Induction motor performance improvement using a five-level inverter topology and sliding mode controllers

This research intends to establish a robust vector control (VC) of a 3-ϕ induction motor (IM). The classical 2-level inverter is displaced by a 5-level neutral-point-clamped (NPC) inverter. The 2-level inverter may only supply 8 voltage vectors, while the 5-level NPC inverter can furnish 125 voltage vectors. The objective is to bring about a command voltage vector that converges to the reference voltage vector as closely as possible; hence, guaranteeing a quick response on one hand and improving the dynamic performance on the other hand. A robust sliding mode controller (SMC) structure is used in all regulation loops. Satisfactory results are obtained for various speed zones. The quality and robustness of the global system are tested under resistive torque disturbance, reversal, high, and low-speed ranges in order to prove system stability. All the simulations have been performed under MATLAB/Simulink. This is an open access article under the CC BY-SA license.

INTRODUCTION Towards the middle of the 1970s, a new concept of induction machine control, called vector control (VC) or field-oriented control (FOC) appeared to be competitive with other control techniques, especially scalar control (SC) [1]. Unlike the last, which is based on pointed but strict mathematical formalisms, VC schemes were initially based on qualitative and clarified knowledge of the conduct of the machine [2]. Often tuning actions were taken on using classical PI controllers and pulse width modulators (PWM). The implementation of these algorithms was therefore simpler, at a time when computing resources were constantly improving in power and speed [3].
The decisive advantages attributed to conventional VC techniques (dynamics, robustness, ease of implementation, performance at low speeds) [4] are nevertheless counterbalanced by the use of a sampled hysteresis or PI regulators; in theory, the regulator drives to a variable frequency action which increases the risks of excitation of mechanical or acoustic resonances [5], and on the other hand, limit frequency sampling outcomes in a pseudo-random exceed of the hysteresis strip. These two factors contribute to making the harmonic content of the various output signals difficult to predict [6]. Simultaneously, new and promising static conversion topologies, called multilevel, have been proposed and increasingly used in high-power variable speed drive ❒ ISSN: 2302-9285 applications [7]. Compared to conventional two-level structures, in which the output voltage can only be modulated by acting on the duration of use of the high state and the low state, pulse width modulation, multilevel  structures indeed open up a new dimension, it's the amplitude modulation [8], [9]. In the present study, our main objective is to propose new strategies of the VC type, compatible with multilevel voltage inverters (more particularly multicellular), having any number of levels. Their application to conventional two-level inverters will only be seen as a special case [10]. We will endeavor to show that a control judiciously exploiting the degrees of freedom offered by these new conversion structures allows to minimize the drawbacks of conventional VC strategies while retaining their advantages [11].
The principal aim of this research is to enhance the performance of the VC applied to the induction machine. We propose a control plan established on nonlinear sliding mode controller (SMC) [12], [13] (without the use of hysteresis or PI controllers) and a five-level neutral point clamped (NPC) inverter in order to obtain an optimal voltage control allowing the best choice of the sequence of the voltage vector to be carried out to the machine while respecting the constraints on the flux and the electromagnetic torque. This will produce a robust VC scheme without resorting to the conventional PI controllers used in the classical VC scheme [14], [15].

IM STATE-SPACE MATHEMATICAL MODEL
The state-space modeling representation of an IM could be mathematically written as: The state vector was represented as X, the input as U , and the output as Y . As stated by [16], the state and the input vectors of an IM can be specified by the stator current and the rotor flux components based on their rotational d-q frame. Thus, they can be defined as: t . I s d and I sq are components of the stator current in the d-q reference axes. Φ r d and Φ rq are components of the rotor flux. V s d and V sq are components of the stator voltage. Thus, components of matrices in the state-space representing could be obtained by construing differential equations of the stator currents and the rotor fluxes [17], as in the equation: LsLr ; τ r = Lr Rr . The electrical power is written as: The expression of the torque is came by dividing the electromechanical power P e over Ω r , whence: The rotor mechanical speed is formulated by: J is the inertia coefficient of the motor, T l is the torque of the load, and F r is the coefficient of the friction [18]. The block diagram of the state-space modeling of IM could be seen in Figure 1.

VECTOR CONTROL BASIS
The direct scheme of VC demands a right acquaintance of the modulus and phase of the rotor fluxes. The basic idea is to place sensors in the motor air gap to access the flux [19]. Nevertheless, the installation of these sensors leads to a rise in the size and a weakening of the motor [20]. Moreover, these sensors are responsive to mechanical shocks and heat. Rather, gauged quantities such stator current and voltage might be used to estimate rotor fluxes [21]. The stator flux may be estimated then by an integration: And the rotor fluxes might be estimated from the stator flux and the real stator current [22]: Subsequently, the flux normΦ r and its positionθ s utilized for coordinate transformation are determined by [23]:Φ

SLIDING MODE SPEED CONTROLLER
Generally, Jean-Jacques Slotine suggested an equation way to define the sliding surface which assure variable converging to the wanted result [24]: E(X)=X * -X: gap variable to be settled, λ: coefficient which is strictly positive, n: relative degree that represents the number of times to derive the output to get the appropriate control [25], [26]. By selecting (n=1) in Jean-Jacques Slotine general (9), the sliding surface of the speed is specified by: Its derivative is: By inserting the control current I * sq =I sqeq +I sqn in (11): Throughout the sliding mode and steady state S(Ω r )=0,Ṡ(Ω r )=0, and I sqn =0, we next obtain the equivalent control expression I sqeq : ❒

ISSN: 2302-9285
Throughout the converging mode, the discontinued control form i sqn should fulfill the conditionṠ(Ω r )S(Ω r )<0. By substituting I sqeq expression in (12), we obtain: The discontinued control form is then put as:

FIVE-LEVEL NPC INVERTER DESIGN
The general schema of the 5-Level NPC inverter is given in Figure 2. This structure consists of 3 symmetrical arms; each arm contains 8 bi-directional switches mounted in series. These interrupters should not be opened or closed at the same instant, to avert the short-circuit of the inverter input continuous voltage [27]. Each switch is made up of a bi-controllable semiconductor S ij (i=A, B, C and j=1, . . . , 8) and a diode posed in anti-parallel. The number of floating diodes is 10 per arm D k (k=1, . . . , 10) ensuring the appliance of various voltage levels at each arm output [28].

Figure 2. The schema of the five-level NPC inverter
This inverter is called a 5-level because it issues five voltage levels per arm ( . By combining the twelve switches of the same arm, seven different voltage levels can be applied to the same phase: The 125 positions of the output voltage vector separate the vector diagram into 6 triangular sectors. Each sector is made up of thirty-six triangular regions. There are thus two hundred sixteen triangular regions in the complete vector diagram. Multilevel inverters are a good choice for many system applications, especially for drive systems. This is because they provide many advantages like power factor improvement and THD reduction [30]. The block diagram of the suggested VC scheme with the SMC and the 5-level NPC inverter is illustrated in Figure 3.

Results analysis
The results illustrated in Figure 4 prove good tracking of the reference speed. The speed regulation loop-based SMC reject quickly the disturbance of the applied load (Figure 4(a)). The response time is less than 0.2 seconds for a reference of +100 rad/s. Once the steady state is reached, the system no longer needs torque. The speed controller cuts the torque demand; it is never zero because it should overcome the friction of the machine which is represented by the resistive torque (Figure 4(b)-(f)). Figure 5 demonstrates the manner the system can act with an instant reverse speed ( Figure 5(a)). The proposed scheme maintains high performance even when reversing the direction of rotation. Strong torque is noticed at the time of the transition of the reference, this high value of approximately -17 N.m is a reaction of the VC to keep the fast pursuit ( Figure  5(b)-(f)). In Figures 6(a)-(f) and 7(a)-(f), the good performance of high and low-speed tracking is obtained with less static error. The system keeps the good tracking of the speed, and the torque is responding accordingly with the speed reference.

CONCLUSION
In this paper, the operation of the VC-based five-level topology that appealed to the induction motor (IM) has been elaborated on and simulated. The attained results have affirmed the effectiveness and the accuracy of the suggested control scheme over sudden resistive torque, reversal, and high and low-speed regions. The proposed technique ensures better control and robustness; the wrench is the five-level NPC inverter that generates a wide interval of the voltage control sequence. Besides, the SMC ensure high resistance toward the instant load application. Satisfactory results have been obtained by numerical simulation, and a detailed discussion has been presented. Multilevel inverters base generally on symmetrical triangle carriers. Their arrangement characterizes the modulation method. The combination of the comparison signals determines the modulated signal and hence directs the control signals. Four alternate carriers are utilized by the PWM unit to control the five-level inverter switches. The alternate carriers have the advantage of allowing sampling at twice the carrier frequency, which results in a signal that is generally of better quality.