Artificial Neural Networks Direct Torque Control of Single Inverter Feed Two Induction Motors

Induction machines have small size and high reliability economical, self-starting and more advantages make them the most widely used machines in residential, commercial, and industrial settings [1].

To control of IMs different methods was proposed in the literature for example in the middle of the 80s, Takahashi et al. [2, 3] and Depenbrock [4]. proposed a new strategy to control induction machine under the name of DTC (direct torque control of induction machine (Figure 1)). This new control is about to make the control of stator flux and torque uncoupled witch provide to AC drive control a robust and fast response with a simple control structure however it has his disadvantages [5, 6], variable switching frequency (causes noises), torque and flux waves around the hysteresis bands, at low speeds the control of flow is difficult; To improved it several works appeared we marked.

• DTC SVM: Space vector Modulation present by Lascu et al. [5] and Zhao and Peng [7] based on the predictive calculation of the applied reference voltage vector using the approximate machine model.
• DMTC: Direct Mean Torque Control Proposed by Flach and Hofmann [8] in 1997. For this control in each sampling period, they did apply two voltage vectors to impose an average torque in the period equal to the torque of reference.
• DSVM: Discrete Space vector Modulation [9] in this method using 5-level hysteresis comparator increase Number of voltage vectors generated which improve the torque response and make switching frequency constant.
• DTC applied to Three-Level Inverters several works applied DTC to three level inverters [9, 10] for these methods the increase level of inverter allowed us to generated a number of high voltage vectors, which makes it possible to reduce torque ripples; minimize the switching frequency However, the cost of this arrangement is high. so, its limited to high power controls.
• DTC by intelligent techniques (Artificial Neural Network, Fuzzy Logic, Neuro-Fuzzy) [11].

These techniques had considerable success in the fields of control and identification of non-linear systems; for DTC, these techniques allow the control of switching frequency and they have fast flow and torque responses with less noises.

In this paper we combined the tow last method to obtain a fast flow and torque responses with less noise

1.png

Figure 1. Block diagram of the classic 2-level DTC control

In classic DTC, one inverter generally drives one induction motor; are called single-machine single inverter systems; but this control cannot satisfy the needs of industrial applications such as electrical railway and high-power drive systems [5] and multi-machine multi-converter systems are expensive and can be just extensions of traditional drives. So, we need new system topology where one inverter supply more than one machines, this topology gives us more comfortable solution because its economical in cost, a smaller number of electronic components [12-15]. These systems are named Multi-Machine Single-Converter systems. There control is the topic of this study. A NPC level converter fed two inductions motors. This study proposes a new application of the average and master slave algorithms with implementation of artificial neural networks DTC.

The performance of the single-inverter multi-motor DTC system is verified with MATLAB Simulink.

3.1 Average algorithm

The concept of the control single-inverter dual motor system is based on the average algorithm where we vectored the operation states of multiple motors and averaging them to obtain an average motor. When there are differences in working conditions, the multiple motors can be driven according to this algorithm. In related theoretical derivation, the differences should be calculated by Eq. (1). [15, 16]:

$\left\{\begin{array}{l}

x y=z \\

\Delta x=\frac{x_{2}-x_{1}}{2}, \quad \bar{x}=\frac{x_{2}+x_{1}}{2} \\

\Delta y=\frac{y_{2}-y_{1}}{2}, \quad \bar{y}=\frac{y_{2}+y_{1}}{2} \\

\Delta x \bar{y}+\bar{x} \Delta y=\Delta z \\

\Delta x \Delta y+\overline{y x}=\bar{z}

\end{array}\right.$        (1)

where, x and y are variable grandeur.

3.2 Average direct torque control algorithm of single-inverter dual motor

Multi-machine with single inverter system is always controlled as one machine but if the operating condition of the machines changes situation or lost; the current distribution of the two motors is unbalance. Vector control and direct torque control is proposed for two levels single-inverter fed dual machine [16-18]. In our study we discuss the implementation of the average algorithm to the direct torque control of NPC single inverter feeds two IM parallel-connected. In the practical applications, as electric traction generally uses only one inverter to fed two motors [18, 19]. When the number of motors is 2, it means the parameters of the two motors are same, the stator resistance, stator and rotor inductance and mutual inductance are all equal, then their variation is zero and to realize the DTC control we need the value of stator and rotor flux and torque. Figure 3 represent the flowing current provide by the inverter this current is equally divided to the dual induction motors connected in parallel. When the loads on motors are balanced, is1 is equal to is2. On other side when the tow motors had unbalanced loads is1 is different to is2 the average of is1 and is2 flowing in each stator coil winding and ∆is the current flowing directly from motor 1 into motor 2. Finally, to obtain the average model of the two motor we use Eq. (1) [16, 18].

3.png

Figure 3. Current flow for parallel connected IM

Then the average current in stator winding is:

$\left\{\begin{array}{l}

\overline{i_{s}}=\frac{1}{2}\left(i_{s 1}+i_{s 2}\right) \\

\Delta \overline{i_{s 12}}=\frac{1}{2}\left(i_{s 2}-i_{s 1}\right)

\end{array}\right.$        (2)

where, i_s1 represent the current of motor one and i_s2 for the second motor. After the alpha-beta (α β) transformation (Clarke transformation) we obtain new equation system.

$\left\{\begin{array}{l}

\overline{i_{s \alpha}}=\frac{1}{2}\left(i_{s \alpha 1}+i_{s \alpha 2}\right) \\

\overline{i_{s \beta}}=\frac{1}{2}\left(i_{s \beta 1}+i_{s \beta 2}\right) \\

\Delta \overline{i_{s \alpha}}=\frac{1}{2}\left(i_{s \alpha 2}-i_{s \alpha 1}\right) \\

\Delta \overline{i_{s \beta}}=\frac{1}{2}\left(i_{s \beta 2}-i_{s \beta 1}\right)

\end{array}\right.$        (3)

Similarly for magnetic induction flux, the average is presented in static α β coordinate Figure 4.

4.png

Figure 4. The average flux in dual-motor system

where, ϕs1 and ϕs2 is respectively the flux of the motor number one and motor tow. The stator flux of ϕs single motor:

$\phi_{s}=\int\left(V_{s}-R_{s} i_{s}\right)$        (4)

where, V_s is the stator voltage and is is the current of the phase and Rs is the resistance of stator. Then the stator flux of dual motors is:

$\left\{\begin{array}{l}

\frac{\mathrm{d} \overline{\phi_{s}}}{\mathrm{~d} t}=V_{s}-R_{s} \overline{i_{s}} \\

\overline{\phi_{s}}=\frac{1}{2}\left(\phi_{s 1}+\phi_{s 2}\right)

\end{array}\right.$        (5)

As shown in Figure 2, the average flux formula in the (α β) plane is:

$\left\{\begin{array}{l}

\overline{\phi_{s \alpha}}=\frac{1}{2}\left(\phi_{s \alpha 1}+\phi_{s \alpha 2}\right) \\

\overline{\phi_{s \beta}}=\frac{1}{2}\left(\phi_{s \beta 1}+\phi_{s \beta 2}\right) \\

\Delta \overline{\phi_{s \alpha}}=\frac{1}{2}\left(\phi_{s \alpha 2}-\phi_{s \alpha 1}\right) \\

{\Delta \overline{\phi_{s \beta}}}=\frac{1}{2}\left(\phi_{s \beta 2}-\phi_{s \beta 1}\right)

\end{array}\right.$        (6)

The rotor flux on single motor,

$\phi_{r}=\int\left(\frac{M}{\sigma L_{s}} \frac{1}{T_{r}}\left(\phi_{s}-\frac{L_{s}}{M} \phi_{r}\right)+j \omega_{r} \phi_{r}\right) \mathrm{d} t$        (7)

Finally, we applied the Eq. (1) the average torque of bi motors is:

$\left\{\begin{array}{l}

T_{e}=p\left(\overline{\varphi_{s} \times i_{s}}\right) \\

=p\left[\bar{\varphi}_{s} \times \bar{i}_{s}+\left(\Delta \varphi_{s} \times \Delta_{s}\right)\right] \\

=p\left(\overline{\varphi_{s \alpha} \times i_{s \beta}-\varphi_{s \beta} \times i_{s \alpha}}\right) \\

=p\left[{\overline{\varphi_{s \alpha}} \times\overline{{i}_{s \beta}}-\overline{{\varphi}_{s \beta}} \times \overline{{i}_{s \alpha}}}+\left(\Delta \varphi_{s \alpha} \times \Delta_{s \beta}\right)-\left(\Delta \varphi_{s \beta} \times \Delta_{s \alpha}\right)\right]

\end{array}\right.$        (8)

Figure 21 represents the principal of the new algorithm control, on the conventional DTC of induction motors to control the flux and electromagnetic torque the magnitude and position of the stator flux are adjusted respectively from that in this strategy some changes are made in order to make it applicable in a multi-machine system. There are two control loops for torque and one for the stator flux after the choice of the master machine because in this strategy, only the master machine is controlled without any consideration of the slave machine response or load changes. We clarified both control loop in the next section.

21.png

Figure 21. DTC of a two- induction machine master-slave control

5.1 Stator flux control loop

For this new algorithm, merely the master machine is controlled without any consideration of the slave machine response or load changes.

Choice of the master machine can be governed by certain factors such as the machine flux and torque. To prevent flux saturation at different situations, switch table algorithm is employed to choose the master motor which will be his stator flux controlled. this selection is based to an index. The product of stator resistance and electromagnetic torque Figure 21. The motor with the smallest product is chosen to be the master motor Figure 21 [15-26].

5.2 Electromagnetic torque control loops

Previously we have seen the direct torque control is choosing the appropriate voltage vector to fed the machine, this voltage allowed us to control on the same time stator flux and torque, this choice depends on the error of comparison between controlled and reference magnitude.

In two induction motor feds by one inverter, we have two torques for that we need to designing a new algorithm to find this error; first each motor had a classical control loop (5 level comparator) and then second control loop for the result of these two comparators the design of this control can be explained from Figure 22. Figure 21 represent the employment of this technique.

22.png

Figure 22. Possibilities of torque errors, (a) the torque should be kept constant, (b) the torque should be increased, (c) the torque should be reduced

In Figure 22, we see the possibilities of torque errors in torque control loop.

The black points characterize the electromagnetic torque typical situation for the both motors for the conditions depicted in Figure 22 (a), a voltage vector is applied to maintain the torque constant. and form the second conditions presented in Figure 22 (b), a voltage vector is applied to increase the torque finally, the last conditions showing in Figure 22 (c), a voltage vector is applied to reduction torque [15, 26]. We can resume the algorithm control in several pointe

• If both motors require a reduction in torque, a vector is applied to decrease torque.
• If no motor requires a torque change, then a vector is applied such that the torque is kept constant.
• If both motors require an increase in torque, then a vector is applied to increase the torque.
• If one motor requires a decrease in torque but the other does not, then a vector is applied to decrease the torque.
• If one motor requires an increase in torque but the other does not, then a vector is applied to increase the torque.
• If one motor requires a decrease in torque but the other one requires an increase, then a vector is applied such that the torque is kept constant.

From this point we obtain the next table.

Table 2. Proposed table in torque control loop

Finally, using the output of this table and the output of the stator flux control loop, the appropriate voltage vector is selected based on the conventional DTC switching look-up Table 2.