In an event when the circuit breaker is closed between a transformer and a power source, a transient current (which could be as high as ten times the transformer rated current) follows for a short period before reaching a steady state. This transient current, known as magnetizing inrush current of a transformer, is caused by the transformer’s saturated core.

The excitation characteristic of the transformer core is expressed by a nonlinear relationship between the flux and magnetizing current. In the steady state, transformers are designed to operate below the knee point of their saturation curve. However, when transformers are energized, flux can rise to a high value in the saturation region such that the magnetizing current increases drastically.

Transformer inrush current has long been considered a critical event in the operation of electric power systems [1]. Due to its high magnitude, inrush current may cause mal-trip of protection relays. In addition, it contains significant dc and harmonic components which can affect the sensitive protection functions by artificially changing actual user settings during transformer energization [2,3]. Moreover, inrush current introduces power quality issues [4,5], and imposes mechanical stress on the windings of transformer [6].

Many researchers have worked on calculation and mitigation of transformer inrush currents [7-21]. Authors in [7], proposed an analytical formula to estimate the maximum inrush current. Some others have used a simulated model to study the behavior of the inrush current [8]. In fact, there are various factors affecting the magnitude and duration of the inrush current [3,5]:

• The value of the residual flux in the transformer core;

• The nonlinear magnetizing characteristics of the transformer core;

• The phase of the supplying source voltage at the instant of energizing transformer;

• The impedance and short circuit power of the supplying source.

In fact, the techniques for inrush current mitigation are generally developed based on these factors. While the first two factors are internal and depend on the transformer design and the core material, the other factors are related to the supplying grid characteristics. The solutions based on changing the design of the transformer such as changing the core material or adding an auxiliary winding on the core [9], may be costly and not suitable for all the operation conditions [10]. Using series compensators as inrush current reduction methods, described in [10,11], is complex and expensive to implement. A number of other techniques have been proposed to reduce the core flux prior to circuit energization [12-15]. This approach appears to be simple, based on waveform measurements at the transformer connection point, but inrush currents may not be reduced when the transformer is energized without any history [14]. A more complex method was proposed by [15] which used a low frequency voltage source as transformer demagnetizer. Recently, several studies have been conducted to mitigate inrush currents based on controlling the switching instant of the breaker. It has been shown that the inrush current can be reduced by using a series resistance at the neutral point of a transformer and sequential switching of each phase of the transformer at the time of energization [16- 18]. In a case that a delta-star transformer is energized from the delta side, series resistance can only be inserted in the line and not in the delta winding of the transformer. Authors in [19] argue that controlled switching in this case can only limit the inrush current in one line. There are also some practical issues in using controlled energization such as deviation in actual breaker switching times, and difficulties in correct measurement of residual flux [20].

As the power grid is moving toward accommodating more distributed generation, the need to study the effect of inrush current during the start of these units is evident. An installation of distributed generation from an IPP may be comprised of several parallel generation units. Since each generator is connected through a transformer, simultaneous switching of all the units can induce a significant inrush current in the system. In this paper, a distributed generation system is modeled and the possibility of energizing a set of parallel transformers through a single generator is investigated. Next, a new approach using an auxiliary transformer is proposed to further mitigate the inrush current of a main transformer in a distributed generation facility. In order to evaluate the proposed method, the worst case scenario is simulated where the power of the magnetizing source is not limited. The results demonstrate the effectiveness of the proposed method in inrush current mitigation.

In the event in which a transformer is energized by the utility line, a typical inrush current would be about 10 times its rated current. If energized by a less capable source, such as a generator set, the current inrush would be somewhat less than when energized by a utility line, but still very large because of the large short circuit current capability of a synchronous generator. In either case, the severe power transient induced by switching on transformers can be very disruptive to the electrical system, particularly when it is being powered up.

For example, consider the case of black starting of a distributed generation system of an IPP installation. In this case, a set of up to 16 transformers and generators is being energized. This part of the IPP system is schematically shown in Figure 1. If the utility line is live, switching on transformers T1 through T16 would not induce a significant inrush current if the transformers were to be energized in a stagger mode allowing sufficient time for the inrush current on each transfer to decay sufficiently (typically 2 to 3 seconds) before switching on the next transformer. However, typically due to cost constraints, in most cases the connection between the transformer and the utility line would be made using a fuse protected switch which would not allow for staggering transformer switch-on, and therefore, all transformers would be energized simultaneously. Energizing multiple transformers at once would then induce a much stronger inrush current onto the utility line, but with a reasonable stiff power source it would be well within the utility source capabilities.

On the other hand, if a stiff power source was not available, there is a degree of uncertainty as to how many generator sets would be able to handle the large inrush current from all transformers switched on at once. In case that multiple generators were needed for energization, their output would need to be synchronized prior to connection to the main electrical bus. Some IPP plants have the capability of using dead-field paralleling of multiple generators to energize the electrical bus under a black start condition. The presumption is that by gradually raising the generator excitation voltage as multiple units come up to speed, the generators would boot-strap themselves into synchronization and energize all transformers simultaneously. In theory, a large inrush would be avoided because generator voltage would be ramped up from null to nominal over a couple of seconds. In practice, however, dead-field paralleling can be rough on equipment because of the potentially high circulating stator currents that occur when paralleling unloaded generators, and in the IPP case the situation is aggravated because the generators are not unloaded as they would be energizing multiple transformers. In this scenario, the generators would be further stressed by the use of dead-field paralleling and the risk of failing to synchronize would be higher.

To avoid these issues, this paper investigates the possibility of handling the inrush from multiple transformers, with a configuration similar to Figure 1, using a single generator as an energizing source. In addition, an auxiliary transformer is used to further mitigate the inrush current when a large capacity source is energizing the main transformer.

The model of the simulated system (Figure 1) is built using DIgSILENT software. The system comprises of 16 generator-transformers connected to a single bus. This bus is also connected to an external grid that represents the equivalent model of the rest of the network. However, during a black start the external grid is disconnected; and it will not contribute to the inrush current of the transformers. All transformers are identical and so are the generators. The transformers are 13.2/0.48 kV, with a Delta/Wye connection, and their specifications are provided in Table 1. Nonlinear magnetizing characteristics of the transformer are modeled using two different magnetizing reactances before and after the saturation point. The diesel generators have a power rating of 2.5 MW, and their other electrical characteristics are listed in Table 2.

In addition to the restrictions mentioned in the introduction section, the inrush current of the transformer is also limited by the instantaneous current capability of the generator as shown in Figure 2.

The output current of the generator lies below this curve at different time cycles as verified during the simulation.

Representative models for AVR, prime mover unitand governor are also included in the simulated model. These models enable the generator to stabilize after being subjected to a high inrush current, and reach to the steady state condition after the transient time is passed.

This study examines the inrush current during energizing different number of transformers connected to a busbar while energized by a single generator (G1 in Figure 1).

Figure 3 shows a flux-current characteristic with two slope representation of a transformer’s magnetic flux before and after saturation point denoted by L_m and L_s, respectively. With a sinusoidal phase voltage of v(t) = V_msin(ωt + θ) applied to the transformer, magnetic flux can be calculated by integration as: