Keywords

1 Introduction

Compensation of reactive power ka we know is especially relevant for industrial enterprises, the main electrical consumers of which are asynchronous motors, as a result of which the power factor without taking compensation measures is 0.7–0.85. Compensation of reactive power, at present, is an important factor in solving the issue of energy saving and reducing the load on the power grid [1,2,3,4].

This inductive load during operation is a source of reactive electricity (reactive power), which oscillates between the load and the source (generator), is not associated with the performance of useful work, but is spent on creating electromagnetic fields and creates an additional load on the power supply lines. Therefore, the reactive power compensator is very important [5,6,7,8,9].

Fig. 1.
figure 1

Structure of reactive power consumers in power systems (by installed active power).

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As we can see from Fig. 1, the main load in industrial power grids is induction motors and distribution transformers. The most effective and efficient way to reduce the reactive power consumed from the network is to use reactive power compensation units (capacitor units) [10,11,12,13,14,15,16].

Measures for reactive power compensation, the use of capacitor units as a reactive power compensator for an enterprise allows:

  • reduce the load on transformers, increase their service life;

  • use wires, cables of a smaller cross-section by reducing the load on them;

  • improve the quality of electricity at electrical receivers (by reducing the distortion of the voltage waveform);

  • to reduce the load on the switching equipment by reducing the currents in the cir-cuits;

  • to reduce energy costs;

  • unload power supply lines, transformers and switchgear;

  • when using a certain type of installations, reduce the level of higher harmonics;

  • suppress mains interference, reduce phase imbalance;

  • to make distribution networks more reliable and economical.

2 Methodology

The research object was the North-East industrial zone of Khujand City, Sughd region, Republic of Tajikistan. Power supply to the North-East industrial zone of Khujand City is carried out through two independent power sources. The first is the «Zarechnaya-110/10» substation, and the second is the «Radiy-110/10» substation. Both substations are located not far from the North-East industrial zone and were operated in the last century. Substation «Zarechnaya-110/10» has two transformers of the TDN-16000/110/10 type. The power of each transformer is 16,000 kVA, and the Radiy-110/10 substation also has two transformers of the TDN-10000/110/10 type, the power of each transformer is 10,000 kVA. From the substation to consumers, the distribution of electricity is carried out through overhead high-voltage power lines, wires of the AABLU-240–3 type. The characteristics of the transformers of the Zarechnaya-110/10 and Radium-110/10 substations are shown in Table 1.

As we have noted, the main power sources of our enterprises are substations «Zarechnaya - 110/10» and «Radiy-110/10». Both substations are powered from the «Khujand - 220/110» substation.OJSC JV «Javoni» has two power transformers with a capacity of 1600 kVA each. Power is supplied from the Zarechnaya - 110/10 substation through 10 kV lines with AABLU-3x240 wire with a distance of 3.35 km and through the Radiy-110/10 substation of a 10 kV line with AABLU-3x240 wire with a distance of 1.43 km. OJSC«MMK» has one 630 kVA transformer in its balance sheet. The power source for this enterprise is only the substation «Zarechnaya - 110/10» with a wire of the type AABLU-3x240. The distance from the source to our consumer is 1.87 km.A detailed description of the types of transformers in industrial enterprises is given in Table 2.

OJSC «Niku Khujand» has two power transformers with a capacity of 630 kVA each. And power is supplied from two substations, ie, «Zarechnaya - 110/10» and «Radiy-110/10» through 10 kV lines with a wire of the type AABLU-3x240. The distance from the «Radiy-110/10» substation to OJSC «Niku Khujand» is 1.45 km, and from the «Zarechnaya - 110/10» substation is about 2.13 km.To reduce the mains voltage from 10 kV to 0.4 kV, industrial enterprises have their own step-down transformers.

The scheme of power supply to consumers without taking into account distributed generation shown in Fig. 2.

Taking into account the prospects for the development of industrial enterprises and justifying the fact that our enterprises will increase production in the future, we take the actual load equal to 20% as a potential load [17,18,19,20,21,22].

Using this formula, we will calculate the current of an industrial enterprise:

Table 1. Characteristics of the transformer substation «Zarechnaya - 110/10» and «Radiy - 110/10».
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Table 2. Power supply of the industrial enterprise and the type of transformers.
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Fig. 2.
figure 2

Power supply system of industrial enterprises from the substation «Zarechnaya - 110/10» and «Radiy-110/10».

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$$ I = \frac{S}{{\sqrt 3 \cdot U_{n} \cdot cos\varphi }} $$
(1)

where \(I\) - current of industrial enterprises, A; \(S\) - full power of industrial enterprises, kVA; \(U_{n}\) - rated voltage, kV; \(cos\varphi\) - power factor.

The following is used to calculate the reactive power of industrial plants, kvar

$$ Q_{r} = P_{r} \cdot tg\varphi $$
(2)

where \(P_{r}\) - rated active power, kW; \(Q_{r}\) - rated reactive power, kvar; \(tg\varphi\) - active power factor.

The active power factor is calculated using the following formula:

$$ tg\varphi = \sqrt {\frac{{1 - cos^{2} \varphi }}{{cos^{2} \varphi }}} $$
(3)

Using the following formula, we will calculate the estimated capacity of the enterprise, kW:

$$ P_{{\text{p}}} = I \cdot U $$
(4)

With the formula below, we will now calculate the total capacity of our industrial plants, kVA:

$$ S_{{\text{p}}} = \sqrt {P_{{\text{p}}}^{2} + Q_{{\text{p}}}^{2} } $$
(5)

3 Calculation Results

Due to the fact that 10 kV is taken on the low voltage side of the supply transformers, the voltage by distributed generation will be taken as 10 kV.

The possibility of using distributed generation sources provides good conditions for the integration of both centralized and decentralized power generation sectors, both for a common network with centralized sources and for individual consumers. In the decentralized sector, distributed generation sources have the advantage, although a local power supply system can also be installed here, combining several distributed sources to work together on the same network.

When introducing distributed generation systems, a potential load is assumed at each power source.

Determination of the compensated reactive power is made by the following formula

$$ {\text{Q}}^{{\prime}} = P_{{\text{p}}} \cdot \left( {tg\varphi\uppi - tg\varphi {\text{e}}} \right) $$
(6)

where \(Q^{\prime}\) - compensated reactive power, kvar; \(P_{p}\) - calculated active power, kW; \(tg\varphi\uppi \)- consumer reactive power factor; \(tg\varphi e\) - reactive power factor of the network.

The determination of the compensated reactive power can be calculated using the following formula:

$$ Q^{\prime\prime} = Q_{{\text{p}}} - Q^{\prime} $$
(7)

where \(Q^{\prime\prime}\) - compensated reactive power, kvar; \(Q_{p}\) - rated reactive power, kvar (Table 3).

Table 3. Calculation of the forecast for active and reactive loads, taking into account the length of the power lines of these enterprises.
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We calculate the total power according to the following formula, kVA

$$ S_{{}}^{{{\prime \prime }}} = \sqrt {P_{{\text{p}}}^{2} + Q^{{{\prime \prime }2}} } $$
(8)

where \(S_{{}}^{^{\prime\prime}}\) - apparent power, kVA; \(P_{p}\) - calculated active power, kW; \(Q^{\prime\prime}\) - compensated reactive power, kvar.

The power factor is determined by the following formula

$$ cos\varphi = \frac{{P_{{\text{p}}} }}{{S_{{}} {^{\prime\prime}}}} $$
(9)

Now let’s calculate the current of industrial enterprises after reactive power compensation according to the following formula

$$ I^{{{\prime \prime }}} = \frac{{S_{{}}^{{{\prime \prime }}} }}{{\sqrt 3 \cdot U_{{H}} \cdot cos\varphi }} $$
(10)

The calculation results and the proposed choice of compensating devices are shown in Table 5.

4 Conclusion

For our industrial enterprises, we choose capacitor units of the AUKRM type - a reac-tive power compensation unit with automatic regulation, for a nominal voltage on the side of 0.4 kV. Based on the location of our factories and sources of electrical energy, the distribution scheme is changed i.e. a common nodal load with three sources of electrical energy is formed between industrial enterprises (Fig. 3 and Table 4).

We will use the two-node method to calculate electrical loads taking into account distributed generation. This method of calculating electrical circuits is based on the adoption of voltage between two nodes of the circuit. When calculating currents by the method of two nodes, the voltage between the nodes is first determined, and then, according to Ohm's law, currents are found for a section of the circuit.

Table 4. Data after reactive power compensation.
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Table 5. Selection of power and type of compensating devices (CD).
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Fig. 3.
figure 3

Scheme taking into account distributed generation sources: \(Z_{1}\) - total resistance of OJSC JV «JAVONI» Ohm; \(Z_{2}\) - total resistance of OJSC “NikuKhujand” Ohm; \(Z_{3}\) - total resistance of OJSC “MMK” Ohm; \(X_{c1,} X_{c2}\) - system resistance.

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