Microsoft Word-13__ISSN_1392-1215_Simulation of Frequency Converters Operation in Industrial Power Net

Induction motors are widely used in various industry enterprises. Its construction is simple, motor work reliability is high, costs is not high. Main problem of using induction motors is it’s speed regulation. Frequency converters are widely used for this purpose in industry enterprises. Inverters with semiconductor based power switches in this output generates voltage with different from power net frequency. Voltage and frequency is changing according to necessary induction motor speed and load. But in this time frequency converter takes from power net non sinusoidal current, with may cause voltage non sinusoid in power net and to disturb normal job of other customers. Level of voltage distortion depends from frequency inverter parameters and power net impedance. Percent of motors with frequency converters in industry is growing, and power quality problem became actually at present. Rectifier of frequency converter cause main influence to current harmonic distortion (Fig. 1), because it’s current from power network is non sinusoid. The traditional solutions for current harmonics reducing are as follows: line chokes and DC chokes (Fig. 1). Choke is inductance; voltage drop in choke for nominal current is about 3-5 %. These solutions typically reduce the THDI (total harmonic distortion of current) to a level less than 48 %. If a choke is not added, the THDI is generally between 60 and 130 % [1]. Depending on their type, external or internal chokes are most often offered as an option and have the following disadvantages: increased cost, installation time, overall size, drive losses with a DC choke. In order to overcome these disadvantages, for example, the ALTIVAR 21 drive integrates new reduced capacitor technology [1]. This technology makes it possible to obtain a THDI less than 35 % without having to add a choke, offering the following advantages: optimized technology through the reduction of current harmonics by decreasing the value of filter capacitors [1]. Method advance is greater reduction of current harmonics compared with traditional solutions: line chokes and DC chokes.


Introduction
Induction motors are widely used in various industry enterprises.Its construction is simple, motor work reliability is high, costs is not high.Main problem of using induction motors is it's speed regulation.Frequency converters are widely used for this purpose in industry enterprises.Inverters with semiconductor based power switches in this output generates voltage with different from power net frequency.Voltage and frequency is changing according to necessary induction motor speed and load.But in this time frequency converter takes from power net non sinusoidal current, with may cause voltage non sinusoid in power net and to disturb normal job of other customers.Level of voltage distortion depends from frequency inverter parameters and power net impedance.Percent of motors with frequency converters in industry is growing, and power quality problem became actually at present.Rectifier of frequency converter cause main influence to current harmonic distortion (Fig. 1), because it's current from power network is non sinusoid.
The traditional solutions for current harmonics reducing are as follows: line chokes and DC chokes (Fig. 1).Choke is inductance; voltage drop in choke for nominal current is about 3-5 %.These solutions typically reduce the THDI (total harmonic distortion of current) to a level less than 48 %.If a choke is not added, the THDI is generally between 60 and 130 % [1].Depending on their type, external or internal chokes are most often offered as an option and have the following disadvantages: increased cost, installation time, overall size, drive losses with a DC choke.
In order to overcome these disadvantages, for example, the ALTIVAR 21 drive integrates new reduced capacitor technology [1].This technology makes it possible to obtain a THDI less than 35 % without having to add a choke, offering the following advantages: optimized technology through the reduction of current harmonics by decreasing the value of filter capacitors [1].Method advance is greater reduction of current harmonics compared with traditional solutions: line chokes and DC chokes.According to [2] value of DC link capacitor depends upon power of frequency converter and is about 80-160 μF/kW.But if this capacity there is smaller, a new problem begins.Small DC link capacitor causes large variations in the DC link voltage on inverter commutation frequency [3].Due to these reasons, the most promising substitute of small capacitor has been the metalized polypropylene (MPPF) capacitor [3].
But in these and other research all attention is about frequency converter job and no attention to harmonic voltage level in industry enterprise network.So it is necessary to simulate industry enterprise power network model with frequency converter and after that estimate voltage distortion level, changing frequency converter load and DC link capacitor value.

Industry enterprise power net model
In industry enterprise power network frequency converters usually are connected to 0,4 kV bus.Bus is connected to 6 or 10 kV power distribution network over 10/0,4kV transformer.Frequency converter is connected to the busses by cable line.According [4], harmonic distribution in power network is calculating according diagram in Fig. 3.

Fig. 3. Electric scheme of power net model, used for higher voltage harmonic level calculation in industry enterprise power net
Later it is necessary to choose structure and parameters for industrial power net in Fig. 2 (Tables 1, 2).Length of cable line is usually small, not more than 100 meters length and its resistance and inductance is necessary to estimate together with transformer parameters, if frequency converter power is big.Typical transformer of 100-1000 kV•A has significant inductance, comparing with its resistance, necessary to estimate this in scheme.Parameters of transformer are calculated to 0,4 kV voltage level.Resistance R con is total resistance of all connections between elements of low voltage net and it's value is 0,015 -0,03 Ω in case of short-circuit current calculation.In our situation we'll use value of R con equal to 5 mΩ, because of electric arc absence.Influence of this resistance is significant, when network parameters with big power transformer and short cable lines are calculating.

Numerical integration rectifier model and its current from electric supply net
It is necessary to say that authors of this article have a deal with modeling of frequency converters input currents for some time [5,6], but previous models have several disadvantages comparing with model, designed here.
Numerical integration rectifier (NIR) model (Fig. 4) consists of six ideal diodes, capacitor network resistance and inductance and load resistor.Different current harmonic level in supply net is modeled by changing R, L, and C values.Rectifier is simulated with software MATLAB, using specially written software.It is modified version of software, described in [5].Operating of converter is described using series of small time intervals transients method, by calculation capacitor charging or discharging in fixed current in period of one interval.Time interval Δt is choosen equal 1µs.Main difference between this model and model in [5] is ability to estimate inductance of power net (X T , and X L in Fig. 3, in [5] only R was estimated), this ability rapidly change results of simulating.Main advantages of NIR model comparing with model, described in [6], are simpler algorithm and ability to calculate input currents in continuous mode of rectifier.
Resultant wiring diagrams are used in model for calculation of currents and voltages (Fig. 5).Three wiring diagrams, depending upon input voltages phases and levels are used for calculation.
Meanings of voltages in Fig. 5 are voltages of power net at moment t.U 1 -maximum source voltage from all phases in this moment, U 2 -minimum source voltage from all phases in this moment), U 3 -voltage between U 1 and U 2 .These meanings are determined in each time step of calculation time.Currents i 1 , i 2 and i 3 in wiring diagram are determined in same way like voltages.
Current in wiring diagrams is calculated according Ohm's law.For example, equations for one of wiring diagram in Fig. 5 (Fig. 5, a) look as follows: It is possible to calculate currents derivatives from (1) expression:

Fig. 5. Three possible variants of wiring diagram, used for frequency converter currents and voltages calculation
This algorithm (Fig. 6) works very stable in wide interval possible meanings of L, R and C, so it is easy to simulate various situations in power net.

Voltage harmonic level in power supply net calculated using NIR and MatLab/Simulink models
Using rectifier and network model in Fig. 3, 6 and 7 dependency of total voltage harmonic distortion level on rectifier load was calculated.Calculations were done using typical 630 kV•A 10/0,4 kV transformer parameters (Table 1).Such kind transformer is very often used in industry electric power supply nets.Connection of converter to power transformer was done by 100 m length cable of 95 mm 2 cross section (Table 2).Transformer was loaded by frequency converters with 20, 50, 100 and 200 μF/kW capacitor; its load was changed during simulation.
Results of calculation, obtained by using of both models were very similar each to other, which confirms their adequacy.9 shows that with rise of transformer load, consisting of frequency converters, THDI of input current is decreasing.Reason is influence of transformer inductance to rectifier job; it is become significant when load of transformer is relatively big.When load of transformer reaches 48% (300 kW), THDI is about 34% and it's further decreasing becomes difficult.For this reason, using of line-chokes in case of great power frequency converters is unnecessary, because transformer inductance itself works like line-chokes.
Levels of THDI and THDU depends on capacitor value and is rising when it's value is decreasing.It is necessary to note that in [5] publication was done the opposite conclusion, but it is true only without estimation of network inductance.
However, low value of DC-link capacitor causes other problems.In Fig. 11 we can see that in mentioned case high-frequency oscillations in rectifier input currents occurs, and that phenomenon is the reason of unalike nature of 20 μF capacity case line in Fig. 9. Fig. 12 shows a typical converter input current form when influence of power net inductance is not significant.In Fig. 13 there's other sample of rectifier work -power net inductance has the greater value.The curves of rectifier input currents, presented in Fig. 13, are very similar to According to result, presented in Fig. 10, it is possible to say, that transformer of 630 kV•A may be loaded of frequency converter with 250 kW power to not to exceed the allowed by [7] value of voltage THD, which is equal to 8%.

Conclusions
Parameters of electric power net cause the great influence on input current curves of frequency converter, especially if the converter power is significant.
Using of line-chokes, offered by manufacturers as an option to frequency converters for current THD decreasing, in case of great converter power is unnecessary, because transformer inductance itself works like line-choke.
To avoid total harmonic voltage distortions more than 8%, it is necessary to limit power of frequency converters, connected to power net transformer.

Fig. 2 .
Fig. 2. Typical electric power net of industry enterprise with frequency converters

Table 1 .
Values of transformer parameters

Table 2 .
Values of cable line parameters