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A Z-source Inverter (ZSI) is a DC-to-AC converter that can perform both buck and boost functions as a single stage. A unique attempt of ZSI is the shoot through state, by which two switches of the same phase leg can be turned ON at same instant. So, no dead time is required and output distortion is greatly reduced to provide improved output without the LC filter. The ZSI overcomes the conceptual and theoretical barriers and limitations of the traditional systems. ZSI can boost DC input voltage without the help of a DC-DC boost converter or a step-up transformer.

Permanent magnet brushless DC (BLDC) motors are being used in several applications due to their higher efficiency, larger power-to-weight ratio and lower maintenance. The trapezoidal electromotive force (EMF) BLDC motors demand rotor positional information for sequencing the inverter drive. This positional information is generally generated by three Hall-effect sensors placed in the non-driven end of the motor. However, these temperature sensitive sensors increase the cost of the motor and need special mechanical provision for mounting.

This article aims at contributing the performance enhancement of BLDC motor drive systems. It proposes a ZSI drive for sensorless controlled BLDC motors with an ingenious random pulse width modulation (RPWM) technique. The proposed system employs back-EMF (BEMF) sensing for the position estimation and the ZSI drive leads to provide a wider range of boost voltage. A devious twosome randomness simple boost pulse width modulation (DTRSBPWM) is proposed for ZSI-BLDC motor drives, which attains randomness in two ways with four initial carrier waves.

The two carriers are normal and inverted versions of a fixed frequency triangular wave. While the third and fourth carriers are variable frequency triangular waves obtained through the chaotic frequency generator and its inverter version. The developed DTRSBPWM method of distributing the harmonic power, triumphs over the simple boost PWM (SBPWM) method. The simulation study of the proposed drive system is done in MATLAB software and the corroboration is performed using a SPARTAN-6 field programmable gate array (FPGA) (XC6SLX45) device. The discussion includes the total harmonic distortion (THD) in the output line voltage, DC bus utilization and the harmonic spread factor (HSF).

**Workings of ZSI**

The ZSI is a DC-to-AC converter that can perform both buck and boost functions as a single stage. The ZSI overcomes the conceptual and theoretical barriers and limitations of the traditional methods. ZSI can boost DC input voltage without the help of a step-up transformer. The working of ZSI can be detailed in four modes. The first mode is the traditional active state mode where the inverter bridge acts as the current source from the DC link. The second mode is the Shoot-through state mode where the inverter bridge operates in any one of the two traditional zero vectors and shorts through the upper and lower three devices of the inverter. The third mode is the Non-shoot-through mode where the inductor current contributes to the line current’s harmonic reduction. The fourth mode is the traditional zero state where the inverter bridge is operating in one of the zero states

**Simple boost PWM**

The most extensively used switching strategy in ZSI is the simple boost PWM. It is this simple strategy, which needs two straight lines to control the shoot-through states. When the triangular wave form is higher than the upper envelope Vp, or lower than the bottom envelope V_{N}, the circuit operates in the shoot-through state. Otherwise it operates just as a traditional carrier-based PWM. During simple boost PWM, the resulting voltage stress across the device is high.

**Sensorless control of ZSI-fed BLDC motors**

The sensorless control of ZSI is pictured as a block diagram in the **Figure 1**. This study performs the sensorless control of a BLDC motor by estimating the zero-crossing instant of the Back EMF (from the terminal voltages) and from which the correct commutation instant is estimated and fed to the ZSI circuit. The speed control of the motor is sensed and compared with the reference speed for control action by a proportional integral controller (PIC).

**Figure 1 **Sensorless control of ZSI fed BLDC motor

**Proposed RPWM method**

The proposed DTRSBPWM method involves two levels of randomness, where four (two sets) of triangular carriers are utilized. The set is generated with the help of a chaotic number generator. The basic principle of the chaos-based PWM is to use a chaotic signal to vary the switching or carrier frequency. The chaotic number, which is bounded with a pre-set limit, is fed to the triangular generator. This number is fixed as the frequency for present carrier cycle and a carrier is generated. The number, and hence frequency for the carrier, changes for every cycle. The chaotic sequence incised by the equation (1) is engaged in this study.

Where, f_{n} is the n^{th} switching frequency of chaotic PWM, chaotic sequences x_{n} may be generated simply by iteration. Thus, the switching frequency may be varied from lower limit, f_{low }to upper limit, f_{high}. The Arbitrary periodic orbit can be arrived at by using the diverse value of c. A typical triangular carrier obtained through chaotic sequence is shown in **Figure 2**. This form of carrier and its 180º phase-shifted (inverter form) are considered as the first set of carriers.

**Figure 2 **Triangular carrier through chaotic sequence

The second set of carriers is obtained from the common triangular and its inverter form. The double randomness carrier is formulated by a pseudorandom binary sequence (PRBS). For the 4×1 multiplexer (MUX), all the four carriers are given as input while the cycle-wise selection is done by two selection bits from the linear feedback shift register (LFSR) as indicated in **Figure 3**. The output of the Multiplexer (MUX) is the required random carrier which is compared with the sinusoidal reference, as in the case of a conventional Sinusoidal PWM (SPWM), to get the pulses.

**Figure 3 **Logic diagram for DTRSBPWM generator

[Continue reading on EDN US: Simulation and experimental investigations]

**Related articles**:

- Brushless DC Motors: Construction and Operating Principles
- TIA Input Z: Infinite… or Zero? What is it, really?
- Introduction to Pulse Width Modulation

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