Unbalanced mains power supply

All results defined in the previous sections are obtained with balanced 3-phase mains power supply. This section considers unbalanced mains power supply. The unbalanced power supply used by the drive are phase-to-phase voltages created by a star system where the phase shift is 120° with different amplitude values.

Unbalance definition

The original star system (v₁, v₂, v₃) is defined as follows:

	associated with the complex number

When the power supply is balanced V₁ = V₂ = V₃.

The resulting phase-to-phase system (u₁₂, u₂₃, u₃₁) that will be used by the drive as mains input power voltage is defined by:

	associated with the complex number

Using the operator
This system can be broken down in 3 different balanced 3-phase systems:

A direct system (u_d, a² · u_d, a · u_d) defined by

associated with the complex number

A reverse system (u_i, a · u_i, a² · u_i) defined by

associated with the complex number

And a zero sequence (homopolar) system (u_o, u_o, u_o) defined by

associated with the complex number

The unbalance factor τ is defined by the ratio of the module of the reverse component to the module of the direct component:

NEMA has defined an approximation of this unbalance factor by the following formula, which is valid for unbalance values up to about 10%.

Evaluation of input voltage unbalance on drives

To define an unbalanced phase-to-phase system, the original star system phase shift is kept constant to 120° and only the amplitudes are modified. The resulting delta system has amplitudes and phase modifications compared to a balanced system. There are many ways to get an increasing unbalance ratio. The method selected in this document is to modify the amplitudes of the original star system in the following way.

V₂ is kept constant.
V₁ is increased from its rated value up to +4% more, and then it is kept constant.
V₃ is then decreased from its rated value down to –4%.

This creates an unbalance factor starting from 0 up to about 2%, increasing in a linear way, which allows us to use it on the X-axis of a graph to display how the DC bus voltage and the mains input current vary depending on it. The unbalance value obtained when V₁ stops increasing and V₃ starts decreasing is 1.2%. This can be seen on the graphs by a change in the slope of some curves.

For different values of the input unbalance factor, an electrical simulation of the input stage of the drive is performed with PSIM software to get the values of the DC bus and input currents, which are copied in an Excel file to get the graphs shown in this section.

Drive with DC choke

The 20 hp drive with the integrated 4.3% DC choke is used as in the previous sections to make electrical simulations to display the impact of the input voltage unbalance.

Influence of DC choke on the drive DC bus voltage

Figure 16 shows the internal DC bus voltage (maximum, minimum, and average voltage) in blue, and its peak-to-peak ripple voltage in red. The frequency of the DC bus voltage ripple is twice the input line frequency. The drive’s mains input voltages resulting from the unbalanced star system are shown in green.

Influence on the drive DC bus voltage

The DC bus voltage ripple starts at about 7 V with balanced mains input voltage and increases up to 53 V with 2% unbalance.

Influence of DC choke on the input line currents

Figure 17 shows the RMS values of the input current variation with the input voltage unbalance. The X-axis for the unbalance ratio and the auxiliary Y-axis for the DC bus voltage ripple are the same as in the previous graph.

Influence of DC choke on the input line currents

Drive with AC line reactor

The same 20 hp, 480 V, 60 Hz drive, without its 4.3% internal DC choke but with the external 2.8% 3-phase AC line reactor, is used to perform the same electrical simulations to compare the results with the DC choke in case of unbalanced mains power supply.

Influence of AC line reactor on the drive DC bus voltage

Influence of AC line reactor on the input line currents

Figures 19 and 20 (next page) show the same voltage and current curves as with the DC choke, with the same input voltage unbalance. In the same input unbalance conditions, the internal DC bus of the drive has a little less ripple with an AC line reactor than with a DC choke. At the same time, the DC bus voltage ripple is also a little less with an AC line reactor.

Drive with DC choke and an additional AC line reactor

To evaluate the influence of an additional AC line reactor on a drive already equipped with a DC choke, the maximum input lines voltage unbalance of 2.1% is kept constant. The additional AC line reactor value is increased from 0 to the same value already used to compare the DC choke and AC line reactor in the previous section.

With the example of the 20 hp drive, the maximum value of the AC line reactor is 1 mH (corresponding to 2.8% impedance). Figure 20 shows that with an additional AC line reactor, the DC bus voltage ripple is reduced. The most important part of the reduction is reached at about half of the value of the AC line reactor.

Drive with DC choke and an additional AC line reactor

Conclusions

In cases of voltage unbalance at the drive input, both a DC choke and an AC line reactor reduce DC bus voltage ripple. DC voltage harmonic rank 2 is created by the input voltage unbalance.

At the same time, input line current unbalance is also created at the drive input. If we consider the AC line reactor and the DC choke which give the same input current THDi in cases of balanced input voltage, the DC bus ripple voltage is a little less with the AC line reactor.

Using an additional AC line reactor with a drive already equipped with a DC choke helps to reduce the DC bus voltage ripple.

DC bus voltage ripple caused by the unbalance reduces the DC bus capacitors’ life by increasing the RMS current through the DC bus capacitors at twice the input frequency.

It is clear that adding an input line reactor in combination with DC chokes reduces DC bus voltage ripple. This reduction of DC bus voltage ripple results in longer life of the DC bus capacitors in the drive.