Voltage Regulation in Load Supply Centers Based on an Integral Criterion of Voltage Quality

R. I. Borisov, V. V. Litvak

(Recommended by the scientific seminar of the departments of power stations and electrical systems and networks.)

The use of transformers and autotransformers with on-load tap changers for interconnecting networks of different voltage levels makes it possible to pose the problem of finding optimal voltage regulation at nodal, reference points of networks [1]. The transformation ratios must be changed in such a way as to ensure the smallest value of the damage determined by integral criteria of voltage quality over the time period under consideration at the required points of the scheme. Such regulation may also be carried out by autonomous generators when they operate on a selected part of the scheme, or by other devices in the form of synchronous compensators, provided that there is sufficient available reactive power in the system. Establishing the required law of voltage regulation at reference points of schemes can be carried out simultaneously with determining the values of the transformation ratios of all available transformers with longitudinal voltage regulation.

Let us assume that the voltage desired by the consumer, \(U^*\), is optimal for the consumer. For operating conditions, the difference in the reduced calculated costs will be determined by the damage from nonuniformity of voltage and by the difference in losses in the elements of the network.

The voltage-related damage, as was shown earlier, can be determined by formula (2), in which the value \(U_0\) may be regarded as an independent variable [2].

If, in the first approximation, changes in power and energy losses at different values of \(k_t\) are not taken into account, then minimization of the damage with respect to \(U_0\) makes it possible to establish the values of the voltage of the supply source, the regulated transformation ratios \(k_{tr}\) for each load condition, and the unregulated transformation ratios \(k_{tn}\) for the entire calculation period.

The dependences for determining the regulated \(k_{tr}\) and the unregulated values \(k_{tn}\) are presented in [2]. For \(U_0\), an expression of the following form is obtained:

\[ U_0 = \frac{1}{ 2 \displaystyle\sum_{q=1}^{n-1} \frac{k_{tq}}{U_{zh q}^{2}} } \left[ 2 \displaystyle\sum_{q=1}^{n-1} \frac{k_{tq}}{U_{zh q}} + \displaystyle\sum_{q=1}^{n-1} \frac{k_{tq}^{2}}{U_{zh q}^{2}} \displaystyle\sum_{q=1}^{n-1} I_{np}(z_{op}+z_{oq}-z_{pq}) \right]. \tag{1} \]

As can be seen, implementation of regulation according to the obtained law presents certain difficulties because the voltage \(U_0\) is...

function of many variables, as well as of the desired voltages of all nodes and the unknown transformation ratios of all transformers.

Equation (1) is a more general form of writing the optimal regulation conditions than that given in [1], because step-down transformers are taken into account.

As a result of a number of calculations, it was found that the voltage at load supply centers can be represented in the form of a functional dependence on the total active load. The approximation errors of \(U_0\) increase with an increase in the degree of nonuniformity of the loads. In the example presented below, \(U_0\) is approximated by a linear characteristic (Fig. 2), and the errors do not exceed \(\pm 3\%\) in any load condition.

It is recommended to solve equations (3–4) [2] and equation (1) jointly by successive approximations in the following order:

1. Specify the values of \(k_{\mathrm{Tq}}\) for the first approximation.

2. For each load condition, determine the voltage of the power-supply source \(U_0\).

3. The relations obtained in item 2 between the voltage \(U_0\) and the total active load are approximated by a functional dependence; the coefficients of the equation may be determined by the method of least squares.

4. For each load condition, determine the transformation ratios for all regulated transformers. Round the values of \(k_{\mathrm{T}p}\) to the nearest standard values.

5. Determine and round the values of \(k_{\mathrm{T}n}\) for unregulated transformers.

6. Refine the voltage \(U_0\) and repeat the calculation until stable values of \(U_0\) and \(k_{\mathrm{Tq}}\) are obtained.

Calculations have shown that usually 4–5 approximations are sufficient, and the rate of convergence of the process is higher the more uniform the load curves of the consumers are.

Figure 1 shows a diagram of a network supplying consumers with characteristic load curves: H1, a repair and mechanical plant \((P_{1\mathrm{m}} = 6.8\ \mathrm{MW},\ \cos\varphi = 0.92)\); H2, a coal mine \((P_{2\mathrm{m}} = 8.5\ \mathrm{MW},\ \cos\varphi = 0.89)\); H3, a municipal and household load \((P_{3\mathrm{m}} = 9\ \mathrm{MW},\ \cos\varphi =\)

Fig. 1.

\(=0.9\). Transformers of capacity T1—7.5 MVA, T2—10 MVA, T3—10 MVA are installed. Double-circuit power-transmission lines at a voltage of 35 kV have lengths \(l_1=8\) km, \(l_2=8\) km, \(l_3=15\) km and conductor types L1-AC150, L2-AC95, L3-AC95. Transformer T3 is equipped with an on-load tap changer.

As a result of the calculation, the law of voltage regulation of the supply source \(U_0\) was obtained, which proves to be very close to the law of counter-regulation:

\[ U_0 = U_{\mathrm{n}}(1.023+0.078P_{*\Sigma});\quad U_{\mathrm{n}}=35\ \text{kV}. \tag{2} \]

Fig. 2 shows the dependence of \(U_0\) on the total active load \(P_{*\Sigma}\). The unregulated transformation ratios ultimately turned out to be equal to \(k_{\mathrm{T}1}=0.293,\ k_{\mathrm{T}2}=0.308\).

The results of calculating the desired and actual voltages on the low-voltage buses of the substations, the voltage \(U_0\), and the regulated transformation ratio \(k_{\mathrm{T}3}\) are presented in Table 1.

Table 1

Fig. 2.

The voltage values at consumers for the selected values of \(k_{\mathrm{t}}\) and the established control law have a maximum deviation of 2.4%, which is much lower than the voltage-deviation values standardized by the PUE.

REFERENCES

1. L. P. Padalko, V. G. Pekelis. On the choice of a voltage-control law in distribution-network supply centers. Elektrichestvo, No. 7, 1966.

2. R. I. Borisov, V. V. Litvak. Selection of load transformer transformation ratios according to qualitative indicators of power supply to consumers. Proceedings of the East Siberian Technological Institute, issue 3, vol. 4, 1969.