Induction Motors Under Voltage Unbalance Combined with Voltage Subharmonics

Abstract

In power systems, various power quality disturbances are present, including voltage deviation, voltage unbalance, and voltage waveform distortions. Voltage waveform distortions are usually identified with harmonics, but in some systems, subharmonics (subsynchronous interharmonics) and interharmonics may also occur—that is, components of frequency less than the fundamental frequency, or not an integer multiple of it. This study examines torque pulsations of an induction motor under voltage subharmonics combined with voltage unbalance. The motor and the driven DC generator vibrations were analysed under the power quality disturbances. Investigations were carried out using finite element and empirical methods. Experimental tests were performed for the maximal levels of the power quality disturbances specified or proposed in the relevant standards. For the investigated motor, under voltage subharmonics or voltage unbalance occurring as a single power quality disturbance, the vibration level was within the prescribed limit. However, under unbalance combined with subharmonics, the level could be accepted for only a limited time. Consequently, the permissible level of voltage subharmonics in non-generation installations should be interconnected with the voltage unbalance in the power system.

1. Introduction

In the land power system, multi-area power quality disturbances commonly occur, such as voltage deviation, voltage unbalance, voltage waveform distortions, and voltage fluctuations. The marine power system also experiences frequency deviations and fluctuations [1,2,3]. Voltage waveform distortions are usually identified with harmonics, but in certain systems [4,5,6], subharmonics (subsynchronous interharmonics) and interharmonics (SaIs) are found—that is, components of frequency less than the fundamental frequency, or not an integer multiple of it. Notably, subharmonics are often regarded as a special case of interharmonics. However, in some studies [7,8,9,10,11], they are distinguished because of their specific influence on power system components and energy receivers [7,8,9,10,11,12,13,14,15,16,17]. In addition, periodic voltage fluctuations [13,14,18,19,20] are the superposition of SaIs and the fundamental voltage component [9,13,14,17,21].

SaIs are generated by power electronic equipment, whose motors driving working machines of pulsating anti-torque and renewable sources of energy—wind power stations and photovoltaic plants [22,23,24,25,26,27,28,29,30,31,32,33,34]. The most critical SaI sources are double-frequency conversion systems (DFCSs)—inverters and high-voltage DC links [5,27,30]. DFCSs generate SaIs because of voltage or current ripples in a DC link, i.e., a capacitor or an inductor interconnecting an input rectifier and an output inverter [30]. Notably, the ripples are transferred to the input and output sites of the DFCS [27,30,31]. Consequently, the input current of the DFCS and the produced output voltage may contain SaIs [27,30,31]. An example of significant SaI contamination due to the work of high-power inverters was reported in [5]. The voltage waveform contained a subharmonic frequency of 45 Hz with a value of 0.9%, and interharmonic frequencies of 135, 225, and 405 Hz with values of 1.17%, 0.89%, and 0.931%, respectively. The rated voltage frequency was 60 Hz.

The primary source of voltage unbalance is an unequal distribution of single-phase loads between three phases: large single-phase loads, like arc furnaces and traction drive systems; unbalanced inductances and capacitances of transmission lines; and unbalanced magnetisation currents of three-phase transformers [13].

Power quality (PQ) disturbances exert harmful impacts on various types of electrical equipment, including the most common industry prime mover, the cage induction motor, which experiences increasing magnetic flux density and power losses, overheating, torque pulsations, a reduction in load-carrying capacity, vibration, and torsional vibration [8,9,10,11,12,13,14,15,16,17,21,27,31,35,36,37]. One of the most harmful phenomena caused by voltage unbalance and SaIs is vibration [9,10,11,35,36]. In some cases [9,10,11], the vibration reaches extremely high levels. According to standards [38,39], the observed vibration is “normally considered to be of sufficient severity to cause damage to the machine”.

To prevent malfunctions in energy receivers, power quality standards impose limitations on PQ disturbances. As per “Standard EN 50160—Voltage Characteristics of Electricity Supplied by Public Distribution Systems” [40], the permissible level of the ratio of negative- to positive-sequence voltage components [13] (i.e., voltage unbalance factor (VUF) [13]) is 2%. This standard does not limit voltage SaIs, for which permissible levels are “under consideration” [40]. Also, the “IEEE Standard for Harmonic Control in Electric Power Systems”, IEEE 519-2022 [41], does not specify permissible levels of voltage SaIs, but contains two proposals of SaI limit curves that are applicable for non-generation installations. The more restrictive proposal generally limits SaIs to 0.3%, while the less stringent one has a limit of 0.5%.

Induction motors supplied with voltage containing SaIs have been considered in many previous studies [8,9,10,11,15,16,17,21,31]. These studies discuss various phenomena in the induction motor, including the flow of current SaIs through windings, increased power losses and windings temperature, speed fluctuations, torque pulsations, vibration, and torsional vibration. To the authors’ knowledge, the effect of SaIs on vibration has only been analysed in the same authors’ previous works [9,10,11], which were restricted to SaIs occurring as a single PQ disturbance. No studies have compared the vibration due to SaIs and other PQ disturbances for the same drivetrain, or examined the vibration under the simultaneous occurrence of SaIs and voltage unbalance. However, one study [35] proved that voltage harmonics can significantly boost vibration caused by voltage unbalance.

This paper aims to formulate an indication concerning subharmonic limitation. Additionally, this study compares the vibration caused by voltage subharmonics and voltage unbalance occurring as single and simultaneous PQ disturbances. The scope of this study is limited to drivetrains equipped with low-power cage induction motors.

2. Methodology

The effects of considered power quality disturbances on torque pulsations and vibration were investigated with the finite element method (FEM) and experimental method, correspondingly. FEM analysis was performed for a 3 kW, four-pole cage induction motor type TSg100L (motor1 manufactured by Indukta, Bielsko-Biała, Poland,

Table 1. Chosen parameters of the investigated motors.

Motor	Type	Rated Power (kW)	Rated Speed (rpm)	Rated Voltage (V)	Rated Current (A)
motor1	TSg100L-4B	3	1420	380	6.9
motor2	1LE1003-1BB22-2AA4	4	1460	400	7.9

). For numerical analysis, the ANSYS Electronics Desktop 2024R1.1 (previously called ANSYS Maxwell) was used. The model was elaborated using the RMxprt module, Maxwell2D—a part of ANSYS Electronics Destop 2024R1.1 (Southpointe 2600 Ansys Drive Canonsburg, PA 15317 USA), and the technical documentation received from the manufacturer, containing all the required geometrical dimensions and windings parameters.

Then, based on solution convergence analysis, a denser mesh of ~22,000 elements was applied. The maximum lengths of the finite element edges were ~2.5 mm in the rotor core, ~4.9 mm in the stator core, and ~0.8 mm in the rotor cage. The applied tau-type mesh is shown in Figure 1. Of note, the convergence analysis was also performed for the calculation step.

Some model parameters, such as the moment of inertia and the damping coefficient, were identified based on the design data of the motor, while others relied on experimental testing. The influence of vibrations and deformations was omitted, and full magnetic balance was assumed. Computations were carried out with a transient-type solver. For each point, the calculations (lasting 8–10 h) corresponded to a motor work time of 1.8 s. The first 0.8 s was rejected, as it contained transients.

The presence of subharmonics in the voltage can be described with the following voltage equations, as introduced into the model:

$$e_1\left(t\right)=E_{m1}\mathrm{s}\mathrm{i}\mathrm{n}\left(2\pi f_{1}t+{\psi }_1\right)+a·E_{m1}\mathrm{s}\mathrm{i}\mathrm{n}\left(2\pi f_{sh}t+{\psi }_{sh1}\right),$$

(1)

$$e_2\left(t\right)=E_{m2}\mathrm{s}\mathrm{i}\mathrm{n}\left(2\pi f_{1}t+{\psi }_2\right)+a·E_{m2}\mathrm{s}\mathrm{i}\mathrm{n}\left(2\pi f_{sh}t+{\psi }_{sh2}\right),$$

(2)

$$e_3\left(t\right)=E_{m3}\mathrm{s}\mathrm{i}\mathrm{n}\left(2\pi f_{1}t+{\psi }_3\right)+a·E_{m3}\mathrm{s}\mathrm{i}\mathrm{n}\left(2\pi f_{sh}t+{\psi }_{sh3}\right),$$

(3)

$$e_{12}\left(t\right)=e_1\left(t\right)-e_2\left(t\right),$$

(4)

$$e_{23}\left(t\right)=e_2\left(t\right)-e_3\left(t\right),$$

(5)

$$e_{31}\left(t\right)=e_3\left(t\right)-e_1\left(t\right),$$

(6)

where $e_1$, $e_2$, and $e_3$ are the instantaneous values of phase voltages; $E_{m1}$, $E_{m2}$, and $E_{m3}$ are the amplitudes of the fundamental harmonic for each phase voltage; $f_1$ is the fundamental harmonic frequency and $f_{sh}$ is the subharmonic frequency; ${\psi }_1$, ${\psi }_2$, and ${\psi }_3$ are the initial phases of fundamental harmonic waveforms; ${\psi }_{sh1}$, ${\psi }_{sh2}$, and ${\psi }_{sh3}$ are initial phases of subharmonic component waveforms; a is the per-unit amplitude of the voltage subharmonic; and $e_{12}$, $e_{23}$, and $e_{31}$ are instantaneous values of phase-to-phase voltages.

The current version of the model has certain limitations. For example, the calculations can only apply for a constant torque load (assumed in this study), linear torque load (where the anti-torque is proportional to the rotational speed), and parabolic torque load (where the anti-torque is proportional to the squared rotational speed). In addition, the electromagnetic model is not coupled with an advanced mechanical model, and cannot be used for drivetrain analysis under elastic-mode torsional resonance.

The FEM model was experimentally validated in the authors’ previous works (e.g., [8,10]) for both the purely sinusoidal supply (i.e., no load and rated load) and various PQ disturbances, including voltage unbalance, voltage deviation, and voltage SaIs. During the validation process, the computed currents or their frequency components (e.g., subharmonics) were compared with measurements. An additional validation was performed for the FEM electromagnetic model indirectly coupled with a thermal model (which was not used in this study) [8]. As the differences between measured and calculated temperatures inside the motor were acceptable (e.g., [8]), the electromagnetic model could also determine the power loss distributions under PQ disturbances with satisfactory accuracy. Additional information on the motor model was also provided in the authors’ former studies, for example in [8,9,10].

The test stand contained a programmable power source (PPS), the three-phase induction motor under investigation, a PQ analyser, and a vibration measurement system (VMS). The motor under consideration was supplied with PPS type Chroma 61512+A615103, with a rated power of 36 kVA. It could generate voltage waveforms with programmable PQ disturbances, including voltage and frequency fluctuations, harmonics, a subharmonic or interharmonic component, and phase or magnitude voltage unbalance. The measurement setup contained a 4 kW cage induction motor type 1LE1003-1BB22-2AA4 (motor2 manufactured by Siemens), coupled with an unloaded DC generator. The chief motor parameters are presented in Table 1. The frame of the drivetrain was fixed with bolts to a dedicated concrete pedestal (Figure 2). In practice, the machine set can be considered a drivetrain model consisting of an induction motor and a working machine. Notably, as the drivetrain was modified (changing the DC generator) and relocated, the investigations presented in this study cannot be directly compared with previous results on the same motor.

The Bruel and Kjaer (B&K) VMS consisted of a four-channel data acquisition module (B&K model 3676-B-040), a computer equipped with B&K Connect software (BK Connect 2023 program version 27.0.0.317), a calibrator (B&K model 4294), and an accelerometer (B&K model 4529-B [42]), which was suitable for magnetic mounting. It could be fixed directly to the DC generator, or to a dedicated steel stand (Figure 2) screwed into the aluminium motor casing. The vibration was analysed following the main recommendations of the standard “ISO 20816-1 Mechanical vibration—measurement and evaluation of machine vibration—Part 1: General guidelines” [39].

A diagram of the test bench is presented in Figure 3 [10].

3. Results

3.1. Torque Pulsations

The most harmful phenomena occurring in induction motors under SaIs are vibration and torsional vibration, which are induced by tangential electromagnetic forces—in practice, by torque pulsations (based on [9,10,11,43]). They are caused by the interaction of the rotating magnetic flux and the additional current components flowing through the windings—the negative-sequence current component [13], current harmonics, and current SaIs. Notably, positive-sequence voltage subharmonics, aside from the flow of current subharmonics, also result in current interharmonics of frequency (based on [21]):

f_ih = 2f₁ − f_sh,

(7)

where f_ih is the interharmonic frequency.

The corresponding frequency of torque pulsations (f_p) is as follows (based on [21]):

f_p = f₁ − f_sh,

(8)

Furthermore, the frequency of torque pulsations caused by the voltage unbalance is equal to twice the fundamental frequency [35,36].

Below, the results of the FEM analysis on electromagnetic torque are presented for motor1 working with full load. As the highest torque pulsations under SaIs occur for the driven appliance having a low moment of inertia [10], an additional assumption was that the moment of inertia of the appliance was much less than that of the motor (i.e., the worst possible case). All numerical tests were performed for the subharmonic value u_sh = 0.3%, which generally corresponds to the more restrictive proposal of SaI limitation included in the “IEEE Standard for Harmonic Control in Electric Power Systems”, IEEE 519 [41]. The assumed voltage unbalance factor (VUF) was 2%, corresponding to the maximal permissible value according to the standard [40]. In practice, to reach the required VUF, the phase voltages are changed appropriately (magnitude voltage unbalance), keeping the positive-sequence voltage component equal to the rated motor voltage.

Figure 4 and Figure 5 show the electromagnetic torque waveform and its spectrum, respectively, for the voltage unbalance combined with a voltage subharmonic value of 0.3%, where the frequency f_sh = 20 Hz. Notably, even under purely sinusoidal supply voltage, the torque waveform contains various frequency components because of the presence of slots and teeth. The pulsating torque component caused by voltage unbalance has a frequency of 100 Hz, and reaches 15.7% of the rated torque T_rat. Furthermore, the component corresponding to the subharmonic has a frequency f_p of 30 Hz, and reaches 18.1% of T_rat. For comparison, in [37], for a VUF of 5% (one-phase undervoltage), the amplitude of the torque pulsation caused by voltage unbalance was ~30% of the rated torque of a 4 kW motor. Furthermore, in [36], torque pulsations at twice the supply voltage frequency were ~20–30% of the rated torque for a VUF of 3%, in various motors with a rated power of 5.5–150 kW.

It should be stressed that for the subharmonic frequency f_sh = 20 Hz, a torsional resonance of rigid-body mode occurs [9,10,11,17,22]. It takes place when the frequency of torque pulsations is approximately equal to the natural torsional frequency of rigid-body mode. For small machines, the resonant frequency takes tens of hertz, while for powerful ones, it takes only single hertz [9,10,11,22]. Under the torsional resonance of rigid-body mode, high current SaIs boost torque pulsations, which increase speed fluctuations, resulting in further amplification of current SaIs and torque pulsations.

Figure 6 presents the characteristics of the amplitude of torque pulsations (ATP) versus the frequency of voltage subharmonics for two cases: (i) voltage subharmonics occurring as a single PQ disturbance (SPQD), and (ii) voltage unbalance appearing together with voltage subharmonics. For the former case, the ATP is as high as 43.2% of T_rat, and for the latter, it is 55% of T_rat. For comparison, for purely sinusoidal, balanced supply voltage and full load, the ATP is 25.6% of T_rat. Furthermore, for voltage unbalance occurring as an SPQD and under the assumed test conditions, the ATP is 37.6% of T_rat.

Of note, for both cases presented in Figure 7, the highest torque pulsations appear for the resonant frequency f_sh = 20 Hz. For comparison, for the frequency f_sh = 5 Hz, the ATP is 31.7% of T_rat for voltage subharmonics occurring as an SPQD, and 43.8% of T_rat for voltage subharmonics combined with voltage unbalance. For the frequency f_sh = 45 Hz, the amplitudes are 25.5% of T_rat and 37.6% of T_rat, respectively.

Torque pulsations caused by voltage unbalance or voltage subharmonics occurring as SPQDs have been reported to cause excessive vibration [9,10,11,35,36]. For both PQs appearing simultaneously, the ATP was up to 46% higher than for the disturbances occurring separately; for unbalance combined with subharmonics, high vibration can be expected.

In summary, for voltage unbalance and voltage subharmonics occurring simultaneously, torque pulsations are appreciably greater than for each PQ disturbance appearing alone. Consequently, the simultaneous occurrence of the PQ disturbances may boost the vibration considerably.

3.2. Vibration

The results of the experimental investigations on vibration under voltage unbalance and positive-sequence voltage subharmonics are presented below. As the excessive vibration of induction motors under SaIs has been reported only for those with no load [9,10,11], all the tests were carried out for the motor driving the unloaded DC generator (see Section 2). Motors driving some appliances [44,45] can work with a load much less than the rated load, at least temporarily.

The vibration velocity was measured for both the motor and the DC generator (modelling the driven working machine—see Section 2). For motor2, under the nominal supply (without PQ disturbances), the broad-band vibration velocities (BBVVs) [38,39] are 0.664, 0.386, and 0.586 mm/s in the vertical (V), horizontal (H), and axial (A) directions, respectively. For the DC generator coupled with motor2, these values are 0.711, 0.807, and 1.325 mm/s, correspondingly. For voltage unbalance appearing as an SPQD (VUF = 2%), the BBVV of motor2 does not exceed about 1 mm/s in any direction. For the DC generator, the BBVV reaches 0.646, 0.832, and 1.580 mm/s in the V, H, and A directions, respectively.

Notably, a vibration velocity of 1.580 mm/s corresponds to evaluation zone B (the vibration velocity is 0.71–1.8 mm/s for small electric motors [38]), as defined in the standards [38,39]. This evaluation zone conforms to the vibration that can be accepted for unrestricted, long-time operation [38,39]. On the contrary, the vibration within the upper evaluation zone—Zone C (BBVV within the range of 1.8–4.5 mm/s [38])—can be accepted only for a limited time [38,39]. Furthermore, the vibration of the BBVV exceeding 4.5 mm/s (Zone D) is considered sufficient to cause machine damage [38,39].

It is worth adding that in [36], 5.5 kW motors of the efficiency classes IE3 and IE4 reached a vibration corresponding to Zone C for VUFs of 4.6% and 1.8%, respectively.

The characteristics of the BBVV versus the frequency f_sh are shown in Figure 7 and Figure 8 for subharmonics of the value u_sh = 0.3%, appearing as an SPQD. Figure 7 corresponds to motor2, and Figure 8 corresponds to the DC generator. For the motor (Figure 7), the vibration velocity reaches 0.817 mm/s, far below Zone B’s upper boundaries. In practice, if the frame of the drivetrain is fixed to the concrete pedestal (see Section 2), the motor vibration occurs low for both voltage unbalance and voltage subharmonics. Furthermore, the vibration velocity of the generator (Figure 8) is as high as 1.607 mm/s in the A direction at f_sh = 25 Hz. The highest vibration in the H direction is 1.422 mm/s at f_sh = 26 Hz, while in the V direction, it is 0.971 mm/s at f_sh = 23 Hz. Notably, these values correspond to Zone B. The peak of vibration velocity in Figure 8 can be explained by the torsional resonance of rigid-body mode (see Section 3.1).

Figure 9 and Figure 10 concern the vibration of the DC generator under voltage subharmonics appearing together with a voltage unbalance of VUF = 2%. Figure 9 depicts the characteristics of the BBVV versus the frequency f_sh for u_sh = 0.3%. The maximal vibration velocity of 2.212 mm/s occurs in the A direction at f_sh = 25 Hz. This is appreciably greater than those in the cases of voltage unbalance and voltage subharmonics occurring alone (1.580 and 1.607 mm/s, respectively). Notably, the vibration velocity falls into Zone C, and cannot be accepted for long-time operation. Furthermore, the maximal vibration velocity in the H direction is 1.342 mm/s at f_sh = 25 Hz, and 1.263 mm/s in the V direction at f_sh = 24 Hz. It is also worth mentioning that an analogical characteristic was determined for the motor, but the results of the measurements are similar to those shown in Figure 7.

Figure 10 shows the characteristic of the BBVV versus the value of the voltage subharmonics at a resonant frequency f_sh = 25 Hz with VUF = 2%. The characteristic is strongly non-linear, especially in the A direction, where the highest vibration occurs. For u_sh ≤ 0.2%, the vibration velocity in this direction, of about 1.6 mm/s, is weakly affected by the subharmonics value. Then, between u_sh = 0.2% and u_sh = 0.4%, the vibration velocity rises to ~2.8 mm/s, and maintains this value up to u_sh = 0.6%. The vibration velocity reaches a local maximum (3.703 mm/s) for u_sh = 0.8%, and a local minimum (2.433 mm/s) for u_sh = 1.0%. For u_sh = 1.2%, it rises to 3.808 mm/s. The vibration velocities in the V and H directions are significantly lower—maximising at 2.922 mm/s and 2.279 mm/s, respectively.

As mentioned in Section 2, the frame of the drivetrain was bolted to the dedicated concrete pedestal. For comparison, additional investigations were carried out with unscrewed nuts on these bolts. The vibration behaves differently in such conditions—the motor shows a comparatively high vibration under voltage subharmonics, which, in some cases, is significantly greater than the generator vibration. These results will be presented in a separate paper. The vibration under subharmonics will also be examined for various locations of screws fixing the frame to the pedestal.

In summary, voltage unbalance and voltage subharmonics can cause excessive vibrations in the prime mover and the driven appliance. In practice, the vibrations of the driven appliance are interconnected with torque pulsations [9,10,11,43]. From the point of view of reliability, the prime mover and the working machine should be protected against excessive vibration. In the case of the investigated drivetrain, the motor vibration is low (except in the case of the unscrewed nuts), while the DC generator experiences comparatively high vibration under voltage unbalance and voltage subharmonics. If these occur as SPQDs, the vibrations can be withstood for unrestricted continuous operation. Contrastingly, for voltage unbalance combined with voltage subharmonics, the vibration level is in Zone C, and is acceptable only for a limited time.

4. Discussion

To prevent electrical equipment malfunctions, PQ standards impose limitations [40,41] on various disturbances. However, they do not specify permissible levels of voltage SaIs. The main reason for the lack of appropriate regulations is insufficient experience concerning the impact of SaIs on electrical equipment [40,41]. Notably, previous works have indicated that rotating machinery is especially sensitive to SaIs, and the most harmful phenomena are vibration and torsional vibration [9]. Furthermore, torsional vibration caused by SaIs is particularly harmful for multi-megawatt drivetrains with synchronous machines (based on [24,29]), which are not applied in low-voltage power systems. It is likely that, as a result, the proposals for SaI limitations included in [41] are for non-generation installations.

This study examines torque pulsations and vibrations under voltage subharmonics and voltage unbalance, appearing as SPQDs or combined. The simultaneous occurrence of power quality disturbances results in appreciably higher torque pulsations than for voltage unbalance or voltage subharmonics appearing alone.

At the same time, torque pulsations are considered the chief source of excessive vibration under PQ disturbances (based on [9,11,43]). Furthermore, under the considered power quality disturbances, the vibration of the investigated motor is far below the prescribed limit (for the frame of the drivetrain bolted to the concrete pedestal, see Section 2), whereas the generator (modelling the working machine) shows significantly higher vibration. However, for voltage unbalance or voltage subharmonics occurring as SPQDs, the vibration level is acceptable for long-time continuous operation. In addition, for both considered PQ disturbances appearing simultaneously, the maximal vibration velocity is ~40% higher than for each disturbance alone, falling into Zone C [38,39]. In practice, this vibration is allowable for a limited period. Notably, the motor and the driven working machine need to be protected against excessive vibration.

In the authors’ opinion, to efficiently protect industry drivetrains against excessive vibration, the permissible level of voltage subharmonics in non-generation installations should be interconnected with the voltage unbalance existing in the power system. A possible dependency describing the permissible levels of voltage subharmonics can be expressed as follows:

V_{sth_lim} = V_{sth_lim0} − c VUF,

(9)

where V_{sth_lim} is the permissible level of voltage subharmonics, V_{sth_lim0} is the permissible level of voltage subharmonics for fully balanced voltage, c is a coefficient, and VUF is averaged, for example, over one hour.

Of course, in practice, a more sophisticated dependency may be proposed. Fine-tuning the final proposals of SaI limitations requires further comprehensive investigations, especially on rotating machinery.

5. Conclusions

In this study, torque pulsations and vibration under voltage unbalance and voltage subharmonics were examined for PQ disturbances occurring alone and simultaneously. For test purposes, their assumed values were equal to their maximal permissible levels as specified or proposed in the standards [40,41]. For voltage subharmonics combined with voltage unbalance, the amplitude of torque pulsations was up to 46% higher than for voltage unbalance appearing alone. The vibrations of the investigated motor were comparatively low for all the considered supply conditions. On the contrary, the DC generator coupled with the motor (modelling the driven working machine) showed significant vibration. For each of the SPQDs, the vibration was within the acceptable level for unrestricted long-time continuous operation, while for voltage subharmonics combined with voltage unbalance, it fell into Zone C (specified in [38,39]), which can be accepted only for a limited time. As the presence of voltage unbalance may significantly boost torque pulsations and vibration induced by voltage subharmonics, the permissible level of voltage subharmonics in non-generation installations should be interconnected with the value of the VUF.