1 Introduction
Consumer Electronics Power Transformer products according to size into large transformers (capacity greater than or equal to 8000kVA) and small and medium-sized transformers (capacity less than or equal to 6300kVA); voltage rating can also be divided into 6kV, 10kV, 35kV, 60kV, 110kV , 220kV, 330kV and 500kV. As a voltage conversion device, the transformer is widely used in the field of transmission and distribution, in particular, 10kV and 35kV voltage transformers in electric power, industrial and commercial power distribution system is generally used, and a huge number. In 1999, China’s annual output transformer of about 338 000 units, including 10kV and 35kV level of about 313,000 units, accounting for 92.6%. It is estimated that about 1 billion to the line, 10kV and 35kV transformer kVA above. Due to high volume, long operation time, the transformer on the selection and use, there is a huge energy saving potential, especially the large wide range of 10kV and 35kV transformer. Choose energy efficient products, and of great significance not only for energy conservation, but also can greatly reduce the operating costs of the transformer, an important way for enterprises to improve economic efficiency. China’s 10kV and 35kV class transformers the vast majority of standard design, the product standards experience? Quot; 64 “standard,” 73 “Standard,” 86 “standard” 95 “standard continues to progress to the mid-1990s, the product from development of high-loss type (SJ, of SJL … S7) to the current lower loss type (S9). As of the end of 1998, the S7-type transformers and by the state has announced phase-out, to stop its production and sales. With transformation of the planned economy to a market economy, and social demand for energy saving and environmental protection, the level of efficiency of our transformers will appear in the trend of diversification currently on the market more energy-efficient products than the S9 series, such as S10, S11 series .
Grid transformer of military age over 20 years old transformers still about 10%. These transformers are designed according to the 1960s and 1970s when “64″ and 73 “standard products, the loss is very high. Compared with the S9 series, the average loss above 100%, the energy saving potential is huge. For businesses, how to proceed from the long-term economic benefits, to determine the appropriate level of transformer efficiency and whether it should replace the high energy consumption energy-saving transformer transformer is one of the transformer purchase and management problems to be solved.
International evaluation transformer energy efficiency, all methods are required to compare the transformer price and loss expenses. The United States in the late 1970s, due to rising energy prices, many power companies began to require the design of the transformer should be able to have a minimum length of service costs, thus creating a total cost of ownership (TOC) Act. The TOC France in the United States in the 1981 development has become the industry standard. Purchase in accordance with the TOC standard transformer has been in use since the TOC method is the sum of the initial cost of the transformer and the equivalent present value of the loss costs to express a comprehensive and integrated cost of the purchase of transformers. With TOC France had reviewed the distribution transformer S9 and S7-economic benefits, and compare the results S9 transformer price is higher than about 20% of S7, the loss index about 21% lower than the S7, S9, the support of Village money can be recovered from the loss of electricity savings in two to three years. Similarly, the S9 transformer replacement 80 years ago, the old transformer products to compare performance results show that only pay S9 equipment costs, excluding under the conditions of the recovery value of the old transformer, S9 funds in 2 to 3 years from the savings loss electricity has been repaid.
This article describes the total cost method TOCEFC (hereinafter referred to as TOC) (Equivalent First Cost-EFC) – the equivalent initial cost evaluation transformer cost-effective methods and calculation process.
This article provides a reference to the U.S. National Electrical Manufacturers Association standards: NEMA TP1-1996 standard, combined with China’s actual conditions.
2 total ownership cost method for TOC (Total Cost) of the Owning
The so-called total ownership costs (TOC) is the initial investment of the transformer and its loss in the period of use expenses. Total ownership cost method by comparison with different levels of efficiency and price of the transformer total cost of ownership, the lowest cost of ownership to choose the level of transformer efficiency.
2.1 The formula in the TOC
The TOC = C + A × NL + B × LL
Type in the NL – transformer rated no-load loss or iron loss, kW; LL – Transformer rated load loss or copper loss, kW; – the transformer during the life of no-load loss per kilowatt capital cost, $ / kW; the B- – Transformer load loss during the life of the capital cost per kilowatt, $ / kW; – Transformers initial costs, program comparison can be used to set
Prepare price.
2.2 calculate the parameters
2.2.1 transformer no-load loss NL and load loss LL
Transformer no-load loss NL and load loss LL rated power loss, taking into account the reactive power in the power line of power loss, calculated as follows:
No-load loss NL = P0 + kQ0 = P0 + k (I0% Se/100)
Load loss of the LL = of Pf + kQf = of Pf + k (the Ud% Se/100)
Where P0 – Transformer rated no-load power loss, iron loss kW;
Q0 – Transformer rated excitation power, kvar;
Pf – transformer rated load power loss, copper loss kW;
Qf – transformer rated load magnetic flux leakage power kvar;
k – Reactive economic equivalent of the location of the transformer in the grid values, general desirability k = 0.1kW/kvar;
I0 is% – transformer no-load current;
Ud% – transformer impedance voltage,%;
Se – transformer rated capacity, kVA.
2.2.2 A and B, coefficient
A coefficient is a no-load loss of transformer life during the unit capital cost ($ / kW), the coefficient B is the unit load loss of transformer life of the capital cost ($ / kW). The two coefficients A and B transformer buyers to grasp the transformer no-load loss and load loss value is important. Once you determine the value of A and B, the total cost of the evaluation of the transformer becomes simple.
Electric utilities and non-power companies, A and B coefficients of different ways. A and B coefficient and transformer load loss and load loss of energy costs and capacity costs were a function of. For power companies, the relevant unit energy loss costs and the costs of capacity and power generation, transmission and distribution of the whole process of investment and operation mode is more complex, required by the electric power business professionals to develop in this paper not to repeat a.
For non-electricity businesses, energy costs and capacity costs of the unit loss is mainly related to electricity and transformer operating mode of the burden of enterprises related to this article A and B coefficients calculated, and its data used in a wider range of industries in the appendix.
(1) The coefficient A – load loss of transformer per kilowatt capital costs
Transformer no-load loss per kilowatt capital costs or the coefficient A, can often be seen as a transformer in the life of the same number 24 hours a day, 365 days a year, will remain unchanged for 20 years (located transformer life of 20 years) . A numerical tariff equivalent at the beginning of the present value of expression is as follows:
A = kPW x (the EJL × 12 + EL × hPY), $ / kW
Where kPW – now the value of coefficient = {1 – [(1 + a) / (1 + i)] n-} / (i-a), (Eq. of transformer use of n years, annual interest rate of i-year inflation rate a, which relationship, see instructions below); EJL – two electricity basic tariff ($ / kW, month);
EL – two tariff electricity tariff ($ / kW · h);
hPY – annual operating hours, and generally 8760h.
(2) The coefficient B – Transformer load loss per kilowatt capital costs
Transformer load loss per kilowatt capital cost coefficient B tariff factors, mainly related to the transformer brought the load characteristics, load characteristics of the available maximum load loss of the number of hours (by the highest load hours a Tmax and power factor to determine, see Appendix expressed in Table 1) and load rate. Heavy load, long operation time and load the high rate of production enterprises, the coefficient B, and vice versa small. The value of the coefficient B is equivalent to the present value of the initial cost of expression is as follows:
B = kPW × (EJL × 12 + EL × τ) × P2, $ / kW
The formula kPW – the present value factor, with coefficient A;
EJL – two electricity basic tariff ($ / kW month);
EL – two tariff electricity tariff ($ / kWh);
τ – the annual maximum load loss of the number of hours (the maximum load to determine the number of hours Tmax and the power factor cosφ,
See Appendix Table 1);
÷ p – transformer load = transformer computational load transformer rated capacity.
(3) the present value of the coefficient kPW coefficients A and B
In the early financing of the transformer to use the financing of the costs of years of wear and tear, to consider the time value of money, the transformer run in each of the loss of electricity converted to investment in the initial moment, the A and B coefficients of inclusive the coefficient kPW component of the present value of make it equivalent to the purchase of equipment initial costs for the same time.
Value coefficient kPW is based computing life (transformer life), the annual interest rate i and the annual inflation rate of a three factor, calculated as:
kPW = {1 – [(1 + a) / (1 + i)] n} / (i-a)
Can be seen from the calculation, the known calculation period is n, when the interest rate i, the higher the calculation proceeds kPW present value of the coefficient is smaller, the A and B coefficients of the loss costs are also smaller. When funds are high value (high interest), capital investment is also reduced. The annual inflation rate of a contrary, a higher the calculated kPW present value of the coefficient the greater the loss the cost of A and B coefficients are greater. Because this time rising prices, currency devaluation, monetary time value of money decreased, the capital investment necessary to increase.
(4) commonly used in A, B, coefficient is easier to apply, in the appendix, we provide the value of the prior calculation of good A and B units of the different electricity load category and load rate loss of power costs. Calculated in accordance with the specific circumstances of the project A, B, data may differ, such as the numerical precision can make other calculation.
2.2.3 The price
Transformer prices in the example from the Machinery Industry Press, 1999 electromechanical products offer manual reference price.
Examples of 2.3 the TOC method of calculation
Total ownership costs the calculation S9-800/10 S7-800/10 transformer, the age of 20 years, transformer operation in non-ferrous smelting factory, three shifts of production, the transformer load was 75%.
Solution: (1) the calculation S9-800/10 type, 800kVA transformer no reactive power, including the loss of value;
No-load loss PNL = P0 + kQ0 = P0 + k × (I0% Se/100)
= 1.40 + (0.1 × 0.008 × 800) = 2.04kW
Load loss of PLL = of Pf + kQf = of Pf + k × (the Ud% Se/100)
= 7.5 + (0.1 × 0.045 × 800) = 11.09kW
(2) Similarly, S7-800/10 loss values:
No-load loss: S7 for 2.5kW load loss: S7 is 13.49kW.
(3) of the transformer no-load and load loss costs (useful life 20 years):
Check Appendix Table 1, corresponding to the non-ferrous smelting industry, the load was 75%, A = 48 672 yuan / kW, B = 17 668 yuan / kW.
No-load loss costs:
The S9 transformers on A. × NLS9, = 2.04 × 48672 = $ 99 291
S7 transformer for the A. × NLS7, 2.5 × 48 672 = $ 121 680
Load loss costs:
S9 transformer B × LLS9 = 11.09 × 17 668 = $ 195 938
S7 transformer B × LLS7 = 13.49 × 17 668 = $ 238 341
(4) Transformer Price: S9, 63,640 yuan to 55,340 yuan, S7.
(5) the period of 20 years the TOC total cost of ownership:
TOCS9 = 63.64 thousand + (2.04 × 48 672) + (11.09 × 17668) = 358 869.
TOCS7 = 55340 + (2.5 × 48672) + (13.49 × 17668) = 415361 yuan.
3 the calculation of the payback period of
Investment spreads the recovery period to calculate the two types of algorithms.
3.1 a simple calculation
Does not consider the time factor, only the calculation of expenses, calculate: Investment spreads recovery period = two transformers investment spreads ÷ two transformers in power consumption costs spread
Payback period of 3.2 taking into account the time value of money calculation formula
Calculate the two transformers (two programs) always has a use when the costs equal to the number of years the value of n, will be counted towards the recovery of the time value of money years. Calculation formula: Transformer 1 TOC = Transformers 2, the TOC:
Two transformer investment spreads the = kPW (two transformer power consumption costs spread)
kPW = two transformers investment spreads ÷ two transformers in power consumption costs spread
Department of the kPW here two transformer investment spreads and consumption costs spread equal the present value factor.
Assumptions, the rate of inflation a = 0, the annual interest rate i = 0.07, according to the present value of the coefficient kPW formula to calculate the value of n
n = log (1-0.07kPW) ÷ log [1 / (1 +0.07)]
3.3 recovery calculation example
S9-35kV, 3150kVA transformer replacement of the SJ type 35kV the 3200kVA old transformers, the investment recovery period in the calculation of the S9 replacement. Investment S9 transformer only the purchase cost of 179,800 yuan; net replacement down the the SJ recovery value of the old transformer and replacement process of disassembly costs. Transformer conditions of use the same example.
Solution: (1) a simple calculation the recovery years were calculated between the two transformer loss value SJ load loss of transformer
PN = P0 + kQ0 = 11 + (0.1 × 0.04 × 3200) = 23.8kW
SJ transformer load loss
PL = Pf + kQf = 37 + (0.1 × 0.055 × 3200) = 54.6kW
S9 transformer no-load loss
PN = P0 + kQ0 = 4.5 + (0.1 × 0.010 × 3150) = 7.65kW
S9 transformer load loss
PL = Pf + kQf = 22.0 + (0.1 × 0.07 × 3150) = 44.05kW
Appendix Table 1, Richard A, = 48672, B = 17 668, multiplied by the capital recovery factor (= 1/kPW), the here kPW = 10.59.
The recovery years of S9 = S9, transformer purchase costs / SJ S9 transformer loss of fees spreads
= 179800 / {[48672 × (23.8-7.65) +17668 × (54.6-44.05)] / 10.59}
= 1.96
(2) calculate the time value of money recycling year
kPW = two transformer investment spread ÷ two transformers electric costs spread
= (179800-0) / (200478.4-108651.2) = 1.96
KPW = 1.96 into the calculation formula of the present value of the coefficient can be included in the calculation of the time value of money recycling year n:
n = log (1-0.07 × 1.96) ÷ log [1 / (1 +0.07)] = 2.18 years
4 Appendix: loss coefficients A and B to determine
4.1 Typical electricity industry of A, B
References to other documents, can be found in the typical industry load characteristics, the maximum load and the annual number of hours to Tmax, cosφ = 0.9 and the maximum load loss of the number of hours τ data, calculated in accordance with the TOC formula A, B, coefficient, as shown in Table 1 below.
The calculation conditions of the data in Table 1: Basic Tariff EJL = 18 / month · kW electricity tariff the EL = 0.5 yuan / kWh, transformers, using n = 20 years, the annual interest rate i = 7%, inflation rate, a = 0 , power factor cos φ = 0.9. For ease of calculation, Table 2 shows the relationship between the number of hours Tmax of maximum load under different power factor cosφ loss of hours the number of τ and the maximum load for the calculation of reference.