Stochastic Pulse-Width Modulation and Modification of Direct Torque Control Based on a Three-Level Neutral-Point Clamped Inverter

Abstract

The three-level neutral-point clamped inverter represents a significant advancement in direct torque-control systems for asynchronous motors. A significant achievement of this study lies in the comprehensive analysis of a random frequency-modulation algorithm, which demonstrates its efficacy in substantially reducing the amplitude of harmonic oscillations and minimizing switching losses. This simplifies filter design and minimizes thermal dissipation in power transistors, thereby enhancing the overall reliability and efficiency of the system. Additionally, the implementation of a six-position torque regulator with a fixed sensitivity zone, applied in direct torque control based on the three-level inverter, improves the stability of the stator flux linkage and reduces the switching frequency of transistors. Numerical simulations conducted in the Matlab/Simulink environment indicate that the proposed algorithm reduces switching losses by 15% during transient states and by 2% during steady-state operation while increasing the system’s efficiency by 2% compared to conventional methods. These findings highlight the potential of the proposed solutions for application in energy-efficient drive systems.

1. Introduction

Frequency converters (IGBT or MOSFET) function as sources of harmonics, introducing additional complexity and challenges in maintaining stable system operation [1,2]. The operation of frequency converters inherently involves energy conversion, which consequently generates harmonic components. The harmonics produced via frequency converters intensify distortions in voltage and current waveforms, leading to disruptions in the continuous operation of connected equipment [3,4,5]. Thus, effective measures to mitigate harmonic distortions and the associated challenges are essential to ensure the reliability and longevity of electrical systems dependent on frequency converters [6,7,8].

For asynchronous electric drives, this phenomenon manifests as increased internal motor temperatures, potentially reaching levels that may cause damage [9,10,11]. The complex interaction of harmonic distortions in the electrical waveform poses a threat to system integrity, leading to adverse effects beyond mere performance degradation. The occurrence of errors in data transmission can be attributed to the destructive impact of harmonic distortions, underscoring the necessity of vigilant mitigation strategies to ensure the operational reliability of the system [12,13,14,15].

Various methodologies have been employed to address the above-mentioned issue, including the following: the use of active filters such as SAPF [16] and MPPT [17]; advanced control techniques involving artificial neural networks [18], fuzzy logic controllers [19,20], and ant colony optimization algorithms [21]; and the development of multi-level structures for frequency converters and their control algorithms. Active filters work by introducing compensating currents into a system, effectively mitigating unwanted harmonic distortions. Implementing these filters is a targeted approach to harmonic elimination, thus enhancing the overall quality of the electrical system. However, the application of active filters and advanced control methodologies is not without challenges. The complexity and relatively high number of algorithms associated with such configurations pose difficulties in practical implementation. Therefore, current research has focused on developing a multi-level structure for frequency converters, specifically designed to optimize performance and reduce harmonics in medium- and high-power equipment.

Studies on the direct torque control (DTC) of motors based on three-level inverters, as demonstrated in works such as [22,23,24], reveal the potential for near-future applications. Collectively, these studies illustrate the dynamic landscape of research focused on advancing control methodologies for electric drives, with the overarching goal of enhancing modern motor-control systems. This drive-control method not only provides high performance and accuracy but also offers the advantage of not requiring a complex model for the entire system. Its characteristic of reduced calculation time, inherent to the DTC system, is particularly advantageous, meeting the demand for rapid responsiveness in electric drive applications [25,26]. By minimizing harmonic effects and optimizing drive performance, this approach makes a substantial contribution to the overarching goals of energy efficiency and improved system operation [23,27,28]. Together, these dual achievements represent steps toward a more sustainable and technologically advanced landscape in the fields of energy efficiency, motor control, and harmonic reduction in electrical systems.

A review of the literature on the structure and control algorithms for asynchronous electric drives has led to the proposal of a structural diagram for an automated asynchronous drive based on a three-level autonomous-inverter neutral-point clamped inverter (NPC), as shown in Figure 1.

This system comprises several key components: a DC power source represented by a battery, a three-level neutral-point clamped inverter, an induction motor (IM) serving as the drive motor, voltage sensors (VSs), current sensors (CSs), rotational speed sensors (RFSs), a motor-control system (MC), and a modulation control system (MCS). The interaction of these components is managed by the motor-control system (MC), which, based on the control task from the drive-control system, generates a reference voltage signal for the three-level inverter (U*_A, U*_B, and U*_C). Simultaneously, the modulation control system (MCS) plays a crucial role by generating switching functions (Sx) for the inverter based on the specified voltage signals. This configuration is designed to optimize the interaction between the battery, the three-level inverter NPC, and the induction motor, thereby achieving desired performance characteristics in terms of stator flux linkage, rotational speed, and overall system efficiency.

In this paper, the authors assess a novel solution for induction motor control using a three-level autonomous-inverter neutral-point clamped inverter. The article is organized as follows: Section 2 delves into an investigation of control algorithms for frequency converters, including an analysis of the impact of constant and random switching frequencies on the performance of nonlinear loads (RL). Section 3 focuses on modifications to the direct torque-control algorithm for the induction motor, incorporating the development of a control algorithm based on a six-position torque controller with an unchanged sensitivity zone. Finally, Section 4 presents a summary of the conclusions drawn from the research results discussed in the preceding sections.

2. Analysis of Algorithms in a Modulation Control System Based on a Three-Level Autonomous-Inverter Neutral-Point Clamped Inverter

The current common practice for constructing modulation control systems for power inverters is the use of pulse-width modulation (PWM) with a constant switching frequency. Based on PWM, a constant switching frequency, are systems such as SinPWM and its modified variants: PWM with premodulation (PWMWP) and space vector PWM (SVPWM) [29,30].

Figure 2a presents the oscillograms of the control and carrier signals, while Figure 2b illustrates the output voltages of the three-level inverter using SinPWM. The oscillograms were generated through computer simulation modeling of the equivalent circuit of an automated asynchronous drive. The equivalent circuit includes a DC voltage source of U_dc = 100 V, a network frequency of f₀ = 50 Hz, and an equivalent three-phase symmetrical load with an active resistance of 1 Ω and an inductance of 0.5 mH.

The control signals are shaped within a three-phase coordinate system, expressed as follows:

$$U_A^{\ast }=sin \left(2\pi f_0\right);\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}{U}_B^{\ast }=sin \left(2\pi f_0-{\displaystyle \frac{2\pi }{3}} \right);\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}{U}_C^{\ast }=sin \left(2\pi f_0+{\displaystyle \frac{2\pi }{3}} \right).$$

(1)

U_set—the carrier signal, also known as the reference or sweep signal, is typically a high-frequency fixed triangular waveform signal. The carrier signal’s frequency is critical in pulse-width modulation (PWM) schemes, where it interacts with the control signals to generate switching pulses that control the inverter’s output. The carrier signals for a three-level neutral-point clamped inverter are represented as follows:

$$\begin{array}{l}{U}_{set1}={\displaystyle \frac{1}{\pi }}\arcsin (2\pi f_{set})+0.5;\\ U_{set2}={\displaystyle \frac{1}{\pi }}\arcsin (2\pi f_{set})-0.5.\end{array}$$

(2)

Computer modeling was performed for the following carrier signal frequencies (f_set): 1000 Hz, 2000 Hz, 3000 Hz, 4000 Hz, and 5000 Hz. The resulting oscillograms of the aforementioned variables were supplemented with spectrograms of the output voltage of the three-level inverter using SinPWM, which are presented in Figure 2.

The analysis of the obtained oscillograms and spectrograms allows for the following conclusions:

−

Increasing the switching frequency from 1000 Hz to 5000 Hz results in a fivefold increase in the carrier signal frequency (Figure 2a), accompanied by a reduction in the width of the voltage pulses and an increase in their number (Figure 2b).

−

Most frequency components of the higher harmonics are multiples of the switching frequency, thus forming a packet of higher harmonics (Figure 3).

Based on the conducted analysis, several problems associated with the use of pulse-width modulation with a constant switching frequency can be highlighted:

−

The generation of high-frequency harmonics by systems with a constant switching frequency may cause significant electromagnetic compatibility problems, negatively impacting the operation of other electronic devices and systems in close proximity.

−

Constant switching frequency can lead to the occurrence of resonance phenomena with system components, such as filters and loads. This could elevate harmonic levels or cause current distortion, resulting in the reduced overall efficiency and stability of the system.

These findings underline the necessity of further study and the optimization of pulse-width modulation to minimize negative effects associated with high harmonic content and resonance phenomena, which would improve the performance characteristics of electric drives and the system as a whole.

To eliminate the high-order harmonic components from the spectrum of the output-line voltage and the related issues with the use of three-level inverters in automated electric drives, various methods can be applied [31]. However, the best solution to these issues is to modify the modulation control system by transitioning from carrier signals with a constant frequency to carrier signals with a variable frequency.

The challenge with variable-frequency PWM lies in the potential for a significant increase in the inverter’s switching frequency when used in automated electric drives. This can lead to higher power losses in their frequency converters, which is generally accompanied by increased heat generation and a higher risk of thermal damage [32,33]. To address these problems, direct-control systems are often equipped with PWM with constant carrier-frequency SinPWM [34] and SVPWM [35], which does not match the operational characteristics of the former. This prevents the full utilization of their advantages and introduces the aforementioned drawbacks inherent to SinPWM, PWMWP, and SVPWM systems into the automated electric drive with a direct-control system.

In this regard, a random-frequency PWM (RFPWM) was developed and studied using computer simulation models. Figure 4a shows the oscillograms of control and carrier signals, and Figure 4b shows the output voltages of the three-level inverter with RFPWM:

−

Variant 1: with random switching frequency variation from 1000 Hz to 5000 Hz;

−

Variant 2: with random switching frequency variation from 2000 Hz to 5000 Hz;

−

Variant 3: with random switching frequency variation from 3000 Hz to 5000 Hz;

−

Variant 4: with random switching frequency variation from 4000 Hz to 5000 Hz.

The obtained oscillograms of the above variables are supplemented by spectrograms of the output voltages of the three-level inverter with SinPWM, presented in Figure 4.

An analysis of the obtained oscillograms and spectrograms allows the following conclusions:

−

Random switching frequency variation from fmin Hz to fmax Hz leads to changes in the carrier signal frequency (Figure 4a), which results in varying pulse widths and counts within the switching period (Figure 4b);

−

Harmonics are spread across the entire frequency range under investigation (Figure 5), and the maximum harmonic amplitudes of the output line voltage of the three-level inverter with RFPWM are lower than when using constant-frequency PWM (

Table 1. Maximum harmonic amplitude of the output voltage.

Frequency, Hz	Maximum Harmonic Amplitude of the Output Voltage, V
	fset, Hz
	1000	2000	3000	4000	5000	1000:5000	2000:5000	3000:5000	4000:5000
1000	11	-	-	-	-	2	2	-	-
2000	12	11	-	-	-	2	3	-	-
3000	3	-	11	-	-	2	3	2	2
4000	6	12	-	11	-	3	2	4	6
5000	5	-	-	-	11	2	3	4	6
6000	2	3	12	-	-	2	2	3	-
7000	3	-	-	-	-	2	1	3	-
8000	2	6	-	12	-	1	1	2	3
9000	2	-	3	-	-	2	2	2	5
10,000	2	3	-	-	12	1	1	2	4

).

The study results suggest that using a three-level inverter with RFPWM allows for the elimination of high-order harmonic component clusters in the spectrum of the output line voltage.

To assess the impact of using a three-level inverter with RFPWM on the energy and dynamic characteristics, oscillograms of the output currents of the three-level inverter (Figure 6) and their spectrograms (Figure 7) were constructed. The obtained oscillograms of the above variables are supplemented by diagrams of the dynamic characteristics of the asynchronous drive (Figure 8), which show the dependence of output voltages and currents on the modulation index. The number of state transitions of inverter with different switching frequencies is shown in Figure 9.

The study results allow us to conclude that applying RFPWM achieves the following advantages:

−

Reduction in electromagnetic interference (EMI): based on the analysis of Table 1 and

Table 2. Maximum harmonic amplitude of the output current.

Frequency, Hz	Maximum Harmonic Amplitude of the Output Current, A
	fset, Hz
	1000	5000	1000:5000	2000:5000	3000:5000	4000:5000
1000	10	-	1	-	-	-
2000	10	-	2	1	-	-
3000	3	-	3	2	1
4000	4	-	2	2	3	3
5000	2	8	1	1	3	3
6000	2	-	1	1	-	-
7000	2	-	1	1	1	-
8000	1	-	-	-	-	-
9000	1	-	-	-	-	3
10,000	1	4	-	-	-	1

, it can be concluded that the maximum harmonic amplitude under random switching frequency maintains low values across all frequency ranges.

−

Reduction in the current ripple: as shown in Figure 6, the current ripple decreases, and the total harmonic distortion (THD) in the current is significantly reduced.

−

Narrowing of the switching-frequency deviation band: With a smaller deviation in the switching-frequency band, maximum amplitudes tend to concentrate at the extreme switching frequencies, f_max and f_min. The significant reduction in maximum harmonic amplitudes greatly simplifies the design of LC filters for asynchronous drives and enhances the electromagnetic compatibility of the overall system (Figure 7).

−

Improved energy-conversion efficiency: since EMI is reduced, the losses due to EMI are also minimized, leading to an improvement in overall energy-conversion efficiency.

−

Preservation of asynchronous drive’s energy and dynamic characteristics: as indicated in Figure 8, the system’s energy and dynamic characteristics remain consistent.

−

Reduction in the system operating temperature: The diagrams of inverter–transistor-state transitions (VT) (Figure 9) show that random switching frequency results in an average value between f_max and f_min. This allows the switching frequency to be effectively halved, reducing switching losses in the transistors by approximately 50%. Additionally, the dispersion of harmonic energy helps reduce localized thermal stress on components.

Disadvantages of Applying Random-Frequency PWM

−

Algorithm complexity: compared to fixed-frequency PWM, RFPWM employs more complex algorithms, which require high-performance signal-processing components, thereby increasing production costs.

−

Filter optimization challenges: due to the random variation in the switching frequency, determining the optimal filter design becomes more challenging, potentially affecting the stability of systems with high precision requirements.

In summary, the use of RFPWM effectively eliminates higher harmonic-frequency components without compromising the energy and dynamic characteristics of the asynchronous drive, and it even reduces switching losses compared to fixed-frequency PWM. Currently, converters with RFPWM are being implemented in direct torque-control systems.

3. Modification of Direct Torque Control Based on a Three-Level Neutral-Point Clamped Inverter

Direct torque control (DTC) is a method that allows for instantaneous control of the stator flux linkage (Ψ_s) and the torque (M) of a motor. The change in torque, M, is crucial in designing the control table, and this change is determined via the following formula:

$$M=-{\displaystyle \frac{3}{2}}{\displaystyle \frac{k_s{k}_r}{\sigma L_m}}\left|{\mathrm{\Psi }}_s\right|\left|{\mathrm{\Psi }}_r\right|\sin \theta$$

(3)

where the following applies: $k_s={\displaystyle \frac{L_m}{L_s}};$$k_r={\displaystyle \frac{L_m}{L_r}};$$\sigma =1-{\displaystyle \frac{k_s}{k_r}}$ denotes the constants value;

L_S, L_r—indicate the stator and rotor inductance;

L_m—represents the mutual inductance;

Ψ_s, Ψ_r—denote the stator and rotor flux;

θ—represents the angle between the stator and the rotor flux.

3.1. Direct Torque Control Based on a Three-Level Inverter with a Three-Position Torque Regulator (3 Level)

From

Table 3. Possible switching states of the voltage rows.

State	Sx1	Sx2	Sx3	Sx4
P	1	1	0	0
O	0	1	1	0
N	0	0	1	1

, it can be concluded that the voltage vectors of the three-level inverter include four main groups, examples of output voltage are illustrated in Figure 10a:

−

Zero vectors: V0 OOO, V7 PPP, and V26 NNN.

−

Short vectors: V1 POO, V2 PPO, V3 OPO, V4 OPP, V5 OOP, V6 POP, V8 ONN, V9 OON, V10 NON, V11 NOO, V12 NNO, and V13 ONO.

−

Long vectors: V14 PNN, V17 NPP, V15 PPN, V18 NNP, V16 NPN, and V19 PNP.

−

Medium vectors: V20 PON, V21 OPN, V22 NPO, V23 NOP, V24 ONP, and V25 PNO.

The voltage vector space of the three-level inverter with a three-level neutral-point clamped inverter is divided into 12 sectors, each covering 30° (Figure 10b): Sectors I [−15°;15°], II [15°;45°], III [−45°;75°], IV [−75°;105°], V [105°;135°], VI [135°;175°], VII [175°;205°], VIII [205°;235°], IX [235°;265°], X [265°;295°], XI [295°;315°], and XII [315°;345°]. The voltage switching table is presented in

Table 4. Voltage switching table with three-position torque regulator for three-level inverter.

dΨ	dM	Sector
		I	II	III	IV	V	VI	VII	VIII	IX	X	XI	XII
+1	+3	V15	V21	V16	V22	V17	V23	V18	V24	V19	V25	V14	V20
	0	V0	V0	V7	V7	V26	V26	V0	V0	V7	V7	V26	V26
	−3	V19	V25	V14	V20	V15	V21	V16	V22	V17	V23	V18	V24
0	+3	V16	V22	V17	V23	V18	V24	V19	V25	V14	V20	V15	V21
	0	V26	V26	V0	V0	V7	V7	V26	V26	V0	V0	V7	V7
	−3	V18	V24	V19	V25	V14	V20	V15	V21	V16	V22	V17	V23

.

A structural diagram of the direct-control system based on a three-level inverter with a three-position torque regulator is shown in Figure 11. The basic direct torque-control system for the three-level inverter also employs three-position and two-position relay controllers to detect deviations in the stator flux linkage and torque. The two-position relay controller checks two states of the stator flux linkage: 1 and 0 (Figure 12). The three-position relay controller checks three torque states: 1, 0, and −1 (Figure 13).

3.2. Direct Torque Control Based on a Three-Level Inverter with a Six-Position Torque Regulator (3 Level_m)

The evaluation of the output voltage vectors of the three-level autonomous-inverter neutral-point clamped inverter allows us to conclude that the output voltage vectors are formed into three groups with values ${\displaystyle \frac{1}{3}}{U}_{dc}$, ${\displaystyle \frac{\sqrt{3}}{3}}{U}_{dc}$, and ${\displaystyle \frac{2}{3}}{U}_{dc}$. Therefore, a new control algorithm is developed that considers this feature (

Table 5. Voltage switching table with six-position torque regulator.

dΨ	dM	Sector
		I	II	III	IV	V	VI	VII	VIII	IX	X	XI	XII
+1	+3	V15	V21	V16	V22	V17	V23	V18	V24	V19	V25	V14	V20
	+2	V20	V15	V21	V16	V22	V17	V23	V18	V24	V19	V25	V14
	+1	V9	V9	V10	V10	V11	V11	V12	V12	V13	V13	V8	V8
	−1	V6	V6	V1	V1	V2	V2	V3	V3	V4	V4	V5	V5
	−2	V25	V14	V20	V15	V21	V16	V11	V17	V23	V18	V24	V19
	−3	V19	V25	V14	V20	V15	V21	V16	V22	V17	V23	V18	V24
0	+3	V16	V22	V17	V23	V18	V24	V19	V25	V14	V20	V15	V21
	+2	V21	V16	V22	V17	V23	V18	V24	V19	V25	V14	V20	V15
	+1	V10	V10	V11	V11	V12	V12	V13	V13	V8	V8	V9	V9
	−1	V5	V5	V6	V6	V1	V1	V2	V2	V3	V3	V4	V4
	−2	V24	V19	V25	V14	V20	V15	V21	V16	V22	V17	V23	V18
	−3	V18	V24	V19	V25	V14	V20	V15	V21	V16	V22	V17	V23

). The distinction of this table is that it utilizes a six-position relay regulator to detect deviations in torque, with states dM = +3, +2, +1, −1, −2, and −3 (Figure 13).

The novelty of this method lies in two key aspects:

−

Maintaining a constant sensitivity zone (c = const) while increasing the number of torque-regulator positions from three to six (Figure 14 and Figure 15): This approach can be understood as a transition from direct switching between levels from dM = −3 to dM = 0 or from dM = −3 to dM = 3. Instead, the system sequentially moves from dM = −3 to dM = −2 and then to dM = −1 or through stages dM = −3 to dM = −2, dM = −1, dM = 1, dM = 2, and finally dM = 3. This gradual transition creates a short interval that improves motor stability and significantly reduces the required switching frequency for each inverter.

−

Vector selection for levels dM = [3; 2; 1; −1; −2; −3]: The primary goal of this research is to minimize the switching frequency. Thus, the transitional vectors for levels dM = −2, dM = −1, dM = 1, and dM = 2 are chosen to closely approximate the vectors of levels dM = −3 and dM = 3 while satisfying the conditions of Equation (3). For instance, at dM = 3, vector V15 (PPN) is used, at dM = 2, vector V20 (PON) is applied, and at dM = 1, vector V9 (OON) is used. Similarly, at dM = −3, vector V19 (PNP) is applied, while vectors V24 (PNO) and V5 (ONO) are used for levels dM = −2 and dM = −1, respectively.

These innovations contribute to enhanced operational stability, reduced switching frequency, and optimized vector control within the three-level inverter NPC system.

The direct torque-control (DTC) system configuration is based on a three-level inverter NPC with a six-position torque controller consisting of two DC voltage sources with voltage Udc₁ = Udc₂ = 300 V directly connected to two capacitors of the three-level inverter NPC, each with a capacitance of 0.15 F, and an asynchronous motor. The specifications of the asynchronous motor are detailed in

Table A1. Asynchronous motor parameters.

Parameter	Measurement	Value
Nominal power (P0)	kW	15
Nominal voltage (U0)	V	380
Frequency (f)	Hz	50
Stator resistance (Rs)	Ohm	0.12
Stator inductance (Ls)	mH	0.19
Nominal speed (ω0)	rad/s	151
Nominal load (M0)	H.м	100
Asynchronous motor efficiency		0.89
Rotor resistance (Rr)	Ohm	0.4258
Rotor inductance (Lr)	mH	5.3
Mutual inductance (Lm)	mH	51
Moment of inertia (J)	kg·m2	0.4
Number of pole pairs		2

. Other specifications are as follows: a two-position relay controller for stator flux (a′ = 0.02); a three-position relay controller for torque (c = 0.3 and a = 0.1); a six-position relay controller for torque (a = 0.1; b = 0.2 and c = 0.3); and a PI controller (P = 12; I = 17.5). To assess the feasibility of using six-position and three-position torque regulators with a three-level inverter NPC, oscillograms were generated for the following variables:

−

Rotational speed: evaluates the drive’s response to speed control and stability under different torque regulators (Figure 16).

−

Stator flux linkage: monitors the stability and control precision of the flux linkage, impacting motor efficiency and response (Figure 17).

−

Electrical torque: analyzes the torque ripple and control accuracy in response to various load conditions (Figure 18).

−

Stator current and its THD in a steady state: measures the waveform quality and harmonic content, reflecting the effectiveness of each torque regulator (Figure 19).

−

Average switching frequency of the transistors (VT): indicates the switching losses and operational stress on inverter components (Figure 20a).

−

Efficiency of the asynchronous drive: assesses the overall system efficiency, considering losses related to switching and motor operation (Figure 20b).

−

The voltage balance of the input capacitors (Figure 21).

These oscillograms provide insight into the performance and efficiency impacts of both torque regulator configurations when integrated with a three-level inverter NPC. The simulation results are presented in Figure 16, Figure 17, Figure 18, Figure 19, Figure 20 and Figure 21, including the following:

−

From 0.5 s to 2.5 s: increase the motor rotation frequency from 0 to 151 rad/s (nominal speed); from 16 s to 17 s: reduce the motor rotation frequency from 151 to 0 rad/s.

−

From 2.5 s to 4 s, and from 17 s to 19 s: the system works with zero load (Mc = 0 N.m).

−

From 4 s to 7 s: the system works with a load of Mc = 50 N.m; from 7 s to 10 s: Mc = 100 N.m; from 10 s to 13 s: Mc = 150 N.m; from 13 s to 16 s: Mc = 200 N.m.

Conclusions based on research findings for the direct torque-control system using a three-level inverter with a six-position torque controller compared to three-level inverters with three-position torque controllers:

Advantages:

−

The implementation of direct torque control based on a three-level inverter with a six-position torque controller does not degrade the performance of the asynchronous motor across various load conditions (Figure 16).

−

Compared to the standard three-position torque controller, the proposed six-position torque controller algorithm reduces stator flux linkage oscillations (Figure 17), enhancing system stability when load changes occur.

−

The reduction in the current ripple decreases the current distortion factor across various load levels (Figure 19), which in turn reduces the torque ripple (Figure 18). Additionally, lower current distortion significantly enhances the current amplitude.

−

The switching frequency is reduced by ~15% during transient processes and by 1–2% in steady-state operation, which consequently lowers switching losses and reduces transistor operating temperatures (Figure 20a). This reduction in thermal stress contributes to an increased lifespan for the frequency converter.

−

An oscilloscope plot of the efficiency factor (EFF) was generated to evaluate the dynamic performance of the asynchronous drive. The results indicate that the proposed six-position torque controller algorithm improves efficiency by 2% compared to the basic three-position torque controller (Figure 20b).

−

This study focuses on minimizing the switching frequency for inverters, making it essential to maintain balanced voltage levels for stable inverter operation, as an imbalance can lead to increased stress on components (Figure 21).

Disadvantages:

−

The proposed algorithm with a six-position torque controller significantly increases the complexity of control algorithms and the requirements for signal processing.

−

Additionally, the random switching frequency associated with direct torque control complicates optimal filter design for a wide frequency range.

Compared to advanced control methods, such as artificial neural network algorithms, fuzzy logic control, and swarm optimization algorithms, as mentioned previously, the described approach represents a novel control method for motor drives based on the three-level inverter NPC.

To study the impact of random-frequency pulse-width modulation (RFPWM) on the efficiency of automated asynchronous drives, sample measurements were taken from 7.99 s to 8.02 s while the equipment operated under a nominal load (Figure 22).

The results indicate the following:

−

RFPWM disperses harmonic energy across a broader frequency spectrum, reducing peak harmonic amplitudes. Consequently, electromagnetic interference (EMI) is reduced, leading to smoother operation and fewer interruptions in sensitive equipment, which ultimately improves system efficiency.

−

Randomized switching in RFPWM helps decrease the current ripple and torque pulsations. This reduction in fluctuations extends the lifespan of components, contributing to improved operational durability and reliability.

However, it is important to note that these results were obtained using Matlab/Simulink R2023a simulation software under idealized device conditions. Practical testing is necessary to assess the complete operational characteristics of the motor, switching losses, and their impact on the battery life of battery-powered vehicles.

4. Conclusions

The application of pulse-width modulation (PWM) with random switching frequency represents an effective approach to eliminating bursts of higher harmonics in the output voltage spectrum of a three-level neutral-point clamped inverter. This method maintains high controllability for the system while significantly reducing switching losses. Another advantage of using PWM with random frequency is the potential for reducing power losses in frequency converters. In the context of traditional PWM with variable frequency, high switching frequencies can lead to substantial losses associated with the switching of power transistors, which is one of the main drawbacks of this method. In contrast, the use of random switching frequency facilitates a uniform distribution of harmonics, which, in turn, minimizes their negative impact on the quality of the output voltage.

The third part of the article was dedicated to the development of an innovative voltage switching table adapted for controlling asynchronous motor drives. This table is based on the use of a six-position torque regulator. Such an approach significantly enhances the accuracy and stability of control, which is especially relevant under dynamically changing operating loads. A comprehensive evaluation of the proposed control table’s effectiveness under various loads corresponding to the nominal speed of the asynchronous drive was conducted using simulations in the Matlab/Simulink environment. The analysis showed that the developed control table optimizes the interaction between drive components, minimizing current distortions and achieving improved torque-control characteristics. These results underscore the significance and potential of utilizing this methodology in modern control systems for asynchronous motor drives.

Further research could focus on adapting this strategy to various operating conditions, which would enhance the versatility of the method. Additionally, a promising direction is the integration with other automation systems, which may contribute to the creation of more comprehensive and adaptive control systems that fully meet the contemporary demands of industrial production.