Transformer Losses, Loading, and Selection Criteria (PDF)

EPRI Underground Distribution Systems Reference Book CHAPTER 16 Transformers and Equipment Authors: Stephen L. Cress, Reviewers: Gordon Hayslip, Snohomish PUD Kinectrics. Inc. John Igielski, Northeast Utilit...

EPRI Underground Distribution Systems Reference Book CHAPTER 16 Transformers and Equipment Authors: Stephen L. Cress, Reviewers: Gordon Hayslip, Snohomish PUD Kinectrics. Inc. John Igielski, Northeast Utilities Ali Naderian, Kinectrics, Inc. Ken Ochs, We Energies Joseph Somma, Consolidated Edison Abstract: This chapter reviews several aspects related to transformers, including transformer losses, loading characteristics, selection criteria for pad-mounted transformers, transformer cooling, interpretation of tests on transformers and oil, and capacitors. Stephen L. Cress graduated in 1976 from The University of Toronto with a Bachelor of Applied Science in Electrical Engineering. He is cur- rently Department Manager – Distribution Asset Management at Kine- ctrics Inc. Stephen has over 33 years’ experience in specialized technical investigations, research, testing, and applications in the power distribu- tion field based on his work at Federal Pioneer, Ontario Hydro Research Division, and Kinectrics Inc. He has conducted major proj- ects for North American distribution utilities dealing with: transformer loading and sizing, transformer losses and efficiency, asset management, asset condition assessment, life extension, distribution protection, equipment failure analysis (transform- ers, switchgear, fuses, capacitors), standard testing, distribution modeling, and develop- ment of utility-oriented engineering software. Stephen is the holder of a U.S. patent on high-voltage current limiting fuses. He is a co-author of the CEATI reference books Application Guide for Distribution Fuses and Engineering Guide for Distribution Overcur- rent Protection. Stephen’s work in the development of probabilistic methods for calculat- ing transformer loss evaluation, loss-of-life, and loading have been incorporated in the commercially available CEATI TRANSIZE TM computer program. He has published papers with international organizations such as IEEE, CIRED, and INTER-RAM, and articles in power industry magazines. He is the Chair of the harmonized CSA and CNC\IEC TC32 Committees dealing with High Voltage Fuses, and a Professional Engineer in the Province of Ontario. Ali Naderian received his B.Sc. and M.Sc. degrees from Sharif Univer- sity of Technology in 1998 and the University of Tehran in 2000, respec- tively. During his studies, his part-time employment experience included ISC (1997-1999) for testing of switchgear and circuit breakers, and ITS (1999-2000) for designing and manufacturing of HV power transform- ers. He was co-designer of a 3*300-kV cascade HV testing transformer. He compared commercially available RTV coatings for outdoor insula- tors in his PhD thesis during his research at the University of Waterloo, Ontario (2003-2006). He has been a project manager of high-voltage testing at Kinectrics, Inc. (formerly Ontario Hydro Research) since 2007, working on diagnostics of power transformers, high-voltage cables, and outdoor insulators. He performs on-line and off- line PD measurements for HV apparatus. His research interests include high-voltage test techniques, dielectric frequency response, and partial discharge. He has published several papers, is actively involved in IEEE transformer working groups, and is a registered engi- neer in the Province of Ontario. 16-1 Chapter 16: Transformers and Equipment EPRI Underground Distribution Systems Reference Book 16.1 INTRODUCTION induced current, called eddy current, produces losses in This edition of the Bronze Book covers only a subset of the core plates. The eddy current loss can be calculated what will be a comprehensive look at underground dis- by Equation 16.2-1 tribution transformers. Included here are sections on π2 transformer losses, loading characteristics, pad- Peddy = σ f 2 d 2 B 2V mounted transformer selection criteria, interpretation 6 16.2-1 of tests on transformers and oil, as well as a discussion Where: on capacitors. σ is the core conductivity. ƒ is frequency. The next edition will also include an overview of trans- d is the core thickness. former types by application, unit components and core B is the peak value of the flux density. construction, installation options, and insulation types. V is the core volume. Additional topics will be transformer cooling, testing and monitoring, and typical examples of failure root As per Equation 16.2-1, eddy current is controlled by causes. using laminated core to cut large current loops at the cross section of the core. The no-load loss is the sum of The reader is encouraged to refer to other sources more hysteresis and eddy current losses, as shown in Equation broadly covering this topic, including the Electric Power 16.2-2. Distribution Handbook by Tom Short (2004), Power Transformers, Principles and Applications by John Wind- P0 = Peddy + Ph 16.2-2 ers (2002), and the ABB Distribution Transformer Guide (2002). 16.2.2 Load Losses Load losses (or copper losses or resistive losses) are pri- 16.2 TRANSFORMER LOSSES marily a function of the winding design of the trans- Losses in distribution transformers are categorized as former. They result from the load current flowing in the load and no-load losses. Load losses vary with the primary and secondary windings. square of the load on the transformer, whereas no-load losses are continuous and constant regardless of load. Components of load loss are I2R and stray losses. For a distribution transformer, I2R is in the range of 92-99% 16.2.1 No-Load Loss of the load loss. The proportion is lower for larger kVA sizes. Load loss is affected by: No-load losses (or excitation losses, iron losses, or core losses) are inherent to the excitation of the transformer. number of turns of winding No-load losses are associated with the core design. They mean length of the primary and secondary turns include core loss, dielectric loss, and the loss in the wind- conductor cross section ings due to exciting current. For distribution transform- ers at 27.6 kV and below, the dielectric loss is negligible. material of the conductor—i.e., copper or aluminum The no-load loss in the transformer core is a function of Stray losses vary inversely as the temperature, thereby the magnitude, frequency, and wavefor m of the making necessary the calculation of load loss at a spe- impressed voltage. No-load losses are affected by volt- cific temperature such as 85°C. Stray losses have three age fluctuations. When an AC voltage is applied to the components: conductor eddy currents, conductor circu- terminals of the transformer, magnetizing current flows lating currents, and stray currents in the core wall and through the winding, and a magnetic flux appears in the core clamps. core. The predominant component is core loss, which is composed of hysteresis and eddy current losses. The current, which is applied to the windings, creates losses due to the winding resistance. The losses of a The hysteresis loss is proportional to the frequency and transformer are losses incident to a specified load car- dependent on the area of the hysteresis loop in the B-H ried by the transformer. Load losses in distribution-class diagram, and, therefore, characteristic of the material transformers mainly include I 2 R loss in the windings and a function of the peak flux density. due to load current. The variable magnetic flux induces current running in Load loss follows Ohm’s law and can be decreased by paths perpendicular to the direction of the flux. The reducing the number of winding turns, by increasing the cross-sectional area of the turn conductor, or by a com- 16-2 EPRI Underground Distribution Systems Reference Book Chapter 16: Transformers and Equipment bination of both. However, reducing the number of Transformer efficiency (η) is the ratio of a transformer’s turns requires an increase of the flux—i.e., an increase useful power output to its total power input as indicated in the core cross-section, which increases the iron weight in Equation 16.2-3 (IEEE 2006). and iron loss. Therefore, a tradeoff has to be made Pout Pin − Ploss between the load loss and the no-load loss. η= = 16.2-3 Pin Pin 16.2.3 Total Loss The following summarizing relationships are useful Where: when considering the losses in distribution transformers: η is the efficiency. Pin is the input power. No Load Loss α Flux Density α 1/# Turns α 1/ Core Pout is the output power. Cross Section Ploss is the total power loss of the transformer to Load Loss α # Turns be introduced. Impedance α Reactance α (# Turns)2 Initial Cost α Core Material α Winding Material In many jurisdictions, government energy agencies have mandated minimum efficiency levels for liquid-filled and Table 16.2-1 summarizes the components of load and dry-type distribution transformers (DOE 2007; NEMA no-load losses. 2002). Table 16.2-3 provides an example of the accepted efficiency levels for liquid-immersed distribution trans- Figure 16.2-1 and Table 16.2-2 provide some typical load and no-load loss values for distribution transform- ers. Figure 16.2-1 illustrates how load losses vary with load on the transformer. 16.2.4 Transformer Efficiency Transformer efficiency is related to the amount of watts losses that occur when the transformer is in operation. Table 16.2-1 Components of Transformer Load and No- Load Loss Type No-Load Lossa Load Lossa I2R from load I Electric I2R from No-load I I2R from I supply- ing Losses Core Hysteresis Loss Conductor Eddy Core Eddy Current Loss Magnetic Current from Stray Eddy Current Loss in Leakage fields Internal components Dielectric Dielectric Loss a. Where I represents current, and I2R is the current Figure 16.2-1 Typical load and no-load losses of squared times the conductor resistance. distribution transformers. Table 16.2-2 Typical Losses for Power Distribution Transformers Rating No-Load Loss Efficiencya KVA Load Loss Watts Watts at 50% load 250 3800 880 0.9925 400 5500 1200 0.9932 667 7900 1700 0.9941 1000 11000 2300 0.9945 1500 15000 3000 0.9950 2500 23000 5000 0.9954 a. Calculated using Equation 16.2-4. 16-3 Chapter 16: Transformers and Equipment EPRI Underground Distribution Systems Reference Book formers. An example of the minimum efficiency for dry- Present distribution transformers are, for the most part, type distribution transformers is shown in Table 16.2-4 between 98% and 99.5% efficient. For the new trans- (DOE 2007). These efficiency values are computed at formers, the guideline from (DOE 2007), presented in 50% of nameplate-rated load. Tables 16.2-3 and 16.2-4, should be followed. Because virtually all-electric energy passes through distribution Efficiency can be expressed directly as a function of the transformers, losses in these devices, though small, are load and no-load losses as in Equation 16.2-4 (NEMA estimated to constitute as much as 2 to 3% of all energy 2002). The efficiency values computed using this for- generated. mula are provided alongside the load and no-load losses in the examples in Table 16.2-2. Generally transformers are at maximum efficiency when they are 50% loaded. When transformers are lightly KVA × Lp.u. loaded, the no-load losses form a large percentage of the η= 16.2-4 KVA × Lp.u. + P0 + Lp.u.2 × PL power utilized, and therefore, the efficiency is low. As the transformer is loaded to higher levels, the load losses Where: dominate the efficiency. The maximum efficiency point KVA is the transformer rated power. is the optimal point of lowest load and no-load losses. It PL is the load loss. is determined by the design of the transformer and theo- P0 is the no-load loss. retically could be designed to occur at any load percent- Lp.u. is the per-unit load (the ratio of actual load age. It typically is designed to occur at 50%, because the to the rated full load). average load tends to be about 50% of the peak load. However, transformers with high no-load losses are Table 16.2-3 Standard Levels of Efficiency for Liquid-immersed Distribution Transformers (DOE 2007) Table 16.2-4 Standard Levels of Efficiency for Dry-type Distribution Transformers (DOE 2007) 16-4 EPRI Underground Distribution Systems Reference Book Chapter 16: Transformers and Equipment most efficient at 60%-80% load, and transformers with tive permeability of the steel, thus reducing the losses, low no-load losses are most efficient at about 40% load. but it also decreases the saturation magnetic flux den- (See Figure 16.2-2.) sity, which increases the amount of material required in the core. Together, these effects reduce the no-load loss 16.2.5 Reduction of Transformer Losses of the core, but the amorphous steel cores are larger, Reduction of transformer losses and improvement in heavier, and more costly to produce. (Permeability efficiency can be achieved by reduction of either load or increases by a factor of 4, but saturation flux density no-load losses. For any given set of core and winding decreases by a factor of 0.75, requiring 1.3 times as materials, reduction of load losses often leads to an much material in the core, so overall loss is lower by a increase in no-load losses and vice versa. factor of 3.) On average, amorphous core loss values are about 30% of that for high-efficiency silicon steel, and Many factors of core design affect no-load losses and only 15% of that for older, less efficient steels. can be altered to reduce these losses. Higher magnetic flux density leads to higher losses. Larger gaps in cut Numerous questions have arisen regarding the mechani- cores lead to higher losses. These gaps can be reduced cal robustness and long-term mechanical performance by manufacturing techniques. The thickness of the of amorphous metals. Short-term testing programs have enamel insulation on the winding conductors affects the not substantiated these beliefs, but the concern persists. size of the core. High-quality enamel can be used in very thin layers to reduce core size and no-load losses. More recently nano-crystalline steel has become avail- Mechanical arrangement of the windings and taps also able for use in transformer cores. affects the efficient use of space and the size of the core. The best are based on an Fe-Zr-B alloy that is formed in Traditionally cores have been made from grain-oriented an amorphous state and then annealed to produce very silicon steel formed into thin sheets and wrapped into a small grain sizes. This approach makes the material less rectangular shape. The loss decreases as the thickness of brittle and thereby decreases production costs. This steel the sheets decrease. Standard grades are M-2 at 0.18 has even higher permeability and also higher saturation mm, M-3 at 0.23 mm, M-4 at 0.27 mm, and M-6 at 0.35 induction than the amorphous materials, but it is not mm. Losses also depend on the permeability of the steel yet available in manufactured transformer cores. The alloy. Higher permeability leads to lower losses. The new steel has 17 times the permeability of steel and 0.89 permeability depends upon the alloy and the orienta- of the saturation flux density; so losses should be tions of the grains. reduced by a factor of 15. A large advance in technology occurred in the 1980s Load losses are caused primarily by the heating of the with the development of amorphous steel cores. These windings by the passage of current (I2R losses). The cur- cores are also built up by wrapping thin sheets or rib- rent is determined by the impedance of the load on the bons, but the steel itself (such as Co-Fe-Si-B alloy) is transformer and the voltage levels and so is not under quenched during manufacture to ensure that no grains the control of the transformer designer. The resistance are formed in the steel. This process increases the effec- depends on the material used in the winding, the cross- sectional area of the wires, and the number of turns. Transformer windings are made of either copper or alu- minum in round wires, square wires, or flat sheets. The resistivity of aluminum is about 1.6 times larger than that of copper, but aluminum has a lower cost. Many different alloys of aluminum and copper are available. In general, the lower resistance alloys are more expen- sive and harder to work with in the manufacturing pro- cesses, leading to higher initial costs. In addition to choice of material, load losses are affected by the cross-sectional area of the wire used. Larger wires produce lower load losses, but then the windings are larger, and this requires a larger core, Figure 16.2-2 Transformer efficiency as a function of load. which increases the no-load losses. 16-5 Chapter 16: Transformers and Equipment EPRI Underground Distribution Systems Reference Book Some load loss is caused by induced currents from adja- 16.2.7 Cost-of-Losses Formula cent windings. These currents can be reduced by using The lifetime cost of a transformer depends on the capi- continuously transposed conductor in the winding and tal cost of the transformer and the cost of the load and thus reducing load losses. This approach also leads to no-load losses during its lifetime. The present value higher initial costs. method is often employed to express the lifetime cost in terms of a dollar value in the present year. Losses from 16.2.6 Transformer Short-circuit Impedance distribution transformers are a significant contribution When provided a customer’s cost of no-load and load to distribution system losses, and their reduction repre- losses, transformer manufacturers will use software that sents an opportunity for improving energy efficiency performs hundreds of iterations, varying core, winding, and tank options, to arrive at a transformer with an A cost-of-losses formula for purchasing purposes is optimal balance of losses and initial cost. often employed to determine the lifetime costs for vari- ous transformer options available to utilities. Compari- The short-circuit impedance of a transformer is used to sons can then be made between more capital intensive calculate the maximum short-circuit current and is low-loss transformers and less expensive higher-loss needed for sizing circuit breakers, fuses, cables, and transformers. other equipment connected to the secondary of the transformer. The following paragraphs describe the general formula- tion of a cost-of-losses formula. Table 16.2-5 defines the Transformer impedance (or short-circuit impedance or quantities used in these equations. impedance voltage) is the percent of per unit voltage that must be applied to the primary side of a trans- former, so that the rated current flows when the second- Table 16.2-5 Definition of Symbols for Cost of Losses ary terminals are short-circuited. This impedance is Formula formulated as Equation 16.2-5. CAP Capital cost ($) CLL Present value of cost of load losses ($/W) U CLL(m) Cost of load losses for month “m” ($/kW) Z % = Z × 100 16.2-5 ZP CLY(y) Cost of load losses for year “y” ($) CNLL Present value of cost of no-load losses ($/W) As the no-load test result is available, the ohmic part of CNLL(m) Cost of no-load losses for month “m” ($/kW) the impedance can be calculated using Equation 16.2-6, D Demand charge, monthly ($/kW) and therefore, the inductive part of the impedance can D(m) Demand charge for month “m” ($/kW) be derived by Equation 16.2-7. E Energy charge, monthly (¢/kWh) EOP(m) Energy charge off-peak for month “m” (¢/kWh) P3ϕ − load − loss EP(m) Energy charge on-peak for month “m” (¢/kWh) R% = × 100 16.2-6 MVA3ϕ.106 FYG(y) Factor for yearly load growth accumulated to year “y” X % = Z %2 − R%2 16.2-7 g(y) Growth of load for year “y” (%/100) HOP(m) Hours off-peak for month “m” (h) In a transformer having a tapped winding, the short-cir- HP(m) Hours on-peak for month “m” (h) cuit impedance is referred to a particular tap. Unless i(y) Interest rate for year “y” (%/100) otherwise specified, the nominal tap applies and is the j(y) Inflation rate for year “y” (%/100) impedance (Z%) that is marked on the nameplate. The PVLC Present value of lifetime cost ($) impedance voltage of distribution transformers with LL Load losses (W) rated power below 630 kVA is usually 4% or less, and LSF Loss factor (average loss/peak loss) this value is usually around 6% for 630 kVA up to NLL No-load losses (W) 2.5 MVA distribution transformers. NY Number of years in economic study period p(y) Growth of power costs for year “y” (%/100) For parallel operation of two or more transformers, PVF Present value factor for a period of years short-circuit impedance is critical. If paralleled trans- PVF(y) Present value factor for year “y” formers do not have the same short-circuit impedance, RATL Rated load for transformer (kVA) the load will be shared in an unbalanced way such that Responsibility factor (load at system peak/peak RF load)2 one transformer can be overloaded and the transformer UF Utilization factor (peak load/rated load) can be underloaded. 16-6 EPRI Underground Distribution Systems Reference Book Chapter 16: Transformers and Equipment The basic form of the cost of losses formula, providing 1 ⎛ E ⎞ the present value of the lifetime cost (PVLC) of a trans- CLL = ⎜12D ∗ RF + 8760 ∗ LSF ⎟ formers, is as expressed in Equation 16.2-8. 1000 ⎝ 100 ⎠ 16.2-10 { } NY ∗∑ [UF ∗ FYG ( y )] ∗ PVF ( y ) 2 PVLC = CAP + NLL ∗ CNLL + LL ∗ CLL 16.2-8 y =1 Where: (1 + p ) y −1 PVF ( y ) = 16.2-11 CAP is the capital cost or initial purchase price (1 + i ) y of the transformer. NY NLL is the no-load losses that occur continu- PVF = ∑ PVF ( y ) 16.2-12 ously when the transformer is energized, y =1 regardless of the loading. FYG ( y ) = (1 + g ) y −1 16.2-13 CNLL is the cost of no-load losses and is inde- pendent of the loading and dependent on the demand and energy charges. Time-of- Where: use energy charges can be considered by UF, the utilization factor, is defined as the ratio of the using on-peak and off-peak energy peak load to the transformer rated load. It repre- charges, and considering the hours that sents the portion of the transformer rated load that the transformer is on-peak or off-peak. is utilized when the transformer is at its highest LL is the load loss at rated load. The value of loading. load loss at rated load is a measured peak load parameter, and load losses at other load- UF = 16.2-14 rated load ings are derived from this value. CLL is the cost of the load losses, and depends on the demand and energy charge rates as RF, the peak responsibility factor, is used to adjust the load to well as on the loading of the transformer reflect the proportion of the asset load that actually contrib- throughout its life. utes to the peak load of the utility as a whole. That is, it indi- cates how much the lo ad lo ss of the particu lar Common cost-of-losses equations use flat-rate demand transformer contributes to the total demand. The and energy charges and fixed annual economic factors, responsibility factor is the ratio of the transformer load such as interest rate, to evaluate the lifetime costs of at system peak to the peak load, all squared. load losses (CLL) and cost of no-load losses (CNLL). 2 ⎛ load at system peak ⎞ The concepts of load factor, loss-factor, utilization fac- RF = ⎜ ⎟ 16.2-15 tor, and responsibility factor are used to describe the ⎝ peak load ⎠ loads on the transformer. A load growth factor can be used to include the influence of rising loads on the LSF, the loss factor, is the ratio of the average loss to the transformer losses over the transformer’s lifetime. Note peak loss. The loss factor can be derived from the load that the load growth factor is 1 in the first year, and then factor. The load factor is a single value that character- changes to a fixed factor at the start of the second year. izes the load profile. The load factor is the ratio of the The present value factor includes the influence of eco- average load to the peak load. nomic factors such as inflation of the cost of power and interest rates. The growth in power costs factor is 1 in Load and loss factors are dependent on the shape of the the first year and then changes to a fixed factor in the load profile. Loading profiles are different for indus- second year. The rate of interest starts in the first year. trial/commercial, urban residential, and rural residential Note that there are 8760 hours in a year. transformers. Industrial/commercial loads are steadier both over the day and over the week. A typical load fac- 1 ⎛ E ⎞ CNLL = ⎜12D + 8760 ⎟ ∗ PVF 16.2-9 tor is 0.85. Residential loads are more variable, with typ- 1000 ⎝ 100 ⎠ ical load factors of 0.4 for a single transformer. Urban residential transformers tend to be more heavily loaded than rural transformers. Theoretically the loss factor may have a value between the value of the load factor and the load factor squared, depending on the load profile shape. A common for- 16-7 Chapter 16: Transformers and Equipment EPRI Underground Distribution Systems Reference Book mula that has been used to calculate loss factor from NY load factor is as shown in Equation 16.2-16. PVF = ∑ PVF ( y ) 16.2-23 y =1 LSF = 0.85 * LDF 2 + 0.15 * LDF 16.2-16 FYG ( y ) = [1 + g ( y )] ∗ FYG ( y − 1) 16.2-24 Where FYG (1) = 1 + g (1) 16.2-25 LDF is the load factor of the daily load profile. Where the variables are as defined in Table 16.2-5. PVF, the present value factor, accounts for the changing value of money and expresses the present worth of dol- With computer assistance the cost of losses formula can lars spent in the future. be further expanded to replace the use of the load factor concept and determine loads directly from daily and Economic factors, of course, are generally not fixed over monthly profiles. long time periods of time. Further, there is considerable utility interest in applying variable or time-of-use rates. Figure 16.2-3 shows a general graph of costs versus With addition of several parameters, the cost of losses transformer mass for a typical distribution transformer. formula can be modified to consider these variable eco- There is an optimum value for total cost. If the loss eval- nomic inputs. uation figures are submitted to the transformer manu- facturers in the request for quotation, they can design a Energy and demand charges can be expressed as being transformer with an optimal cost from the end user dependent on the time of use, either on-peak or off- point of view. The result of this process should be the peak. Economic factors and the load growth can be cheapest transformer in the useful life period—i.e., with allowed in the equation to vary from year to year. Note the lowest total owning cost, optimized for a given that either p(y) or j(y) must be set to zero for all years application. y. To use the initial cost of power in the first year, set p(1) to zero [or j(1) to zero, if you are not using p(y)]. Therefore the components of the cost of losses formula can be further expressed as: ⎡ 1 12 ⎤ CLL = ⎢ ∗ ∑ CLL( m ) ⎥ ⎣1000 m =1 ⎦ 16.2-17 { } NY ∗∑ [UF ∗ FYG ( y )] ∗ PVF ( y ) 2 y =1 CLL( m ) = D( m ) ∗ RF ⎡ EP ( m ) EOP ( m ) ⎤ + ⎢ HP ( m ) ∗ + HOP ( m ) ∗ ⎣ 100 100 ⎥⎦ ∗LSF 16.2-18 Figure 16.2-3 Transformer mass vs. transformer lifetime cost. ⎡ 1 ⎤12 CNLL = ⎢ ∗ ∑ CNLL( m ) ⎥ ∗ PVF 16.2-19 ⎣1000 m =1 ⎦ CNLL( m ) = D( m ) + HP ( m ) EP ( m ) ∗ + HOP ( m ) 16.2-20 100 EOP ( m ) ∗ 100 [1 + p( y )] ∗ [1 + j ( y )] PVF ( y ) = ∗ PVF ( y − 1) 16.2-21 [1 + i ( y ) PVF (1) = [1 + p(1)] ∗ [1 + j (1)] 16.2-22 [1 + i (1)] 16-8 EPRI Underground Distribution Systems Reference Book Chapter 16: Transformers and Equipment 16.3 LOAD CHARACTERISTICS FOR 24-hour load profile is modeled by a series of constant TRANSFORMERS loads of a short duration, usually 1 hour. The equivalent One of the main considerations for selecting the appro- load during the short time steps is determined by using priate transformer is the characteristic of the load. Not the maximum peak load during the short-time period only the number and type of loads, but the load pattern under consideration. An equivalent two-step overload needs to be considered. cycle can be used for determining emergency overload capability, as shown in Figure 16.3-1. The equivalent Because load is a function of human behavior and life- two-step load cycle consists of a prior load and a peak style variables, as well as the type and size of electric load. A constant load that generates total losses the equipment and weather changes, load forecasting has same as a fluctuating load is assumed to be an equiva- some level of uncertainty. lent load from a temperature standpoint. Equivalent load for a specific part of daily load is expressed by 16.3.1 Load Types Equation 16.3-1. Several types of loads occur on a distribution systems: N Domestic (residential): Mainly lights, fans, heaters, ∑L t 2 i i refrigerators, air conditioners, ovens, small pumps, Leq = i =1 N 16.3-1 and other household appliances. ∑ ti i =1 Commercial: Lighting of shops, air-conditioning, heating, and shop appliances. Where: Industrial: Medium and large motors. Li is various load steps in% or per unit. N is the total number of load steps. Municipal (Public): Street lights, and traffic signals. ti is the duration of each load step. Agricultural: Motors and pumps. 16.3.3 Peak Load Commercial loads typically have a dedicated trans- Equivalent peak load is the rms load obtained by Equa- former; however, multiple residences are usually served tion 16.3-1 for the limited period over which the major by a single or three-phase transformer. Public loads usu- part of the actual peak exists. If the peak load duration ally need their own dedicated transformer due to the load is over-estimated, the rms peak value may be consider- size. The daily load profiles of these three load categories ably below the maximum peak demand. To protect are not usually matched. Commercial and industrial against overheating due to high, brief overloads during loads may at times e served on a spot network of multiple the peak overload, the rms value for the peak load transformers in parallel. Some service areas, mainly in period should not be less than 90% of the integrated ½ metropolitan areas of loads including residential and hour maximum demand. commercial loads are serviced from distributed grids of many transformers in parallel via network protectors. Besides daily peak load, seasonal peak load needs to be taken into account. Depending on the geographic loca- Distribution transformers serving primarily residential tion, and due to weather conditions, a winter peak or loads regularly carry average loads that are only 15 to summer peak can be expected. 25% of the transformer's rated capacity but also must be designed to support peak morning and evening loads. An example of a daily load profile with two peak loads Because of the wide gap between peak and non-peak is given in Figure 16.3-2. loads, and the relatively limited amount of time that the transformer is peak-loaded, average transformer load- ing tends to be fairly low. 16.3.2 Load Profiles Transformer loads generally follow cycles that repeat daily, and may have seasonal variation during the year and yearly growth. The daily load variation for many utilities repeats every 24 hours and has two common forms: a single hump shape (as shown in Figure 16.3-1) or a double hump shape. A multistep load cycle calcula- Figure 16.3-1 Example of actual load cycle and tion can be used to describe the load (IEEE 1995b). The equivalent load cycle of IEEE C57.91. 16-9 Chapter 16: Transformers and Equipment EPRI Underground Distribution Systems Reference Book the actual maximum demand on the system as described in Equation 16.3-4. Load Diversity = ∑ Individual Maximum Demands − System Maximum Demand 16.3-4 Diversity factor in a distribution system is the ratio of the sum of the individual maximum demands of the var- ious subdivisions of a system to the maximum demand of the whole system under consideration (see Equation 16.3-5). Loads do not normally all peak at the same time. Therefore, the sum of the individual peak loads is greater than the peak load of the composite system. Therefore, diversity factor is usually more than one. Figure 16.3-2 Morning and evening peak loads (from Pabla 2004). DF = ∑ Individual Maximum Demands 16.3-5 System Maximum Demand 16.3.4 Average Load Demand factor is the ratio of the maximum demand of According to IEEE C57.91, the average continuous load a system, or part of a system, to the total connected is the rms load obtained by Equation 16.3-1 over a cho- load on the system. Demand factor is always less than sen period of the day. A period of 12 hours preceding one. “Demand factor” is a percentage by which the total and following the peak is suggested to be considered for connected load on a service or feeder is multiplied to the time interval of average load calculation. Time inter- determine the greatest probable load that the feeder will vals (t) of 1 hour are suggested as a further simplifica- be called upon to carry. For example, in hospitals, tion of the equation, which for a 12-hour period hotels, apartment complexes, and dwelling units, it is becomes Equation 16.3-2. The dashed line in Figure not likely that all of the loads are connected to every 16.3-2 shows the average load cycle constructed from branch-circuit served by a service or feeder would be the actual load cycle. “on” at the same time. Therefore, instead of sizing the 12 feeder to carry the entire load on all of the branches, a Laverage (12h ) = 0.29 ∑L i =1 2 i 16.3-2 percentage can be applied to this total load, and the components sized accordingly. Equation 16.3-6 formu- lates the size of a distribution transformer considering In fact, the average load determines the kWh billing rev- the incorporated factors: enue that will be obtained from serving the load, whereas peak load determines how much system capac- M N i × kWi × DFi × LFi ity is required to serve that particular load group. ∑ i =1 PFi 16.3-6 S ( kVA) = DivF 16.3.5 Load Factor The ratio of the average demand over a time interval to Where: the maximum demand over the same time interval is the S is the rated power of transformer. load factor. N is the number of loads (appliances) of the same type. Average Demand Power( kW ) kW is the rated power of each load. LDF % = × 100 16.3-3 Peak Load ( kW ) DF is demand factor. LF is the load factor. Load factor can be calculated daily, monthly, and annu- PF is the power factor of each load. ally based on the load profile. M is the number of different type of loads. DivF is the diversity factor. 16.3.6 Load Diversity, Diversity Factor, and Demand Factor Table 16.3-1 suggests typical values for load factor, Load diversity is the difference between the sum of the diversity factor, and demand factor of loads (Pabla individual maximum demands of loads on a system and 2004). 16-10 EPRI Underground Distribution Systems Reference Book Chapter 16: Transformers and Equipment 16.3.7 Load Growth In general, the method to determine the maximum Estimating load growth includes an element of specula- diversified load of a number of houses consists of the tion. Load growth for each year into the future may be following steps: estimated from known factors such as planned installa- Define the type of houses based on major electrical tion and geographically related load patterns. usage, such as space heating, water heating, and air conditioning. If the annual rate of load growth is available, the load Identify all loads in the type of home being consid- growth can be calculated for the transformer useful life- ered. time interval. The modified transformer rating is as shown in Equation 16.3-7. Determine the value of all Connected Loads (Lk) and the Maximum Non-Coincident Demand (MNCD). ST = S (1 + i )n 16.3-7 Determine the maximum peak load for each house type. Where: S is the calculated power from Equation Use demand factors to determine the Maximum 16.3-6. Coincident Demand (MCD) for groups of similar i is the annual growth rate. types of houses. n is the typical expected transformer life. Develop charts of number of kW per home vs. num- ber of homes, and total kW vs. number of homes. 16.3.8 Load Diversity Charts Residential loads can be analyzed to determine the type Load diversity considerations account for the fact that of electrical equipment and its electrical load that would not all loads connected to the distribution transformer be connected in typical homes. Electrical equipment will be drawing power at the same time. Many individual used in residential homes may be general (e.g., clothes loads are thermostatically controlled or cycling and washer, microwave oven, stereo, hair dryer, etc.), high- therefore are not likely to be turned on at the same energy consuming (e.g., electric clothes dryer), or ther- time—that is, not coincident. Transformer loading mostatically controlled (e.g., refrigerator, air-condition- needs to accommodate the diversified or coincident load ing, heating). For an average home, major appliances as opposed to the total connected load. consume the most electrical energy (10.3-kWh/day). Lighting would consume an average of 4.1-kWh/day. For the purpose of characterizing loads on a distribu- Homes with air-conditioning units would utilize tion transformer, it is useful to determine the maximum 7.3-kWh for cooling and motor blower. Houses with peak load that is likely to occur when a group of similar electric heating use, would utilize on average about load types are connected to the transformer. For 120 kWh/day, and average houses with electric water instance, in practice, it is useful to know the ultimate heating consume 14.7-kWh/day. peak load that will result from connecting a number of similar electrically heated residences to a distribution Based on the electrical energy equipment and load, transformer. The total diversified or coincident load on houses can be classified into different major categories the transformer will be less than the sum of the maxi- such as: mum peak demand of all the residences. Natural gas heated with no air conditioning Table 16.3-1 Typical values for Demand Factor, Diversity Natural gas heated with air conditioning Factor, and Load Factor Natural gas heated with air conditioning and electric Demand Diversity water heating Factor% Factor Load Factor% Natural gas heating and cooking with air condition- Domestic 70-100 1.2-1.3 10-15 ing Commercial 90-100 1.1-1.2 25-30 Industrial Central electrical heating, electrical water heating (less than 70-80 - 60-65 with no air conditioning 500 kW) Industrial (Above 500 85-90 - 70-80 The definitions and relations for maximum coincident kW) load, maximum noncoincident load, connected loads, Municipal 100 1 25-30 Agricultural 15-20 1-1.5 90-100 16-11 Chapter 16: Transformers and Equipment EPRI Underground Distribution Systems Reference Book diversity factor, and demand factor are expressed in A second method for developing diversity charts is Equations 16.3-8 and 16.3-9. using the “diversity factor” and the relation as shown in Equation 16.3-10. Maximum Coincident Demand ( MCD ) = DF. Lk Maximum Diversified 16.3-8 ΣkWn ( DF1 ). ⎡⎣1 − P N ⎤⎦ ( Coincident ) Demand = 16.3-10 ( Fact )n Div ( DF )N = 16.3-9 N [1 − P ] Where: Where: Σ kWn is the sum of the maximum non-diversified DF is the demand factor. load. DF1 is the demand factor for one house (ratio of Maximum Demand to Total Connected Table 16.3-2 is an example of a diversity chart for 1 to 20 Load for one house). houses for different scenarios including air conditioned, Lk is the total connected load. electric heating, natural gas appliances, etc. The refer- N is the number of houses. ence size of the house is a range of 1250 to 1750 square P is the probability that one house has the feet. Larger or smaller homes or with a mix of loads same Coincident Loads as other houses would require appropriate adjustments to these load within the same time period. factors. Utilities should develop their own diversity charts based on their regional loading data. With these relations, demand factors for different condi- tions can be established. The demand factor approach was used in Table 16.3-2, where: Demand factor for N = 1 is 0.64. Probability factor is 0.7. Table 16.3-2 Diversity Chart for 1 to 20 Detached Houses Transformer Peak Load (kW) for Detached Houses (1250 to 1750 ft2) Peak Season Number of Houses 1 2 3 4 5 6 7 8 9 10 Demand Factor 0.64 0.55 0.47 0.41 0.36 0.31 0.28 0.25 0.23 0.21 Natural Gas Summer 8.6 14.9 19.4 22.7 25.2 27.1 28.6 29.9 30.9 31.8 Heated – No A/C Natural Gas Heated – Central Summer 10.2 17.9 23.9 28.9 32.9 36.4 39.4 42.1 44.8 47.2 A/C Natural Gas Heated – Natu- Summer 8.8 15.5 20.9 25.2 28.9 32.2 35.0 37.7 40.2 42.5 ral Gas Stove - Central A/C Natural Gas Heated – electric Summer 12.8 22.9 31.2 38.1 44.1 49.5 54.4 59.0 63.4 67.6 Water Heater - Central A/C Electric Space Winter 14.8 27.7 39.1 49.6 59.4 68.8 77.8 68.6 95.2 103.7 and Water Heat 16-12 EPRI Underground Distribution Systems Reference Book Chapter 16: Transformers and Equipment 16.4 PAD-MOUNT TRANSFORMER SELECTION been used for transformers with 65°C average winding temperature rise. 16.4.1 Loading Criteria and Transformer Rating The rated kVA of a transformer is the output that can Top oil temperature alone should not be used as a guide be delivered for the time specified at rated secondary in loading transformers, because the difference between voltage and rated frequency without exceeding the spec- top oil and hot-spot copper temperatures varies with ified temperature-rise limitations and within the limits different designs and with load. Transformers may be established in the design spec. operated above average continuous hottest-spot temper- atures (95°C for 55°C rated transformers and 110°C for Selection of a transformer with an appropriate rating to 65°C rated transformers) for short times, provided they serve to load should be done by considering several fac- are operated over much longer periods at temperatures tors, including: below 95°C and 110°C, respectively. According to Equa- tion 16.4-1, 110°C is the sum of the following: average Transformer internal temperatures, such as hottest winding rise (65°C), ambient (30°C), and hot spot rise spot in the winding, top oil temperature, and average (15°C). winding temperatures, Transformer loss of life, and Two characteristic modes of operation can be identified Total lifetime cost of the transformer with respect to the aging of insulation: Normal operation—corresponds to the normal life Hottest-spot, Top Oil Temperatures, and Average Winding expectancy where the deterioration under varying Temperature conditions of load and ambient temperature is nor- Transformer loading causes heat to be generated due to mal. the winding and core losses, which results in a tempera- ture rise of the oil and solid insulation. In addition, ele- Overload operation—which is permitted when neces- vated loading increases the presence of oxygen, moisture, sary without risking the reliability of the transformer. and their byproducts, and will accelerate the process of insulation aging. It is, therefore, important to ensure that Loading of transformers above nameplate is a contro- the temperature rise is kept within the design limits. It is versial subject. Transformers, at some time, may have to possible to relate normal and abnormal loading to the be overloaded during power system emergencies, in transformer hottest-spot temperature in order to under- order to preserve system reliability. The maximum con- stand how loading affects the life of the insulation. tinuous load-carrying capacity of the transformer depends on its rating, on the temperature of the cooling The hot-spot winding temperature is the principal factor medium, ambient temperature, and the level of accepted in determining the degradation of the transformer due insulation aging governed by the effect of temperature to loading and hence has major bearing on the trans- and time. former life. The hottest-spot temperature can be consid- ered as the sum of the temperature of the cooling Overload capacity of a transformer is the maximum medium, the average temperature rise of the copper, and load for which the transformer can be subjected for a the hot-spot allowance. It is given by Equation 16.4-1 particular duration and considering a particular ambi- ent temperature. θ H = θ A + ΔθT + Δθ H 16.4-1 ΔθT = θT − θ A The overload capacity depends on the average winding temperature rise that has been used to design the trans- Where: former. This temperature can be 55°C or 65°C, depend- θΑ is the average ambient temperature. ing on the standard or request of end user at purchase ΔθΤ is the top-oil rise over ambient temperature. time. ΔθΗ is the winding hottest-spot rise over top-oil temperature. When transformer purchase specifications include over- loadability requirements for specific load profiles, in It is not possible to measure the hottest-spot tempera- duration, frequency, and magnitude of overload, the ture directly in a traditional transformer because of the manufacturer will adjust the design accordingly to guar- hazards in placing a temperature detector at the proper antee such overload operation as normal, and can also location. Standard allowances for hottest-spot rise over do so with no loss of life as specified. This design adjust- top-oil temperature have been obtained from laboratory ment usually results in a more substantial design and/or tests. A hottest-spot allowance at rated load of 15°C has lower loss unit. 16-13 Chapter 16: Transformers and Equipment EPRI Underground Distribution Systems Reference Book According to IEEE C57.91, normal life expectancy will bushings, leads, soldered connections, and tap changers; result from operating continuously with hottest-spot and heating of associated equipment such as cables, cir- conductor temperature of 110°C or with an equivalent cuit breakers, fuses, disconnecting switches, and current daily transient cycle. Distribution transformer tests indi- transformers are examples of associated equipment. cate that the normal life expectancy at a continuous hot- Any one of these may constitute the practical limit in test-spot temperature of 110°C is 20 years. load-carrying ability. Long-term and Short-time Emergency Overloads If the loading strategy is based on the average winding The permissible loading of transformers for normal life temperature, as a typical value, for each degree Celsius expectancy depends on the design of the particular in excess of 5°C that the average winding test tempera- transformer, its temperature rise at rated load, tempera- ture rise is below 65 °C, the transformer load may be ture of the cooling medium, duration of the overloads, increased above rated kVA by 1.0%. The 5°C margin is the load factor, and the altitude above sea level if air is taken to provide a tolerance in the measurement of tem- used as the cooling medium. ANSI-IEEE C57.92 perature rise. The load value thus obtained is the kVA (ANSI/IEEE 1981) has developed several permissible load, which the transformer can carry at 65°C rise. overload graphs for different types of transformers with respect to a number of factors. Figure 16.4-1 shows a For a very short-time loading that is less than ½ hour, it typical overload capability curve for oil-immersed trans- is possible to load transformers up to 300%, with the formers from ANSI C57.92 for ambient temperature of maximum hottest spot of 200oC and top-oil temperature 30oC and oil temperature rise of 65oC. For example, a of 120oC. If the high loading factor continues more than liquid-filled transformer with a 50% continuous equiva- ½ hour, the insulation aging takes place. It should be lent base load at 30°C ambient temperature could be clearly understood that, while the insulation aging rate loaded to 120% of full load nameplate rating for five information is considered to be conservative and helpful hours without excessive loss of insulation life. in estimating the relative loss of life due to loads above nameplate rating under various conditions, this infor- Overloading of transformers should not be practiced mation is not intended to furnish the sole basis for cal- without investigation of the various limitations culating the normal life expectancy of transformer involved, other than winding and oil temperature. Oil insulation. The uncertainty of service conditions and expansion; pressure in sealed- type units; heating of the wide range in ratings covered should be considered in determining a loading schedule. As a guide, utilities consider an average loss of life of 4% per day in any one emergency operation to be reasonable. Percent Loss-of-Life due to Loading Aging or deterioration of insulation is a function of time and temperature. When cellulose ages, the cellulose chains are cut in a process called chain scission, reduc- ing the average length of the cellulose chains and result- ing in shorter fibers. This can be measured by Degree of Polymerization, or so-called DP. The rate of degrada- tion is very slow at room temperature. At elevated tem- peratures, however, the rate of degradation increases exponentially, effectively doubling for approximately every 8°C increase in temperature. Because the tempera- ture distribution in most apparatus is not uniform, the part that is operating at the highest temperature will ordinarily undergo the greatest deterioration. Therefore, it is usual to consider the effects produced by the highest temperature, or the hottest spot. Traditionally NEMA developed graphs of % of loss of life of transformers versus the hottest spot temperature, Figure 16.4-1 Permissible overload for varying periods of as shown in Figure 16.4-2. The basis of the aging factor time for oil-filled transformers with 65oC rise based on the modeled by IEEE is the exponential curve of aging ver- initial load, normal life expectancy, ambient = 30oC (ANSI sus temperature. C57.92). 16-14 EPRI Underground Distribution Systems Reference Book Chapter 16: Transformers and Equipment IEEE C57.91-1995 (IEEE 1995) has a well-defined types. This standard defines “insulation aging rate”, model for transformer aging and life of insulation. It FAA, as shown in Equation 16.4-3. includes a per unit life model to calculate the aging of ⎛ A A ⎞ transformers, as shown in Equation 16.4-2. ⎜ ⎜θ − ⎟ + 273 θ HS + 273 ⎟⎠ 16.4-3 FAA = e ⎝ HS ,R B PerUnit Life = Ae θH + 273 16.4-2 Where FAA is the insulation aging rate, θHS,R is the refer- ence hot spot temperature for the insulation, and θHS is where θΗ is the winding hottest spot in °C, A = 2 × 10−18 the hot spot temperature at which aging is evaluated. and B is a constant equal to 15,000 for most insulation A curve of FAA versus hottest-spot temperature for a 65°C rise insulation system is shown in Figure 16.4-3. FAA has a value greater than 1 for winding hottest-spot temperatures greater than the reference temperature 110°C and less than 1 for temperatures below 110°C. Reduced Life Expectancy with Heavy Loading IEEE C57.91 has defined a method to calculate the reduced life expectancy based on “aging accelerated fac- tor”, FAA as shown in Figure 16.4-3. The reduced life expectancy, RLF , is calculated from Equation 16.4-4. Feq × t % RLF = × 100 16.4-4 Normal Life N ( ∑ FAAn Δtn ) Feq = n =1 N 16.4-5 ∑ Δt n =1 n Where: Feq is equivalent aging factor for the total time period. N is the total number of intervals. FAAn is aging acceleration factor for the tempera- Figure 16.4-2 Loss of life versus temperature for different ture that exists during the time interval time periods, 65oC rise time (NEMA TR-98-1964). Δ tn. t is the time period in hours. Figure 16.4-3 Insulation’s aging acceleration factor (IEEE C57.91-1995). 16-15 Chapter 16: Transformers and Equipment EPRI Underground Distribution Systems Reference Book Normal Life is defined by manufacturer. As a bench- roof gratings, a higher ambient temperature than the mark for a distribution transformer, normal life is 20 outdoor air is expected. The amount of increase years for a well-dried, oxygen-free 65oC average winding depends on the design of the manholes and vaults, net temperature rise insulation at a reference temperature of opening area of the roof gratings, and the adjacent sub- 110oC. surface structures. Therefore, the increase in effective ambient temperature for expected transformer losses Unusual Service Condition must be determined before loading limitations can be A number of factors related to transformer loading are estimated. considered unusual service conditions such as: Increase of ambient temperature Total Lifetime Cost As discussed in Section 16.2.7, “Cost of Loss Formula,” Installation in a height more than 1000 m (3300 ft) the transformer cost has three components: capital investment, no-load loss, and load loss. If the end-user The design of distribution transformers usually consid- provides the energy price with the purchase request, the ers ambient temperature of 30oC. If the average of ambi- designer can develop a transformer design that will min- ent temperature increases, the loading should be imize the total lifetime cost including the cost of losses. lowered to keep the normal life expectancy. A guideline The result of this process is the cheapest transformer in provided by IEEE C57.91 suggests a load de-rating of the useful life period—i.e., with the lowest total owning 1.5% for each o C up to 50 o C. The load is allowed to cost—optimized for a given application. increase by 1% for each oC lower than 30o C. Average ambient temperatures can be considered to cover The following considers the total cost of losses for trans- 24-hour periods. The maximum ambient temperature in formers loaded at different fractions of their rating. 24 hours should not be more than 10°C above the aver- Typically a transformer is designed to have a minimum age temperature. loss when operated at about 50% of rating. However, a larger transformer operated at a lower fraction of rat- The effect of the decreased air density due to high alti- ing, may have a smaller cost of losses than a smaller unit tude is to increase the temperature rise of transformers, operated at 50% of rating. This circumstance will be because they are dependent upon air for the dissipation particularly true in situations with significant annual of heat losses. If the transformer is installed at a height load growth. of 1000 m (3300 ft) above sea level, a de-rating factor needs to be considered as shown in Figure 16.4-4. The present value of the total cost of losses can be cal- culated by calculating the loss in each of the next 40 Note that if enough information has been delivered to years and then applying a discount factor to account for the transformer designer, the effect of de-rating due to inflation, and the cost of capital or the expected rate of high ambient temperature or high altitude level is usu- return on capital investment. The losses in any one year ally considered by the designer. Therefore, the name- are calculated as the sum of load and no-load losses. plate ratings do not need to be de-rated. The no-load power loss is simply the no-load loss expressed as a percent of rating times the rating of the For transformers installed in subsurface manholes and transformer. Because the no-load loss is constant, this vaults of minimum size with natural ventilation through power loss is simply multiplied by the hours in a year to obtain the energy loss. The load losses in a transformer vary with the load. The manufacturer usually states load losses at rated load as a percentage of transformer rating. The value of loss at other loads can be estimated by multiplying by the ratio of the loads squared, because the loss increases with the square of the current. This procedure ignores the decrease in loss at lower temperatures caused by the decrease in resistance as the temperature decreases (approximately 25% from 90ºC to 20ºC), because this decrease is small compared to the quadratic decrease. Figure 16.4-4 Permissible KVA loading and ambient The peak power loss is calculated at the peak load, and temperature for altitude above 1000 m (ANSI C.57.12.00). the energy loss is calculated at the peak loss (at peak load) multiplied by the loss factor to give the energy 16-16 EPRI Underground Distribution Systems Reference Book Chapter 16: Transformers and Equipment loss. The loss factor can be an input parameter, or it can on the time for which the peak load occurs, the previous be calculated from the load factor using an assumed load condition, and the thermal time constant of the load profile by the empirical equation LF = 0.85(LD2) + transformer. Short time peaks of up to 200% of rating 0.15 LD, where LF is the loss factor and LD is the load can be justifiable. factor. If the exact load profile of a transformer is known, such as hourly load for a year, then the loss fac- Optimal transformer sizing can be determined using the tor can be calculated from the load data, and the loss Diversity Chart and Figure 16.4-5. Using the peak load calculation will be exact. calculation from Table 7 of IEEE C57, the first vertical intercept with a transformer plot determines the most The input parameters to the calculation procedure are: optimum size in terms of lifetime ownership cost. Load loss for each transformer rating Transformer size selection, at any specific load level, is Noload loss for each transformer rating controlled by the thermal load limit, not by the cost of Cost of losses (kW and kWh) losses. This conclusion depends on the ratio of no-load Real discount rate loss to load loss for the particular set of transformers. It will be true as long as the difference in no-load loss from Annual load growth rate one transformer size to the next is larger than the load Load factor loss of the smaller size transformer when loaded near its Loss factor rating. Figure 16.4-5 shows the present value of the cost of The overall conclusion is that a utility cannot reduce losses over a 40-year life versus peak load in the first transformer losses by going to a larger size transformer year. Single–phase, 4-kV polemount transformer data that will have lower load losses. The minimum loss costs are used in this example for sizes ranging between 10 are achieved if the smallest possible transformer is and 100 kVA to provide the widest data coverage. The selected based on thermal loading limits. lowest losses are often for a transformer that is severely undersized. To make a reasonable limit on the loading, 16.4.2 Other Parameters for Transformer the “thermal limits” are shown as vertical dashed lines Selection based on IEEE C57 – Distribution, Power and Regulat- Selection of the appropriate transformer should also ing Transformers (Table 7, 2-hour peak load duration at include consideration of: 10 °C and 30° C [winter and summer operation] 65 ° C Preferred power ratings rise.). For winter and summer operation, the peak limit was set at 1.87 and 1.57, respectively. This is not a firm Short-circuit capacity limit, because the loss of life of a transformer depends Noise level Figure 16.4-5 Cost of ownership vs. initial load – 4 kV pole transformers – single phase. 16-17 Chapter 16: Transformers and Equipment EPRI Underground Distribution Systems Reference Book Preferred Power Ratings The symmetrical short-circuit current can be calculated Despite the selection of an exact power rating that may as follows: be optimal for an application, distribution transformers are generally produced in a number of preferred ratings. U I SC = 3( ZS + ZT ) 16.4-7 Preferred continuous kVA ratings of single-phase and IR I three-phase distribution and power transformers based = ≅ R ZS % + ZT % ZT % on an average winding rise by resistance of 65o C are defined as following: Where: ISC is the symmetrical short-circuit current. Single-Phase (kVA): 5, 10, 15, 25, 37.5, 50, 75, 100, 167, IR is the rated current. 250, 333, 500, 800,1250, 1600, 2500, 3300 ZS is the system impedance connected to the transformer. Three-Phase (kVA): 15, 30, 45, 75, 112.5, 150, 225, 300, ZT is the transformer short-circuit impedance. 500, 750, 1000, 1500, 2000, 2500, 3750, 5000 Based on IEEE Std C57.12.00, multi-winding trans- To reduce inventory, some utilities seek to further limit formers shall be considered to have system fault power the ratings of the transformers that they purchase. supplied at no more than two sets of un-faulted termi- Short-circuit Capacity nals rated greater than 35% of the terminal kVA of the Another of the important factors for selecting a trans- highest capacity winding. former is the short-circuit capacity. Transformers Noise Level should be designed and constructed to withstand the Transformers in service cause sound, which may cause mechanical and thermal stresses produced by external discomfort to people in the environment in the long short circuits. The external short circuits shall include term. This is mainly the problem of power transformers. three-phase, single line-to-ground, double line-to- However, it can be an issue for large distribution trans- ground, and line-to-line faults on any one set of termi- formers too. Sound can be defined as the pressure varia- nals at a time. tion in air that the human ear can detect. The normal range of hearing of a healthy young person is from IEEE Std C57.12.00 limits determine the short-circuit approximately 20 Hz to 20 kHz. The weakest sound that current duration of distribution transformers as shown an ear can detect is dependent on the frequency. in Equation 16.4-6. 1250 Sound pressure level, LP, expressed in dB, is defined in ts = if S ≤ 500kVA Equation 16.4-8 I2 16.4-6 ts = 2 if S > 500kVA p2 LP = 10 log 16.4-8 p02 Accordingly, the above standard has determined the short-circuit withstand capability of distribution trans- Where: formers based on the symmetrical short-circuit current po is the reference level equal to 20μPa. shown in Table 16.4-1. p is the sound pressure measured by a micro- phone. Table 16.4-1 Short-circuit Withstand Capability (ANSI/IEEE C57.12.00) Withstand Capability per Unit of Base Current Single Phase (kVA) Three Phase (kVA) (Symmetrical) 5-25 15-75 40 37.5-110 112.5-300 35 167-500 500 25 Should be calculated using trans- Above 500 kVA former impedance only. 16-18 EPRI Underground Distribution Systems Reference Book Chapter 16: Transformers and Equipment To provide a feeling, a quiet living area has a sound option, it is suggested to order transformers designed at pressure level of about 45 dB, and a city street with 3 dB below NEMA standard sound levels. heavy traffic can have 95 dB sound pressure. Methods are available to the transformer designer to The dominant generating source of transformer sound control the transformer noise: is core magnetization. When the magnetic flux changes, Reducing the core flux density from 1.5 T - 1.6 T to a the magnetic domains change their directions. There- range of 1.2 T-1.3 T. This can be done either by fore, when excited by a sinusoidal flux, the core sounds. increasing the core cross section, or by increasing the In three-phase cores, the changes of magnetic domain number of turns in the winding. for each core limb do not occur simultaneously, which means that the whole core is subjected to pulsating dis- Making a heavier framework for the core tortions. Comprehensive investigations are made to cor- Inserting pad of damping material between core lay- relate human perception of loudness at various ers, or between active part and tank frequencies and sound pressure. To imitate the response curves of the human ear, three different filters are Dimensions and Relation between KVA and Size inserted in the measuring equipment, named A- There is a certain fundamental relationship between the weighted, B-weighted, and C-weighted filters. They imi- KVA rating of transformers and their physical size. A tate the curves going through 40, 70, and 100 dB, rather obvious relationship is the fact that large trans- respectively. For transformers, the frequency spectra of formers of the same voltage have lower loss than smaller the audible sound consists primarily of the even har- units. monics of the power frequency; thus, for a 60-Hz power system, the audible sound spectra consists of tones at As a typical scaling rule, the length, width, and height 120 Hz, 240 Hz, 360 Hz, 480 Hz, etc. A transformer are scaled as.