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ELSEVIER Procedía Engineering 165 (2016) 1529 - 1535 =

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15th International scientific conference "Underground Urbanisation as a Prerequisite for

Sustainable Development"

PWM algorithms synthesis

Alexander Gulyaev a, Dmitriy Fokin Evgeniy Ten a, Vladislav Vlasyevsky a

aFar Eastern State Transport University, Serysheva str. 47, Khabarovsk, 680021, Russia

Abstract

The paper describes various modified algorithms of classical sinusoidal pulse width modulation (PWM) serving for a three-phase two-level inverter control. The paper presents the results of a research of 3 PWM versions with varying duty cycle parameters and frequency of the pulse signal modulation. The method is to divide the modulated sinusoidal signal cycle (half-cycle) into intervals in order to change the modulation frequency within the separate sectors of forming the quasi-sinusoidal output voltage waves. In addition, algorithmic ways to compensate the additional losses in the inverter and the induction motor at high modulation frequencies of a discrete control signal are investigated and described in the paper. Calculations and simulations are performed by NI Multisim simulation program and NI Lab VIEW visual programming environment. Theoretical studies are performed using the electric drive theories, discrete control systems and spectral analysis. The practical implementation performed by Texas Instruments Stellaris Launchpad using the Energia prototyping platform, field-programmable gate arrays (FPGA) of National Instruments CompactRIO-9074 and NI Single-Board RIO GPIC (sbRIO-9606, NI 9683 (GPIC), LX45 FPGA) using NI LabVIEW software and add-on modules (LabVIEW Real Time, LabVIEW FPGA). The suggested inverter control methods make it possible to reduce the distortion of the output quasi-sinusoidal signal and reduce the power consumption of the DC link while significantly reducing the number of inverter transistor switching in comparison with the classical method without premodulation or technical devices (filter-compensating devices). © 2016PublishedbyElsevierLtd. Thisisanopenaccess article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-reviewunderresponsibility ofthescientific committee ofthe 15th International scientific conference "Underground Urbanisation as a Prerequisite for Sustainable Development

Keywords: induction motor, inverter, PWM, power loss, harmonics, THDi, modulation losses, coefficient of performance (COP), frequency converter, duty cycle.

CrossMar]

* Corresponding author. Tel.: +7-962-501-23-28. E-mail address: dimkof27@mail.ru

1877-7058 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the scientific committee of the 15 th International scientific conference "Underground Urbanisation as a Prerequisite for Sustainable Development doi: 10.1016/j.proeng.2016.11.889

1. Introduction

High harmonics have a negative impact on the induction motor and three-phase power supply system [1]. Currents with frequencies that are multiples of the fundamental frequency of the power supply, are superimposed on the fundamental harmonic. That distorts the voltage shape in the power network. Suppression systems of high harmonic components in the current curve developed from passive filters, filter-compensating devices to the active serial and parallel filters. Despite the high efficiency of the current filters that reduce current distortion 8-10% [1], their use has been hampered due to a number of substantial drawbacks: weight and overall dimensions, operating frequency limit, sensitivity to changes in the form of a harmonic structure and temperature, decrease in performance when nominal values of the electrical network parameters deviate, power transistors high cost. Currently, however, there are technical solutions that provide motor connection without output filters and chokes. For example, low-voltage motor Siemens series N-compact is a special version designed to work directly from the frequency converter. These motors are equipped with reinforced insulation windings and insulated bearings. However, many industries mainly use active filtering methods through PWM voltage inverters. This fact is related to the high cost of special series drives, as well as the spread of the IGBT-modules, the development of digital signal processors and transistor multifunction device management microprocessors systems. The use of active harmonic filters, implemented in frequency converter, is also caused by the successful introduction of variable frequency drive to solve technological problems.

Since the industrial and transport systems commonly use inverters with no special ventilation channels and no continuous mechanical ventilation (particularly necessary for the variable frequency drives using and operating in not nominal conditions at low speeds), it is a promising direction to develop algorithms for converting devices, which allow to eliminate the current shape distortions in the induction motor supply circuit (inverter output).

To increase the use of the DC link they apply method based on the overmodulation [2-4, 5], the third harmonic premodulation [5, 6] and the vector PWM using the two-input comparator or three-level comparator [6, 12, 13, 14]. The main drawback of vector PWM is the impact of the 'dead' time [2, 3, 15], so there are different ways to compensate for it [15-18]. There are different options of the two-phase piecewise sinusoidal PWM to keep the line voltage sinusoidal [19]. To reduce THDi, when the drive is powered by a voltage inverter with the classic sinusoidal PWM, the modulation frequency is increased thereby reducing the losses in the induction motor. However, not any increase of discrete signal frequency leads to a positive effect. Firstly, one of the disadvantages of this method of suppressing the current ripple is the increase in the inverter losses on switching. Secondly, as a result of these losses there is an additional current waveform distortion. Since the greatest duration of the winding connection is provided in the middle of the half-cycle and the pulse duration is small in the beginning and at the end of half-cycle, if the discrete signal frequency is significantly increased, pulse width aim for the pulse part that has been lost during the switching of the transistor (Figure 1). Thereby, the amount of energy spent on switching becomes relatively large per time unit, and the 'useful' pulse width reduces, since the value of burned down during switching pulse is always the same at any level of the reference signal frequency. This is a really important key point in the interaction between the intellectual control part (control system) and the inverter. Currently there are no algorithms for PWM which allow the microprocessor control system to take into account the difference between the pulse generated by the computer system and its real 'useful' duration on the transistor collector. Current form in the motor power network is made up of exponents fragments and becomes quasi-sinusoidal. But modulated by the control system algorithm the signal does not correspond to the real pulse sequence at the output of frequency converter due to distortions introduced by transistors switching losses at high switching frequency. This is due to mismatch of exponents fragments form of theoretical construction and implementation as the pulse width decreases because of the transition to comparable values area of the of the transistor switch-on duration and the process duration at high modulation frequencies. Used today PWM methods don't provide correction algorithms for generated pulse signal to compensate for the partial pulse loss when switching by recalculating the transistors switching-on duration at high modulation frequencies.

Fig. 1. Visualization of shape distortion process due to switching with modulation frequency increasing.

The sinusoidal form [6, 20-22] and the symmetry of the three-phase currents are the main indicators in assessing the electric power quality. When the induction motor is powered by a frequency converter there are no problems with the currents symmetry as opposed to the currents shape distortion. At high frequencies, the additional switching losses in the inverter also cause the sinusoidal form distortion of the quasi-sinusoidal signal at the beginning and the end of half-cycle (in the range of 60 electrical degrees) due to the small pulse width/duration. The high frequency pulse generating is only required in the maximum values of the sinusoidal modulating signal (approximately corresponds to the value greater than 0.7 when y = sin x and y is in the range [-1, 1]). At the beginning and at the end of half cycle for small values of the sinusoidal modulation function due to the imperfection of the inverter key elements (the transistors opening/closing delays, the variation in characteristics of the different transistors in the circuit, the variable/nondeterministic current rate of rise in the switched circuit, etc.) high frequency pulse signals create greater distortion of the sinusoidal inverter output signal in comparison with a low frequency digital signal for given modulation sectors. Thereby the increase of the modulation frequency in frequency converters, not only leads to additional losses at switching, but also to distortion of the sinusoidal signal form, so that frequency modulation in the range from 1,500 to 15,000 Hz is used for different applications of the frequency converter.

Figure 2 shows the THDi coefficient range of values for the various switching frequency of inverter power components in the range from 1500 to 15,000 Hz. You can see that an increase in the pulse frequency can lead to a significant increase in the THDi coefficient. Therefore, increasing the modulation frequency should be carried out in accordance with the implementing regulation PWM algorithm. In order to compensate for the amplitude increase of higher harmonics and harmonic multiples of three (3rd, 9th, 15th, etc.) modulated signal frequency has to be an odd multiple of the modulating pulse signal frequency [9]. This means that the modulation frequency is a critical parameter for the PWM algorithm implementation and must be variable and adapted to various conditions when modulating sinusoidal signal. The parameters of existing frequency converters don't allow to adjust the modulation frequency for different sectors of the modulating function period (half-cycle). Currently the frequency of the generated pulse sequence is a constant for all inverter control systems.

In the papers [7, 8, 10, 11] they describe the algorithms that allow to reduce significantly the current sine wave distortion of the induction motor stator when working with voltage inverter and to use the power supply system of the induction motor on the frequency inverter without additional smoothing filters. In the papers [7, 8, 10, 11] they investigate an algorithm characterized by the absence of the sawtooth reference signal, used in the classical sinusoidal PWM methods. In this case, the creation of the sinusoidal current in the power network of the induction motor is carried out by an auxiliary signal which is a copy of the modulating signal, but with a smaller amplitude. Modulating sinusoidal function is defined as follows [9]

UM = UmsinwMt (1)

Since the auxiliary signal is given the same function as the modulating signal then the PWM of the inverter

output voltage is also carried out according to a sinusoidal principle. The values of the function are submitted directly to the generator of the discrete pulses sequence for determining the duty cycle (Figure 3) [11]. THD i coefficient for this method is shown in Figure 2 (method 1). This algorithm has been implemented on a fast FPGA system. By changing the method for determining the duty cycle of the discrete inverter control signal, the algorithm can create quasi-sinusoidal network current with improved distortion factor.

Classical

Multiples —Nonmultiples

♦ Method 1

Method 2

# Method 2 average frequency

_ Power

(Classical)

y- 5E-08xJ 0,0011m 19,544

- Power

(Method 2 average frequency)

y = SEO&K- 0.0014*+ 19.582

Fig. 2. THDi coefficient for different modulation methods in the frequency range from 1,500 to 15,000 Hz.

In the paper [8] they also consider a modified sinusoidal PWM method in which the reference signal frequency changes stepwise two times at equal 60 degrees intervals in a half-cycle. The idea of forming the inverter control signal by the pulse system is to divide the half-cycle of the modulating function into 3 sectors. The modulation frequency at the beginning and the end of half-cycle is less than the middle 60 degrees sector. THDi factor for this method is shown in Figure 2 ("Method 2" - the figure shows coefficients values for the maximum frequency values, "Method 2 average frequency" - the average rate for the cycle/half-cycle). Analyzing Figure 2 you can see that the application of the algorithm for inverter control allows you to change the points area of THDi coefficient values. The power function is plotted using MS Excel software tools for the values group of classical PWM method and the modified two-step (with a change of the reference signal frequency / bilevel sawtooth ) method. Trendlines show an offset of the THDi coefficient values to lower values for the two-level PWM method compared to the classical algorithm. This approach to the inverter control allows you to simultaneously reduce the THDi coefficient and the number of transistors switching during the half-cycle by reducing the modulation frequency in 2/3 the switching period. This helps to minimize power loss in the inverter as well as in the induction motor, which has a positive effect on the efficiency of the plant "inverter - induction motor". This algorithm can be applied in low power and inexpensive computer systems such as microcontrollers. The number of frequency change sectors may be increased, but this requires expensive high-speed powerful computing systems. This is due to the switching between

frequencies at the intervals boundaries may also bring additional distortions in the signal, especially when using microcontrollers without parallelization function of computing operations. The reference signal function can be set by the system of equations:

Uy < a1, Aop arcsiwï'Çsi Uy < a2, Aop arcsiri

Uy < at, Aoparcsiv)J^t > at+1, Aop arcsMiÇi

opwd t)) oPwc2t))

opWcjt)) W, 1))

opwj +11

where i, j are the number of frequency change ranges of the reference signal, a is the modulating function value at the transition point between the sectors.

This paper consider the algorithm study results of pulse signal modulation of the inverter transistor switches control, which is a synthesis of two modified versions of the above-described PWM [7, 8]. Analytical expression of this modulation method is also a system of equations like in "method 2", but the sinusoidal auxiliary signal of "method 1" is used instead of the reference sawtooth or triangular shape signal. The control signal is set as follows:

y _ < y' Ua = UBSi™t, HPK fgi =

a ~ \uB > y, ua = UBsinœt, npH f6

where UB is the value of the auxiliary signal function; y is the value of the modulation function at the transition point between the sectors; n, m - are the values of frequencies of the extreme and medium sectors, respectively; /rH is the frequency of the pulse signal generator. Figure 3 is a functional diagram of the inverter control system.

Fig. 3. Functional diagram of inverter control system with the control signals of frequency and duty cycle.

The proposed algorithm ("method 3") reduces the stator current distortion of the induction motor as compared to the classical PWM method or to the modified methods described above. The comparison of the different algorithms results was performed for the entire frequency range from 1,500 to 15,000 Hz in various combinations of two-level algorithms. Table 1 shows the best results in harmonic distortion coefficient, since this parameter is the main criterion for assessing the efficiency of the frequency converter [6, 20-22].

Table 1. Comparison of dual-frequency PWM methods.

Frequency at the beginning

and the end

of the half-cycle, Hz

The frequency in the middle of the half-cycle, Hz

Method 2, %

Method 3, %

consumption Method 2, W

consumption Method 3, W

2000 4000 4000 2500

4000 6000 10000 4000

9.9 8.17 8.7 16

11.8 9.28 12 10.5

36150 33730 32460 30520

35355 33600 33233 30598

2500 5000 10.2 7.07 32000 30780

2000 6000 8.9 13 34420 34455

3000 5000 9.3 6.98 35400 33440

2000 5000 9.96 - 36600 -

2000 3000 8.6 12.9 35360 35570

6000 10000 7.47 - 33928 -

5000 10000 8.1 12.3 32850 30671

2500 3000 - 75 - 29675

2500 10000 - 16.5 - 30600

In this paper 3 different modified method of classical PWM are given. All of these methods can reduce the THDi coefficient in the stator winding of the motor, ensure rational energy consumption by plant "inverter - induction motor", increase the energy efficiency of the frequency converter, improve the plant "inverter - induction motor" efficiency. The suggested algorithms are easy to implement and can be implemented on different hardware platforms with different performance and of different cost, for any voltage inverters with different number of D.C. convert levels and the phases number. For example, this approach can be an alternative to the vector PWM based on a three-phase three-level inverter [23-37]. The positive effect is achieved without increasing the modulation coefficient and without the use of premodulation algorithms by the third harmonic, etc. The synthesis of "Method 1" and "Method 2" ("Method 3") makes it possible to get the algorithm which provides a power plant efficiency increase by 9% compared to "Method 2" and by 20% compared to the classical sinusoidal PWM algorithm. Simultaneous regulation of the pulses duty cycle and repetition frequency in the modulating signal of the inverter control has a positive impact on the energy performance of both the inverter and the motor.

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