The demand for high efficiency from wind turbines makes permanent magnet generators (PMGs) the optimum choice for wind turbine manufacturers. The capacity factor of wind turbines is normally in the range of 0.4 in the best operating locations, and therefore, wind turbines mainly operate at partial loads, where PMG technology is the best choice [1]. Other technologies, such as the double-fed induction generator (DFIG) and squirrel cage induction generators (SCGs) also exist on the market.

In many applications, the generator interfaces with the grid by means of a back-to-back converter as shown in Figure 1. In the case of low voltage (<1000 VAC), the back-to-back converter comprises two 3-phase Insulated-gate bipolar transistor bridges, generating pulse-width modulation sequences, which are usually filtered to improve the generator terminal or grid supply voltage harmonic spectra. Structurally, PMG, DFIG and SCG drives, designed for operation in a variable speed wind turbines, resemble each other [1-3]: they contain a back-to-back converter, which is connected either to the stator winding (PMG, SCG) or to the rotor winding via slip rings (DFIG).

Taking into account this similarity, let us further consider the PMG drive as an example, remembering, however, that the considerations and outcomes of this paper are also applicable to other drives, containing frequency converters, with some modifications.

2 Equivalent Electrical Circuits

Typically, the low-voltage side of the three-phase transformer is star-connected with a galvanically grounded star point. This potential is, therefore, the reference potential of the whole drive train. All the other potentials of the drive train can be assumed connected to this basic potential through different impedances. As follows from Figure 1, the back-to-back converter comprises two frequency converters. A frequency converter generates common-mode noise, which can cause failures in the electrical machine windings and bearings [4]. The common-mode noise, generated by the frequency converter, can appear either at the phase terminals, if the system is grounded on its direct-current (DC) side, or in the DC link potentials, if the system is grounded on its alternating-current side, when measured versus electrical ground.

Electrical filters are very effective in common-mode noise prevention in single-converter systems [5-9]. However, in the back-to-back converter, common-mode noise is mainly generated by two sources, one of which, produced by the grid-side converter, is the reference for the other one, produced by the generator-side converter [10-13]. This is illustrated in Figure 2 for one phase of the three-phase system. In Figure 2, u_{cm_gr} is the common-mode voltage of the grid-side converter, u_{c_gen_ph} is the generator converter one-phase voltage, u_{cm_gen} and u′_{cm_gen} are the common-mode voltage parts produced by other two phases of the three-phase generator converter, e_{gen_ph} is the back-electromotive force in the PMG's phase, L_{f&cab}, C_{f&cab} and R_{f&cab} are respectively the sum filter and cable inductance, capacitance and resistance, and L_{ph} is the PMG's phase inductance. For simplicity, in further investigation, we neglect filter capacitances and resistances, presented in Figure 2. However, they are usually needed to provide the best possible high-frequency attenuation. If the filter resistance is small (or negligible), the estimations, presented in the succeeding text, may provide too optimistic results. Also, cable representation as a lumped LCR circuit is simplified.

Ideally, if the system is symmetrical, common-mode voltages do not appear in the phase-to-phase voltages. Thus, an equivalent circuit for the phase-to-phase voltage generation is depicted in Figure 3, where u_{c_gen_phph} is the phase-to-phase voltage at generator converter terminals and e_{gen_phph} is the back-electromotive force between the PMG phases. In practice, phase-to-phase voltages may contain some portions of the common-mode voltages, but Figure 3 is usually valid.

Figure 2 indicates that the generator filter cannot affect the common-mode voltage generated by the grid-side converter. This means that the back-to-back converter can place more stress on the PMG winding and bearings than single converters do. Special pulse-width modulation techniques have been invented to minimize the common-mode emission of the frequency converters [11, 12, 14]. They can be successfully implemented in the back-to-back converter. However, the risk of winding insulation damage for badly insulated generators can still be high.

Both phase-to-ground and phase-to-phase voltages can be harmful to the generator winding. Therefore, they have to be estimated during system design. A way of such estimation is presented further in this article.

3 Generator Terminal Voltages Estimation

The switching of the grid-side and generator-side converters is usually unsynchronized, and often, they even have different switching frequencies, indicating a variety of switching combinations that exist in phase-to-ground voltages at the PMG terminals. Thus, it is reasonable to assume that the phase-to-ground voltage is at its maximum level when all voltage sources in Figure 2 are at their maximum levels.

As follows from Figure 2, if the RC-damping chain is neglected, then the peak voltage applied at the generator terminals can be described as

Let us estimate peak values. Common-mode voltage, generated by the grid-side frequency converter, can be seen, e.g., in the DC link potentials measured versus earth. The shape of this voltage is shown in Figure 4 (experimental data).

It is worth observing that the grid-side common-mode voltage, presented in Figure 4, is highly oscillatory. Usually, these oscillations are hardly possible to prevent: they can be explained by the LC resonances between the phase inductances and the stray capacitances present in a generator. The resistances of the stray paths are rather low, which explains the hard oscillations existing in the common-mode voltage. Grid-side common-mode voltage varies in the range of [−U_{DC}/2; U_{DC}/2] by U_{DC}/3 steps [4]. Each step creates an oscillation with the amplitude U_{DC}/3. Therefore, peak common-mode voltage in the DC link can be estimated as follows:

Ucm_gr.m=5/3⋅UDC/2(2)

where U_{DC} is the voltage between the DC link potentials.

Equation (2) can be also used for the generator-side converter peak common-mode voltage u_{cm_gen} estimation.

Furthermore, the generator converter voltage is typically filtered by a du/dt filter, which is usually an LCR circuit, characterized by voltage overshoot. Connections between phases via stray cable capacitances and filter damping circuit create voltage disturbances, which may exceed overshoot on filter output. These disturbances in the phase voltage happen every time when the converter switches controlling other phases commutated and they distort the converter voltage U_{c_gen_ph.m}. This effect is demonstrated in Figure 5 (measured data). Typically,

Uc_gen_ph.m≥UDC.(3)

Generator back-electromotive force e_{gen_ph} can be thought to be sinusoidal, and its peak value e_{gen_ph.m} is easy to find by multiplying the generator nominal root mean square value by a factor of 2

Since the common-mode voltage is practically the same for all three phases, it is not visible in the phase-to-phase voltages. Thus, the peak phase-to-phase voltage can be expressed as

where e_{gen_phph.m} = 3e_{gen_ph.m}, k_{σ} = (100 + σ)/100 and σ is voltage overshoot provided by the LCR filter.

If filtering is not implemented, k_{σ} in equation (4) can be assumed to be 2, which describes the worst case when the cable creates a double voltage overshoot at the generator terminals.

Let us now put equations (2) and (3) in (1) and then divide equation (1) by (2) assuming that L_{ph} > > L_{f&cab}. This way, we can find the relation of phase-to-phase voltage to phase-to-ground voltage for a typical converter, designed for operation inside a multi-megawatt turbine

Uphg.m/Uphph.m=1.84/kσ.(5)

As follows from equation (5), if k_{σ} < 1.84, (i.e., overshoot after the generator filter is lower than 84 %, which is commonly true), then phase-to-ground voltage spikes U_{phg.m} represent a dominating threat for the PMG's winding insulation.

As an example, let us consider a typical case for a wind generator with a power range from hundreds of kilowatts to multi-megawatts, when U_{DC} = 1050 V and L_{ph} > > L_{f&cab}. If the voltage overshoot after filtering is 10%, an estimated peak voltage applied to the generator terminals, calculated with equation (4), is 1926 V. The peak phase-to-phase voltage at the generator terminals is equal to 1155 V. Calculated values should be taken into account during the system design.

4 Experimental Results

Experimental investigations were performed in Lappeenranta, Finland, at The Switch facilities. The test drive setup is presented in Figure 6. The test VEM 2.2 kW, 230/400 V three-phase induction motor was supplied through a full-power converter based on Vacon NXP modules. The grid-side bridge switching frequency was set at 3.6 kHz, whereas the generator-side switching frequency was set at 10 kHz, for the main tests, and 2.1 kHz to provide the clearly visible oscillograms in Figure 7. Measured magnetizing inductance of the motor's phase is 11 mH, and phase resistance is 2.4 Ω. The induction motor was connected to the converter by a 3 m long cable.

First measurements were provided without filter inductance. After that, 1.7, 3.7 and 6.7 mH three-phase wire wound inductors were utilized. The measurements were made with a Tektronix TDS3014B scope. Testec TT-SI9002 differential voltage probes were used for the phase-to-phase and phase-to-ground voltage measurements at the motor terminals.

The measured results with and without the extra inductor are presented in Figure 7. Phase-to-ground voltage is noisier than phase-to-phase voltage, since the common-mode sources and the grid-side and generator-side converters affect it. Sinusoidal content appears in both measured voltages when the extra inductor is utilized. This content rises along with the increase in extra inductance at the converter terminals. Since the levels of voltages with and without the extra inductor for the cases presented are approximately equal, we can conclude that the extra inductor changed the relation of voltages at the motor terminals so that the motor's back-electromotive force portion is increased and converter's voltage portion is reduced. All these facts confirm the validity of the equivalent electrical circuit presented in Figures 2 and 3.

The measured and calculated maximum voltages at the generator terminals are compared in Figure 8 with regard to inductance L_{f} between the motor and converter. Deviations between measured and calculated curves can be explained by the fact that the maximum values of the overshoots were used for estimations, neglecting damping in the system, as the actual values are usually unknown in practice. Also, we did not take into account motor winding resistance. It must be noted that the winding resistance is small enough in generators, ranging from hundreds of kilowatts to multi-megawatts, which are the main subject of the current investigation. In addition, for the points measured with scalable inductance, we should remember that the inductor's equivalent series resistance contributes to the damping of the cable-caused oscillations at the generator terminals.

Particularly at high frequencies, where spikes occur, winding resistance increases because of skin and proximity effects. In summary, experimental results have confirmed the validity of the analysis proposed in this paper.

5 Conclusion

This paper proposes a way to estimate the generator terminal voltages when it is controlled by the back-to-back converter. Estimations are based on theoretical equations and practical knowledge and also supported by small-scale measurements.

It is shown that phase-to-ground voltages typically represent the dominating threat to the generator windings. This is explained by the fact that the back-to-back converter contains two common-mode voltage sources: grid-side and generator-side Insulated-gate bipolar transistor bridges.

Phase-to-ground and phase-to-phase voltages generation is explained with the help of equivalent circuits. On the basis of these simplified representations, practical equations for peak voltages estimation are presented.

Estimations presented in the paper are recommended for the system design procedure in order to agree on generator voltage levels between the wind turbine, wind generator and power converter manufacturers. The analysis presented in this paper is applicable to DFIGs, PMG drives, SCGs (for variable speed wind turbines) and for other systems containing back-to-back converters.