1、2009 ASHRAE 369This paper is based on findings resulting from ASHRAE Research Project RP-1395.ABSTRACTHeat dissipated by medium and low voltage switchgear is determined by use of a spreadsheet model. In the first part of this paper, mathematical models of a switchgear component that produces a signi
2、ficant portion of the total heat loss is examined. Rectangular bus bars are used in switchgear for carrying large current loads and the loss contribution of this one component is significant. The heat loss mechanisms of bus bars consist of eddy current loss, loss from proximity effect, and stray or
3、enclosure loss. Each of these losses is considered in turn to develop a complete model of the bus bar loss process. Where possible, portions of the loss model are compared to information developed elsewhere with excellent agreement. The eddy current and proximity effect loss models are devel-oped in
4、 such a way that the model allows evaluation with a spreadsheet. The same can be said for the stray or enclosure loss model. The goal of this work is to produce a switchgear power loss model suitable for use by HVAC engineers for heat load prediction. INTRODUCTIONAccurate prediction of building heat
5、 gains relies on accu-rate data and/or equipment models. For three decades, the paper by Rubin (1979) has served as a primary tool for esti-mating building heat gain caused by electrical distribution equipment. Owing to a built-in conservatism, heat gain esti-mations based on Rubins work exceeded th
6、e heat gains occur-ring in practice. White, Pahwa, and Cruz (2004, 2004a) provided new data and procedures for better estimation of the heat gain. The publications by White et al. stemmed from the work performed in ASHRAE RP 1104 and represented the first step in determining a better means of heat g
7、ain prediction.Part of the effort in RP 1104 involved spreadsheet models of low and medium voltage switchgear. The data used in the switchgear models were taken from unverified manufacturer heat loss figures found in catalogues and displayed on websites. One of the goals of ASHRAE RP 1395 is to prov
8、ide verification of that published manufacturer data used in the switchgear models. This two-part paper describes an analyti-cal and experimental approach taken to develop the required verification.The first of these two papers describes an analytic approach taken to develop a loss model of the elec
9、trical bus. Not only is the bus important in estimating heat losses occur-ring in switchgear, it also plays a significant role in heat loss production occurring in other equipment such as motor control centers and panelboards. The bus is the conduit for power transfer within distribution equipment a
10、s well as between equipment pieces. As a result, accurate bus heat losses require an accurate model for prediction. It is well to spend time discussing the bus model because it plays a major roll in elec-trical distribution equipment heat losses. Parts of the calcula-tion will be verified by compari
11、ng basic results with those obtained experimentally. By comparing analytically produced heat loss values to both measured data and data obtained through other analytical means, the bus loss model will be verified.RP 1104 provided information on medium and low volt-age circuit breaker heat losses. So
12、me of this information stemmed from measurements and some from manufacturer published data. In the second paper, circuit breaker heat losses Building Heat Load Contributions from Medium and Low Voltage SwitchgearPart I: Solid Rectangular Bus Bar Heat LossesWarren N. White, PhD Emilio C. Piesciorovsk
13、yWarren N. White is an associate professor in the Department of Mechanical and Nuclear Engineering and Emilio C. Piesciorovsky is a grad-uate student in the Department of Electrical and Computer Engineering, Kansas State University, Manhattan, KS.LO-09-034 (RP-1395) 2009, American Society of Heating
14、, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2009, vol. 115, part 2. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission.370
15、ASHRAE Transactionsdetermined by both measurements and manufacturer data are used with the model to be presented in order to predict the switchgear heat loss. In some switchgear applications, fused switches are employed. The bus and breaker (fused switch) are the two leading heat-producing component
16、s of switchgear. There is a collection of special equipment employed in switch-gear for tasks such as metering and climate adjustment having loss values that are much smaller than those associated with buses and breakers. The heat losses associated with the special equipment are included in the swit
17、chgear model. Another topic of the second paper is the general construction tech-niques of switchgear. The second paper concludes with exam-ples of the spreadsheet use.Types of BusesBusways and bus bars are used to transmit large electrical currents. Although the bus conductors can consist of flexib
18、le cables, buses usually consist of copper or aluminum bars or tubes. The busway usually houses a three phase supply which is in contrast to cables and cable trays where several three phase circuits could be laid side by side. There are three types of bus configurations, all found in industrial plan
19、ts. The first configuration is the non-segregated phase bus where all conductors are enclosed in a common structure with no barri-ers between the phases. If the size of the enclosing structure is allowed to grow and the bus is not symmetrically placed inside the structure, then this configuration ap
20、proximates the bus inside electrical equipment where the bus might be passing close to a sheet metal wall. The next configuration is the segre-gated phase bus where all conductors are enclosed by a common structure in addition to barriers that are placed between the phase conductors. The final categ
21、ory is the isolated-phase bus where each conductor is surrounded by an electrically grounded metal housing that is separate from the other phases. Figure 1 illustrates the different configurations.Instances of isolated phase buses include factories and power plants, however inside electrical equipme
22、nt, bus bars are usually bare or have a thin coating of electrical insulation. The losses of isolated phase buses are well documented in the standard IEEE C37.23-2003. As stated earlier, the non-segre-gated bus best approximates the bus configuration inside elec-trical equipment for the purpose of d
23、etermining heat losses.Ohmic Heating Loss MechanismsThe discussion of heat losses in electrical power conduc-tors centers on losses in either copper or aluminum materials. Because electrical conductors consist of nonmagnetic mate-rial, magnetic hysteresis is excluded from consideration as a loss mec
24、hanism. The discussion that follows divides the heat generation into three parts. The first part is skin effect which increases the electrical resistance of the conductor. The second part is proximity effect which can both decrease and increase the heat losses. The final part is stray loss which inv
25、olves currents being induced in surrounding structures. Each of these loss mechanisms will be described in the following text.Ohmic heat dissipation in a conductor carrying a DC current is well understood, however when alternating current flows, the changing magnetic field created by the alternating
26、 current induces voltages in the conducting material that cause other currents to also flow in the conductor. The net result is that the current crowds to the edges of the conductor while little current flows in the center of the conductor. Recall that the resistance of a conductor is given by(1)whe
27、reR = the electrical resistance in ohm, = the electrical resistivity of the material in ohm-m,L = the length of the conductor in m, andA = the cross-sectional area in m2.Because the current flows through an effectively smaller area, equation (1) shows that the resistance will be greater. This larger
28、 resistance provides for proportionally larger heat losses. This phenomenon is called skin effect and depending upon the size of the conductor its contribution to the heat losses is to increase the electrical resistance of the conductor, thus providing greater heat loss than that caused by a DC curr
29、ent of the same magnitude as the RMS (root mean square) AC current.A current carrying conductor sets up a magnetic field. When this current is an alternating current, the current created magnetic field is able to induce voltages in surrounding metal-lic objects that can cause currents to flow. When
30、a surrounding metallic object is another conductor, then the induced voltage will cause a current to flow and there is ohmic heating asso-ciated with that induced current. If the nearby conductor is Figure 1 Busway configurations.R LA-=ASHRAE Transactions 371carrying its own current, then the induce
31、d current can alter the current distribution over the cross-section. This rearrange-ment of current can both increase and decrease the total ohmic losses. Likewise, the alternating current in the nearby conduc-tor also sets up a magnetic field that can induce currents in the original conductor and r
32、edistribute the current there. The influence the conductors have on the current distributions in adjacent conductors is called “proximity effect.” The result of proximity effect can change the ohmic heating loss. Whether the change is a greater, a smaller, or an unvarying amount depends on the condu
33、ctor shape, current, and relative place-ment of the conductors.In some published literature regarding proximity effect, such as IEC 60278 2002 (also, see the references cited in Chapter 1of this IEC standard), the proximity effect is sepa-rated from skin effect. It can be argued that owing to linear
34、ity the total magnetic field of the collection of conductors is the superposition of the individual magnetic fields, which is true. However, the losses do not superimpose because the losses depend upon the square of the current density integrated over the cross-sectional area of the conductor. In or
35、der to develop an estimate of the ohmic losses, we need to consider all conductors at the same time. The bus model presented later in this paper does take into account all current carrying conduc-tors at the same time, thus, skin and proximity effect are considered together.As stated earlier, voltag
36、es (and thus currents) can be induced in surrounding metal structures in the vicinity of alter-nating current carrying conductors. The surrounding struc-tures could be beams for switchgear cabinets and conductor supports and metallic cabinet walls. The currents induced in these structures cause heat
37、ing and the ohmic heating associ-ated with these structures is called “stray loss.” Another term used to describe this type of heating is “enclosure loss.” The prediction of stray loss values is complicated owing to the geometry of surrounding structures. The most common attri-bute of the geometry i
38、s that the bus bars parallel a conducting plane over most of switchgear enclosed conductor length.The model of bus bar heating losses to be presented accounts for each of the three ohmic loss mechanisms just described.Single Phase ModelThe succeeding development shows the model used to predict the e
39、ddy current augmented power production in a single phase, rectangular bus bar. The model to be presented is a numerical one that is sufficiently simple to allow spread-sheet implementation. Because a single conductor is being considered, skin effect provides the only means of increasing the resistiv
40、e heating relative to that occurring for DC current. The calculated results will be compared to measured values as a test of the validity of the model.During the early part of the 20thcentury, the increase in ohmic losses caused by skin effect was investigated in hollow cylindrical, hollow square, a
41、nd solid rectangular conductors. The analysis of hollow circular and square conductors covered the range from very thin tubes up to and including solid conductors. The IEEE Standard C37.23 2003 covers the cylindrical and square conductors very well. Notable contri-butions to this investigation of si
42、ngle phase losses are Dwight (1947) and the references cited in Dwights paper. Figure 1 of Dwights paper consisted of a compilation of all known measurement results of the ratio of AC to DC resistance for nonmagnetic solid rectangular conductors as a function of frequency, resistivity, and width to
43、height ratio. Dwight was able to reduce the dependence of the resistance ratio to two parameters being the width to height ratio and the dimension-less quantity P given by(2)whereP = dimensionless parameter,f = the alternating current frequency in Hz,a = the conductor height in meters,b = the conduc
44、tor width in meters, and = the conductor electrical resistivity in ohm-m.The use of P with absolute (cgs) units dates back to the earlier work of Dwight (1918). The width to height ratio (b/a)ranged from unity for square conductors to several hundred for wide flat conducting straps. Arnold (1938) ha
45、s adequately treated the problem of square conductors producing an analyt-ical formula that forms the basis for the results presented in IEEE Standard C37.23 2003. In general, for rectangular conductors there are three regions of Dwights Figure 1 of interest being the low, mid, and high value region
46、s for P. Dwight (1918) treated the low P region where the width to height ratio played only a minor role in determining the AC to DC resistance ratio. Thus, the analysis results, which consisted of an analytical formula, were widely applicable. Cockcroft (1929) treated the high P region of the curve
47、 where the skin effect limits the current to a thin layer at the conductor surface. Cockcroft was able to produce an analytical result. The mid P range of Dwights Figure 1 presents problems in that the simplifying approximations invoked by Dwight (1918) and by Cockcroft are not applicable. Furthermo
48、re, the analysis must be approached from the point of view of solving the partial differential equations that govern the magnetic field inside the conductor. The partial differential equation solution is complicated by the lack of known boundary conditions at the conductor surface. Silvester (1967)
49、points out this compli-cation in a paper where he presented a numerical approach for determining the AC to DC resistance ratio for rectangular conductors. Mocanu (1975) presented an approximate analy-sis for arbitrary cross section based on an iteration method similar to that used by Dwight (1918). For mid-range frequen-cies, numerical methods have essentially provided the way of predicting the AC to DC resistance ratio.P8fab-=372 ASHRAE TransactionsLacking an analytical formula for the midrange P values, a numerical method must be used to predict the AC to
