Influence of Short-Circuit Current Levels on the Reliability and Quality Indicators of Power Supply
Abstract Generated abstract
The paper examines how the level of short-circuit currents in 6 to 20 kV distribution networks affects reliability, voltage quality, losses, equipment requirements, and overall economic performance. It formulates the choice of reactor ratings and network schemes as a techno-economic optimization problem using reduced calculated costs that include capital investment, annual costs, and damage from supply interruptions, loss of motor stability, and voltage deviations. A sample calculation for a 10 kV supply scheme with varying reactor resistance indicates a cost minimum at a short-circuit current of 20 kA, corresponding to a reactor resistance of about 2.1 percent and a short-circuit power of 350 MVA. The authors suggest that short-circuit current level can serve as a criterion for rational distribution-network design and for selecting optimal configurations.
Full Text
INFLUENCE OF SHORT-CIRCUIT CURRENT LEVELS ON THE RELIABILITY AND QUALITY INDICATORS OF POWER SUPPLY
R. I. BORISOV, V. D. KOZYREV
(Presented by the scientific seminar of the Departments of Electric Stations and Electrical Systems and Networks)
The values of short-circuit currents in distribution networks depend on the degree of reactoring of the circuits and have a major influence on their operational reliability and on the quality indicators of power supply.
In operating practice, short-circuit currents at supply centers downstream of reactors are usually reduced to 10 kA or less, instead of 20 kA (for VMG-133 and VMP-10 circuit breakers) [1]. Some drives do not correspond to the characteristics of the circuit breakers. Thus, according to the emergency circular of the Ministry of Power Engineering [2], the breaking current of a VMG-133 circuit breaker with a PS-10 type drive was established as 15 kA [3].
An increase in the values of short-circuit currents is achieved by several methods:
1) shunting reactors;
2) connecting paired reactors in parallel;
3) shunting booster transformers;
4) removing reactors from the circuits;
5) drawing up operating power-supply schemes with allowance for the levels of short-circuit currents, etc.—gives the following advantages:
1) it increases the reliability of consumer operation by reducing interruptions in power supply and maintaining stable operation of electric motors during external short circuits and voltage drops at their terminals;
2) it reduces voltage fluctuations under load changes, which improves the quality of the electric power supplied to consumers and reduces the limits of voltage regulation;
3) under normal conditions, active and reactive power losses decrease and, consequently, energy losses decrease;
4) capital expenditures in the network are somewhat reduced through limiting the field of application of current-limiting and starting reactors, simplifying devices for voltage regulation, compensating devices, and rheostatic starting of induction motors.
On the other hand, increasing short-circuit currents requires more powerful and expensive equipment, leads to an increase in cable cross sections according to the condition of thermal stability, requires the installation of high-speed protections, and complicates automation.
The level of short-circuit current values in distribution networks is one of the technical-and-economic categories that must be substantiated for different power-supply schemes and parameters, and it can be used as a criterion for constructing rational power-supply schemes. Therefore, in order to determine optimal values of short-circuit currents, it appears possible to establish relationships among reliability, power-supply quality indicators, power and energy losses in electrical networks, and the levels of short-circuit current values; this can be done using the mathematical apparatus for multifactor problems.
When selecting technical solutions for determining the optimal values of short-circuit currents in 6–20 kV distribution networks by changing the degree of reactance, we shall use the following reduced calculated costs \(Z_{\mathrm{p}}\):
\[ Z_{\mathrm{p}} = p_{\mathrm{n}}K + I_{\mathrm{g}} + Y, \tag{1} \]
where
\(K\) — capital investments for the power-supply option, thousand rubles;
\(I_{\mathrm{g}}\) — annual costs, thousand rubles;
\(Y\) — national-economic damage, thousand rubles.
\[ Y = Y_1 + Y_2 + Y_3, \tag{2} \]
where
\(Y_1\) — damage caused by interruptions in power supply to consumers;
\(Y_2\) — damage due to a violation of load stability;
\(Y_3\) — damage from voltage deviations at consumers.
The reliability of consumers’ power supply is characterized by the components of national-economic damage: \(Y_1\) and \(Y_2\).
\[ Y_1 = y_0 E_{\mathrm{g}}, \tag{3} \]
where
\(y_0\) — specific damage from interruptions in power supply, rubles/kWh;
\(E_{\mathrm{g}}\) — electric energy not supplied over a year, kWh,
\[ E_{\mathrm{g}} = h_{\mathrm{e}} T_{\max} P_{\max}, \tag{4} \]
\(h_{\mathrm{e}}\) — probable duration of power-supply interruptions, relative units;
\(T_{\max}\) — time of maximum load, hours;
\(P_{\max}\) — maximum load, kW.
For each load node and power-supply option, the critical voltage \((U_{\mathrm{cr}})\) is determined, at which motors overturn, i.e., to check load stability we shall use one of the practical criteria of load stability:
\[ \frac{dE}{dU} > 0 \left(U_{\mathrm{cr}} \sim \frac{dE}{dU} = 0\right). \]
To construct the dependencies \(E = f(U)\), we use the static characteristics of the composite load. It should be noted that determining the calculated margins of static voltage stability of the load by means of practical stability criteria provides the accuracy necessary for engineering calculations [4]. Next, we determine the recovering voltage \((U_{\mathrm{v}})\) on the busbars of the load node after disconnection of the short circuit and operation of automatic reclosing. The value \(U_{\mathrm{v}}\) is compared with \(U_{\mathrm{cr}}\), and the conditions for self-starting of the electric motors are identified. With large external resistances, self-starting of all motors is not-
is possible; therefore some of the electric motors have to be disconnected, which leads to a certain loss:
\[ Y_2 = y_0 h_\varepsilon' P_{\text{disc}} \cdot T, \tag{5} \]
where
\[ h_\varepsilon' \]
is the probable duration of disconnection of electric motors, relative units;
\[ P_{\text{disc}} \]
is the load power of the disconnected electric motors;
\[ T = 8760\ \text{h}. \]
The change in voltage deviations from the optimum value at consumers, caused by different reactor ratings, is assessed by integral indicators of the national-economic loss, the magnitude of which is determined by the “nonuniformity” of the voltage.
\[ Y_3 = k_y N, \tag{6} \]
where
\[ k_y \]
is the coefficient of loss due to voltage, thousand rubles/\((\%)^2\);
\[ N \]
is the “nonuniformity” of voltage, \((\%)^2\).
The criterion of voltage “nonuniformity” is used only in economic calculations of loss for approximately homogeneous electrical receivers or technological processes with voltage deviations at the terminals of the electrical receivers.
Fig. 1
Calculations were performed to determine the optimum value of the short-circuit current for the scheme shown in Fig. 1. The calculated costs were determined by formula (1):
\[ Z_p = f\left[ C_p(x_p, I_n, U_n);\ C_B(U_n, I_n, I_{kz});\ C_{\text{cable}}(I_{kz});\ Y \right]. \]
The load was specified by a duration curve with \(T_{\max}=5440\ \text{h}\), \(P_{\max}=5\ \text{MW}\), \(\cos\varphi=0.85\).
The reactor resistance was varied from 1 to 8%. The short-circuit currents at points \(K_1\) and \(K_2\) were calculated.
The dependence of \(Z_p\) on \(I_{k1}\) \((S_{k1})\) is shown in Fig. 2. The minimum of the costs was obtained for \(I_{k1}=20\ \text{kA}\), which corresponds to \(x_p=2.1\%\) and to the limiting value of the short-circuit power of 350 MVA (for a voltage of 10 kV), adopted for domestic networks at the present time.
Fig. 2
The proposed formulation of the problem of studying the reduced calculated costs as a function of short-circuit currents requires deriving cost relationships of the following form:
\[ C = f(I_{\mathrm{kz}}, \Pi_{\mathrm{n}}), \tag{7} \]
where
\(C\) and \(\Pi_{\mathrm{n}}\) are the calculated cost (thousand rubles) and the nominal parameters of the electrical equipment used.
Further studies show that the level of short-circuit current values can be used as a criterion for the rational design of electrical-network schemes, employing the base-point method in techno-economic calculations. It appears possible to use an algorithm for selecting the optimal configuration which, by varying the scheme parameter \(k\), which may be the short-circuit power, makes it possible to find a number of power-supply schemes, including the variant with the lowest reduced costs.
REFERENCES
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