Analysis of cascaded H-bridge multilevel inverter with current control methods

Received Aug 30, 2021 Revised Mar 2, 2022 Accepted Mar 25, 2022 A detailed model and analysis of a five-level cascaded H-bridge (CHB) multilevel inverter with different current control methods are presented. Simulation models of the CHB inverter with hysteresis current controller, PI current controller using SPWM technique and predictive current controller have been built to demonstrate the CHB inverter system performance with regard to load current THD and reference current tracking. In controlling the load current, the hysteresis and the PI current controllers have the problem of current ripple and phase lag, respectively. The proposed predictive current control method effectively addresses these issues. The current control methods are analyzed for varying reference current and unbalanced load conditions. The simulation results are observed and analyzed using the MATLAB Simulink software to validate the current control methods.


INTRODUCTION
In modern days, plentiful industries have initiated to utilize higher power machineries. Multilevel inverters (MLI) are extensively applicable for higher power machineries due to the prolific benefits [1]- [3]. The inverters have the ability to provide required voltage and power by exploiting switching devices as an alternative for transformers. The THD and the electromagnetic interference in the output voltage and current waveform decreases as the number of output levels rises. The fundamental idea of the MLI is to obtain high power by utilizing power semiconductor switches with more than a few lower dc voltage sources. The deeprooted topologies of MLI [4] have plentiful reward when compared to the traditional inverters. In recent days, the CHB inverter has become widely implemented topology for high-power variable-speed drive applications [5]- [7] such as conveyors, steel and paper rolling mills, locomotive traction drives, ship propulsion drives and battery operated and hybrid vehicle drives. The three phase CHB inverters are designed with a number of Hbridge units. The foremost emphasis is on the CHB-MLI for analyzing its performance with diverse current control methods including hysteresis current control [8]- [11], PI current control using SPWM technique [12], and predictive current control [13]- [17]. The main problem with hysteresis current control is its variable switching frequency that roots high switching losses and higher order harmonics in the load current, thereby increasing ripple current [18], [19]. The PI current controller has the problems of steady-state magnitude error, phase lag and limited disturbance rejection capability in controlling the load current [20], [21]. The current control methods are analyzed with the level of load current THD, reference current tracking capability and unbalanced load conditions. The five-level CHB inverter with the hysteresis, PI and predictive current control methods is simulated using the MATLAB Simulink.

MODULATION TECHNIQUES FOR CHB INVERTER
Numerous modulation methods [22]- [26] have been adopted for the CHB inverter based on specific requirements and distinctive applications. PS-PWM and LS-PWM are advancement of the conventional PWM techniques. Modulating signal of pure sinusoidal wave and multi carrier signals of triangular waves have been considered for generating the gate signals to the switching devices in the CHB inverter. The number of carrier signals needed for an m-level inverter is calculated by (m-1). The (m-1) carrier signals are arranged in vertical shifts in LS-PWM technique. The PS-PWM method is implemented for generating gate signals to the inverter. The least THD for the inverter can be obtained when 180 or 360/h (where h is the number of cells) phase shifts are provided between the carrier signals.

Hysteresis controller
In the hysteresis current controller, the load current tracks the reference current within a hysteresis band. Figure 2(a) shows the block diagram of a hysteresis current controller for the inverter. The operating principle of the hysteresis modulation is shows in Figure 2(b). It has the upper and lower hysteresis band limits. When the load current surpasses the upper band limit, higher voltage level is selected until the current error reaches to zero. Similarly, When the load current surpasses the lower band limit, next voltage level is selected until the current error reaches to zero. Hence the load current is controlled with in the upper and lower hysteresis band limits. The changes in the load parameters and operating constraints continuously modifies the switching frequency, which creates resonance problems and switching losses. This is considered as a main downside in the hysteresis current control method.

Proportional-integral controller
The PI control method is a modest control technique with widespread industrial applications. The PI controller employing PSPWM is shown in Figure 3. The controller is comprised of a feedback loop for measuring the actual load current. The controller generates the reference voltages by processing the error between the reference current and the load current. The PSPWM scheme is used as a modulator to produce switching signals for the inverter.

Predictive control method
The predictive current control method [27] is a modern control technique that is expected to control the load current very effectively when compared with traditional control methods. The predictive current control method involves mathematical modeling of the CHB inverter and the predictive control model. The circuit diagram of the inverter with RL load as shown in the Figure 4 is used for mathematical modeling.

Modeling of CHB inverter
The probable voltage levels for each phase are: where, m is count of voltage levels, and h is the count of H-Bridge cells per leg. The number of voltage level combinations L m in the three-phase CHB inverter is: All the cells in the CHB inverter requires two gate pulses, the inverter voltage per leg is: where, Saj, 1 and Saj, 2 are the gate pulses of the phase a and cell j. The conceivable switching amalgamation PS is: The differential equation for a leg of the RL load is: where, van is the potential difference with reference to neutral point of the load.
The potential difference across the load with respect to the inverter voltage is: va0 = vaN + vn0 va0 = vaN + vn0 (6) where, vn0 is the common-mode voltage (vcm), given by Using vectorial transformation, the load model is formulated as, where a, b, and c are the three-phase parameters, and α and β are the vectorial variables. In (5) can be formulated in relation to the vectorial variables α−β as, where iα, β is the current vector and Vα, β is the voltage vector.

Predictive current controller
In the predictive current controller shown in Figure 5, a mathematical model of the CHB inverter and the load is formulated to forecast the future behavior of the current for each and every diverse voltage vector produced by the inverter. The voltage vector that minimizes a cost function is nominated to be applied as a switching signal. The predictive current control method avoids the application of any modulation method in the CHB inverter.
and substituting it in (9), the forthcoming load current vector is obtained as (11).  (12) is solved for all the conceivable voltage vector. The voltage vector which reduces the cost function is nominated and made functional.

SIMULATION RESULTS
The CHB inverter with different current control methods is simulated in MATLAB/Simulink software. The RL load is used to obtain simulation results. The parameters used for the simulation are specified in Table 1. The current control methods are examined and related with respect to current THD, varying reference current and unbalanced load conditions.

Current THD
The THD spectrum of the load current is evaluated with the aid of the FFT tool in MATLAB/Simulink. The THD level of the load current for various values of load are measured. The load current waveforms for hysteresis controller, PI controller, and predictive controller are shown in Figures 6, 7 and 8, respectively. The THD for different load values were compared as shown in the Figure 9 to analyze the effect of the hysteresis, PI, and predictive current control.

Reference current variations
The amplitude of the reference current is varied from 0.9 A to 0.7 A at instant t= 0.04 ms to 0.08 ms. The current tracking performance of the hysteresis control, PI control and predictive control methods are shown in Figures 10, 11, and 12, respectively. The Hysteresis current control method shows time lag in tracking the reference current, and has more current ripple. The PI control method shows phase lag in tracking the reference current. The predictive control method tracks the reference current perfectly when the reference current is varied.

Unbalanced load condition
A three-phase load can be considered unbalanced when the phase impedances are not equal to each other. The magnitudes of each phase current are different. The response (load current) of the hysteresis control, PI control, and predictive control are shown in Figures 13, 14, and 15, respectively. The load values assumed for phase 'a' is R=42 Ω, L=10 mH, phase 'b' is R=47 Ω, L=15 mH and phase 'c' R=52 Ω, L=20 mH. The predictive current control method tracks the reference current perfectly during the unbalanced load currents.

CONCLUSION
The performance of hysteresis, PI and Predictive controller for the five-level CHB multilevel inverter were analyzed for various load conditions. The current THD spectra for the three control methods are compared, and the current spectrum attained with predictive current control method showed lower THD than the other two control methods. The simulation results for varying reference current shows more current ripple in the current tracked by hysteresis controller and phase lag in the current tracked by the PI controller. These two limitations are addressed by the predictive controller, and hence better performance of the predictive controller is observed in tracking the set reference current. When compared with other two current control methods, it is also noticed that the predictive controller effectively controls the load current within the preset limit during the unbalanced load conditions.