Transformer Magnetizing Inrush Currents Using a Directly Coupled Voltage-Source Inverter

The connection of a power transformer to the grid is associated with magnetizing inrush currents that may result in power quality issues as well as faulty relay tripping. In distributed generation, ...


Introduction
When energizing a power transformer, the magnetizing inrush currents that follow may be several times higher than the rated currents for the transformer. The magnitude of the inrush currents may cause voltage dips in the local grid, resulting in poor power quality [1]. Also, the magnetizing inrush currents are rich in harmonic content, usually have a high direct current component, and may erroneously trigger transformer overcurrent protections [2]. Much work has been conducted in making the protective relays recognize the difference between overcurrents at a fault and a magnetizing inrush current [3].
The magnitude of the inrush currents depends on the circuit reactance, the phase angle of the voltage source, and the transformer remanent magnetic flux . The remanent flux in the transformer is the flux that exists in the transformer after it is powered down. This phenomenon has long been studied, and various methods and models can be found in the literature. To measure the remanent flux is not easy but may be approximated with measurements of the voltage integral during deenergization.
Several ways to reduce or eliminate the inrush currents have been presented. Ways to handle the issues are through controlled switching and removal of remanent flux [4,5], sequential phase energization [6,7], insertion of damping resistors [8], capacitive loading, or thyristor switching control [9].
Work that uses PWM inverters to inject a cancelling-out current via the inverter during powerup of the transformer has also been presented [10] along with methods to detect the remanent flux by analysing the DC component during switching [11].
Many renewable energy sources are nonsynchronous with the grid, which will require a power electronics conversion stage for grid connection. A commonly used conversion is the voltage-source inverter (VSI), followed by an LCL-filter and a step-up transformer. The full control of the VSI allows the transformer magnetization to be handled by the source rather than the grid, which can give a great advantage in handling the magnetizing inrush currents.
In this paper, the power transformer is directly magnetized by a VSI. The LCL filter is put on the secondary side of the transformer to reduce the ampacity of the filter inductors, as discussed in [12]. No external circuitry is required for the transformer magnetization. Three different strategies of magnetization are experimentally evaluated with variations in the remanent flux, and the peak inrush currents are detected.   Figure 2: Three different typical paths in the B-H plane. is assumed to be maximum for all cases. In strategy 1, the core is directly pushed into saturation and it can take a long time before it stabilizes. In strategy 2, is pulled down to zero for all phases, which reduces the magnitude of the inrush current. In strategy 3, the voltage ramping will slowly converge to the stable B-H-path while avoiding large inrush currents.

Theory
When a variable voltage source V 1 ( ) is applied to the transformer windings, a resulting flux ( ) will be induced in the transformer core according to Faraday's law as follows: where is the natural frequency of the applied voltage, is the start angle, and , the number of winding turns. The induced flux may be derived by computing the voltage integral over time as follows: where is the remanent flux. Figure 1 shows how this is used to derive the classical --curve or --curve. It is clear how even a small saturation in the magnetic flux may result in a large magnitude of the magnetizing current . As a worst case scenario, the peak amplitude of may be approximated by [1]̂= where is the source impedance, is the winding impedance, and (min) is the minimum magnetization impedance. When the core is completely saturated, it may be treated as an air core, and it has been shown that may be approximated by the short-circuit impedance SC [13].
More accurately, the magnetizing inrush current is calculated bŷ= where is the normal rated flux density, is the remanent flux density, and is the saturation flux density. For more detailed analysis, a finite-element method (FEM) model has to be set up for the transformer.

Magnetizing Strategies
With the VSI directly connected to the power transformer, three different magnetization strategies have been evaluated for start-up of the transformer: (1) step response with remanent flux,  In the first strategy, the inverter is started abruptly, giving full magnetization to the transformer. This becomes similar to an immediate grid connection and will be used as a reference case. In Figure 2(a), the remanent flux was positive at startup, and the transformer core is pushed into saturation as the starting angle = 0 ∘ . If instead = 180 ∘ for this case, a minimal inrush current would have been obtained for this phase.
In the second strategy, the inverter is started at zero amplitude modulation , which will slowly force the core flux to zero for all the transformer legs. The switching frequency of the inverter is much faster than the transformer time constant, resulting in only a small pulse ripple in the transformer core flux. This essentially results in a removal of the remanent flux, that is, = 0, and becomes a special case of strategy 1 when = 90 ∘ or 270 ∘ . Once the transformer has settled, a step response is made in the induced voltage to 1 pu. This is illustrated in Figure 2(b) where the flux is forced to circle around origo before energization.
The third strategy starts at = 0 and slowly increases the applied voltage with a constant ramping function until full magnetization is reached in the transformer core. The applied voltage can be described as where V is the nominal voltage, is the slope of the ramp, and − 0 is the duration of the voltage ramping. The major benefit of this method is that it becomes rather insensitive to the initial , and the core flux will smoothly settle

Hardware Implementation.
A three-phase two-level voltage-source inverter (VSI) has been designed as shown in Figure 3(a). It is made from three dual-package 400GB126D insulated-gate bipolar transistor (IGBT) modules with 2SC0108T2Ax-17 driver boards mounted on top. These have in-built desaturation (desat) protections set to trigger 2.5 s after a fault detection of an overcurrent of 250 A or above. The de-sat protection circuit is shown in Figure 4(a). The collector-emitter voltage, CE , across the IGBT is continuously detected, and if it goes above a set threshold value th during conduction, this is recognized as a faulty current, and the IGBT is turned off. CE is a function of the the collector current as shown in Figure 4(b). The IGBT will be turned on again after a delay time, but after multiple fault detections, it will stop to avoid overheating.
The inverter is directly connected to a three-phase 345 V/1 kV YY-connected transformer, shown in Figure 3(b). The transformer ratings are given in Table 1. The VSI is controlled by sinusoidal pulse-width modulation (SPWM), where a sinusoidal reference waveform is compared with sawtooth carrier waveforms to generate the output logic to the IGBTs. It is possible to control the start angle and stop angle as well as the voltage ramping slope.

Results and Discussion
The transformer was magnetized to its rated voltage of 1 kV using the three different strategies proposed above, while measuring the peak magnetizing inrush currents. In strategy 1, the transformer was stopped at different angles to evaluate the variations in the remanent flux. In strategy 2, this becomes redundant, as always converges to zero before start-up. In strategy 3, = 0 ∘ and = 180 ∘ are used to evaluate max,− and max,+ . Figure 5, the magnetizing inrush currents are plotted for two different and in phase A. These samples are shown to illustrate the worst scenarios with maximum remanent flux in the core. As expected, the highest inrush currents are obtained when is shifted half a period from , and here the peak currents easily reach above 250 A. To minimize the peak currents for this strategy, should be in phase with , which here results in peak currents of about 100 A. It is clear from Figures 5(a) and 5(c) how de-sat protection is activated, which otherwise could have resulted in much higher currents.

Strategy 1 Results. In
In Figure 6, the peak current values are sampled and displayed, for fixed values of . The variation between phases is due to not only and , but also unbalances in the transformer core, where the center leg will have a lower reluctance path than the outer legs. This was not compensated for in the transformer design.

Strategy 2 Results.
In strategy 2, the remanent flux is essentially removed, resulting in the special case of strategy 1 when = 0 ∘ for phase A. Also the remanent fluxes for phases B and C are removed, which was not the case in strategy 1. In Figure 7, currents are displayed for the two worst case scenarios in phase A, = 0 ∘ and = 180 ∘ . The worst inrush currents are less than half compared to those in strategy 1 and never sufficiently high to trigger the de-sat protection. In Figure 8, the peak phase currents are shown while varying . Figure 9, the applied voltage starts from zero and is linearly ramped to 1 pu. In Figure 9(a), the ramping time duration is one fundamental cycle (20 ms); in Figure 9(b) this is increased to 3 cycles (60 ms) and in Figure 9(c) 5 cycles. was set to 0 ∘ for all cases, but it has negligible impact for this strategy. Already at 1 cycle ramping time, the peak current has reduced by half compared to that in strategy 1, and it continues to drop for longer time durations. Inrush current peak vs. number of cycles is displayed in Figure 10. As the ramping time increases, the inrush currents are effectively removed.

Conclusions
The magnitude of the magnetizing inrush currents for a power transformer with direct VSI connection has been evaluated, where no external circuitry for the grid connection is required. Three magnetization strategies have been suggested and experimentally investigated: step response with remanent flux, step response without remanent flux, and voltage ramping. A de-sat protection is used to limit the highest currents. By removing the remanent flux, the peak inrush current is reduced to at least half in the worst cases. However, with voltage ramping, the peak currents may be more or less completely removed depending on the time duration of voltage ramping. All strategies are easy to implement in the FPGA-based control system.