ON THE ISSUE OF IMPROVING THE POWER FACTOR OF INDUSTRIAL ENTERPRISES

A. I. ZAITSEV

(Presented by the scientific seminar of the Electromechanical Faculty)

By a government decree, in order to reduce losses in electrical networks and to make the most economical use of equipment, all operating enterprises with an installed capacity of 100 kVA and above, receiving electric power from the power systems of the Ministry of Electric Power Stations and Electrical Industry, are obliged to carry out measures to increase the power factor and bring it to a value of 0.92–0.95. Raising the power factor of the electrical installations of industrial enterprises is an integral part of the problem of increasing the efficiency of the electrical system and of revealing the internal reserves of the large energy economy of each enterprise.

Questions of improving the power factor of electrical installations are stimulated by a whole series of organizational and technical measures. Such measures include a scale of discounts and surcharges for the power factor, as well as a bonus payment system at enterprises for engineering and technical workers and service personnel for carrying out measures to save electric power and reduce the consumption of reactive power.

The widespread use of asynchronous motors, transformers, and electric welding, while producing a large industrial effect, inevitably entails the appearance of large reactive loads and a decrease in the power factor of electrical installations. A feature of the operation of any electrical system is the complete balance both in active and in reactive power, i.e., the numerical equality of their production and consumption at any moment in time. An increase in the consumption of reactive power in the system causes an increase in the current in the conductors of any link of the electrical system. An increase in current, i.e., an increase in the apparent power, in turn leads to the need to increase the carrying capacity of the corresponding links. With an unchanged nominal carrying capacity of a link, determined by the magnitude of the apparent power, the presence of reactive power entails an unproductive expenditure of energy in this link. Therefore it is desirable, where possible, to avoid the flow of reactive power through the conductors, covering the demand for it locally. In addition, the surcharges paid by enterprises to the electricity tariff for a reduced power factor of electrical installations are not included in the planned cost of industrial production.

From what has been said it follows that the most decisive measures must be taken to carry out measures for improving the power factor of enterprises’ electrical installations. From the technical literature on questions of improving the power factor it is known that the most expedient—

Expedient measures for improving $\cos\varphi$ are measures aimed at improving the natural power factor [1, 2]. Such measures consist mainly of the following:

1) replacing lightly loaded asynchronous motors with motors of lower power;

2) reducing the voltage for lightly loaded asynchronous motors;

3) limiting the no-load running of operating asynchronous motors, etc.

Let us dwell on one of these measures.

Reducing the voltage for lightly loaded asynchronous motors by switching the stator windings from delta to star is not always possible, either because of a load greater than 50%, or when, owing to the network voltage, the motor must be connected in star. In these cases reverse connection can sometimes be used, i.e., supplying power to the rotor and connecting the stator winding according to the rotor circuit. Such a measure is possible only in those cases when the phase voltage of the rotor is greater than the phase voltage of the network. In this case, if the change in saturation of the rotor iron is neglected, the effect of reducing reactive-energy consumption will be determined by the square of the ratio of the rotor phase voltage to the network phase voltage,

\[ g=\left(\frac{U_{\phi\ \text{rot}}}{U_{\phi\ \text{network}}}\right)^2. \]

The factor by which reactive-power consumption is reduced in this case will differ from the value 3, as occurs when switching from delta to star, and may assume different values depending on the design of the motor rotor. Carrying out such a measure makes it possible to broaden the possibilities for reducing the consumption of reactive power by motors that usually cannot be switched from delta to star for the reasons indicated.

As operating practice with electrical equipment shows, the value of the weighted-average power factor almost never reaches the neutral value ($\cos\varphi=0.85$). To ensure a high value of $\cos\varphi=0.92 \div 0.95$, it is necessary to carry out additional measures that make it possible to relieve network elements from the flow of reactive energy. This becomes possible if the required reactive energy is generated directly at the consumer. The most economical means of obtaining leading reactive power under the conditions of industrial enterprises with an installed transformer capacity at the substation of up to 3–5 MVA are:

a) installation of static capacitors;

b) replacement of asynchronous motors with synchronous ones;

c) synchronization of asynchronous motors.

The application of one measure or another must be decided on the basis of technical and economic calculations. The installation of static capacitors is an inexpensive method of compensation because of their small active losses. A capacitor bank may be installed on the high- and low-voltage side. Installing capacitors on the high-voltage side reduces losses only in the high-voltage line and in generators, and, from this point of view, the economic effect of using high-voltage capacitors is limited, since the losses themselves in high-voltage distribution lines are relatively small, while such network elements as step-down transformers and the low-voltage distribution network are not relieved of the flow of reactive currents.

Such conclusions can be drawn if the distribution of energy is carried out at generator voltage.

The installation of capacitors on the low-voltage side can relieve transformers of the flow of reactive currents in addition to the high-voltage line, and, in the case of installing capacitors at the motors, also the low-voltage network. When determining the economic effect of compensation on the low-voltage side, it is necessary to take into account the reduction of losses in the low-voltage line, in the transformer windings, and in the high-voltage line. In addition, it is necessary to take into account the value of the released transformer capacity, which is determined by the cost of the transformer’s connected kVA per year. If these factors are taken into account, then even with the very high cost of low-voltage capacitors, the annual expenditures for such compensation turn out to be comparable with the annual expenditures for compensation by high-voltage capacitors, and sometimes these expenditures are smaller. Therefore, if the problem of improving \(\cos\varphi\) is considered as a nationwide one, it is necessary to raise the question of introducing low-voltage capacitors. This will make it possible to increase the additional active load of substations without connecting other transformers.

As is known [1; 2], replacing induction motors with synchronous ones gives the greatest economic effect, since in this case the compensating effect is determined not only by the reactive power supplied by the motor to the network, but also by the reactive power that was consumed by the induction motor before its replacement. Taking into account the fact that at present the output of synchronous motors does not fully satisfy the needs of the national economy, the synchronization of induction motors can be applied with great success. When the wound rotor of an induction motor is supplied with direct current, the latter is pulled into synchronism and becomes capable of operating with a leading power factor, acquiring properties similar to those of a synchronous motor. The compensating effect of a synchronized motor should be considered as that for a synchronous motor installed in place of an induction motor,

\[ Q_k = Q_c + Q_{ac}, \]

where \(Q_c\) is the leading power of the synchronized induction motor;

\[ Q_{ac} \]

is the lagging power of the induction motor.

A characteristic indicator of the operation of a compensating device is the loss coefficient. In the present case this loss coefficient is determined by the following equation:

\[ K_k=\frac{\Delta P}{Q_k}= \frac{\dfrac{P_{dv}}{\eta_2}-\dfrac{P_{dv}}{\eta_1}}{Q_c+Q_{ac}}, \]

where \(\Delta P\) is the increase in active losses in the motor during synchronization;

\(\eta_2\) is the efficiency of the synchronized motor;

\(\eta_1\) is the efficiency of the motor before synchronization. For example, it is required to determine the loss coefficient for a synchronized motor with a power of 155 kW, having \(\eta_1=0.92\) and \(\cos\varphi=0.82\). After synchronization \(\eta_2=0.91\) and \(\cos\varphi_{\text{lead}}=0.75\). The motor load is 100 kW.

\[ Q_{ac}=\frac{P_{\text{nom}}\cdot \tg\varphi}{\eta_1} =\frac{155\cdot 0.7}{0.92}=118\ \text{kvar}, \]

\[ Q_c=\frac{P_{\text{nom}}\cdot \tg\varphi_{\text{lead}}}{\eta_2} =\frac{155\cdot 0.865}{0.91}=149\ \text{kvar}, \]

\[ K_k=\frac{\dfrac{100}{0.91}-\dfrac{100}{0.92}}{118+149} =\frac{110-109}{267}=0.00375. \]

The obtained loss coefficient proved to be less than the loss coefficient for static capacitors (0.004). If it is possible to obtain a lower leading power factor of the synchronized motor, the loss coefficient will be still smaller. Therefore, synchronization of induction motors is the most advantageous from the economic point of view. In this case we obtain the lowest cost of 1 kvar-hour, while the capital investments will be determined by the cost of the installation for obtaining direct current.

At present there are a number of schemes for synchronizing induction motors. The DAG scheme, used in the coal industry, has become the most widespread. This scheme provides for automatic control. However, as was shown by the discussion “On measures for increasing the power factor of electrical installations of industrial enterprises” [3; 4; 5; 6], the DAG scheme has a number of shortcomings and is complex in its construction. The main shortcomings are the dependence of the excitation current on the applied voltage, as a result of which stability decreases when the voltage drops, and the short service life of selenium rectifiers. Therefore, from the point of view of reliability this scheme cannot be adopted as the basic one.

The most reliable synchronization scheme is obtained if low-voltage, high-current direct-current generators are used as the direct-current source. Welding generators and two-collector generators for electrolysis at a voltage of 6/12 V are well suited for this purpose.

Under the author’s direction, at one of the plants two induction motors of 155 and 135 kW were synchronized with the aid of a two-collector motor-generator of the AND type and a welding generator.

The synchronization scheme is shown in Fig. 1. The indicated scheme provides for automatic control of synchronization.

Let us consider very briefly the operation of this scheme.

1. Starting the motor

The starting mode is carried out in the usual way with the aid of a starting rheostat. To ensure accident-free starting, a block contact \(K_3\) is installed, which will not allow the motor starter \(P_1\) to be switched on until the resistance of the starting rheostat has been completely inserted.

2. Synchronization

As soon as the starting rheostat has been completely cut out, block contact \(K_2\) closes; through the normally closed contact of the direct-action current relay \(K_1\), it closes the circuit of the holding coil of starter \(P_2\). The exciter motor will begin to accelerate, and the generator will be excited. Then direct current will flow through the rotor windings of the motor, and the motor will enter synchronous operation.

3. Falling Out of Synchronous Operation

In the event of a motor load at which the motor will fall out of synchronism, the direct-acting current relay of the maximum automatic device of type \(A\) operates; to its moving armature there is attached a normally closed pair of contacts \(K_1\). When the current relay operates, it opens contact \(K_1\), and starter \(P_2\) of the exciter motor is disconnected. With the exciter motor stopped, the constant field disappears, and the motor passes into asynchronous operation. In this case one of the phases will be connected to the others through the armature winding of the exciter.

Fig. 1.

4. Automatic Synchronization

After the load has decreased, the current relay will close its contact \(K_1\); thereby starter \(P_2\), the exciter motor, will be switched on. As the exciter accelerates, the direct current flowing through the rotor windings will gradually increase, and the motor will again enter synchronism. Such a synchronization circuit makes it possible to avoid strong surges of stator current when entering synchronism. The maximum current relay has a very small reset coefficient, which in this case is very important.

To change the reset current of the current relay, it is necessary to vary the magnitude of the air gap between the movable armature and the core of the stationary magnetic system. By changing the gap, one can determine that value of load current at which the motor is again brought into synchronous operation. Thus, by using only one direct-acting current relay of the maximum automatic device, it is possible to ensure complete automation of the operation of the synchronization circuit.

Synchronized motors operate with sharply varying load; however, falling out of synchronism occurs very rarely and with

at overloads greater than 110–120% of the rated value. Thus, assertions [1; 2] that a synchronized motor falls out of synchronism at a load factor equal to 70–80% are unfounded. As experience and the theory of stability of parallel operation of a synchronous motor show, the limiting load of the motor depends on the excitation current and is determined from the following equation [7]

\[ P=\frac{\dot U \cdot \dot E_d}{X_d}\sin\hat{\delta}, \]

where \(U\) is the network voltage;
\(E_d\) is the counter-emf of the synchronized motor, which depends on the magnitude of the excitation current, i.e., on the current flowing through the motor rotor;
\(X_d\) is the inductance along the longitudinal axis of the motor;
\(\hat{\delta}\) is the angle of divergence between the vectors \(U\) and \(E_d\).

The maximum power will occur when the angle \(\hat{\delta}\) takes the value \(90^\circ\). Then the equation takes the form

\[ P_{\max}=\frac{U \cdot E_d}{X_d}. \]

A further increase in the angle leads to loss of synchronous operation.

The equation given shows that the smaller the value of the leading power factor, the greater the limiting power obtained. Thus, it is necessary to create such conditions under which the excitation current would be as large as possible and close to the nominal value of the rotor current during asynchronous operation; thereby the value of the economic coefficient will also decrease.

When selecting a motor to be synchronized, preference should be given to more powerful and higher-speed motors, since in such motors, owing to the high speed, a much greater compensating effect can be obtained with the same excitation current and number of turns per phase than in low-speed motors.

The economic effect from synchronizing asynchronous motors is still more appreciable than compensation by means of static capacitors because of the low cost of the additional capital expenditures (the cost of the generator installation).

Analysis of the system of power-factor compensation at industrial enterprises indicates the need for compensation both on the low-voltage side, relieving the low-voltage network and transformers from the flow of reactive currents, and on the high-voltage side. Let us call this method of compensation combined.

With the combined method of compensation, the required capacity of the capacitor bank on the high-voltage side will depend on the power factor on the low-voltage side, and on the type and capacity of the connected transformers.

The resulting load on the high-voltage side will consist of the sum of the load on the low-voltage side, the losses of active and reactive power in the transformer windings, and the reactive magnetizing power of the transformers.

\[ S_{tr}=P_{lv}-jQ_{lv}+\Delta P_t-j\Delta Q_t-jg_{\mu}=P_{hv}-jQ_{hv}, \]

where \(P_{lv}\) and \(Q_{lv}\) are the transformer loads on the low-voltage busbars;
\(\Delta P_t\) and \(\Delta Q_t\) are the losses of active and reactive power in the transformer windings;
\(g_{\mu}\) is the magnetizing power of the transformer.

The quantities \(\Delta P_m\) and \(\Delta Q_m\), when \(\cos\varphi\) worsens, increase and thereby worsen \(\cos\varphi\) on the high-voltage side. The power factor also worsens on account of the magnetizing power. Thus, even when \(\cos\varphi = 1\) on the low-voltage side, it will not be equal to unity on the high-voltage side.

The required power of the capacitor bank, for the desired power factor on the high-voltage side \(\cos\varphi_{\text{des}}\), can be determined from the expression

\[ Q_{\text{bank}} = Q_{\text{hv}} - P_{\text{hv}}\cdot \tg \varphi_{\text{des}} . \]

It is evident from the formula that, as the power factor on the low-voltage side increases, the required power of the capacitor bank continually decreases. In addition, improvement of \(\cos\varphi\) on the low-voltage side makes it possible to load the substation transformers with additional active power, which may be determined as the difference between the possible active load at the new value of the power factor—\(\cos\varphi_{\text{des}\cdot\text{lv}}\)—and the possible active load at the initial value \(\cos\varphi_{\text{lv}}\), i.e., before compensation:

\[ P_{\text{add}} = S\cdot \cos\varphi_{\text{des}\cdot\text{lv}} - S\cdot \cos\varphi_{\text{lv}} . \]

In the interests of the state, it is necessary first of all to attain a high \(\cos\varphi\) on the low-voltage side, and only then to carry out compensation on the high-voltage side.

Conclusions

1. The synchronization of asynchronous motors, along with static capacitors, is a very effective means of improving the \(\cos\varphi\) of factory electrical installations.

2. It is necessary in every way to limit \(\cos\varphi\) compensation on the high-voltage side when there is no deficit of reactive energy in the system, since the effect of such compensation on a nationwide scale is very small if the distribution network is made at generator voltage and there are no intermediate transformations.

3. It is necessary in every way to popularize \(\cos\varphi\) compensation on the low-voltage side, since this makes it possible additionally to draw upon internal reserves in the form of additional connections of active power to substation transformers and to reduce energy losses significantly in all links of the system.

4. In determining the economic effect of compensation on the low-voltage side, it is necessary also to take into account the cost of the released kVA of installed transformer capacity, as is done with respect to released generator capacity.

5. In view of the fact that synchronization of large asynchronous motors, when they operate with leading \(\cos\varphi\), has a loss coefficient smaller than that for capacitors, and the capital expenditures are likewise small, it is necessary to continue work on finding the simplest synchronization schemes and obtaining inexpensive direct-current sources, such as mechanical converters of alternating current into direct current may be. The converter of Engineer S. G. Tamantsev [8] deserves special attention here.

Literature

1. A. A. Fedorov and B. A. Knyazevsky. Electric Power Supply of Industrial Enterprises. GEI, 1951.

2. Yu. L. Mukoseev. Problems of Electric Power Supply of Industrial Enterprises. GEI, 1951.

1. Skorkin K. I. Synchronization of asynchronous electric motors at the mines of the Stalinugol Combine. Elektrichestvo 5, 1952.

2. Shishkin O. P. Results of the introduction of synchronization in the Grozny oil fields. Elektrichestvo 5, 1952.

3. Kiselev A. F. and Beskov M. Ya. Synchronization of asynchronous motors according to the DAG scheme in the asbestos industry. Elektrichestvo 2, 1952.

4. Discussion. On measures to increase the power factor of electrical installations at industrial enterprises. Elektrichestvo 2, 1953 and 1, 1954.

5. Berger A. Ya. Synchronous machines. GONTI, 1938.

6. Artapov S. G. Study of a synchronous motor with a mechanical rectifier. Abstract, Moscow, 1954.