Imposed Switching Frequency Direct Torque Control of Induction Machine Using Five Level Flying Capacitors Inverter

MUTLILEVEL inverters have received a great deal of research attention in the recent years and are nowadays widely used in high to medium voltage AC drives [1]. Large number of output voltage levels can be produced from the multilevel converters, which brings about lower harmonic contents, lower switching loss, high voltage capability and high power quality. The principal function of multilevel converter is to synthesize a desired ac voltage from several dc voltage levels [2]

Generally speaking, there are three kinds of multilevel converter topologies: Diode-clamped topology, Capacitor–clamped topology and Cascade H-bridge topology [3].

Among these multilevel inverters, the diode-clamping inverter, which is called the neutral-point clamped (NPC) inverter, has been commonly used [4]. However, it is difficult to control real power flow for balancing the neutral-point voltage. On the other hand, although the flying-capacitor inverter has demerits to require additional flying-capacitors and voltage control, these capacitors are smaller than DC-link capacitance and they are a simple mechanism to control charging and discharging voltage of flying-capacitors [2, 3].

There have been main three approaches to balance the voltage of dc link series capacitors in the reported papers:1) adopting separate dc sources; 2) using some auxiliary balancing circuits; 3) improving the control method by selecting redundant switching states [2].

Direct torque control (DTC) is the control strategies that are commonly used for variable-speed AC drives. It is characterized by the simple structure, excellent transient response and parametric robustness [3].

Nonetheless, classical DTC suffers from issues such as high torque and flux ripples and variable switching frequency. These demerits can be attributed mainly to three reasons: 1) the nature of varying torque and flux slopes in the motors; 2) the use of hysteresis controllers with fixed bands; 3) the availability of only a limited number of voltage vectors, which are predetermined by specific inverter topology used. Therefore, low sampling periods, leading to high switching frequencies, are often required in classical DTC to keep the torque and flux ripples to an acceptable level.

Several advanced control methods have been proposed to improve the performance of classical two-level inverter fed DTC drives. Techniques such as space vector modulation [3], predictive control [5] and duty cycle based DTC [6 of Deep] are frequently employed to improve the torque and flux regulation in the DTC drives. Both SVM-DTC and predictive-DTC are also capable of obtaining constant inverter switching frequency [6]. Although these advanced methods contribute to alleviate the major drawbacks of the classical DTC in two Level-DTC drives, their extension to n level-DTC drives is not straightforward due to the increased degree of freedom.

In This paper the Imposed Switching Frequency Direct Torque Control (ISFDTC) strategy is generic and compatible with static converters with any number of levels. Its basic principle is applicable to different converter topologies including choppers, single-phase or three-phase inverters. However, the main application, as described in [7], is a multilevel three-phase voltage inverter-controlled induction motor. The ISFDTC strategy is designed to improve the quality of the supplied torque to achieve enhanced dynamics, low ripple amplitudes and harmonics frequency imposition. On the other hand, the ISFDTC strategy makes it possible to impose the average switching frequency of the inverter which leads to several advantages such as improved operation of the machine (audible noise) and the inverter and this for a wide range of torque and speed of the induction machine. Like all the control laws described as "direct", the ISFDTC acts in such a way that, at each sampling time, an instantaneous voltage vector is applied to the machine based to its current state and the performance characteristics imposed by the user. In addition, the ISFDTC strategy is based on three stages corresponding to the degrees of freedom offered by the multi-level inverters. It is well known that the number of voltage vectors at the output of a three-phase multi-level inverter increases with the number of levels of the inverter. This better meet the requirements of the regulation of the variables of the load. This degree of freedom has been classified as type I. In addition, the fact that the same voltage vector at the output of a multi-level inverter can be synthesized from several phase level sequences can be considered as a second degree of freedom which has been called type II.

Finally, a third degree of freedom for flying capacitors inverters name type III, is the ability of this type of converter to generate the same voltage level in each of its three arms with several arm configurations.

The remaining of the paper is organized as follows: Section 2 describes the model of induction machine using stationary reference frame, the operating principle and vectors generated by five level flaying capacitors inverter are presented in section 3, next section 4 describe the conventional direct torque control DTC, the three steps of proposed method of imposed switching frequency and direct torque control ISFDTC are explained in section 5, the developed method of balancing voltage of floating capacitors discussed in the section 6,  simulation results are illustrated in section 7. Finally, the concluding remarks are drawn in section 8.

The flying capacitors inverter structure is characterized by a nested connection of the switching cells as shown in Figure 1 [8]. Each arm of the inverter consists of four cells.

1.png

Figure 1. Flying capacitors inverter arm with N-levels (p = N-1 cell)

Table 1 shows the different states of a N-levels (p-1 cells) flying capacitors converters.

Table 1. Possible states of the p-cell nested cell inverter $\Delta \mathrm{U}=E_{c} / p$  

The combinations of states of the three arms of the inverter allow us to generate125 vectors in total including 61 distinct vectors as shown in Figure 2.

2.png

Figure 2. Voltages that can be supplied by the inverter with five voltage levels

5.png

Figure 5. The three steps principle of ISFDTC applied to the torque of the asynchronous machine fed by a multilevel inverter

5.1 Selection of the voltage vector of the inverter

This step allows an instantaneous regulation of the torque and flux of the machine and can generalized to any multilevel inverter topology. The selection method proposed in [11] is applied here. For the control of the flux, the error ε_ϕ is localized in one of the three associated intervals and which are fixed by the constraints:

$\varepsilon_{\phi}<\varepsilon_{\phi \min }$

$\varepsilon_{\phi \min } \leq \varepsilon_{\phi} \leq \varepsilon_{\phi \max }$

$\varepsilon_{\phi}>\varepsilon_{\phi \max }$         (12)

In steady-state, the electromagnetic torque is equal to the load torque. To improve the control of the torque, five control regions are defined based on the following constraints on the torque error  $\varepsilon_{T}$:

$\varepsilon_{\Gamma}<\varepsilon_{\Gamma \min 2}$

$\varepsilon_{\Gamma \min 2} \leq \varepsilon_{\Gamma} \leq \varepsilon_{\Gamma \min 1}$

$\varepsilon_{\Gamma \min 1} \leq \varepsilon_{\Gamma} \leq \varepsilon_{\Gamma \max 1}$

$\varepsilon_{\Gamma \max 1} \leq \varepsilon_{\Gamma} \leq \varepsilon_{\Gamma \max 2}$

$\varepsilon_{\Gamma \max 2}<\varepsilon_{\Gamma}$           (13)

6.png

Figure 6. Hysteresis control regions of the torque.

The switching table is determined based onto the outputs of the flux and torque hysteresis controllers and the flux position zone, as shown in Table 2.

Table 2. Switching table used with twelve angular sectors

Ɵ 1

Ɵ 2

Ɵ 3

Ɵ 4

Ɵ 5

Ɵ 6

Ɵ 7

Ɵ 8

Ɵ 9

Ɵ 10

Ɵ 11

Ɵ 12

5.2 Selection of the phase voltage sequence

This step is also executed recursively and consists in determining, the sequence of phase levels at the next sampling period, using the degree of freedom of type II for flying capacitors inverters. It allows the balancing of commutations among the three phases.

5.3 Selection of the configuration

Once the sequence of phase levels is known, a separate phase-dependent floating capacitor balancing procedure can be used to determine the conduction states of the III cells of the three phases of the inverter, by exploiting the degrees of Type III freedom. Note that, this step is applied only for flying capacitors inverters.

In this subsection, the transient and steady state performances of the proposed algorithm ISFDTC are compared to the conventional DTC method in [8], which is referred to as CDTCM in the continuation of this paper for simplicity. In the simulations, both classical DTC method and the proposed ISFDTC operate with a sampling frequency of 20 kHz. The torque regulator in the proposed ISFDTC operates with a imposed frequency $\left(f_{i}\right)$  to 1.25 kHz $f_{i}=\frac{f_{s}}{4 \rho}$  where $\rho$ : number of cell and $f_{s}$  is sampling frequency , while the average inverter switching frequency of classical DTC method is variable, with a mean value of approximately 1 to 20 kHz Figure 9.

The ISFDTC strategy is applied to direct torque control of an induction machine driven by a 5-level inverter.

Figure 10 shows the waveforms of the main quantities of the induction machine controlled by the ISFDTC strategy compared to the direct torque control with conventional method where the waveforms are shows in Figure 9. It can be observed that the torque and stator flux are successfully controlled within their respective hysteresis band. The amplitude of the flux vector increases then remains constant and equal to its reference value with a low ripple. This demonstrates a good regulation of the flux and effective decoupling with the torque during the transient conditions. The waveforms of the steady-state capacitor voltages are shown in Figure 10. Hence, it can be confirmed by simulation that, independently of the phase voltage level, it is always possible to select an arm configuration that makes it possible to confine the evolution of the capacitor voltages within their hysteresis band. Figure 10(e) shows the voltages at the terminals of each floating capacitor. All capacitor voltages converge to their respective set points. The average switching frequency ( $f_{i}=1.25 k H z$ ) is practically constant. It is important to remember that this ability to correctly impose the switching frequency is a major advantage of the ISFDTC strategy that did was not found in conventional DTC strategies.

9.png

Figure 9. Response of conventional DTC: torque, flux, stator current, voltage

10.png

Figure 10. Response of ISFDTC torque, flux, stator current, voltage, evolution of voltages at floating capacitor terminals, and average switching frequency per cell