Technical and Economic Justification for the Selection of the Number and Capacity of Transformers at a Substation
Abstract Generated abstract
This paper presents a technical and economic procedure for choosing the number and rated capacity of transformers at industrial substations under reliability requirements for category I and II consumers. It outlines how permissible transformer overloads may be assessed using the one percent and three percent rules, then develops calculations for active and reactive transformer losses, annual energy consumption, power factor, and electricity cost under a two rate tariff. The proposed comparison method selects among technically feasible substation variants by minimizing annual operating expenses, including energy costs, depreciation, and repairs, with an additional payback period check when the lower cost variant requires higher capital investment.
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Technical-Economic Justification for Selecting the Number and Capacity of Transformers at a Substation
A. I. Zaitsev
(Presented by the scientific seminar of the Department of Electrification of Industrial Enterprises)
High requirements are imposed on the reliability of operation of the modern electric-power supply system. To supply industrial enterprises as a whole, as well as large shops having consumers of categories I and II, it is necessary to install at least two or more transformers. This number must be such that, if one of the transformers fails, those remaining in operation would fully supply category-I consumers and partially supply category-II consumers. The percentage of reserve supply for category-II consumers must be established individually, depending on the type of enterprise, or by means of technical-economic calculations. In design organizations these data are available.
When assigning equivalent alternatives for the number of transformers at the substation being designed, it is necessary to proceed from the condition that, during prolonged operation, the current-carrying parts and insulation should not heat above the permissible temperature. Depending on the form of the load curve, in some cases a certain overload of transformers may be permitted during the passage of the maximum load, taking into account that, when the load decreases, the temperature of the transformer will decrease. The magnitude of the permissible overload of transformers is determined from the condition that the service life of the insulation remains within the established limits.
In determining the limiting value of transformer overload, one must be guided by the one-percent and three-percent rules.
The one-percent rule. It consists in the following: if the maximum of the typical summer curve is below the rated capacity of the transformer, then in the winter months an overload of the transformer is permitted in the amount of 1% for each percent of underloading in summer, but not more than 15%.
The three-percent rule. It consists in the following: if the daily load curve of a transformer has a load factor of less than 100%, then for each 10% decrease in the load factor below 100%, an overload of the transformer by 3% above its rated capacity is permitted. Both rules may be used jointly. In this case, the total overload of the transformer must not exceed, for transformers installed in the open air,
30%, and for transformers installed in enclosed premises, no more than 20%.
Taking into account the one-percent and three-percent rules, the rated capacity of the transformer may be determined from the equation
\[ \sum S_{NT} \geq \frac{S_{\max}}{1+\frac{z_{30}}{100}-\frac{z_{1h}}{100}}, \]
where \(z_{30}\) is the permissible value of transformer overload according to the three-percent rule
\[ z_{30}=0.3(1-k_{z.o})100; \]
\(z_{1h}\) is the permissible value of transformer overload according to the one-percent rule
\[ z_{1h}=\frac{\sum S_{NT}-S_{\max \,\text{summer}}}{\sum S_{NT}}\,100. \]
Thus, in order to satisfy the conditions of reliable power supply, any number of equivalent variants may be outlined. It is obvious that the more transformers are installed at the substation, the smaller the specific weight of each individual transformer will be, and its outage will have less effect on the overall power-supply system. However, as the number of transformers increases, the capital costs for construction of the substation rise very sharply, the construction portion increases, more switching equipment is required, the arrangement of the primary and secondary connections of the substation becomes more complicated, and operation and maintenance of the installations become more difficult. Therefore it is necessary to choose a variant that, as far as possible, would satisfy these two contradictory requirements.
To decide which of the outlined technically equivalent variants is the most advisable, it is necessary to carry out an economic comparison of these variants. The criterion for selecting the variant here should be the annual operating costs of the substation being designed.
In the economic comparison it is necessary to take into account only those components of the annual costs that depend on the variant. These components include:
- Deductions for depreciation of equipment.
- Costs for current repair of the substation.
- Cost of the electric power consumed by the substation.
The numerical values of the percentage deductions from the total cost are characterized by the following table.
| Name of facilities | Depreciation deductions, % | Current repair deductions, % | Total deductions, % |
|---|---|---|---|
| Transformers and electrical equipment of substations | 6 | 2--6 | 8--12 |
| Buildings | 3 | 1.5 | 4.5 |
The cost of the energy consumed by the substation must be calculated according to a two-rate tariff, taking into account electric-power losses in the transformers.
The active electric energy consumed over a year, \(Э_a\), on the low-voltage side is determined from the aggregate load curve, or from the maximum calculated power and the time of utilization of the maximum. The consumed reactive power \(Э_p\) is determined analogously. For a given weighted-average value of the load power factor, the reactive energy may be determined from the equation
\[ Э_p = Э_a \operatorname{tg}\varphi_{\text{avg. wt.}} . \]
To the active and reactive energy consumed by the consumer it is necessary to add the energy losses in the transformers. Losses in transformers may be divided into two groups: losses dependent on load, and losses not dependent on load.
The active losses in a transformer at any load can be determined from the equation
\[ \Delta P_T = \Delta P_c + \Delta P_{\text{m.nom}}\beta^2 , \]
where
\(\beta\) is the transformer load factor;
\(\Delta P_c\) are the losses in the steel of the transformer;
\(\Delta P_{\text{m.nom}}\) are the losses in the copper when the rated current flows.
For \(n\) transformers operating in parallel, these losses increase by a factor of \(n\).
\[ \Delta P_T = n(\Delta P_c + \Delta P_{\text{m.nom}}\beta^2) = \]
\[ = n\Delta P_c + n\Delta P_{\text{m.nom}} \left(\frac{S}{nS_{\text{nom}}}\right)^2 = n\Delta P_c + \frac{1}{n}\Delta P_{\text{m.n}} \left(\frac{S}{S_{\text{nom}}}\right)^2 , \]
where \(S\) is the total load on the substation at the given moment of time;
\(S_n\) is the rated capacity of one transformer.
The active-energy losses can be determined from the load curve, taking into account the most economical operating mode of the transformers,
\[ \Delta Э_{aT} = n \cdot \Delta P_c \cdot t_0 + \frac{1}{n}\Delta P_{\text{m.n}} \sum_{1}^{n}\left(\frac{S}{S_n}\right)^2 \cdot t , \]
where \(t_0\) is the actual operating time of \(n\) transformers during the year;
\(t\) is the operating time of \(n\) transformers with load \(S\).
Reactive losses in transformers at any load are determined from the equation
\[ \Delta Q_T = \Delta Q_0 + \Delta Q_{\text{m.n}}\beta^2 , \]
where \(\Delta Q_0\) is the reactive magnetizing power;
\(\Delta Q_{\text{m.n}}\) are the reactive-power losses at the rated load current of the transformer.
For \(n\) transformers operating in parallel, the losses are determined as
\[ \Delta Q_T = n(\Delta Q_0 + \Delta Q_{\text{m.n}}\beta^2) = n\Delta Q_0 + \frac{1}{n}\Delta Q_{\text{m.n}} \left(\frac{S}{S_n}\right)^2 . \]
The reactive-energy losses are determined from the load curve
\[ \Delta Э_{pT} = n \cdot \Delta Q_0 \cdot t_0 + \frac{1}{n}\Delta Q_{\text{m.n}} \sum_{1}^{n}\left(\frac{S}{S_n}\right)^2 \cdot t . \]
The consumed active energy, referred to the high-voltage buses of the transformers, can be determined from the equation
\[ E_a = E_{a\,\text{load}} + \Delta E_{aT}. \]
Reactive energy is determined from the equation
\[ E_p = E_{p\,\text{load}} + \Delta E_{pT}. \]
Let us determine the weighted-average value of \(\cos \varphi\), taking into account energy losses in the transformers,
\[ \cos \varphi = \frac{E_a}{\sqrt{E_a^2 + E_p^2}}. \]
For this value of \(\cos \varphi\), the cost of the consumed energy is determined according to the two-rate tariff
\[ A = S \cdot s + p' \cdot E_a, \]
where
\(S\) is the connected transformer capacity at the high-voltage buses;
\(s\) is the cost of one connected kVA of installed capacity for the given power system;
\(p' = p(1 \pm g)\) is the cost of a kilowatt-hour, taking into account the actual value of the power factor, with allowance for the scale of discounts and surcharges relative to the cost of electricity at the neutral value of the power factor \(p\).
The annual expenses associated with the variant under consideration will be equal to the sum of the cost of consumed electricity and deductions for depreciation and repairs:
\[ B = A + nK, \]
where \(n\) denotes deductions for depreciation and repairs;
\(K\) denotes the capital costs for constructing the given variant of the number and capacity of transformers.
The annual expenses for other variants of the transformer substation design are determined analogously.
By comparing the obtained economic data, the variant that gives the lowest annual expenses is selected. If the selected variant with lower annual expenses has larger capital investments, it is necessary to check it by the payback period
\[ t = \frac{K_1 - K_2}{B_2 - B_1}. \]
If the payback period exceeds more than 8–10 years, the variant with lower capital investments should be selected.