INSTITUTE OF INTEGRATED ELECTRICAL ENGINEERS
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Transformer Loss Cost Evaluation R. F. Corpuz, G. R. Pagobo
Table I I NCLUSION OF L OSSES IN B ID E VALUATION
Abstract—This paper establishes the monetary value of National Grid Corporation’s (NGCP) transformer losses. Based on IEEE Standard C57.120-1991, the results could be used to assess the relative economic benefits of investment on capacity of say, a high-first-cost1 , low-loss unit over one with low-first cost but with higher losses. The use of the results in this paper facilitates what could be a tedious, perplexing optimization process enabling NGCP as a buyer and even its potential supplier to respectively purchase and manufacture transformers economically. Index Terms—Loss evaluation, No-Load Loss, Load Loss, Auxillary Power Loss, Copper Loss, Core Loss
I. I NTRODUCTION RANSFORMER losses evaluated using IEEE Std. C57.120-1991 fall into three categories namely No-Load Loss (NLL), Load Loss (LL) and Auxiliary Power Loss (APL). No-Load Losses are inherent transformer losses and are more commonly referred to as excitation losses. These losses include dielectric loss, conductor loss in the winding due to excitation current, conductor loss due to circulating current in parallel windings and core loss. Load Losses are transformer losses that are dependent on the transformer loading. Commonly referred to as “copper losses” these include losses due to transformer loading, eddy currents, leakage flux in the windings, core clamps and circulating currents in parallel windings. Mathematically load losses are expressed as I 2 R. Auxiliary Power Loss are losses that are required in order to operate the transformer. These include power required for cooling fans, oil pumps and other ancillary equipment. NLL, LL and APL are factors and come in the form of $/kW. NGCP uses these values in evaluating supplier’s total bid for transformers. These factors multiplied by its respective supplier’s guaranteed loss will be added to transformer bid to arrive at the total supplier’s bid. To understand the concepts, an example is shown in Table I. The total bid in Table I represents the total suppliers’ bid which take into account the transformer losses. For the example above, the most economical transformer to purchase is Bid 4 despite having a relatively high initial cost. The values of the factors NLL, LL, APL1 and APL2 which are respectively $4,500/kW, $3,200/kW, $1,750/kW and $1,300/kW are the “rate” currently used by NGCP. Such values however need to be updated to reflect the present economic factors. To make it consistent with IEEE Standard C57.1201991, NLL, LL, APL1 and APL2 will be referred to as respectively, No-Load Loss Cost Rate (NLLCR), Load Loss Cost Rate (LLCR) and Auxiliary Load Cost Rate (ALCR1 and ALCR2). Numerical indexes 1 and 2 in ALCR1 and ALCR2 correspond to loss cost rates for stage 1 and stage 2 cooling, respectively.
T
1 Unless
otherwise specified, all costs appearing in this paper is in US$.
Notes: NLL =$4,500/kW LL = $3,200/kW APL1 = $1,750/kW APL2 = $1,300 /kW Column G = NLL x Column C Column H = LL x Column D Column I = APL1 x Column E Column J = APL2 x Column F
In this paper the principles of loss evaluation is first presented, followed by the assessment of each of the cost rates, defining and supplying values to variables along. II. L OSS E VALUATION P RINCIPLE In evaluating the cost of transformer losses, the cost of energy actually consumed by the losses, the generator investment needed to supply the energy and the transmission line to transmit the generation shall be considered. As such, it consists of a demand portion and energy portion. Mathematically, the loss cost rate is formulated as follows; LCR =
$ (GIC × F CRG + SIC × F CRS) + ( kwh × h) F CRT
Where: (GIC×F CRG+SIC×F CRS) is the F CRT $ ( kwh ×h) F CRT is the energy portion
demand portion
LCR the Loss Cost Rate GIC is the cost of installing a kW of power plant
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SIC is the cost installing transmission line with a kW of capacity Loss Cost Rate refers to NLLCR or LLCR or ALCR1/ALCR2 FCRG is the Fixed Charge Rate of Generating Plant FCRT is the Fixed Charge Rate of Transformer FCRS is the Fixed Charge Rate of Transmission h is the number of hours per year that transformer is energized The Fixed Charge Rate of Plant/Transformer refers to that portion of investment needed per year to support the capital investment. In its simplest form, it represents the required yearly income from the investment. Its components are as follows; 1) Minimum Acceptable Rate of Return 2) Annual Cost of Depreciation and 3) Taxes For purposes of this study, FCRT and FCRS are equated to NGCP’s Weighted Average Cost of Capital (WACC) for the second regulatory period which is 15.87%. FCRG is set equivalent to 15%, NEDA’s Social Discount Rate. The numerator in the equation for the Loss Cost Rate represents the cost per year to provide a continuous kW of loss. The first term (GIC × F CRG + SIC × F CRS) represents that portion of investment cost on a generation and transmission needed per year to support transformer losses while the second term represents the cost of the energy under the present prevailing energy cost. For Luzon, the current year energy cost, CYEC, is set to $0.1444/kWh This is based on P7.04/kWh2 energy rate and P48.65/$13 peso-dollar exchange rate. III. N O L OAD L OSS C OST R ATE Following the principles in Section II, the No Load Loss Cost Rate is determined as follows; N LLCR =
(GIC×F CRG + SIC×F CRS) + LECN ET ×F CRT ×IF
Except for ET and IF terms in the denominator, the formula for NLLCR is similar to the equation for transformer loss in Section II. Note that LECN, the Levelized No Load Energy cost, is the energy portion in Section II equivalent to US$ 1,573.43/kWyear for Luzon. LECN is determined in Section VI. ET and IF are dimensionless factors introduced to reflect the Efficiency of Transmission and Increase Factor respectively. ET is determined through power flow simulations and is set to 0.9783 for Luzon Grid. To simplify calculations, IF is set to 1.0074 and only reflects project overhead cost. By introducing ET, the calculated energy, in terms of cost is marked-up to include other costs dissipated through inefficiency. IF further increments this cost in proportion to project’s overhead cost. 2 Figures
from PSALM rate forecast from Economist Intelligence Unit as used by NGCP in the 3rd Reg. Filing 4 Based on actual budget 3 Exchange
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Values for other variables are as follows; Generation Installation Cost GIC = $1,600/kW Generation Installation Cost SIC = $2.74/kW 5 Solving for NLLCR for Luzon Grid; (1, 600×0.15 + 2.74×0.1444) + 1, 573.43 (0.9783×0.1587×1.007)
N LLCR =
N LLCR = $11, 601.60/kW
IV. L OAD L OSS C OST R ATE For the Load Loss Cost Rate, there is a need to remove the impact of the Availability Factor AF6 from LECN, as calculated in Section VI since for this loss rate Transformer Loading Factor TLF will be used. Modifying LECN in this manner results to LECL or the Levelized Load Energy Cost, LECL is determined as follows: LECL =
1, 573.43 1, 589.8 LECN = = year AF 0.9897 kW
With the denominator remaining the same as that for NoLoad Loss Cost Rate, the equation for the Load Loss Cost Rate is: LLCR =
(GIC×F CRG + SIC×F CRS)×P RF 2 ×P U L2 (ET ×F CRT ×IF ) +
LECL×T LF 2 (ET ×F CRT ×IF )
The new terms in the numerator are dimensionless adjustment factors introduced to enable realistic assessment. The Peak-Per Unit Load (PUL) relates demand-associated losses to full rated transformer and not to the peak transformer load7 . It is the average of yearly peaks over the lifetime of transformer divided by the rating at which the load losses are guaranteed to be tested. For this study, load losses are assumed to be tested at full-load transformer rating. Using load forecast data for 2009, PUL is set to 1.114 for Luzon. The Peak Responsibility Factor (PRF) is the transformer’s load during system peak8 , divided the transformer’s peak load. This factor is intended to compensate for the transformer peak load losses not occurring at the system peak losses. The rationale is, if the entire transformer peak does not occur during the system peak, then there is no need to put up additional generation since the transformer load and its losses could be supplied by the system. That is reason behind inclusion of PRF in the demand portion of the loss assessment equation. The data used in the determination of this parameter 5 Based on $27,365.00/km, 2008 Price Level of 5km, 69kV ST/SC, 1-336.4 MCM ACSR 6 Availability Factor AF is the expected percentage of time the transformer will be energize. AF = 0.9897 7 Guide for the Evaluation of Large Power Transformer Losses, USDA 8 System Peak assumed to occur at 1900H
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was surveyed from various NGCP substations. Using the data, PRF for Luzon is set to 0.8643. The Transformer Loading Factor is the ratio of the average transformer losses to the peak transformer losses during a specific period of time . To simplify calculations, it is assumed constant and does not change significantly over the life of transformer. It is formulated as;
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For Stage 2 Cooling: LAEC2 = 1, 573.43×
ALCR2 = T LF = 0.8 × LF 2 + 0.2 × LF
(1, 600×0.15 + 2.74×0.1587) + 562.60) (0.9783×0.1587×1.007) ALCR2 =
Where: LF is the Load Factor Using the equation above and the surveyed data from various NGCP substations, the average TLF for Luzon Grid is 0.6480. Substituting values and calculating for the Load Loss Cost Rate for Luzon Grid; LLCR =
3, 100 $562.605 = year 8, 669.77 kW
$5, 136.38 kW
Table II is a summary of the Loss Cost Rate for Luzon, Visayas and Mindanao Grids determined through the methodology presented above. Table II T RANSFORMER L OSS E VALUATION FOR L UZON , V ISAYAS AND M INDANAO G RIDS
(1, 600×0.15 + 2.74×0.1587)×0.86432 ×1.1142 ) (0.97742×0.1587×1.007) +
1, 589.80×0.64802 (0.97742×0.1587×1.007)
LLCR = $5, 695.54/kW
V. AUXILIARY L OAD L OSS C OST R ATE For the Auxiliary Loss Cost Rate Stage 1 (ALCR1), only the energy portion of the loss equation has to be modified. LECN has to be proportionately adjusted to the average number of hours that stage 1 cooling is expected to operate. The Levelized Auxiliary Energy Loss Cost – Stage 1 Cooling (LAEC1) is computed as follows; LAEC1 = LECN ×
hstage1 8760×AF
Where: hstage1 is the average hours stage 1 cooling is running Substituting: LAEC1 = 1, 573.43 ×
4, 700 $852.98 = year 8, 669.77 kW
Using the value determined for LAEC1, the Auxiliary Loss Cost Rate Stage 1 (ALCR1) is calculated as follows: ALCR1 =
(GIC×F CRG + SIC×F CRS) (ET ×F CRT ×IF ) +
ALCR1 =
LAEC1 (ET ×F CRT ×IF )
(1, 600×0.15 + 2.74×0.1587) + 852.978) (0.9783×0.1587×1.007) ALCR1 = $6, 993.67/kW
VI. D ETERMINATION OF L EVELIZED N O -L OAD E NERGY C OST The cost of energy, as with any other commodity, is subject to inflation. Economic studies, such as this transformer loss evaluation, would require more complicated techniques to assess exponential variables. One method of simplifying the problem is to levelize the values of the variables, this way the rate of energy would be equal during the entire booklife of the transformer. As an example consider a cost of $1/kWh escalating at 5% per annum, that is, its rate after a year is 1(1.05), after two years 1(1.05)(1.05) and so on until N years when its rate becomes 1(1.05)N. In the Figure 1 below the exponential cost of energy is the increasing curve below. The dashed line results after levelling. Levelling is achieved by multiplying the Net Present Value of all yearly energy rates by the Capital Recovery Factor (CRF) given by the following equation: CRF =
r(1 + r)N (1 + r)N − 1
Where: r is the Rate of Return, in the context of this study it is equal to WACC = 15.87% N is equal to 35 years, the booklife of transformer
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Figure 2.
Figure 1.
Illustration of Levelization
Applying the values and solving for CRF: CRF =
0.1587(1 + 0.1587)35 = 0.159621 (1 + 0.1587)35 − 1
The Net Present Value (NPV) is determined using the following equation:
NPV =
35 X
Cash Flow. Concept of Net Present Value
LECN =
The value 0.9897 appearing in the equation above is the Availability Factor (AF). This figure was determined from 2005-2009 transformer outage statistics from System Operations. Following the same methodology, LECN for Visayas and Mindanao Grids are as follows: LECN =
$1, 367.81 year kW
LECN =
$2, 219.34 year kW
(1 + r)−N (1 + i)N (CY EC)
N =1
$1, 573.32 year kW
Where: r and N is as given in CRF calculation i is the escalation rate equivalent to 3%9 CYEC is the Current Year Energy Cost equivalent to $0.1444/kWh The first term in the NPV equation equates the rate of energy in the Nth year which is (1 + i)N (CY EC) in terms of the present values. In other words it determines how much must be invested today at an interest rate “r” in order to have (1 + i)N (CY EC) in the future. Figure 2 illustrates the principle. The sum of these present values is the Net Present Value. Substituting variables and solving for NPV:
NPV =
35 X
Rex F. Corpuz is a former Sr. VP of the National Transmission Corporation and a former President of National Grid Corporation of the Philippines (NGCP). He is presently the Sr. Technical Adviser at the Office of the President, NGCP. He is also a former Regional Governor of IIEE Region 1., e-mail: rfcorpuz@gmail.com
(1 + 0.1587)−N (1 + 0.03)N (0.1444) = 1.13697
N =1
The Calculated Levelized No-Load Energy Cost (LECN) for Luzon Grid is equal to: LECN = N P V ×CRF ×8760×AF LECN = 1.13697×0.159621×8760×0.9897 9 Escalation rate for 2009 figures as used by Project Management. Note a constant rate of 3% is assumed for the entire book life of transformer
Gerald R. Pagobo is a Power System Consultant and formerly worked with the research group of NGCP. He received his MS in Electrical Engineering degree from the University of the Philippines in 2009. His research interests include reliability engineering, power system dynamic stability, electricity market optimization, and computer-based power system modeling and analysis. Email: grpagobo@gmail.com