Building heat load contributions from medium and low voltage switchgear--part II: component and overall switchgear heat gains.
General description, classification, and construction details are explained for low and medium voltage switchgear. Common construction techniques and components are detailed and described, especially those components giving rise to environmental heat gain. In RP 1104, rudimentary spreadsheet models for LV and MV switchgear were presented. The low and medium voltage switchgear spread-sheets have been greatly improved and use updated component power losses. These switchgear components include circuit breakers, transformers, bus bars, enclosures, space heaters, in addition to relaying and control systems. These updated power losses were obtained from manufacturers (brochures and data sheets), previous research papers, and the bus model of White and Piesciorovsky (2009). In this paper, efficiency is defined as
Efficiency = Switchgear Output Power x 100/Switchgear Input Power [%]
while the power loss of the equipment is defined as
Power Loss = Switchgear Input Power - Switchgear Output Power [watts, Btu/h]
The low and medium voltage switchgear spreadsheets are used to estimate the power losses of two practical problems considering actual loadings. However, the power losses for the same problems are also estimated using the rated current loads for the bus and breakers showing a considerable increase in the estimated dissipation. Comparing the estimated power losses for these two situations, an important conclusion is presented at the end of this paper.
SWITCHGEAR CLASSIFICATION AND GENERAL COMPONENTS
Before classifying the switchgear, it is important to understand the difference between low voltage switchboards and low voltage switchgear, equipment that sometimes look similar but have different power distribution applications and characteristics. These differences are demonstrated in Table 1.
Table 1. Low Voltage Switchboard versus Low Voltage Switchgear Characteristics Low Voltage Switchboard Low Voltage Switchgear Application Load distribution before the Substation application panelboards before the switchboards Stand-alone enclosure mounted Stand-alone enclosure away from a wall. mounted away from a wall. Design Construction with internal Construction with barriers between devices and internal barriers busses is optional. between devices and busses. Breakers fully compartmentalized with barriers. Bus Bars Horizontal and vertical bus Horizontal and vertical bars (3 phases and ground) bus bars (3 Phases) Breaker Ampere 150/5000 amperes 800/5000 amperes Ratings (Minimum/Maximum) (Minimum/Maximum) Access Front and rear access Front and rear access Disconnect Fusible switches, molded case Fused and non-fused low Devices circuit breakers, insulated voltage power circuit case circuit breakers, and breakers fused and non-fused low voltage power circuit breakers Standards UL 891(dead front ANSI C37.20.1, UL 1558, switchboards), NEMA PB-2 ANSI C37.13, UL 1066 (switchboards), UL 489 (circuit breakers) (circuit breakers)
Switchgear are classified as either outdoor or indoor equipment. However, this paper only treats indoor switchgear. Switchgear are also segregated according to the voltage level as illustrated in Figure 1.
[FIGURE 1 OMITTED]
The total power loss of the LV or MV switchgear can be calculated by the sum of all the partial power losses produced by each switchgear component and device. The LV and MV switchgear components and devices include the enclosures, horizontal and vertical bus bars, circuit breakers, current transformers, power transformers, control power transformers, relaying and control systems (electromechanical and microprocessor type), and space heaters.
LOW VOLTAGE AND MEDIUM VOLTAGE SWITCHGEAR CHARACTERISTICS
The circuit breakers used in low voltage switchgear are given the designation of "Low Voltage Power Circuit Breaker" (LVPCB) and these breakers are rated from 800 to 5000 amp at 600 volt. The LVPCB has an interrupting current capability, up to 200 kA. This type of breaker can be used as a fused circuit breaker (non automatic) and a non-fused circuit breaker (automatic). The type of mechanism used to open the breaker is a stored energy spring system while the trip sensor type is a microprocessor based RMS (root mean square) sensor. The LVPCB are drawn out mounted (can be slid out from the switchgear) allowing easy inspection operations.
The power circuit breaker losses follow the [I.sup.2]R calculation. Table 2 shows a range of power circuit breaker frame sizes. For each frame size power loss figures are provided for the cases of fused and non-fused application. These power loss figures represent the power losses that occur when rated frame current flows in the breaker. For smaller currents, the resistance values shown in Table 2 are used to predict the power loss through an [I.sup.2]R calculation.
Table 2. Power Circuit Breaker Heat Losses for Low Voltage Switchgear Fused Low Voltage Power Non-Fused Low Voltage Power Circuit Breaker Circuit Breaker Frame Current, Power Loss, Heat Loss Power Loss, Heat Loss amps watts, Resistance, watts, Resistance, (Btu/h) ohms (Btu/h) ohms 800 600 (2047) 0.0009375 95 (324) 0.0001484 1200 1050 (3582) 0.0008681 212 (723) 0.0001472 1600 1500 (5118) 0.0005859 378 (1289) 0.0001477 2000 2250 (7677) 0.0005625 500 (1706) 0.0001250 3000 3375 (11529) 0.0003750 1042 (3559) 0.0001157 3200 3600 (12283) 0.0003516 1150 (3923) 0.0001123 4000 4500 (15354) 0.0002813 1372 (4681) 0.0000858 5000 4700 (16036) 0.0001880 1650 (5629) 0.0000660
The most common medium voltage switchgear circuit breaker found in buildings and factories (5/15 kV) is the vacuum circuit breaker type. It is classified as a vacuum circuit breaker with either a magnetic or spring actuator mechanism. The vacuum circuit breaker is rated from 1200 to 4000 amp. This medium voltage circuit breaker is drawn out mounted and it is a non-fused breaker. The power losses of medium voltage circuit breakers can be calculated as previously reported in White, Pahwa and Cruz (2004).
The compartments, cabinets, and the horizontal and vertical bus dimensions are different for low and medium voltage switchgear. They are designed by manufacturers according to industrial standards. The differences between low and medium voltage switchgear influence the dissipated heat loss. The bus heat loss is given by the proximity and skin effect while the enclosure heat loss is given by the stray loss.
Skin effect causes the current in an AC conductor to crowd to the outer edges creating an increase in electrical resistance and correspondingly higher heat loses than those caused by the same size DC current. The proximity effect occurs when the magnetic field of one conductor induces a magnetic field in an adjacent conductor that creates losses through a process that is similar to induction heating. The magnetic fields produced by the phase conductors interact, altering the current distribution in one another. The stray loss of the enclosure involves losses induced in surrounding conducting structures.
Using the described analytical models for the skin, proximity and the stray loss effect (White and Piesciorovsky 2009), several Visual Basic programs and spreadsheets were created. Bus bar and enclosure power losses were calculated for low and medium voltage switchgear, considering the switchgear dimensions from several manufacturers.
Tables 3 and 4 show the horizontal & vertical bus bar, enclosure, and total heat loss resistances for low voltage (600V) and medium voltage (5-15Kv) switchgear considering copper bus bars, galvanized sheet steel enclosures, 60 Hz frequency, 40[degrees]C (104[degrees]F) ambient temperature, and 65[degrees]C (149[degrees]F) bus bar temperature rise.
Table 3. Horizontal and Vertical Bus Bar, Enclosure, and Total Heat Loss Resistance for Low Voltage Switchgear Horizontal Bus Bar and Enclosure Heat Loss Resistance per Phase, [mu][OMEGA]/m ([mu][OMEGA]/ft) Ampere Bus Bar Enclosure Total Rating, Resistance Resistance Resistance amps 800 51.6 (15.7) 0.35 (0.11) 51.95 (15.81) 1600 28.9 (8.8) 0.76 (0.23) 29.66 (9.03) 2000 22.5 (6.8) 1.33 (0.40) 23.83 (7.20) 3200 17.9 (5.4) 1.49 (0.45) 19.39 (5.85) 4000 14.8 (4.5) 2.20 (0.67) 17.00 (5.17) 5000 12.0 (3.7) 3.22 (0.98) 15.22 (4.68) Vertical Bus Bar and Enclosure Heat Loss Resistance per Phase, [mu][OMEGA]/m ([mu][OMEGA]/ft) Ampere Bus Bar Enclosure Total Rating, Resistance Resistance Resistance amps 800 50.0 (15.2) 5.31 (1.62) 55.31 (16.82) 1600 28.5 (8.7) 5.48 (1.67) 33.98 (10.37) 2000 22.0 (6.7) 5.66 (1.72) 27.66 (8.42) 3200 17.5 (5.3) 7.96 (2.42) 25.46 (7.72) 4000 14.5 (4.4) 9.64 (2.94) 24.14 (7.34) 5000 11.8 (3.6) 11.61 (3.54) 23.41 (7.14) Table 4. Horizontal and Vertical Bus Bar, Enclosure, and Total Heat Loss Resistance for Medium Voltage Switchgear Horizontal Bus Bar and Enclosure Heat Loss Resistance per Phase, [mu][OMEGA]/m ([mu][OMEGA]/ft) Ampere Rating, Bus Bar Enclosure Total amps Resistance Resistance Resistance 1200 21.97 (6.69) 12.07 (3.67) 34.04 (10.36) 2000 17.43 (5.31) 12.07 (3.67) 29.50 (8.98) 3000 8.73 (2.66) 12.09 (3.68) 20.82 (6.34) 4000 6.84 (2.08) 12.11 (3.69) 18.95 (5.77) Vertical Bus Bar and Enclosure Heat Loss Resistance per Phase, [mu][OMEGA]/m ([mu][OMEGA]/ft) Ampere Rating, Bus Bar Enclosure Total amps Resistance Resistance Resistance 1200 21.97 8.35 30.32 (6.69) (2.54) (9.23) 2000 17.43 8.36 25.79 (5.31) (2.54) (7.85) 3000 8.73 8.39 17.12 (2.66) (2.55) (5.21) 4000 6.84 8.41 15.25 (2.08) (2.56) (4.64) Riser Bus Bar and Enclosure Heat Loss Resistance per Phase, [mu][OMEGA]/m ([mu][OMEGA]/ft) Ampere Rating, Bus Bar Enclosure Total amps Resistance Resistance Resistance 1200 21.97 23.20 45.17 (6.69) (7.07) (13.76) 2000 17.43 22.91 40.34 (5.31) (6.98) (12.29) 3000 8.73 21.34 30.07 (2.66) (6.50) (9.16) 4000 6.84 20.65 27.49 (2.08) (6.29) (8.37)
Special Equipment Losses
The LV and MV switchgear are composed of different special equipment belonging to the control, protection and metering electrical circuits of the system. This equipment consists of transformers, usually protected by fuses at both sides (primary/secondary coil) together with relaying and control systems.
Transformers can be classified, according to their use, as potential, control power, and current transformers. Potential transformers (PTs) are also called voltage transformers (VTs). They are designed to offer a negligible load to the secondary through a voltage ratio, converting high voltage into low voltage and feeding input signals for metering, control, and protective devices. Control power transformers (CPT) are larger than potential transformers, because these transformers are used to provide the necessary input energy to feed all the metering, control, and protective circuits in the MV and LV switchgear. The CPT primary coils are connected to the LV or MV supply (600V or 5/15 kV). They can have one phase (1, 3, 5, 7.5, 10, 15, 25, or 50 kVA) and three phases (45 or 75 kVA). Current transformers (CTs) are designed to provide a current in its secondary coil proportional to the current flowing in its primary. The CT primary is connected to breakers, buses and other power devices, transforming the primary high current into a secondary low current. They are used to offer a negligible current to the secondary through the current ratio and this low current is used to feed the input signals for metering, control, and protective devices.
Relaying and control systems can be classified according to their technology into either the electromechanical or microprocessor type. The electromechanical type (EM) is characterized by electromechanical relays (switches). Each relay can have several auxiliary contacts that have different characteristics (normally closed, normally open, single pole, double pole, etc). The EM relay is operated by an energized coil and provides different outputs using the auxiliary contacts characterized by the electromechanical relay construction. Each EM relay has moving components and an electrical coil that dissipates heat. Depending on the complexity of the relaying and control circuit used (number of relays involved in the system), the electromechanical type relaying and control system can be classified into either electromechanical simple type or the electromechanical complex type. The microprocessor type is characterized by solid state switches so that these relays do not have any moving components, increasing their lifetime. Microprocessor switches are more efficient and dissipate less heat loss than EM relays. For this reason, new relaying and control systems use the microprocessor type.
SWITCHGEAR SPREADSHEET MODELS
The following sections present two spreadsheet models that can calculate the power loss for low and medium voltage switchgear. Practical examples are shown for each case. Before the spreadsheets are presented some considerations about the spreadsheets will be covered.
* If the loading is unknown, 0.8 (expected load equal to 80% of the full load) is a reasonable value to use.
* For each circuit breaker, one current transformer of 3 coils has to be included, the size of which depends upon the rating of the circuit breaker.
* The circuit breaker and current transformer power losses have to be calculated using the actual breaker amperage. For each circuit breaker, a relaying and control system module has to be included.
* If the bus ampere ratings are unknown, then they can be selected according to the ampere ratings of the breakers that are connected to the bus and the standard bus ampere ratings for LV and MV switchgear which are included in Tables 3 and 4, respectively.
* The bus power losses have to be calculated using the actual or expected current flowing in the bus. For this reason, the one line circuit (it represents a three phase electrical circuit by a single line circuit) of the LV or MV switchgear needs to be known to determine the actual loadings. Also, the switchgear connections for normal and/or contingency operation (see below) need to be known in order to complete the actual loading information.
* If the number of space heaters used is not known then allot one space heater per vertical section.
Low Voltage Switchgear (Unit Substation)
The LV (600V) switchgear one line circuit of Figure 2 is used for this example. This LV switchgear has six vertical sections as illustrated in Figures 3 and 4. All low voltage power circuit breakers (LVPCBs) work as fused breakers. The LV switchgear can be analyzed while it is operating in one of two modes which are:
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
* Normal operation as illustrated in Figure 2a. The 4000 amp tie breaker is open so each 4000 amp main breaker and 1600 amp feeder breaker located at either side is carrying 1300 amp. The 800 amp breakers are carrying 350 amp (4 units) and 300 amp (4 units).
* Contingency operation as shown in Figure 2b. The 4000 amp tie breaker is closed because one 4000 amp main breaker is out of service. Therefore, the other 4000 amp main breaker is carrying 2600 amp, the 4000 amp tie breaker is carrying 1300 amp while each 1600 amp feeder breaker is carrying 1300 amp. The 800 amp breakers are carrying 350 amp (4 units) and 300 amp (4 units). The LV switchgear contingency operation is shown in Figure 3 specifying the breaker amp rating/breaker actual load in each breaker frame (section).
For example, considering the contingency operation of the LV switchgear, the total power loss was calculated when one main breaker had interrupted the power flow and both branches were fed by one 4000 amp main breaker and the 4000 amp tie breaker. For this reason, the current of the main horizontal bus was 1300 amp and the rest of the bus is carrying the currents shown in Figure 3. The bus amp ratings were chosen according to the amp ratings of the breakers because they were designed to support the future breaker amp loadings as shown in Figure 4. The data necessary to calculate the low voltage switchgear power loss is shown in Tables 5, 6, and 7.
Table 5. Low Voltage Switchgear Main Devices Data Item Number Main Devices Actual Load, Ampere Rating, amps amps 1 1 Main Breaker 2600 4000 2 1 Tie Breaker 1300 4000 3 2 Feeder Breaker 1300 1600 4 4 Breakers 350 800 5 4 Breakers 300 800 6 4 Current Transformer (3 Set) 350 800:5 7 4 Current Transformer (3 Set) 300 800:5 8 2 Current Transformer (3 Set) 1300 1600:5 9 1 Current Transformer (3 Set) 2600 4000:5 10 1 Current Transformer (3 Set) 1300 4000:5 Table 6. Low Voltage Switchgear Horizontal and Vertical Bus Bar Data Item Bus Bars Frames * Actual Load, Ampere Rating, amps amps 1 Main Horizontal Bus Bar 6 1300 4000 2 Horizontal Bus Bar 4 1300 3200 3 Vertical Bus Bar 6 1300 3200 4 Vertical Bus Bar 2 950 3200 5 Vertical Bus Bar 2 650 3200 6 Vertical Bus Bar 2 350 3200 * The Frame or Section is a dimension unit which correspond to the module height (vertical bus bars) or width (horizontal bus bars) Table 7. Low Voltage Switchgear Equipment Data Item Number Equipment Characteristics 2 1 Control Power Transformer Single Phase-15 kVA 1 2 Potential Transformer (PTs) 600 Volt/120 Volt 3 5 Auxiliary Compartments Instrument Compartments 4 6 Space Heater per Vertical 400 watts per section section 5 13 Relaying and Control System per Microprocessor Type Breaker
Considering a loading of 0.8 (expected load equal to 80% of the full load) and using the data from Tables 5, 6, and 7, the spreadsheet was completed as illustrated in Figure 5. The low voltage switchgear power loss was calculated using the contingency operation mode.
The result from the spreadsheet is shown in Figure 5 using the 0.8 loading and the data provided by the Tables 5, 6, and 7 and selecting the LV switchgear contingency operation mode. The low voltage switchgear power loss was calculated to be 8309 watts (28351 Btu/h).
Medium Voltage Switchgear
The medium voltage (15 kV) switchgear one-line circuit diagram in Figure 6 is used for this example. This switchgear is given by eight vertical sections according to Figures 7 and 8. The MV switchgear can only work in normal operation because this system has only one 2000 amp main breaker.
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
For example, considering the normal operation of the medium voltage switchgear, the 2000 amp main breaker located at a low central area was carrying 1900 amp and it was feeding three 1200 amp breakers with a load of 300 amp for each left side breaker and five 1200 amp breakers with a load of 200 amp for each one on the right side as shown in Figure 7. The bus amp ratings were chosen according to the amp ratings of the breakers because they were designed to support the future breaker amp ratings as shown in Figure 8. In the present example, the current of the main horizontal bus was different at either sides of the 2000 amp main breaker because the loads on each side were different. However, the main horizontal bus amp rating had to be 2000 amp because the main breaker was given as 2000 amp. On the other hand, the ampere rating for each vertical bus bar has to be 1200 amp because each vertical bus is connected to a 1200 amp breaker as shown in Figure 8. Tables 8, 9, and 10 show the data to find the MV (15 kV) switchgear power loss.
Table 8. Medium Voltage Switchgear Main Devices Data Item Number Main Devices Actual Load, Ampere Rating, amps amps 1 1 Main Breaker 1900 2000 2 3 Breaker 300 1200 3 5 Breaker 200 1200 4 1 Current Transformer (3 Set) 1900 2000:5 5 3 Current Transformer (3 Set) 300 600:5 6 5 Current Transformer (3 Set) 200 600:5 Table 9. Medium Voltage Switchgear Horizontal and Vertical Bus Bar Data Item Bus Bars Frames * Actual Load, Ampere Rating, amps amps 1 Main Horizontal Bus Bar 1 400 2000 2 Main Horizontal Bus Bar 1 800 2000 3 Main Horizontal Bus Bar 1 1000 2000 4 Main Horizontal Bus Bar 2 900 2000 5 Main Horizontal Bus Bar 1 600 2000 6 Main Horizontal Bus Bar 1 300 2000 7 Vertical Bus Bar 3 300 1200 8 Vertical Bus Bar 5 200 1200 9 Vertical Riser Bus Bar ** 1 1900 2000 * The Frame or Section is a dimension unit, which corresponds to the module height (vertical bus bars) or width (horizontal bus bars) ** The vertical riser bus bar corresponds to the 2000 Amperes main breaker incoming bus bar. Table 10. Medium Voltage Switchgear Equipment Data Item Number Equipment Characteristics 1 1 Control Power Transformer Single Phase-15 kVA 2 1 Potential Transformers (PTs) 15 kV/100 Volt 3 8 Auxiliary Compartments Instrument Compartments 4 8 Space Heater per Vertical 400 watts per section section 5 9 Relaying and Control System per Microprocessor Type Breaker
Considering a load of 0.8 (expected load equal to 80% of the full load) and using the data from Tables 8, 9, and 10, the spreadsheet was completed as illustrated in Figure 9. The medium voltage switchgear power loss was calculated for normal operation mode.
The result from the spreadsheet is in Figure 9 using the 0.8 loadings. In the present example, the medium voltage switchgear power loss was calculated to be 7533 watts (25703 Btu/h).
Another Load Case
The results from the spreadsheets presented here provide a realistic estimated dissipated power loss in LV and MV switchgear. If instead of using actual loadings, the breaker and bus bar ampere ratings (unknown loading case) were used, the results obtained with the spreadsheets would have been larger. If in the present examples power loss of low and medium voltage switchgear had been calculated using breaker and bus amp ratings, the results of the LV and MV spreadsheets would have been 22131 watts (75513 Btu/h) and 18260 watts (62304 Btu/h), respectively. Therefore, if breaker and bus ampere rating (unknown loading case) are used, the dissipated power loss of the LV and MV switchgear is overestimated by the spreadsheets. It is always important to use the actual loading for each bus bar and circuit breaker to improve the accuracy of the results.
The power loss dissipated by LV and MV switchgear is considered. Construction details and the various components that make up each switchgear type have been described. Tables have been constructed that predict the ohmic heating of the various components when operated at 100% load. These tables are based on manufacturer data, measured data, and the non-segregated bus model developed by White and Piesciorovsky (2009). By scaling these power loss figures according to the actual loading (most components scale according to the square of the current) and summing the component power losses produces a realistic estimate of the equipment heat contribution to the environment. Two spreadsheets, one for LV and another for MV switchgear have been constructed that make use of the information gathered and developed in this study. Examples have been presented for the use of these spreadsheets. It is demonstrated that the estimated power loss dissipated by the switchgear is much larger when using rated bus and circuit breaker amperage as compared to the power loss dissipated under the conditions of a partial loading. In the examples presented, loading the switchgear to 80% of rated load reduced the dissipated power losses by a factor of approximately 1/2 when compared to the dissipated power losses occurring at breaker and bus ampere ratings (unknown loading case). This work forms a useful contribution to the heat load estimation for sizing HVAC equipment.
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.
ANSI/IEEE C37.13-1990, "Standard for Low-Voltage AC Power Circuit Breakers Used in Enclosures, American National Standards Institute and Institute of Electrical and Electronics Engineers," May 1, 1990.
ANSI-IEEE C37.20.1-1993, "Standard for Metal-Enclosed Low-Voltage Power Circuit Breaker Switchgear, "American National Standards Institute and Institute of Electrical and Electronics Engineers, May 1, 1993.
NEMA PB2-2006, "Deadfront Distribution Switchboards," National Electrical Manufacturers Association, January 1, 1995.
UL 1558, "Metal-Enclosed Low-Voltage Power Circuit Breaker Switchgear," Underwriters Laboratories Standard, Fourth Edition, February 25, 1999.
UL 1066, "Low-Voltage AC and DC Power Circuit Breakers Used in Enclosures," Underwriters Laboratories Standard, Third Edition, May 30, 1997.
UL 891, "Dead-Front Switchboards," Underwriters Laboratories Standard, Tenth Edition, December 23, 1998.
UL 489, "Molded-Case Circuit Breakers, Molded-Case Switches, and Circuit Breaker Enclosures," Underwriters Laboratories Standard, Ninth Edition, 1996.
White, W. N., A. Pahwa, A. and C. Cruz, "Heat Loss from Electrical and Control Equipment in Industrial Plants: Part II--Results and Comparisons," ASHRAE Transactions, Vol. 110 (2) pp. 852-870, 2004.
White, W. N. and E. C. Piesciorovsky, "Building Heat Load Contributions from Medium and Low Voltage Switchgear: Part I--Solid Rectangular Bus Bar Heat Losses," ASHRAE Transactions--to appear, 2009.
Emilio C. Piesciorovsky: The indoor MV and LV switchgear power loss model spreadsheets were based on
[P.sub.TOTAL LOSS] = [P.sub.LOSS](I) + [P.sub.LOSS],
where [P.sub.LOSS] (I) is the estimated power loss in watts produced by the electrical devices in which losses depend on the actual loadings (circuit breakers, current transformers, bus bars, and enclosures), and [P.sub.LOSS] is the estimated power loss in watts produced by the electrical devices in which losses do not depend on the loadings (space heaters, relaying control systems, control power transformers, voltage transformers, and instrument modules). The previous equation can also be written as
[P.sub.TOTAL LOSS] = [[m.summation over (i = 1)][([D.sub.f] x [I.sub.i]).sup.2] x [R.sub.i] x [10.sup.6]] + [[n.summation over (j = 1)][P.sub.j]],
where m is the total number of electrical devices which losses depend on the actual loadings of the device, [D.sub.f] is the diversity factor applied to the switchgear equipment, [I.sub.i] is the actual loading in amperes for the ith electrical device, [R.sub.i] is the heat loss resistance in micro-ohms for the ith electrical device, n is the total number of electrical devices which losses do not depend on the loadings of the device, and [P.sub.j] is the power loss in watts for the jth electrical device.
Emilio C. Piesciorovsky
Warren N. White, PhD
This paper is based on findings resulting from ASHRAE Research Project RP-1395.
E.C. Piesciorovsky is a graduate student in the Department of Electrical and Computer Engineering, and W.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.|
|Date:||Jul 1, 2009|
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