On Specific Cost Indicators of Electricity Production
Abstract Generated abstract
The article addresses the need for generalized techno-economic unit indicators for evaluating power transmission lines, network sections, substations, power-supply schemes, and electrical equipment designs. It proposes formulas for unit capital costs per kilowatt delivered to consumers and for the calculated cost of electricity at the consumption point, incorporating station reserve, auxiliary consumption, fuel extraction and transport capacity, network transmission capacity, losses, and consumer connection level. Approximate numerical indicators are presented for several network categories and load durations, and existing official methods are criticized for omitting several cost components. The author argues that the proposed approach remains relatively simple while reducing potentially significant errors, though some assumptions are presented as open to further discussion.
Full Text
ON UNIT COST INDICATORS OF ELECTRICITY GENERATION
I. D. Kutyavin
For the techno-economic evaluation of variants of power-transmission lines, individual sections of a network, power-supply schemes and substations, and for the techno-economic study of series of transformers and motors when designing them, it is necessary to use such techno-economic unit indicators as unit capital costs in the system per one kilowatt of consumed capacity and the calculated cost of electricity at the point of consumption.
The author is aware of two official methodologies devoted to this question*. As is evident from their titles, they are of a particular nature and, unfortunately, contain substantial shortcomings, which will be discussed below. Therefore the need has become ripe for the development of generalized techno-economic unit indicators of the kind under consideration.
The unit calculated capital costs per one kilowatt of capacity delivered to the consumer, or lost in a network or transformer, consist of the following components:
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Capital costs for the additional capacity of the system’s power stations required to transmit 1 kW to the consumer.
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Capital costs for the additional output capacity of the station’s fuel-producing shop, required to generate the additional capacity of the system.
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Capital costs for the additional transmission capacity of the system’s electrical networks up to the point of consumption of 1 kW.
To simplify the problem, the capital costs for electrical networks may be taken as proportional to the total capital costs for construction of the system’s power stations and as constituting (40–50)% of these costs.
To transmit to a consumer 1 kW of capacity connected at some section of the network, it is necessary to deliver from the busbars of the power station a capacity \(P_{\text{sh}} > 1\), allowing for losses in the preceding network. Then
* Guiding and normative instructions on the selection of the economic current density for power-transmission lines. Teploelektroproekt, Moscow, 1961; P. G. Grudinskii, Draft instructions on the techno-economic substantiation of the choice of the level and ratio of losses in electric motors and transformers in the design of mass-produced series. (See: P. M. Tikhomirov, Calculation of Transformers. GEI, 1962).
additional capacity of the system, taking into account the station’s own consumption and the capacity reserve in the system
\[ P_{\mathrm{d}}=k_{\mathrm{sn}}k_{\mathrm{r}}P_{\mathrm{sh}}, \tag{1} \]
where \(P_{\mathrm{sh}}=1.0\text{--}1.15\) is the capacity delivered from the station busbars to transmit \(1\ \mathrm{kW}\) to the consumer;
\[ k_{\mathrm{r}}=1.1\text{--}1.15 \]
is the system reserve coefficient;
\(k_{\mathrm{sn}}\) is the coefficient taking into account the consumption of capacity for the station’s own needs and the capacity consumed by the station’s fuel-mining shop (mine, open-pit coal mine).
The station’s own-use capacity consumption is usually taken within the range of \(6\text{--}8\%\). The capacity consumption of the station’s fuel-mining shop, in relative units, may be determined from the expression
\[ P_{\mathrm{t}}=q w_{\mathrm{y}}\frac{T_{\mathrm{mp}}}{T_{\mathrm{mt}}}, \tag{2} \]
where \(q\) is the specific consumption of standard fuel (s.f.) per \(1\ \mathrm{kWh}\), \(\dfrac{\mathrm{t}\cdot \mathrm{s.f.}}{\mathrm{kWh}}\);
\(w_{\mathrm{y}}\) is the specific electricity consumption for mining one tonne of standard fuel, \(\dfrac{\mathrm{kWh}}{\mathrm{t}\cdot \mathrm{s.f.}}\);
\(T_{\mathrm{mt}}\) is the annual duration of use of the maximum of the fuel-mining shop;
\(T_{\mathrm{mp}}\) is the same for the consumer.
Then the coefficient
\[ k_{\mathrm{sn}}=1.07+P_{\mathrm{t}}=1.07+q w_{\mathrm{y}}\frac{T_{\mathrm{mp}}}{T_{\mathrm{mt}}}. \tag{3} \]
The maximum capacity, as a percentage, consumed by the fuel-mining shop at \(w_{\mathrm{y}}=(30\text{--}60)\), \(q=0.35\cdot 10^{-3}\):
\[ P_{\mathrm{t}}=100\cdot 0.35\cdot 10^{-3}(30\text{--}60)=(1.0\text{--}2.1)\%. \]
This is a substantial capacity, and it cannot be neglected.
The capital expenditures for constructing the additional capacity of power stations and networks, referred to \(1\ \mathrm{kW}\) of capacity transmitted to the consumer, are
\[ Z_{\mathrm{es}}=C_{\mathrm{s}}k_{\mathrm{es}}P_{\mathrm{d}}, \tag{4} \]
where \(C_{\mathrm{s}}\) is the specific capital expenditure per one installed kilowatt of power-station capacity,
\(k_{\mathrm{es}}=1.0\text{--}1.5\) is the coefficient taking into account capital expenditures for creating additional network transmission capacity up to the point of consumption of \(1\ \mathrm{kW}\).
For station consumers \(k_{\mathrm{es}}=1\), and for the most remote consumers \(k_{\mathrm{es}}=1.5\).
The annual consumption of standard fuel per \(1\ \mathrm{kW}\) of consumer capacity is
\[ Q_{\mathrm{t}}=k_{\mathrm{sn}}P_{\mathrm{sh}}T_{\mathrm{mp}}q. \tag{5} \]
The capital expenditures for creating additional productivity of the fuel-mining shop and fuel transport in connection with transmitting \(1\ \mathrm{kW}\) to the consumer are
\[ Z_{\mathrm{yt}}=C_{\mathrm{t}}Q_{\mathrm{t}}=C_{\mathrm{t}}k_{\mathrm{sn}}P_{\mathrm{sh}}T_{\mathrm{mp}}q, \tag{6} \]
where \(C_{\mathrm{t}}\) is the specific capital expenditure for constructing a fuel base and fuel transport with productivity of one tonne of standard fuel per year, rub./t s.f.
Total capital expenditures for the additional system capacity per 1 kW of power delivered to the consumer
\[ Z_{\mathrm{uk}} = Z_{\mathrm{us}} + Z_{\mathrm{ug}} = k_{\mathrm{si}} P_{\mathrm{sh}} (C_{\mathrm{s}} k_{\mathrm{p}} k_{\mathrm{es}} + C_{\mathrm{t}} q T_{\mathrm{m}}). \tag{7} \]
The table gives approximate values of \(Z_{\mathrm{uk}}\), calculated from (7) for \(k_{\mathrm{sn}} = 1.085\); \(k_{\mathrm{p}} = 1.1\); \(C_{\mathrm{t}} = 30\ \frac{\text{rub}}{\text{t}\cdot\text{s.f.}}\) and \(C_{\mathrm{s}} = 130\ \frac{\text{rub}}{\text{kW}}\) (in 1969 prices); \(q = 0.35 \cdot 10^{-3}\ \frac{\text{t}\cdot\text{s.f.}}{\text{kW}\cdot\text{h}}\).
The remaining initial data are indicated in the table.
Table
| Place of consumer connection | \(P\) | \(k_{\mathrm{es}}\) | \(Z_{\mathrm{u}}\) | 2000 | 3000 | 4000 | 5000 | 6000 |
|---|---|---|---|---|---|---|---|---|
| 1. Station consumers | 1 | 1.0 | \(Z_{\mathrm{uk}}\) \(Z_{\mathrm{ue}}\) |
179 0.006 |
188 0.006 |
200 0.006 |
212 0.006 |
224 0.006 |
| 2. Consumers of networks of 110 kV and above | 1.06 | 1.25 | \(Z_{\mathrm{uk}}\) \(Z_{\mathrm{ue}}\) |
230 0.0080 |
242 0.0074 |
254 0.0072 |
266 0.0070 |
278 0.0069 |
| 3. Consumers of secondary networks 6–35 kV | 1.09 | 1.35 | \(Z_{\mathrm{uk}}\) \(Z_{\mathrm{ue}}\) |
254 0.0088 |
265 0.0081 |
278 0.0077 |
290 0.0075 |
303 0.0073 |
| 4. Consumers of tertiary networks 0.4–6 kV | 1.12 | 1.5 | \(Z_{\mathrm{uk}}\) \(Z_{\mathrm{ue}}\) |
286 0.0099 |
298 0.0089 |
311 0.0083 |
323 0.0080 |
336 0.0078 |
When determining \(Z_{\mathrm{uk}}\) in guiding and normative instructions, the following indicators are not taken into account:
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Capital expenditures for the additional transmission capacity of the network up to the point of consumption of 1 kW.
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Capital expenditures for the additional system capacity and the additional productivity of the fuel base required to cover the capacity of losses in the network up to the point of consumption of 1 kW.
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Consumption for auxiliary needs in the fuel component of capital expenditures.
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Capital expenditures for the additional system capacity required to supply the fuel-extraction shop.
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The coefficient of coincidence with the system maximum \(k_{\mathrm{m}}\) in the capital expenditures for the creation of the additional fuel base.
Further, it is generally more expedient not to introduce into the expression for \(Z_{\mathrm{uk}}\) the coefficient \(k_{\mathrm{m}}\) and the coefficient of economic efficiency \(p_{\mathrm{n}}\), but to use the product \(k_{\mathrm{m}} p_{\mathrm{n}} Z_{\mathrm{uk}}\), since the values of \(k_{\mathrm{m}}\) and \(p_{\mathrm{n}}\) for consumers may be different.
In the work of Prof. P. G. Grudinsky, the complete specific capital investments in the system \((k_{\mathrm{s}})\), in rub/kW, are used as \(Z_{\mathrm{uk}}\). We have not found an interpretation of this concept.
The calculated cost of electricity at the point of consumption consists of the following components:
- From the cost of electricity delivered from the busbars of the power plant when transmitting 1 kW to the consumer.
- From deductions for depreciation, repair, and maintenance from the total capital expenditures for the network up to the place of consumption of 1 kW.
The annual cost of electricity delivered from the plant busbars when transmitting 1 kW to the consumer is:
\[ Z_{\text{sh}} = C_{\text{esh}} P_{\text{sh}} T_{\text{mp}}. \tag{8} \]
Deductions from capital expenditures for the network up to the place of consumption of 1 kW:
\[ Z_a = c_c p_{\text{ar}}(k_{\text{es}} - 1), \tag{9} \]
where \(p_{\text{ar}}\) is the rate of deductions for depreciation, repair, and maintenance in relative units,
\(C_{\text{esh}}\) is the cost of electricity delivered from the busbars of the power plant.
Then the total annual operating costs per 1 kW are:
\[ Z_e = Z_{\text{sh}} + Z_a = C_{\text{esh}} P_{\text{sh}} T_{\text{mp}} + c_c p_{\text{ar}}(k_{\text{es}} - 1). \tag{10} \]
The calculated cost of electricity (rubles/kWh) is
\[ Z_{\text{ue}} = C_{\text{esh}} P_{\text{sh}} + \frac{c_c p_{\text{ar}}}{T_{\text{mp}}}(k_{\text{es}} - 1). \tag{11} \]
Indicative values of the calculated cost of electricity at the place of consumption, computed from (11) for \(C_{\text{esh}} = 0.006 \dfrac{\text{rub}}{\text{kWh}}\),
\[ c_c = 130 \frac{\text{rub}}{\text{kW}}; \qquad p_{\text{ar}} = 0.10, \]
are given in the table.
To determine the calculated cost of electricity losses due to the no-load operation of transformers, in (11) \(T_{\text{mp}}\) must be replaced by the total time the transformer is switched on during the year; and for losses in network conductors and transformer windings, by the loss duration time \(\tau\).
In the methods indicated above, only the fuel component and depreciation deductions from capital expenditures for additional capacity are taken into account in the cost of electricity. The fuel cost does not take into account consumption for the plant’s own needs. This may lead to an impermissible error in estimating the calculated cost of electricity.
Determining the calculated cost of electricity by the proposed method is hardly more complicated than estimating it only by the two components indicated.
In conclusion, it should be noted that a number of the issues touched upon in the article are debatable; therefore, it is desirable that the material of this article be subjected to discussion.