**1. Introduction**

The replacement of obsolete electric motors with new, more efficient ones could provide considerable advantages in terms of polluting emissions, energy resources exploitation, and manufacturing costs. For this reason, the mandatory compliance of industrial electromechanical systems with gradually increasing efficiency requisites has been enforced all over the world in the last decades. This can be accomplished either by increasing the efficiency of motors, for example, according to European Union (EU) IE2 and IE3 efficiency levels [1], or by replacing direct online electric motors with electric drives.

Despite the wide variety of electric motors available on the market, low- and mediumpower three-phase direct online induction motors (DOL-IM) are by far the most dominant in the industrial sector, providing a wide variety of constant speeds and variable load applications where dynamic response requirements are not critical, such as pumps, fans, and compressors. Affordability, durability, easy functioning, and easy maintenance are some of the major factors driving the ever-increasing demand for induction motors. Highefficiency DOL-IMs [1] in industrial applications provide a significant reduction in energy consumption and environmental impact; however, they are still burdened by a low power factor (PF) at partial loads, which can be only mitigated by adding power factor correction capacitors. Moreover, large in-rush current is very commonly generated at start-up, leading to voltage dip, speed loss, torque pulsations, and possible activation of protection devices. A wide diffusion of variable speed drives (VSDs), featuring either torque or speed control, has been experienced in the past thirty years due to the advances in power electronics technology and control strategies, which have allowed an increase in the efficiency and reliability of electric drives [1–4]. Suitable Pulse Width Modulation (PWM) strategies have been developed that are able to cope with adverse effects related to shaft voltages,

**Citation:** Tornello, L.D.; Foti, S.; Cacciato, M.; Testa, A.; Scelba, G.; De Caro, S.; Scarcella, G.; Rizzo, S.A. Performance Improvement of Grid-Connected Induction Motors through an Auxiliary Winding Set. *Energies* **2021**, *14*, 2178. https:// doi.org/10.3390/en14082178

Academic Editor: Emilio Gomez-Lazaro

Received: 1 March 2021 Accepted: 6 April 2021 Published: 13 April 2021

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bearing currents, motor insulation breakdown, and electromagnetic interference (EMI) issues [5–11]. However, despite clear advantages achieved in terms of efficiency, induction motor drives are much more expensive than DOL-IMs, leading to the development of some intermediate or hybrid solutions. One of these solutions is represented by direct online double-winding IMs (DOL DWIM) [12–14]. They were proposed to overcome some typical drawbacks of conventional induction motors, mainly poor efficiency and power factor, by exploiting a partial power converter, which means an inverter rated at only a fraction of the motor rated power, cutting the cost. According to the DOL-DWIM approach, a special induction machine is used, encompassing two full sets of stator windings: one being directly connected to the grid and a second one being fed by an inverter supplied through a floating capacitor [12–17]. According to the basic DOL-DWIM configuration, the two winding sets feature the same number of turns; thus, the inverter supplying the second set is rated at the grid voltage, although at remarkably lower power. DOL-DWIMs are generally managed by simple control algorithms, mainly developed in order to control the PF under sinusoidal steady state operation [12–17].

An advanced DOL-DWIM configuration is presented in this paper, aimed at achieving new valuable functions in a cost-effective way, such as dynamic, active, and reactive power control; a reduction in in-rush current; and the mitigation of torsional vibrations generated by periodical torque disturbances or distorted grid voltages [18], which lead to acoustic noise and additional mechanical stress.

As shown in Figure 1, the proposed DOL-DWIM configuration features a gridconnected main winding and an auxiliary three-phase winding set featuring a lower number of turns, located in the same stator slots of the main one. The auxiliary winding is supplied by a voltage inverter featuring a floating DC-bus capacitor. As the auxiliary winding has less turns than the main one, the inverter power and voltage ratings are much lower than those of the motor.

**Figure 1.** Double-winding induction motor (DWIM) featuring an auxiliary winding set, fed by a three-phase low power, low voltage, Voltage Source Inverter (VSI).

The outline of this paper is as follows: First, the modeling of the electromechanical system is presented in Section 2, and the control strategy implemented in the auxiliary winding set is described in detail in Section 3. Thereafter, the capability of the combined multi-winding sets motor, floating capacitor inverter, and control strategy to efficiently control the power factor PF, mitigate the detrimental effects related to distorted main grid voltages and mechanical torque vibrations, and reduce the large inrush current driven by the induction motor during the starting period is thoroughly investigated in Section 4. Finally, the conclusions are stated in the last section.

#### **2. DWIM Model**

It is assumed that the two polyphase stator windings [19–23] are distributed in order to produce sinusoidal magneto-motive forces; moreover, the effects of the saturation of the magnetic core are neglected, while iron losses are considered according to [24]. The voltage and flux equations of the DOL-DWIM, written in complex form *fqd* = *fq* − *j fd*, according to an orthogonal *qd* reference frame rotating at the angular frequency *ω<sup>e</sup>* of the input stator voltage vector, are given by [23]:

$$
\upsilon\_{qds1} = r\_{s1} i\_{qds1} + \frac{d\lambda\_{qds1}}{dt} + j\omega\_c \lambda\_{qds1} \tag{1}
$$

$$
v\_{qds2}' = r\_{s2}'i\_{qds2}' + \frac{d\lambda\_{qds2}'}{dt} + j\omega\_{\mathfrak{c}}\lambda\_{qds1}' \tag{2}$$

$$
\omega\_{qdr}' = r\_r' i\_{qdr}' + \frac{d\lambda\_{qdr}'}{dt} + j(\omega\_{\varepsilon} - \omega\_{r\varepsilon})\lambda\_{qdr}' \tag{3}
$$

$$L\_{qds1} = L\_{ls1} i\_{qds1} + L\_M \left[ i\_{qds1} + i'\_{qds2} + i'\_{qdsr} \right] \tag{4}$$

$$
\lambda\_{qds2}' = L\_{ls2}' i\_{qds2}' + L\_M \left[ i\_{qds1} + i\_{qds2}' + i\_{qdsr}' \right] \tag{5}
$$

$$
\lambda\_{qdsr}' = L\_{1sr}' i\_{qdsr}' + L\_M \left[ i\_{qds1} + i\_{qds2}' + i\_{qdsr}' \right] \tag{6}
$$

$$R\_{F\varepsilon}i\_{qdF\varepsilon} = \frac{d\lambda'\_{qdr}}{dt} + j\omega\_{\varepsilon}\lambda\_{qdm}\lambda\_{qdm} = L\_M i\_{qdm} \tag{7}$$

$$i\_{qds1} + i\_{qds2}' + i\_{qdsr}' = i\_{qdm} + i\_{qdFc} \tag{8}$$

where *vqds*1, *λqds*<sup>1</sup> and *v qds*2, *λ qds*<sup>2</sup> are the stator voltages and fluxes of the two winding sets, separately; *v qdsr* and *λ qdr* are the rotor voltages and fluxes, respectively; *r <sup>r</sup>*, *rs*<sup>1</sup> and *r <sup>s</sup>*<sup>2</sup> are the rotor and stator resistances, respectively; *LM* is the mutual inductance; and *L lr*, *Lls*1, and *L ls*<sup>2</sup> are the rotor and stator leakage inductances. All electrical quantities of the auxiliary winding set are referred to in the main stator winding. Moreover, *ωre* = *ppωrm*, where *ωrm* is the angular rotor speed and *pp* is the number of pole pairs. The equivalent circuit of the DWIM is depicted in Figure 2.

**Figure 2.** Equivalent circuits of the DWIM in the synchronous reference frame: (**a**) q-axis and (**b**) d-axis.

The electromagnetic torque is expressed in Equation (9), [25,26], and the relationships between the total electromagnetic torque *Te* applied to the motor shaft and the torque related to the mechanical inertia *J*, the load torque *TL*, and the frictional torque *F* are described in Equations (10) and (11). *θrm* is the rotor position.

$$T\_c = 3/2p\,p L\_M [(i\_{qs1} + i\_{qs2}' - i\_{qFe})i\_{dr}' - (i\_{ds1} + i\_{ds2}' - i\_{dFe})i\_{qr}'] \tag{9}$$

$$T\_c = T\_L + f \frac{d\omega\_{rm}}{dt} + F\omega\_{rm} \tag{10}$$

$$
\omega\_{rm} = \frac{d\theta\_{rm}}{dt} \tag{11}
$$
