Issues in Determining the Economic Efficiency of Deep Voltage Regulation in Long-Distance Power Transmission Lines
Abstract Generated abstract
The paper examines how to evaluate the economic efficiency of introducing deep voltage regulation in existing long distance power transmission lines. It compares calculated costs for operating variants with and without such regulation, accounting for transformer cost increases, possible reductions in compensating devices, and changes in energy losses through the duration of maximum losses. The author derives a cost difference expression that separates capital investment effects from fuel cost savings due to reduced losses, and notes practical uncertainties in estimating transformer price increments and discrete compensation equipment changes. The proposed formulation is also suggested as a basis for selecting an optimal voltage regulation range by varying assumed relationships between regulation depth and transformer cost.
Full Text
Proceedings of the Tomsk Polytechnic Institute Named after S. M. Kirov, Holder of the Order of the October Revolution and the Order of the Red Banner of Labor
Vol. 295 1976
Issues in Determining the Economic Efficiency of Deep Voltage Regulation of Long-Distance Power Transmission Lines
A. G. Milyushkin
(Presented by the scientific seminar of the Department of Electrical Systems and Networks)
By comparing the calculated costs for variants with deep voltage regulation (DVR) and without it, one can determine the economic efficiency of deep voltage regulation [1].
This paper considers a methodology for the efficiency of introducing deep voltage regulation for existing power transmission lines; determination of the advisability of DVR for the case of a planned power transmission line is set forth in the literature [2]. The value of the calculated costs for the variant without the use of deep voltage regulation is written as [4]:
\[ Z_{\mathrm{I}}=\varepsilon' K_{\text{line}}^{\mathrm{I}}+\varepsilon'' K_{\text{subst}}^{\mathrm{I}}+\Delta P_m^{\mathrm{I}}\left(k_{\mathrm{ud}}\varepsilon'''+\tau^{\mathrm{I}}\beta\right), \tag{1} \]
where \(\varepsilon\) is the share of deductions from capital investments of the corresponding facility for depreciation and operation, taking into account the normative efficiency coefficient;
\(K\) — capital investments in the corresponding facilities (thousand rubles);
\(k\) — specific capital investments in a power plant (rubles/kW);
\(\tau\) — time of maximum losses (hours);
\(\beta\) — fuel component of costs for the production of electricity (thousand rubles/kW·hour);
\(\Delta P_m\) — maximum power losses in the power transmission line during passage of the load peak (MW).
Substituting all quantities into formula (2) in the indicated dimensions, we obtain the value of the calculated costs in thousand rubles. For the variant with the use of deep voltage regulation, the calculated costs are written as
\[ Z_{\mathrm{II}}=\varepsilon'K_{\text{line}}^{\mathrm{II}}+\varepsilon''K_{\text{subst}}^{\mathrm{II}}+\Delta P_m^{\mathrm{II}}\left(k_{\mathrm{ud}}\varepsilon'''+\tau^{\mathrm{II}}\beta\right). \tag{2} \]
It is obvious that, for the variant of an existing power transmission line, \(K_{\text{line}}^{\mathrm{I}}=K_{\text{line}}^{\mathrm{II}}\); moreover, since DVR is not carried out over the entire range of variation of the transmitted active power, the assumption is justified that when the peak of the load curve is transmitted, DVR is not carried out, i.e., the power transmission line operates at a voltage equal to the nominal one; therefore \(\Delta P_m^{\mathrm{II}}=\Delta P_m^{\mathrm{I}}\). Since the active-power losses in the variant with DVR do not exceed
losses in the variant without DVR, then \(\tau^{II} \leq \tau^I\). Taking into account that \(K_{\text{p/st}}^I\) and \(K_{\text{p/st}}^{II}\) differ in the cost of transformers, since transformers with a deep voltage-regulation range are more expensive than ordinary ones, and in the cost of compensating devices, since the installed capacity of reactive-power sources in the variant with DVR may be smaller, because at low loads the required reactive power of the RPS is smaller for the second variant. Taking into account the conclusions made in [3], where it is stated that CD (shunt reactors) for 500-kV transmission lines are now used not to limit internal overvoltages, but mainly to compensate the charging power of lines, and therefore it is more advantageous to install CD on the secondary side, and knowing that the unit capacity of CD at secondary voltage is comparatively small (20, 90, 100 Mvar), it may turn out that in the variant with DVR the number of CD at secondary voltage at switching stations or intermediate taps can be reduced. On the basis of the above one may write
\[ K_{\text{p/st}}^{II}=K_{\text{p/st}}^{I}+K_{\text{tr}}\cdot n\cdot \lambda-\Delta K_{\text{ku}}, \tag{3} \]
where \(n\) is the number of transformers with an extended regulation range installed at substations instead of ordinary ones and equal to them in unit ratings;
\(K_{\text{tr}}\) is the calculated cost of transformers of ordinary design;
\(\lambda\) is the amount (in fractions of unity) by which transformers with DVR are more expensive than standard ones;
\(\Delta K_{\text{ku}}\) is the reduction in capital investments in CD due to the introduction of DVR.
Comparing the calculated costs of the variants, taking into account the foregoing, one can judge the economic efficiency of applying deep voltage regulation.
\[ Z_I-Z_{II}=\varepsilon''\left(\Delta K_{\text{ku}}-\sum_{i=1}^{n}K_{\text{tr}\,i}\cdot \lambda_i\right)+\Delta P_m\cdot \beta(\tau_I-\tau_{II}). \tag{4} \]
It is obvious that the component \(\Delta P_m\cdot \beta(\tau_I-\tau_{II})\) characterizes the reduction in fuel costs due to the reduction of power losses in the transmission line. The quantities \(\tau_I\) and \(\tau_{II}\) are determined by
\[ \tau=\frac{\Delta A}{\Delta P_m}. \tag{5} \]
Taking into account that \(\Delta P_m\) is the same for both variants, it follows that \(\tau_I\) and \(\tau_{II}\) are unequal because of the different \(\Delta A\)
\[ \Delta A=\sum_{i=1}^{n}\Delta P_i\cdot \Delta t_i=T_{\text{year}}\cdot \sum \Delta P_i\cdot \rho_i, \tag{6} \]
where \(T\) is the number of hours during which the transformers are switched on per year;
\(\Delta P_i\) is the value of the active-power losses at the transmitted power \(P_i\);
\(\rho_i\) is the probability of the load \(P_i\).
It follows from (6) that the energy losses in the variants being compared differ because of the difference in \(\Delta P_i\), since in both cases the same transit schedule over the transmission line is assumed, i.e.,
\[ \Delta A_I=T\cdot M(\Delta P_I);\qquad \Delta A_{II}=T\cdot M(\Delta P_{II}). \tag{7} \]
To determine the economic efficiency of deep voltage regulation, it is necessary to determine \(\tau_I\) and \(\tau_{II}\), as well as the value \(\lambda\), which depends on the capacity of the transformers, their rated voltages, and the depth of the regulation range. Up to the present time, there have been no firm estimates of the increase in transformer cost when their regulation range is increased. There are difficulties in determining the value \(\Delta K_{\text{ku}}\), owing to its discreteness and to limitations of a technical and economic nature. The proposed formula (4) can also be used to determine the optimal regulation range, for which it is necessary:
a) to specify the relationship between the deepening of the transformer voltage regulation range and its increase in cost;
b) by varying the depth of voltage regulation, one can obtain the dependence of the change in calculated costs on the magnitude of the regulation range for the relationship specified in item “a”;
c) by varying the relationships in item “a,” one can obtain a family of dependences of calculated costs on the depth of the voltage regulation range for the family of relationships in item “a.”
References
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T. B. Stepanova. Economic efficiency of deep voltage regulation of long-distance electric-power transmission lines. In: Problems of General Power Engineering and the Unified Energy System. Issue 1, “Nauka,” Alma-Ata, 1965.
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I. S. Davydov, I. Ya. Melzak, A. N. Sherentsis. The present state of 500-kV networks in the USSR. Elektrichestvo, 1971, No. 2.
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Yu. N. Starshinov. On the economic efficiency of operating modes with a voltage drop in 330–500-kV long-distance electric-power transmission lines. Elektrichestvo, 1966, No. 1.