss at rated current for breakers and switches with RK1 and J class fuses. For the same frame size-amps or current rating, the fusible switches dissipate higher losses than breakers.

Motor Starters

The NEMA motor starter has the functions of motor control together with overload and short circuit protection. An overload is caused by a non-normal operation of the motor requiring large torque that can produce a high current flowing through the starter circuit. The short circuit is caused by an electric circuit that allows a high current to travel along a path different from the original motor circuit. These protection functions are provided by a relay for the overloads and a circuit breaker or fusible switch for the short circuits. The motor starter's circuit has a contactor with auxiliary contacts which can control the motor remotely using on and off push buttons. Figure 5 shows the circuit and elements of a full volt-age non-reversing (FVNR) motor starter with a fusible switch.

In the FVNR motor starter circuit, fuses are selected by a rule of thumb: the fuse rating is 1.25 times the current rating of the motor. This paper is focused on FVNR motor starters with fusible switches that can control up to 30 hp motors at 240 VAC and up to 50 hp motors at 480 VAC. The power loss measurements of motor starters reported in RP-1104 (White and Pahwa 2003) are used in this work. In RP-1104, measured power losses of the NEMA 0, 1, 2, and 3 FVNR motor starters were collected at different loads. The power losses of the contactor coil in Figure 5 were measured separately. From the starter power losses that were collected in those experiments, the regression curve of each device was performed and shown in Figures 6 and 7.

The power loss models of FVNR motor starters in RP-1104 did not include fuses. The recommendation is to add the appropriate fuse power loss to those presented in Figures 6 and 7. Because a fuse is placed in series with each phase and each motor starter circuit has three phases, the fuse power losses are three times that of a single fuse. The power loss model for motor starters is

[[P.sub.starter loss] = A + b + [I.sup.2] + 3 x [[P.sub.starter loss] (10)

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

where A is the constant in watts, B is the constant in [watts/amp.sup.2], I is the given starter phase current in amps, and [[P.sub.starter loss]is the power loss of the motor starter in watts. The coil loss is represented by the constant A. Table 4 shows the current rating, maximum horsepower, and values of the constants A and B for NEMA starter sizes from 0 to 3. In Equation 10, fuses are usually selected according to the motor load.

[FIGURE 8 OMITTED]

In order to compare the motor starter power loss models with data from other sources, the power loss was calculated with Equation 10 where the power loss of the fuse was calculated using Equation 6 and J class fuses were sized at 1.25 times the current rating of Table 4. The estimated power losses were compared with McDonald and Hickok (1985) and manufacturer literature in Figure 8. The NEMA 0 motor starter is not compared because data is not reported in the cited paper or the manufacturer literature for a starter of this size. From Figure 8, it is evident that there the manufacturer literature is a better match of the model than McDonald and Hickok (1985). Note, in the cited paper, it was not specified whether the reported starter power losses corresponded to FVNR or full voltage reversing (FVR) starters and whether a fusible switch or breaker was used. Also, the manufacturer literature did not specify if a fusible switch or breaker was used.

Enclosure and Bus Bars

The bus bar power losses in panelboards are produced by electric and electromagnetic power loss effects. The electromagnetic effects usually increase the electrical resistance of the conductor. The enclosure power loss is produced by the stray loss effect when magnetic fields induce current flow in surrounding metallic parts. The bus bar power loss mechanisms consist of the ohmic, skin, and proximity effects. In power panelboards the enclosure is formed by a metallic box made of galvanized steel and the bus bar is made of either copper or aluminum. The bus bars form a three phase main circuit which distributes loads to all circuits that are connected along the bus bars. Each circuit consists of a fusible switch, breaker or motor starter connected to a load. Figure 9 shows the configuration of the enclosure-bus bar power loss construction which is based on information collected from one manufacturer.

[FIGURE 9 OMITTED]

The dimensions of enclosures and bus bars depend on the power panelboard current ratings and the number of disconnecting devices installed (feeder capacity) in the power panel-board. Copper bus bar dimensions for ratings at 250, 400, 600, 800, and 1200 amps were selected from UL 67-1993, and enclosure dimensions were chosen from manufacturer literature. The power loss model of the enclosure-bus bar is based on analytical methods, materials, and dimensions that were reported in the panelboard section of RP-1395 where power loss of the enclosure was estimated by using Del Vecchio (2003) while the power loss of the bus bars was estimated by using White and Piesciorovsky (2009).

The enclosure-bus bar power losses at rated loads are defined as the sum of the watts dissipated by the AC resistance and the stray loss in the enclosure which is expressed as

[P.sub.ebr] = [P.sub.e] + [P.sub.b] (11)

where [P.sub.e] and [P.sub.b] are the enclosure and three phase bus bar power losses at rated loads in watts/m (Btu/h/ft). By using Equation 11, data from RP-1395 were compiled for the enclosure-bus bar model. The compiled data are shown in Table 5. The enclosure-bus bar power losses at rated loads shown in the last column of Table 5 were fitted with the polynomial

[P.sub.ebr] = 0.00004 x [I.sub.bbr.sup.2] + 0.839 x [I.sub.bbr] (12)

[FIGURE 10 OMITTED]

where [I.sub.bbr] is the bus bar rating in amps and [P.sub.ebr] is the enclosure-bus bar power loss at rated loads in watts/m or Btu/h/ft after multiplying Equation 12 by 1.0399. The data of the last column of Table 5 and Equation 12 are shown in Figure 10.

During this study, no enclosure-bus bar power loss measurements were made or found in manufacturer or technical literature. However, as the enclosure-bus bar consists of three bus bars inside of a rectangular metallic enclosure, the power loss model could be considered similar to a 600 VAC busway. As a check on the reasonableness of the presented results, the 600 VAC copper armor-clad busway power losses reported by McDonald & Hickok (1985) were compared with the enclosure-bus bar power loss calculations for rated loads. This information is also shown in Figure 10. Caution must be exercised when comparing these results since the 600 VAC copper busway and panelboard enclosure-bus bar have some design differences, such as panelboard enclosures are greater than busway enclosures. The enclosure-bus bar power loss for a panelboard at a given load is

[P .sub.enc bus loss] = [((lf x I)[I.sub.bbr]).sup.2] x H [p.sub.ebr] = [(lf x I).sup.2] H (0.00004 + 0.0839 x [I.sub.bbr.sup.-1]) (13)

where I is the load current flowing through a single bus bar in amps, H is the bus bar length in meters, lf is the load factor applied to the main bus and [P .sub.enc bus loss] is the enclosurebusbar power loss of the panelboard in watts. Calculation of lf for the main bus will be explained in the following section. Equation 13 is valid at balanced three phase loads and 60 Hz.

PANELBOARD POWER LOSS MODEL

Power Loss Model of Panelboard and Load Factor of Main Bus (lf)

Figure 11 shows a schematic diagram of a power panel-board where there is a main bus or branch that feeds the secondary branches that consist of circuit breakers, fusible-switches, and motor starters. The main branch has power losses from the main disconnecting device (breaker or fusible switch) and enclosure-bus bar losses, while the secondary branches have the breakers, fusible switches, and motor starter power losses.

By inspection of Figure 11, the current of the main branch is given by the sum of all currents from the secondary branches. So, the main branch current, I in amps, is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [I.sub.c] is the secondary branch device load in amps and p is the number of secondary branch devices. Because each secondary branch has its own load factor, the load factor for the main branch needs to be determined. The main branch load factor is chosen to satisfy

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where lf is the main branch load factor, I is the main branch current, and [lf.sub.c] is the load factor of the [c.sup.th] secondary branch. Based on Equation 15, the main branch load factor is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the main branch current, I, is giben by Equation 14.

The panelboard power loss model is the sum of all the partial power losses of each panelboard component. The dissipated power is determined by summing the losses of the main and secondary branches. The panelboard power loss model is given by

[FIGURE 11 OMITTED]

Panelboard.sub.power loss] = Main [Breaker.sub.loss] + Enclosure Bus [Bar.sub.loss] + [Breakers.sub.loss] + Fusible [Switches.sub.loss] + NEMA FVNR Motor [Starters.sub.loss] (17)

By substituting for the partial power loss models of electrical equipment in power panelboard previously described

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the symbols are defined in Table 6.

Power panelboards can use breakers or fusible switches as main disconnecting devices. An alternative loss model of the power panelboard having a fusible switch as the main disconnecting device is also presented. The main fusible switch panelboard loss model is given by Equation 17. But in this case, the first term of Equation 17 is replaced by

[Main Fusible Switch.sub.loss] = [{lf x I}.sup.2] x {0.0003 + 0.0839 x [I.sub.sr.sup.-1]} + (3 x [p.sub.fr] x [I.sub.fr.sup.-2]) (18)

where Main Fusible [Switch.sub.loss] is the power loss of the main fusible switch in watts, [I.sub.sr] is the main switch current rating in amps, [I.sub.fr] is the main fuse current rating in amps, and [P.sub.fr] is the fuse power loss at rated load in watts given by Equations 4 or 5. The power panelboard loss model is valid under the conditions that are shown in Table 7.

To estimate the heat gain from power panelboards, the loss models of the panelboard with main breaker and given by Equation 17 and the panelboard with main fusible switch given by Equation 18 were used in a Visual Basic program that was linked to a spreadsheet. Figure 12 shows this spreadsheet that will be used in the heat gain example to be presented.

Heat Gain Example

A power panelboard with a circuit breaker as the main disconnecting device will be installed in a room and its dissipated power loss has to be estimated to size the HVAC equipment. The line-line voltage is 240 VAC and the current rating of the panel-board is 1200 amps. The power panelboard will operate with balanced three phase loads and 60 Hz. In Table 8, the loads and electrical equipment installed in the front view of the power panelboard are shown. The panelboard has a main breaker that feeds the secondary branch devices which consist of five breakers, three fusible switches, and three FVNR motor starters.

The approach taken for estimating the heat loss rate is to (1) calculate the FVNR motor starter and main branch load currents, (2) determine the load factor of the main branch, and (3) compute the breaker, fusible switch, motor starter, and total power losses.

1. Load Currents

The FVNR motor starter load currents are calculated from

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

where I is the motor starter load in amps, [P.sub.hp] is the motor power in horse-power, [eta] is the motor efficiency in percent, [V .sub.line] is the motor line to line voltage in volts, and pf is the motor power factor. Equation 18 was developed in White et al. (2004). The FVNR motor starter load currents designated as [I.sub.1], [I.sub.2], and [I.sub.3] are determined in Table 9.

The main branch load current, I in amps, is found using Equation 14. The main branch load current is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

2. Load Factor

The load factor of the main branch, lf, is determined by Equation 16 and the data shown in Table 8. The calculated value is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

3. Component and Total Losses

The partial power losses are obtained from the main breaker panelboard loss model given by Equation 17. Table 10 shows the power loss of each panelboard component and the total in watts.

The estimated heat gain rate from the power panelboard is 350 watts. The same result can be found using the spread-sheet of Figure 12. In the example, the power loss of the panel-board can be estimated using a hand or spreadsheet calculation, obtaining similar results. The use of the spreadsheet is recommended instead of the hand calculation because a great number of components are used in power panelboard.

Using the power loss model based on equation (17), the estimated power loss is 350 watts (1197 Btu/h). For the same example, using Table 1 reported by Rubin (1979), the estimated power loss of a panelboard with 12 three pole devices (36 single pole devices) is 450 watts (1539 Btu/h). The estimation from Rubin (1979) is 28% greater than the results obtained with the model presented in this paper. It should be appreciated that the difference between the results presented here and that of Rubin is a function of load. Rubin did not account for part loads.

CONCLUSION

This paper provides information on the heat loss rate at full and part-loads for electrical equipment used in power panelboards. Power loss models at full and part-loads for circuit breakers, fusible switches, motor starters, and bus bars with enclosures are developed based on measurements, manufacturer literature, and published papers. It was shown that the fusible switches dissipate more heat than breakers of the same size ratings. This means breakers are more energy efficient than fusible switches.

The power panelboard loss model at part-load presented in this paper was based on the sum of partial power losses of each panelboard component. A heat gain example at part load was presented showing that the power losses can be predicted. The loss model of the power panelboard at part-load, equation (17), can predict losses more accurately than Rubin (1979), who presented little loss information, did not define all device power losses, and did not consider part loads. A hand or spreadsheet calculation can be used to estimate the heat gain rate of a power panelboard. The use of the spreadsheet is recommended over the hand calculation because power panel-boards can have a large number of electrical devices and the hand calculation could be tedious.

In order to size HVAC equipment in industrial plants and building, realistic heat gain rates from power panel-board can be predicted. This power loss model, equation (17), will be a useful tool for HVAC designers who have to estimate the environmental heat gain rate contributed by power panelboards.

ACKNOWLEDGMENTS

The authors would like to thank the American Society of Heating Refrigeration and Air Conditioning Engineers (ASHRAE) for funding this work, especially TC 9.2 Industrial Air Conditioning and TC 9.1 Large Building Air Conditioning Systems.

REFERENCES

Bene, J. 1994. Specifying 600 volt current-limiting fuses: Applications 600 Amperes or Less. IEEE Transactions on Industry Applications 30(6):1449-55.

Del Vecchio, Robert M. 2003. Eddy-current losses in a con-ducting plate due to a collection of bus bars carrying currents of different magnitudes and phases. IEEE Transactions on Magnetics 39(1):549-52.

IEC 60947-3-2008. 2008. Low-voltage switchgear and controlgear, Part 3: Switches, disconnectors, switch disconnectors, and fuse-combination units, Third ed. International Electrotechnical Commission.

McDonald, William. J., and Herbert N. Hickok. 1985. Energy losses in electrical power systems. IEEE Trans-actions on Industry Applications IA-21(3):803-19.

NEC. 2008, National Electrical Code ANSI/NFPA70. National Fire Protection Association, Quincy, MA, 2007.

NEMA ICS 2-2000. 2000. Industrial control and systems controllers, contactors, and overload relays rated 600 volts. National Electrical Manufacturers Association.

Rubin, I.M. 1979. Heat losses from electrical equipment in generating stations. IEEE Transactions on Power Apparatus and Systems PAS-98(4):1149-52.

UL 67-1993. 1993. Standard for panelboards. Underwriters Laboratories, Eleventh Edition.

UL 98-2004. 2004. Enclosed and dead-front switches. Underwriters Laboratories, Thirteenth Edition.

UL 248-8-2000. 2000. Low-voltage fuses-Part 8: Class J fuses. Underwriters Laboratories, Second Edition.

UL 248-12-2000. 2000. Low-voltage fuses-Part 12: Class R fuses. Underwriters Laboratories, Second Edition.

UL 489-1996. 1996. Molded-case circuit breakers, molded-case switches, and circuit breaker enclosures. Under-writers Laboratories, Ninth Edition.

White, Warren N., and Anil Pahwa. 2003. Heat gain from electrical and control equipment in industrial plants, Part I. ASHRAE Research Project 1104-TRP, American Society of Heating Refrigeration and Air Conditioning Engineers.

White, Warren N., Anil Pahwa, and Chris Cruz. 2004. Heat loss from electrical and control equipment in industrial plants: Part II-Results and comparisons. ASHRAE Transactions 110(2):852-70.

White, Warren N., and Emilio C. Piesciorovsky. 2009. Building heat load contributions from medium and low voltage switchgear, Part I: Solid rectangular bus bar heat losses (RP-1395). ASHRAE Transactions 115(2):369-82.

White, Warren N., and Emilio C. Piesciorovsky. 2010. Heat gain from electrical and control equipment in industrial plants, Part II. ASHRAE Research Project RP-1395, American Society of Heating Refrigeration and Air Conditioning Engineers.

Emilio C. Piesciorovsky is a doctoral student in the Department of Electrical and Computer Engineering and Warren N. White is an associate professor in the Department of Mechanical and Nuclear Engineering, Kansas State University, Manhattan, KS.

INTRODUCTION

The main goal of this paper is to create a model to predict heat gain from power panelboards for three phase balanced loads and 60 Hz so that HVAC equipment in industrial plants and buildings can be sized accordingly. McDonald and Hickok (1985) reported power losses for lighting panelboards but did not report any data for power panelboards. Rubin (1979) reported the same power losses for lighting and power panelboards based on the number of single pole circuit breakers as shown in Table 1.

Table 1. Power and Lighting Panelboards Power Losses (Rubin 1979) Number of Single Pole Power Losses, Circuit Breakers W (Btu/h) 12 150 (512) 24 300 (1024) 36 450 (1535) 42 500 (1706)

In this paper, a panelboard classification is presented and a general description and construction details are given for those panelboard components that lead to environmental heat gain. The loss model of the power panelboard is based on the sum of partial power losses from circuit breakers, fusible switches, motor starters, and bus bars with enclosures. Information obtained from measurements, manufacturer literature, and published papers is used to create the power loss models of the electrical equipment that are used in power panelboards. Most of the component power loss data were reported in RP-1395 (White and Piesciorovsky 2010). In this study, the majority of power loss information was collected from manufacturer literature and electrical equipment designed from Underwriters Laboratories (UL) standards. The list and characteristics for all panelboard components are shown in Table 2.

Table 2. Electrical Equipment Used in Power Panelboard Molded Case Circuit Breakers (MCCBs) Switches Voltage rating: 600 VAC Voltage ratings: 600 or 690 vac Ampere rating: 15 to 1200 amps Ampere rating: 16 to 630 amps Thermal magnetic trip Three poles Three poles J Class-Fuse RK1 Class-Fuse Voltage rating: 600 VAC Voltage ratings: 250 or 600 VAC Ampere ratings:15 to 600 amps Ampere ratings: 70 to 600 amps Single pole Single pole Motor Starters Voltage ratings (Max. motor horsepower): 240 VAC (30 hp) and 480 VAC (50 hp) NEMA sizes: 0, 1, 2, and 3 Disconnecting device: Fusible switch Type: Full voltage non-reversing (FVNR) Enclosure Bus Bars Material: Galvanized steel sheet Material: Copper Thick: 1.74 mm (0.0685 in.) Conductivity: 98.9% IACS or 2.74 mm (0.1079 in.) Current density: 155 amps/[cm.sup.2] (1000 amps/[in.sup.2]) Ampere ratings: 250, 400, 600, 800, and 1200 amps

A power panelboard heat gain example is presented for three phase balanced loads and 60 Hz. A hand and spreadsheet calculation is developed to estimate the heat gain rate for part loads. Although the results obtained from these two methods are the same, the spreadsheet is provided for convenience of use in repetitive calculations. In the example, the estimated heat gain rate is compared with results from Rubin (1979), showing that the presented power loss model has important advantages. The creation of the power panelboard loss model allows HVAC designers to predict heat gain rates in buildings and industrial plants, providing the correct HVAC sizing.

PANELBOARD CLASSIFICATION

The National Electrical Code (NEC) defines a panelboard as a "single panel or group of panel units designed for assembly in the form of a single panel, including buses, automatic overcurrent devices, and equipped with or without switches for the control of light, heat, or power circuits; designed to be placed in a cabinet or cutout box placed in or against a wall, partition, or other support; and accessible only from the front" (NEC 2008).

Panelboards are classified, according to their applications, as lighting or power panelboards. Lighting panelboards are used only in light control applications while power panel-boards are used not only in light but also in control heat or power circuits (motor applications). This paper concentrates on predicting heat gain rates from power panelboards that have current ratings higher than the lighting panelboards.

PARTIAL LOSSES FROM ELECTRICAL EQUIPMENT IN POWER PANELBOARDS

Circuit Breakers

The circuit breakers used in power panelboards have three-poles and are called molded case circuit breakers (MCCB). In power panelboard applications, these breakers are rated from 15 to 1200 amps at 600 VAC. MCCBs are designed and built according to UL 489-1996. In this paper, power loss data from thermal magnetic trip MCCBs were collected from manufacturer literature and measurements and compared with published information. The power loss model of MCCBs was based on collected measurements performed during RP-1395. A comparison of the tested MCCB power losses scaled to rated load with power loss data reported by McDonald and Hickok (1985) and two manufacturers is shown in Figure 1.

In Figure 1, the measured power losses were fitted with a linear regression curve that describes the power losses of the MCCBs at rated load. The curve fit [is

[p.sub.r] = 0.2658 [I.sub.br] (1)

where [I.sub.br] is the frame size or rated current of the breaker in amps and [P.sub.br] is the three phase breaker power loss at rated current in watts or Btu/h after multiplying Equation 1 by 3.412. On the other hand, the power loss of a breaker at any load is given by

[p.sub.breaker loss] = [((lf x I)/br).sup.2] x [p.sub.br] = [(lf x I).sup.2] x (0.2658/[I.subg.br]) (2)

where I is the breaker phase current in amps, lf is the load factor, [P.sub.breaker loss] is the breaker power loss in watts.

[FIGURE 1 OMITTED]

The load factor is the ratio of the average current, [I.sub.AVE], and the maximum current, [I.sub.H], flowing through the breaker. The load usually will vary in a cyclic manner during a period of time. The current flowing through the breaker is averaged so that over the same time span the average current adds the same amount of heat to the environment. The load factor, lf, is defined by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the product of lf and [I.sub.H] is the RMS current.

Low Voltage Fuses

Low-voltage fuses used in power panelboards are rated up to 600 VAC. Low voltage fuse power loss information was obtained from manufacturer literature for RK1 and J class fuses that are used widely in power panelboards in the United States. The J class fuses are rated from 15 to 600 amps and the RK1 class fuses are rated from 70 to 600 amps. According to Bene (1994), both classes of fuses have time delay characteristics to protect motor and transformers and non-delay (fast acting) characteristics to protect branch and feeder circuits. Table 3 shows the characteristics and applications of the RK1 and J class fuses.

Table 3. Characteristics and Applications of RK1 and J Class Fuses UL Standard AC Characteristics Applications Fuse Voltage Class Ratings Time delay Motors and transformers RK1 UL 248-12-2000 250 or 600 volts Nondelay Branch and feeder circuits Time delay Motors and transformers J UL 248-8-2000 600 volts Nondelay Branch and feeder circuits

RK1 and J class fuse power losses at rated current were collected from one manufacturer. Figure 2 shows the collected data for the RK1 and J fuses and the regression analysis that was performed on each fuse class. The power loss model for RK1 class fuses at rated load is

[p.pk1] = -4 x [10.sup.-5] x [I.sub.fr.sup.2] + 0.0160 x [I.sub.fr] (4)

and the power loss model for J class fuses at rated load is

[p.sub.J] = -10 x [I.sub.fr.sup.2] + 0.165 x [I.sub.fr] (5)

where [I.sub.fr] is the fuse current rating in amps, [P.sub.pki] is the power loss in watts for RK1 class fuses, and PJ is the power loss in watts for J class fuses. Note that Equations 4 and 5 provide the power loss at rated fuse current. The fuse power loss for part loads is given by

[p.sub.fuse loss] = [(if x I/[I.sub.fr]).sup.2] x [P.sub.fr] (6)

where [P.sub.fr] is provided by Equations 4 or 5 depending on the fuse class, I is the given current in amps, lf is the load factor of the load protected by the fuse, and [p.sub.fuse loss] is the fuse power loss in watts.

Low-Voltage Fusible Switches

Low-voltage fusible switches used in power panelboards are formed by a three-pole disconnect switch and three low-voltage fuses. The switch works as a disconnecting device and the fuses work as a protection device. The low-voltage switches are rated up to 600 VAC (UL 98-2004) and 690 VAC (IEC 60947-3-2008). The switches are always used with fuses that protect the main elements of the circuit such as cables, heaters, transformers, motors, and lighting from overloads and short circuits. In order to develop a model for these switches that are rated from 16 to 630 amps, data on power losses at rated load and balanced three phase operation were collected from three manufacturers. Figure 3 shows the collected data and the regression curve that was performed on the switches. The power loss model for low-voltage switches at rated load is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [I.sub.sr] is the rated switch current in amps and [p.sub.sr] is the three phase switch power loss at rated current in watts. The switch power loss at a given current is determined by

[p.sub.switch loss] = [(lf x I/[I.sub.sr]).sup.2] x [p.sub.sr] (8)

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

where [P.sub.switch loss] is the low-voltage switch power loss in watts (Btu/h), I is the given phase current flowing through the switch in amps, [I.sub.sr] is the switch current rating in amps, [P.sub.sr] is determined by Equation 7, and lf is the load factor applied to the load connected to the switch. Because each of the three phases of the switch are connected in series with a fuse, the power loss of the fusible-switch is

[P.sub.fusible switch loss] = [P.sub. switch loss] + 3 x [P.sub.fusible loss] (9)

where [P.sub.fusible switch loss] is the fusible-switch power loss in watts (Btu/h). Equation 9 is valid at balanced three phase loads and 60 Hz.

A comparison of Equation 9 using RK1 and J fuses is made with measured data collected from an online loss calculator found at http://pps2.com/b1/ndb/. The power loss calculator was developed by a manufacturer based on laboratory measurements made by the manufacturer. The power losses of the fusible switches are estimated using Equation 9 and with the constraint that the switches and fuses have the same current ratings. Figure 4 shows a comparison of the RK1 and J fusible switch power loss results from Equation 9 with the data from the calculator.

Engineers sometimes have to decide between breakers or fusible switches. Figure 4 shows the comparison of the power loss at rated current for breakers and switches with RK1 and J class fuses. For the same frame size-amps or current rating, the fusible switches dissipate higher losses than breakers.

Motor Starters

The NEMA motor starter has the functions of motor control together with overload and short circuit protection. An overload is caused by a non-normal operation of the motor requiring large torque that can produce a high current flowing through the starter circuit. The short circuit is caused by an electric circuit that allows a high current to travel along a path different from the original motor circuit. These protection functions are provided by a relay for the overloads and a circuit breaker or fusible switch for the short circuits. The motor starter's circuit has a contactor with auxiliary contacts which can control the motor remotely using on and off push buttons. Figure 5 shows the circuit and elements of a full volt-age non-reversing (FVNR) motor starter with a fusible switch.

In the FVNR motor starter circuit, fuses are selected by a rule of thumb: the fuse rating is 1.25 times the current rating of the motor. This paper is focused on FVNR motor starters with fusible switches that can control up to 30 hp motors at 240 VAC and up to 50 hp motors at 480 VAC. The power loss measurements of motor starters reported in RP-1104 (White and Pahwa 2003) are used in this work. In RP-1104, measured power losses of the NEMA 0, 1, 2, and 3 FVNR motor starters were collected at different loads. The power losses of the contactor coil in Figure 5 were measured separately. From the starter power losses that were collected in those experiments, the regression curve of each device was performed and shown in Figures 6 and 7.

The power loss models of FVNR motor starters in RP-1104 did not include fuses. The recommendation is to add the appropriate fuse power loss to those presented in Figures 6 and 7. Because a fuse is placed in series with each phase and each motor starter circuit has three phases, the fuse power losses are three times that of a single fuse. The power loss model for motor starters is

[[P.sub.starter loss] = A + b + [I.sup.2] + 3 x [[P.sub.starter loss] (10)

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

where A is the constant in watts, B is the constant in [watts/amp.sup.2], I is the given starter phase current in amps, and [[P.sub.starter loss]is the power loss of the motor starter in watts. The coil loss is represented by the constant A. Table 4 shows the current rating, maximum horsepower, and values of the constants A and B for NEMA starter sizes from 0 to 3. In Equation 10, fuses are usually selected according to the motor load.

Table 4. NEMA Starter Loss Constants NEMA ICS 2-2000 Standard ASHRAE RP-1104 Maximum Horsepower Starter Current Constant Constant B, Size Rating A, W (Btu/h) W/am[p.sup.2] (Btu/h/am[p.sup.2]) 240 VAC 480 VAC 6 0.005 0 18 3 5 (20.472) (0.18766) 7 0.003 1 27 7 10 (23.884) (0.11259) 8.7 0.018 2 45 15 25 (29.684) (0.06142) 15.5 0.004 3 90 30 50 (52.886) (0.01501)

[FIGURE 8 OMITTED]

In order to compare the motor starter power loss models with data from other sources, the power loss was calculated with Equation 10 where the power loss of the fuse was calculated using Equation 6 and J class fuses were sized at 1.25 times the current rating of Table 4. The estimated power losses were compared with McDonald and Hickok (1985) and manufacturer literature in Figure 8. The NEMA 0 motor starter is not compared because data is not reported in the cited paper or the manufacturer literature for a starter of this size. From Figure 8, it is evident that there the manufacturer literature is a better match of the model than McDonald and Hickok (1985). Note, in the cited paper, it was not specified whether the reported starter power losses corresponded to FVNR or full voltage reversing (FVR) starters and whether a fusible switch or breaker was used. Also, the manufacturer literature did not specify if a fusible switch or breaker was used.

Enclosure and Bus Bars

The bus bar power losses in panelboards are produced by electric and electromagnetic power loss effects. The electromagnetic effects usually increase the electrical resistance of the conductor. The enclosure power loss is produced by the stray loss effect when magnetic fields induce current flow in surrounding metallic parts. The bus bar power loss mechanisms consist of the ohmic, skin, and proximity effects. In power panelboards the enclosure is formed by a metallic box made of galvanized steel and the bus bar is made of either copper or aluminum. The bus bars form a three phase main circuit which distributes loads to all circuits that are connected along the bus bars. Each circuit consists of a fusible switch, breaker or motor starter connected to a load. Figure 9 shows the configuration of the enclosure-bus bar power loss construction which is based on information collected from one manufacturer.

[FIGURE 9 OMITTED]

The dimensions of enclosures and bus bars depend on the power panelboard current ratings and the number of disconnecting devices installed (feeder capacity) in the power panel-board. Copper bus bar dimensions for ratings at 250, 400, 600, 800, and 1200 amps were selected from UL 67-1993, and enclosure dimensions were chosen from manufacturer literature. The power loss model of the enclosure-bus bar is based on analytical methods, materials, and dimensions that were reported in the panelboard section of RP-1395 where power loss of the enclosure was estimated by using Del Vecchio (2003) while the power loss of the bus bars was estimated by using White and Piesciorovsky (2009).

The enclosure-bus bar power losses at rated loads are defined as the sum of the watts dissipated by the AC resistance and the stray loss in the enclosure which is expressed as

[P.sub.ebr] = [P.sub.e] + [P.sub.b] (11)

where [P.sub.e] and [P.sub.b] are the enclosure and three phase bus bar power losses at rated loads in watts/m (Btu/h/ft). By using Equation 11, data from RP-1395 were compiled for the enclosure-bus bar model. The compiled data are shown in Table 5. The enclosure-bus bar power losses at rated loads shown in the last column of Table 5 were fitted with the polynomial

Table 5. Calculated Enclosure and Bus Bar Power Losses at Rated Loads Power Bus Bar Dimensions, m (ft) Calculated Panelboard Enclosure Ampere Power Loss, Ratings, [P.sub.e], W/m [I.sub.bus], (Btu/h/ft) amps b a S 0.0254 0.0064 0.0444 0.13 250 (0.00774) (0.00195) (0.01353) (0.135) 0.0508 0.0064 0.0952 1.45 400 (0.01548) (0.00195) (0.02902) (1.508) 0.0635 0.0064 0.1206 5.01 600 (0.01935) (0.00195) (0.03676) (5.210) 0.0889 0.0064 0.1714 16.58 800 (0.02709) (0.00195) (0.05224) (17.241) 0.0635 0.0127 0.1143 23.63 1200 (0.01935) (0.00387) (0.03484) (24.573) Power Calculated Calculated Panelboard Three-Phase Enclosure-Bus Ampere Bus Bar Bar Power Loss, Ratings, Power Loss, [P.sub.ebr] = [I.sub.bus], [P.sub.b] [P.sub.e] + amps W/m (Btu/h/ft) [P.sub.b] W/m (Btu/h/ft) 25.84 25.97 250 (26.871) (27.006) 33.87 35.32 400 (35.221) (36.729) 61.89 66.90 600 (64.359) (69.569) 78.71 95.29 800 (81.850) (99.091) 136.63 160.26 1200 (142.081) (166.654)

[P.sub.ebr] = 0.00004 x [I.sub.bbr.sup.2] + 0.839 x [I.sub.bbr] (12)

[FIGURE 10 OMITTED]

where [I.sub.bbr] is the bus bar rating in amps and [P.sub.ebr] is the enclosure-bus bar power loss at rated loads in watts/m or Btu/h/ft after multiplying Equation 12 by 1.0399. The data of the last column of Table 5 and Equation 12 are shown in Figure 10.

During this study, no enclosure-bus bar power loss measurements were made or found in manufacturer or technical literature. However, as the enclosure-bus bar consists of three bus bars inside of a rectangular metallic enclosure, the power loss model could be considered similar to a 600 VAC busway. As a check on the reasonableness of the presented results, the 600 VAC copper armor-clad busway power losses reported by McDonald & Hickok (1985) were compared with the enclosure-bus bar power loss calculations for rated loads. This information is also shown in Figure 10. Caution must be exercised when comparing these results since the 600 VAC copper busway and panelboard enclosure-bus bar have some design differences, such as panelboard enclosures are greater than busway enclosures. The enclosure-bus bar power loss for a panelboard at a given load is

[P .sub.enc bus loss] = [((lf x I)[I.sub.bbr]).sup.2] x H [p.sub.ebr] = [(lf x I).sup.2] H (0.00004 + 0.0839 x [I.sub.bbr.sup.-1]) (13)

where I is the load current flowing through a single bus bar in amps, H is the bus bar length in meters, lf is the load factor applied to the main bus and [P .sub.enc bus loss] is the enclosurebusbar power loss of the panelboard in watts. Calculation of lf for the main bus will be explained in the following section. Equation 13 is valid at balanced three phase loads and 60 Hz.

PANELBOARD POWER LOSS MODEL

Power Loss Model of Panelboard and Load Factor of Main Bus (lf)

Figure 11 shows a schematic diagram of a power panel-board where there is a main bus or branch that feeds the secondary branches that consist of circuit breakers, fusible-switches, and motor starters. The main branch has power losses from the main disconnecting device (breaker or fusible switch) and enclosure-bus bar losses, while the secondary branches have the breakers, fusible switches, and motor starter power losses.

By inspection of Figure 11, the current of the main branch is given by the sum of all currents from the secondary branches. So, the main branch current, I in amps, is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [I.sub.c] is the secondary branch device load in amps and p is the number of secondary branch devices. Because each secondary branch has its own load factor, the load factor for the main branch needs to be determined. The main branch load factor is chosen to satisfy

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where lf is the main branch load factor, I is the main branch current, and [lf.sub.c] is the load factor of the [c.sup.th] secondary branch. Based on Equation 15, the main branch load factor is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the main branch current, I, is giben by Equation 14.

The panelboard power loss model is the sum of all the partial power losses of each panelboard component. The dissipated power is determined by summing the losses of the main and secondary branches. The panelboard power loss model is given by

[FIGURE 11 OMITTED]

Panelboard.sub.power loss] = Main [Breaker.sub.loss] + Enclosure Bus [Bar.sub.loss] + [Breakers.sub.loss] + Fusible [Switches.sub.loss] + NEMA FVNR Motor [Starters.sub.loss] (17)

By substituting for the partial power loss models of electrical equipment in power panelboard previously described

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the symbols are defined in Table 6.

Table 6. Symbols, Definitions, and Units of Power Loss Models for Panelboards Symbols Definitions Units [Panelboard.sub.main Panelboard W breaker loss] power loss 1f Load factor 0 to1 of main branch or bus I Main branch amps current [I.sub.br] Main breaker amps ampere rating H Bus bar length metres [I.sub.bbr] Bus bar ampere amps rating of power panelboard 1[f.sub.e] Load factor of breaker in 0 to1 secondary branch [I.sub.e] Breaker load amps of secondary branch Ib[r.sub.e] Breaker amps ampere rating of secondary branch 1[f.sub.g] Load factor 0 to1 of fusible switch in secondary branch [I.sub.e] Load of fusible switch in amps secondary branch I[sr.sub.g] Ampere rating of switch in amps secondary branch I[fr.sub.g] Ampere rating of fuse in amps secondary branch [A.sub.i] Table 4 coefficient W for ith starter [B.sub.i] Table 4 coefficient W/am[p.sup.2] for ith starter 1[f.sub.i] Load factor of NEMA 0 to1 FVNR motor starters [I.sub.i] Load of NEMA FVNR motor starters amps 1f[r.sub.i] Fuse ampere rating of NEMA FVNR amps motor starters Pf[r.sub.I] Fuse power loss at W rated load provides by Equations 4 or 5

Power panelboards can use breakers or fusible switches as main disconnecting devices. An alternative loss model of the power panelboard having a fusible switch as the main disconnecting device is also presented. The main fusible switch panelboard loss model is given by Equation 17. But in this case, the first term of Equation 17 is replaced by

[Main Fusible Switch.sub.loss] = [{lf x I}.sup.2] x {0.0003 + 0.0839 x [I.sub.sr.sup.-1]} + (3 x [p.sub.fr] x [I.sub.fr.sup.-2]) (18)

where Main Fusible [Switch.sub.loss] is the power loss of the main fusible switch in watts, [I.sub.sr] is the main switch current rating in amps, [I.sub.fr] is the main fuse current rating in amps, and [P.sub.fr] is the fuse power loss at rated load in watts given by Equations 4 or 5. The power panelboard loss model is valid under the conditions that are shown in Table 7.

Table 7. Conditions of Power Panelboard Loss Models Location Indoor Maximum operating voltage 600 VAC Frequency 60 Hz Loads Three phase balanced currents Copper bus bar conductivity 98.9% IACS Enclosure Galvanized steel sheet Room temperature 25 [degrees] C (77 [degrees] F) Bus bar temperature rise 65 [degrees] C (149 [degrees] F)

To estimate the heat gain from power panelboards, the loss models of the panelboard with main breaker and given by Equation 17 and the panelboard with main fusible switch given by Equation 18 were used in a Visual Basic program that was linked to a spreadsheet. Figure 12 shows this spreadsheet that will be used in the heat gain example to be presented.

Heat Gain Example

A power panelboard with a circuit breaker as the main disconnecting device will be installed in a room and its dissipated power loss has to be estimated to size the HVAC equipment. The line-line voltage is 240 VAC and the current rating of the panel-board is 1200 amps. The power panelboard will operate with balanced three phase loads and 60 Hz. In Table 8, the loads and electrical equipment installed in the front view of the power panelboard are shown. The panelboard has a main breaker that feeds the secondary branch devices which consist of five breakers, three fusible switches, and three FVNR motor starters.

Table 8. Electrical Equipment of Power Panelboard in the Example Main Branch Main breaker: Main bus bar: Rating = 1000 amps Rating = 1200 amps Load = ?, lf= ? H = 1.327 m Secondary Branches Breaker 1: Breaker 2: Rating = 200 amps Rating = 175 amps Load = 130 amps, lf= 0.9 Load = 90 amps, lf= 0.8 Breaker 3: Breaker 4: Rating = 100 amps Rating = 100 amps Load = 70 amps, If = 0.8 Load = 70 amps, If= 0.8 Breaker 5: J Fuse/switch 1: Rating = 100 amps Ratings = 100/160 amps Load = 70 amps, lf = 0.8 Load = 60 amps, If = 0.8 J Fuse/switch 2: J Fuse/switch 3: Ratings = 200/250 amps Ratings = 100/160 amps Load = 120 amps, lf = 0.8 Load = 80 amps, lf =0.8 NEMA 1 FVNR motor starter: NEMA 3 FVNR motor starter: Rating = 20 amps (J Fuse) Rating = 60 amps (J Fuse) 7hp motor, [eta] = 85%, pf = 0.9 20 hp motor, [eta] = 90%, pf = 0.9 lf = 0.7, Load = ? If = 0.8, Load = ? NEMA 2 FVNR motor starter: Rating = 35 amps (J Fuse) 10 hp motor, [eta] = 85%, pf = 0.8 lf = 0.9, Load = ? where lf = load factor of main breaker, lf = load factor of secondary branches, pf = motor power factor, [eta] = motor efficiency, and H = bus bar length

The approach taken for estimating the heat loss rate is to (1) calculate the FVNR motor starter and main branch load currents, (2) determine the load factor of the main branch, and (3) compute the breaker, fusible switch, motor starter, and total power losses.

1. Load Currents

The FVNR motor starter load currents are calculated from

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

where I is the motor starter load in amps, [P.sub.hp] is the motor power in horse-power, [eta] is the motor efficiency in percent, [V .sub.line] is the motor line to line voltage in volts, and pf is the motor power factor. Equation 18 was developed in White et al. (2004). The FVNR motor starter load currents designated as [I.sub.1], [I.sub.2], and [I.sub.3] are determined in Table 9.

Table 9. Determination of FVNR Motor Starter Load Currents NEMA 1 FVNR motor starter [I.sub.1] = 16.4 amps NEMA 2 FVNR motor starter [I.sub.2] = 26.4 amps NEMA 3 FVNR motor starter [I.sub.3] = 44.3 amps

The main branch load current, I in amps, is found using Equation 14. The main branch load current is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

2. Load Factor

The load factor of the main branch, lf, is determined by Equation 16 and the data shown in Table 8. The calculated value is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

3. Component and Total Losses

The partial power losses are obtained from the main breaker panelboard loss model given by Equation 17. Table 10 shows the power loss of each panelboard component and the total in watts.

Table 10. Power Losses in the Example Main Branch Main breaker: Main bus bar: 107.4 W 58.94 W Secondary Branches Breaker 1: Breaker 2: 18.19 W 7.87 W Breaker 3: Breaker 4: 8.34 W 8.34 W Breaker 5: J Fuse/switch 1: 8.34 W 12.61 W J Fuse/ switch 2: J Fuse/ switch 3: 25.90 W 22.42 W NEMA 1 FVNR motor starter: NEMA 3 FVNR motor starter: 14.57 W 26.68 W NEMA 2 FVNR motor starter: 30.51 W Total Power Loss: 350 W

The estimated heat gain rate from the power panelboard is 350 watts. The same result can be found using the spread-sheet of Figure 12. In the example, the power loss of the panel-board can be estimated using a hand or spreadsheet calculation, obtaining similar results. The use of the spreadsheet is recommended instead of the hand calculation because a great number of components are used in power panelboard.

Using the power loss model based on equation (17), the estimated power loss is 350 watts (1197 Btu/h). For the same example, using Table 1 reported by Rubin (1979), the estimated power loss of a panelboard with 12 three pole devices (36 single pole devices) is 450 watts (1539 Btu/h). The estimation from Rubin (1979) is 28% greater than the results obtained with the model presented in this paper. It should be appreciated that the difference between the results presented here and that of Rubin is a function of load. Rubin did not account for part loads.

CONCLUSION

This paper provides information on the heat loss rate at full and part-loads for electrical equipment used in power panelboards. Power loss models at full and part-loads for circuit breakers, fusible switches, motor starters, and bus bars with enclosures are developed based on measurements, manufacturer literature, and published papers. It was shown that the fusible switches dissipate more heat than breakers of the same size ratings. This means breakers are more energy efficient than fusible switches.

The power panelboard loss model at part-load presented in this paper was based on the sum of partial power losses of each panelboard component. A heat gain example at part load was presented showing that the power losses can be predicted. The loss model of the power panelboard at part-load, equation (17), can predict losses more accurately than Rubin (1979), who presented little loss information, did not define all device power losses, and did not consider part loads. A hand or spreadsheet calculation can be used to estimate the heat gain rate of a power panelboard. The use of the spreadsheet is recommended over the hand calculation because power panel-boards can have a large number of electrical devices and the hand calculation could be tedious.

In order to size HVAC equipment in industrial plants and building, realistic heat gain rates from power panel-board can be predicted. This power loss model, equation (17), will be a useful tool for HVAC designers who have to estimate the environmental heat gain rate contributed by power panelboards.

ACKNOWLEDGMENTS

The authors would like to thank the American Society of Heating Refrigeration and Air Conditioning Engineers (ASHRAE) for funding this work, especially TC 9.2 Industrial Air Conditioning and TC 9.1 Large Building Air Conditioning Systems.

REFERENCES

Bene, J. 1994. Specifying 600 volt current-limiting fuses: Applications 600 Amperes or Less. IEEE Transactions on Industry Applications 30(6):1449-55.

Del Vecchio, Robert M. 2003. Eddy-current losses in a con-ducting plate due to a collection of bus bars carrying currents of different magnitudes and phases. IEEE Transactions on Magnetics 39(1):549-52.

IEC 60947-3-2008. 2008. Low-voltage switchgear and controlgear, Part 3: Switches, disconnectors, switch disconnectors, and fuse-combination units, Third ed. International Electrotechnical Commission.

McDonald, William. J., and Herbert N. Hickok. 1985. Energy losses in electrical power systems. IEEE Trans-actions on Industry Applications IA-21(3):803-19.

NEC. 2008, National Electrical Code ANSI/NFPA70. National Fire Protection Association, Quincy, MA, 2007.

NEMA ICS 2-2000. 2000. Industrial control and systems controllers, contactors, and overload relays rated 600 volts. National Electrical Manufacturers Association.

Rubin, I.M. 1979. Heat losses from electrical equipment in generating stations. IEEE Transactions on Power Apparatus and Systems PAS-98(4):1149-52.

UL 67-1993. 1993. Standard for panelboards. Underwriters Laboratories, Eleventh Edition.

UL 98-2004. 2004. Enclosed and dead-front switches. Underwriters Laboratories, Thirteenth Edition.

UL 248-8-2000. 2000. Low-voltage fuses-Part 8: Class J fuses. Underwriters Laboratories, Second Edition.

UL 248-12-2000. 2000. Low-voltage fuses-Part 12: Class R fuses. Underwriters Laboratories, Second Edition.

UL 489-1996. 1996. Molded-case circuit breakers, molded-case switches, and circuit breaker enclosures. Under-writers Laboratories, Ninth Edition.

White, Warren N., and Anil Pahwa. 2003. Heat gain from electrical and control equipment in industrial plants, Part I. ASHRAE Research Project 1104-TRP, American Society of Heating Refrigeration and Air Conditioning Engineers.

White, Warren N., Anil Pahwa, and Chris Cruz. 2004. Heat loss from electrical and control equipment in industrial plants: Part II-Results and comparisons. ASHRAE Transactions 110(2):852-70.

White, Warren N., and Emilio C. Piesciorovsky. 2009. Building heat load contributions from medium and low voltage switchgear, Part I: Solid rectangular bus bar heat losses (RP-1395). ASHRAE Transactions 115(2):369-82.

White, Warren N., and Emilio C. Piesciorovsky. 2010. Heat gain from electrical and control equipment in industrial plants, Part II. ASHRAE Research Project RP-1395, American Society of Heating Refrigeration and Air Conditioning Engineers.

Emilio C. Piesciorovsky is a doctoral student in the Department of Electrical and Computer Engineering and Warren N. White is an associate professor in the Department of Mechanical and Nuclear Engineering, Kansas State University, Manhattan, KS.

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Author: | Piesciorovsky, Emilio C.; White, Warren N. |
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Publication: | ASHRAE Transactions |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Jul 1, 2011 |

Words: | 5857 |

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