*3.1. Grid Synchronization*

The control system driving the floating capacitor inverter is mainly based on a standard vector control approach approximating a stator flux orientation, which is achieved by transforming the three-phase utility voltages *abc* into a reference frame synchronous with the grid voltage vector phase *θe*. The last quantity can be determined with one of the well-known grid synchronization algorithms available in the literature [27,28]. In this work, a decoupling algorithm was exploited to remove all of the unwanted harmonic components from the measured voltages in order to keep the phase-locked loop (PLL) locked to fundamental harmonic, positive-sequence component at all times [29]. The block diagram of the grid synchronization algorithm based on a multi-harmonic synchronous reference frame (SRF) filtering (MSF) structure is shown in Figure 4. The basic idea is to

estimate each voltage harmonic set by applying a low-pass filtering after a reference frame transformation synchronous with the corresponding harmonic frequency.

**Figure 4.** Block diagram of the multiharmonic SRF filtering (MSF) algorithm.

### *3.2. Active and Reactive Power Control*

The machine active and reactive powers are functions of auxiliary winding currents *iqs*<sup>2</sup> and *ids*2, which can be managed to control the PF under different load conditions. By neglecting the voltage drop due to stator resistances and leakage inductances, the active and reactive power generated by the auxiliary winding can be expressed as:

$$P\_2 = 3/2(v\_{q\approx 2}i\_{q\approx 2} + v\_{ds2}i\_{ds2}) \ Q\_2 = 3/2(v\_{q\approx 2}i\_{ds2} - v\_{ds2}i\_{q\approx 2}) \tag{12}$$

If the *q2*-axis is aligned to the main grid voltage vector *vqds*1, the active and reactive power can be approximated to:

$$P\_2 = 3/2v\_{qs2}i\_{qs2}Q\_2 = 3/2v\_{qs2}i\_{ds2} \tag{13}$$

Hence, it is possible to control the machine reactive power by acting on the d-axis current of the auxiliary winding *ids*<sup>2</sup> in order to track a desired power factor at the main stator winding terminals. The q-axis current *iqs*<sup>2</sup> can be managed to control the active power required to hold a stable voltage in the floating capacitor of the isolated two-level inverter supplying the auxiliary winding. A certain amount of active power is required by the floating capacitor inverter to compensate for power devices and capacitor losses. Hence, two external control loops were included in the control structure in order to achieve the desired PF and DC bus voltage *Vdc*.

### *3.3. Active Mitigation of Mechanical Vibrations*

The auxiliary winding can be also exploited to mitigate vibrations generated by periodical torque disturbances or distorted grid voltages. Torque disturbances Δ*TL* generate harmonic components in the stator currents *iqs*<sup>1</sup> and *ids*1, yielding vibrations in the mechanical system. They can be mitigated by generating compensating components of the electromagnetic torque by means of the auxiliary winding set. In particular, in case of motor operation under a highly distorted grid voltage, some current harmonics set *i* (*k*) *as*<sup>1</sup> , *i* (*k*) *bs*<sup>1</sup> , *i* (*k*) *cs*<sup>1</sup> of amplitude *Ik* and angular frequency *kω<sup>e</sup>* are superimposed to the fundamental current set *i I as*1 , *i I bs*1 , *i I cs*1 , of magnitude *I1* and angular frequency *ωe*. Therefore, it is possible to identify each couple of current harmonic components *i* (*k*) *qs*<sup>1</sup> and *i* (*k*) *ds*<sup>1</sup> in the *qd* current plane by applying a suitable reference frame transformation:

$$\begin{bmatrix} \dot{i}\_{\text{gc1}} \\ \dot{i}\_{\text{ds1}} \end{bmatrix} = K(\theta\_{\varepsilon}) \begin{bmatrix} \dot{i}\_{\text{as1}} \\ \dot{i}\_{\text{bs1}} \\ \dot{i}\_{\text{cs1}} \end{bmatrix} = \frac{2}{3} \begin{bmatrix} \cos(\omega\_{\varepsilon}t) & \cos(\omega\_{\varepsilon}t - \frac{2}{3}\pi) & \cos(\omega\_{\varepsilon}t + \frac{2}{3}\pi) \\ \sin(\omega\_{\varepsilon}t) & \sin(\omega\_{\varepsilon}t - \frac{2}{3}\pi) & \sin(\omega\_{\varepsilon}t + \frac{2}{3}\pi) \end{bmatrix} \begin{bmatrix} \dot{i}\_{\text{ds1}} \\ \dot{i}\_{\text{bs1}} \\ \dot{i}\_{\text{cs1}} \end{bmatrix} \tag{14}$$

$$\begin{cases} i\_{q\pm 1} = i\_{q\pm 1}^{(1)} + \sum\_{k=1}^{+\infty} i\_{q\pm 1}^{(k)} = i\_{q\pm 1}^{(1)} + \sum\_{k=1}^{+\infty} I\_{s1}^{(k)} \cos[(k \pm 1)\omega\_{\ell}t] \\\ i\_{d\pm 1} = i\_{d\pm 1}^{(1)} + \sum\_{k=1}^{+\infty} i\_{d\pm 1}^{(k)} = i\_{d\pm 1}^{(1)} + \sum\_{k=1}^{+\infty} I\_{s1}^{(k)} \sin[(k \pm 1)\omega\_{\ell}t] \end{cases} \quad \left\{ \begin{array}{c} +1 \to if \to k = 2, 5, 8, 11, \ldots \\\ -1 \to if \to k = 4, 7, 10, 13, \ldots \\\ 0 \to if \to k = 3, 6, 9, 12, \ldots \end{array} \right. \tag{15}$$

where *i* (1) *qs*<sup>1</sup> and *i* (*k*) *ds*<sup>1</sup> are the DC components related to the fundamental current harmonic. These current harmonics are identified through a standard harmonic identification algorithm based on fast Fourier transform. Each undesired harmonic present on the main winding current is then reproduced with the opposite sign on the auxiliary winding through a specific closed-loop current control. A control structure composed of some paralleled current control modules is thus required to mitigate mechanical vibrations featuring different frequencies, each module being threshold-activated on the basis of the actual magnitude of the specific stator current harmonic to be attenuated. Similar considerations are valid in case of mechanical vibrations caused by shaft eccentricity, mechanical imbalance phenomena, or bearing aging.

#### *3.4. Inrush Current Mitigation during Startup*

The large line currents that occur on the grid at motor start-up can be mitigated by exploiting the charge stored in the floating capacitor by implementing a proper control strategy in the DOL DWIM. For achieving this additional feature, a suitable selection of the floating capacitor and of the inverter current rating is required. In particular, the inrush current in the main stator winding can be reduced by exploiting the energy stored in the floating capacitor to reduce the power drawn from the grid. This can be accomplished by generating a set of currents exactly in phase with the currents flowing in the main winding during the first few cycles of the grid voltage. The measured main winding currents *iqs*<sup>1</sup> and *ids*<sup>1</sup> are firstly scaled by the turn ratio of the two stator windings; then, they are used as references of the closed loop current controllers managing the auxiliary windings voltages in order to generate three phase currents *iabc*<sup>2</sup> in phase with *iabc*1, thus allowing a sharing between the inrush currents of both windings.

#### **4. Performance Assessment of the Grid-Connected DWIM**

The control strategies described in the previous section were assessed via a simulation analysis realized in Simulink/MATLAB, as shown in Figure 5a. The model of the electromechanical system, shown in Figure 5b, was realized according to the data listed in Table 1. Implementation of the multiharmonic SRF filter and harmonic compensation system are presented, respectively, in Figure 6a,b. According to Table 1, the considered machine features a turns ratio between the main and auxiliary windings *Ns*1/*Ns*<sup>2</sup> = 5. The floating capacitor inverter was driven with a space vector modulation (SVM) at a switching frequency *f s* of 10 kHz and the DC bus voltage control held an average voltage *Vdc* of 150 V. The inverter was equipped with a 5 mF floating DC bus capacitor.


**Table 1.** Multi-winding induction motor data.

**Figure 5.** Simulink block diagram of the: (**a**) power conversion system and control strategies and (**b**) DOL-DWIM model.

**Figure 6.** Simulink block diagram of the: (**a**) MSF algorithm and (**b**) harmonics compensation.

A first set of tests dealt with assessing the capability of the proposed solution to regulate the reactive power exchange between the power conversion system and the AC grid in a wide operating range. The performance of a standard IM featuring a single stator winding was compared with that of the DWIM under same load conditions. Active and reactive power flows associated to the fundamental harmonics in both main and auxiliary windings are shown in Figure 7. The simulation results are shown in Figure 8.

**Figure 7.** Power flow scheme of the DWIM.

**Figure 8.** (**a**) Active and reactive power (*P1* and *Q*1, respectively), (**b**) power factor *PF,* (**c**) main winding current magnitude *Is*1, (**d**) auxiliary winding current magnitude *Is*2, (**e**) p.u. back-electromotive force (EMF) variation Δ*Em,* computed at 20% and 40% of rated torque *Tn* for different values of *ids*<sup>2</sup> (solid lines—standard IM; circles—DWIM).

The active power *P*<sup>1</sup> and reactive power *Q*<sup>1</sup> absorbed by the DWIM are reported in Figure 8a,b as a function of the current *ids*2. The magnitude of currents in both windings, PF, and the per-unit (p.u.) variation of the back-electromotive force (EMF) *Em* are displayed in Figure 8c–e, respectively, considering two different load conditions: 20% and 40% of the rated torque. The same figures include the corresponding quantities computed for the single-winding IM configuration (the same electrical machine without auxiliary winding) operating under the same load conditions, whose values are indicated in the figures with horizontal solid lines. By varying *ids*2, a beneficial effect is achieved, consisting of a reduction in *Q*<sup>1</sup> and leading to an improved PF (Figure 8c). This causes a reduction in the current flowing through the main winding, as shown in Figure 8d. This last result is justified even by the increase in the back-emf *Em* of the DWIM in correspondence with

an increase in *ids*2, as clearly shown in Figure 8e; the last variation is in any case limited to a few percentages of the back-EMF of the DWIM with *ids*<sup>2</sup> = 0. The variation in *Em* is associated to a variation in the magnetizing current.

The proposed approach can lead to a reduction in the active power *P*<sup>1</sup> absorbed by the DWIM at partial load, leading to an efficiency improvement. This result is confirmed by the analysis summarized in Figure 9, where the iron and total Joule losses are computed for the standard single-winding IM configuration and the considered DWIM as a function of the current *ids*2. In particular, Figure 9 displays the difference between the standard IM and DWIM total Joule losses Δ*PJ* (stator and rotor) and iron losses Δ*PFe*, with both motors operating under the same loads. The joule *PJ* and iron *PFe* losses referring to the single-winding IM are the points displayed in the three graphs at *ids*<sup>2</sup> = 0. Notably, in DWIM, by increasing *ids*2, iron losses rise and total joule losses initially drop and then rise. Thus, by suitably selecting *ids*2, the balance between iron losses increase and joule losses drop may lead to a neat reduction in total power losses and to a higher efficiency compared with the conventional IM. This beneficial result is strictly related to the motor design, load condition, and desired power factor PF. If we assume to operate the DWIM at PF = 0.9, thus requiring *ids*<sup>2</sup> ≈ 25*A* (Figure 8c) and a load equal to 40%*Tn*, a total loss reduction Δ*Ploss* equal to 3% can be achieved compared with the standard IM configuration. On the contrary, the same DWIM operated at PF = 0.9 and a load equal to 20%*Tn*, will require a *ids*<sup>2</sup> = 40*A*, yielding a Δ*Ploss*/*Ploss* less than 0.8%, significantly reducing the efficiency improvement of the DWIM. The implementation of a losses minimization algorithm is not the focus of the paper, and more details on how to approach this aspect can be found in [30].

Simulations were performed over a wide load range and the results shown in Figure 10 confirm the effectiveness of the proposed approach in increasing the power factor by acting on *ids*<sup>2</sup> with marginal variations in the additional power losses, although the improvement becomes progressively less relevant as the load increases.

**Figure 9.** (**a**) Total loss variation in p.u. Δ*Ploss*, (**b**) joule losses variation in p.u. Δ*Pj*, and (**c**) iron losses variation in p.u. Δ*PFe*, vs. *ids*2, computed at 20% and 40% of rated torque *Tn*. Joule *PJ* and iron *PFe* losses referring to the single-winding IM are the points displayed in the three graphs at *ids2* = 0.

**Figure 10.** (**a**) *PF*, (**b**) Δ*Ploss*, (**c**) root mean square (RMS) value of the main winding current *IRMS1*, determined under different loads *TL*.

According to Figure 10b, for a given load condition, negative losses Δ*Ploss* can be achieved by suitably selecting *ids*2, leading to higher efficiency compared with the standard IM. Figure 11 deals with some results obtained by holding the PF at 0.9 by means of the control system. As shown, under constant PF operation, *ids*<sup>2</sup> and the reactive power *Q*<sup>2</sup> decrease when decreasing the load torque and the absorbed active power. Moreover, only a small active power *P*<sup>2</sup> is transferred from the grid to the auxiliary winding. Finally, both the active power *P*<sup>1</sup> and reactive power *Q*<sup>1</sup> are changed by the controller in order to keep the power factor constant. The power handled by the auxiliary winding in the worst-case scenario, i.e., a very light load, is roughly one-fifth of the standard IM rated power.

The dynamic behavior of the PF controller was also evaluated and some results are shown in Figure 12, dealing with a sequence of step loads *TL* using a standard DOL IM and the proposed DOL DWIM. A rather satisfying dynamic behavior was achieved with the DOL DWIM, which was able to hold the PF constant.

The test results shown in Figure 13a confirm the effectiveness of the proposed approach in mitigating the oscillations of the rotational speed caused by an externally applied sinusoidal shaft torque disturbance Δ*TL* = 20 Nm (20% of rated torque) at 100 Hz. We note the remarkable speed ripple reduction after the instant *t*1, when the current control in the auxiliary winding set is activated.

Figure 13b depicts the mitigation of the speed ripple generated by a fifth harmonic component (*fd* = 250 Hz) superimposed to the fundamental AC grid voltage. At *t*1, the compensation algorithm is turned on, leading to the reduction in the speed ripple. A very small *Vdc* ripple was also observed in both cases.

The effects of the harmonic compensation on motor quantities are shown in Figure 14. The obtained results confirmed the theorical harmonic distribution given by Equation (15). Specifically, a second-order harmonic disturbance on the electromagnetic torque and on the mechanical speed produced a harmonic of the same order on the *qd* axis currents and therefore a third harmonic disturbance in the phase currents on both main and auxiliary windings. A different case is considered in Figure 15, where a fifth harmonic component is superimposed on the AC grid voltage. Th theoretical findings and the effectiveness of the harmonic compensation were also confirmed in this case.

**Figure 11.** (**a**) Power factor control: *TL* and *PF* vs. *ids2*; (**b**) *P1*, *P2*, *Ptot = P1 + P2*; (**c**) *Q1*, *Q2* and *Qtot = Q1 + Q2*.

**Figure 12.** Dynamic transients under different torque load *TL* conditions: (**a**) in standard IM configuration and (**b**,**c**) in the proposed DWIM configuration.

Finally, the effectiveness of the proposed approach in mitigating inrush currents was evaluated by considering two motors rated at 3 and 15 kW. Figure 16 shows the currents in the two windings during the start-up without and with using the proposed technique for peak current reduction on the two motors. Figure 16a deals with the 3 kW IM using a 5 mF flying capacitor, whereas Figure 16b deals with the 15 kW machine using 120 mF capacitor. In both cases, at *t = t2*, the current control is disabled and the *PF* and *Vdc* controls are activated instead. A remarkable mitigation of the grid current was obtained, as well as an increase of the electromagnetic torque, although at the cost of rather high transitory currents on the auxiliary winding. The floating capacitor has to be charged before the start-up of the DOL DWIM. This goal can be reached in different ways by using low-power, low-voltage circuitries. A viable solution is presented in Figure 17, where a cascade connection of a small power transformer and diode rectifier was used to charge the floating capacitor. The performance in terms of inrush line current mitigation clearly improved by increasing the capacitance of the floating capacitor because this reduced the power drawn from the grid. However, a large flying capacitor may be impractical in some applications; hence, a smaller capacitor complemented by a parallel connected battery can be used instead. An alternative approach consists of operating the start-up at a higher DC-bus voltage in order to increase the energy stored in the floating capacitor. A cost-benefit analysis is also required to establish the inverter ratings and thus the overcurrent mitigation level during the start-up.

**Figure 13.** Simulation results: (**a**) compensation of *ωrm* with Δ*TL = 20 Nm*; (**b**) compensation of *ωrm* with *Vabc5th* = 30 V.

**Figure 14.** Harmonic content of motor quantities with and without the harmonic compensation when a sinusoidal torque disturbance is applied to the shaft: (**a**) main winding phase stator amplitude voltage *Vas1*, auxiliary winding phase stator voltage amplitude *Vas2*, main winding phase stator amplitude current *Ias1*, auxiliary winding phase stator amplitude current *Ias2*; (**b**) qd-axes main winding stator current *Iqs1* and *Ids1*, electromagnetic torque *Te*, mechanical speed *ωrm*.

**Figure 15.** Harmonic content of motor quantities with and without harmonic compensation when a 5th harmonic component is superimposed on the AC grid voltage: (**a**) main winding phase stator amplitude voltage *Vas1*, auxiliary winding phase stator voltage amplitude *Vas2*, main winding phase stator amplitude current *Ias1*, auxiliary winding phase stator amplitude current *Ias2*; (**b**) qd-axes main winding stator current *Iqs1* and *Ids1*, electromagnetic torque *Te*, mechanical speed *ωrm*.

**Figure 16.** Induction motor start-up current: (**a**) standard IM (3 kW), (**b**) standard IM (15 kW), (**c**) 3 kW with the proposed technique, and (**d**) 15 kW with the proposed technique.

**Figure 17.** Floating capacitor low-power, low-voltage charging circuit.
