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SIGNAL PROCESSOR CONTROLLER FOR A THREE-PHASE PWM INVERTER°
Copyright © IFAC Control in Power Electronics and Electrical Drives, Lausanne, Switzerland, 1983
SIGNAL PROCESSOR CONTROLLER FOR A THREE-PHASE PWM INVERTER0 G. S. Buja and W. Zoccarato Istituto di Elettrotecnica
e di Elettronica,
Universitä di Padova, Padova, Italy
Abstract. A new approach to realizing a controller for a subharmonic pulse width modulation (PWM) three-phase inverter is presented, based on the use of a signal processor as a control unit. The approach has the merits of simplifying the implementation of high-quality, three-phase modulation techniques, combining almost all the advantages of the analog approach with the microcomputer, and reducing to a minimum the hardware. All these merits have been experimented by designing, building, and testing an Intel 2920-based controller for an application of interest. The hardware structure of the controller, the procedure of developing its software and the results of the most significant tests are provided. Keywords. Analog microcomputer applications; controllers; control; power inverter control; pulse width modulation.
industrial
INTRODUCTION Among the latest advances in LSI devices are the signal processors which can be considered as special-purpose microcomputers designed especially for digital signal processing. Unlike the conventional microcomputers developed for data rather than signal processing, the signal processors are able to create, alter or detect signals at high speed. As a result, digital, programmable devices with effective real-time signal processing capabilities are ready to be utilized in the control systems of many industrial plants.
Intel 2920, a three-phase, desiderably featured PWM technique, used to control a variable-voltage, fixed-frequency inverter. The utmost simplicity of the hardware of the controller is emphasized and the new fashion of arranging its software is detailed. Some experimental results obtained from the controller with various values of the voltage command are also given.
BASIC REVIEW Subharmonic PWM techniques
In the field of power converters, which is of interest to the authors, a signal processor has already been introduced in the control of a single-phase PWM inverter by Buja and De Nardi (1981). This paper intends to extend the argument, exploring the possibilities offered by these devices in three-phase PWM inverter applications. Inverters modulated with the subharmonic techniques are concerned, as these techniques accomplish the modulation by processing analog signals and therefore are suited to be implemented in a signal processor.
Pulse width modulation is a well-established method of controlling the amplitude and the frequency, and improving the waveform of the basic square-wave voltage at the output of an inverter operating from a fixed-dc supply. The means most used for accomplishing such a modulation are the subharmonic techniques because they afford an easy solution to the problem of synthesizing the widths of the pulses at the inverter output. According to these techniques, the widths result from an electronic comparison of properly shaped and controlled analog signals. Undoubtely, the sinusoidal subharmonic PWM technique proposed by Schönung and Stemmler (1964) is the most direct in conception, whereby a triangular carrier of fixed frequency and amplitude is compared with a sinusoidal reference of frequency and amplitude less than the triangle. Both objectives of a modulation are thus achieved, as the inverter output contains a predominant component of sinusoidal waveform, and the
The contents of the paper is organized as follows. After a review of the subharmonic PWM techniques and the existing controllers, general considerations about the convenience of a signal processor approach are presented. The approach is then illustrated by implementing in one such processor °This work was supported by Contract 12.2.2, from Ministry of Education of Italy.
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amplitude and the frequency of this sine, termed fundamental harmonics, are determined by the reference. Fig. 1. illustrates this PWM technique for a single-phase, half-bridge inverter. Desiderable features for the PWM voltage, v , so obtained are 1? linear relationship between the amplitude of t*he reference and the fundamental harmonics of v , 2) no subharmonics, i. e. harmonics of frequency lower than the fundamental, 3) no harmonics of significant amplitude in a certain frequency band having the fundamental as lower limit.
Fig. 1. Sinusoidal subharmonic modulation technique. Feature 1) is useful in providing a direct control from the reference of the amplitude of the fundamental harmonics of v , in addition to that of frequency. Features 2) and 3) serve to generate a PWM waveform faithfully reproducing the sine even upon rough, low-pass filtering. The spectral analysis of v carried out by Schönung and Stemmler (1964; shows that the features 1 ) , 2) and 3) are satisfied by selecting the carrier to reference frequency ratio, respectively a) greater than 7, b) odd integer, c) as high as possible. Point a) gives feature 1) an accuracy better than 0.5%. Point b) assures the rigorous fulfilment of feature 2) . The condition of odd ratio provides to eliminate the dc harmonics from v ; furthermore it yields to the elimination of all the even harmonics Actually, point b) may be ignored for a frequency ratio greater than 11, whereby the subharmonics are so small in amplitude not to affect any load. Point c) aims at enlarging the frequency band defined in 3) . This result is a theoretical finding; in practice, inverter losses due to the inverter current commutations, working frequency of the turnoff circuits, and, mainly, turnoff time of the inverter devices restrain the possible ratio. According to
whether the inverter devices are thyristors or transistors, this ratio is about 9 or 20 and more, respectively, with a fundamental frequency of 50 Hz. When the frequency ratio is integer, that is the triangle is synchronous with the sine, it is usual to set to zero the time-phase displacement between the signals, as shown in Fig. 1. Features 1 ) , 2) and 3) are desiderable for the phase-to-phase voltages of a three-phase PWM inverter as well. As in the standard three-phase, half-bridge configuration these voltages result from the difference between two different phase voltages waveshaped as in Fig. 1., points a ) , b) and c) are again valid in satisfying the above features. Furthermore, one can utilize this difference to improve the quality of the phase-to-phase voltages. This can be achieved by satisfying the following feature, special for a three-phase system: d) in phase of some harmonics of the same order belonging to different phase voltages. Feature d) intends the suppression of certain harmonics from the phase-to-phase voltages. A performance analysis of these voltages as obtained from a three-phase system of sinusoidal references and various terns of triangular carriers (Buja and Indri, 1976) has shown that very good results are attained by selecting 4) the same carrier for all the three phases and the frequency ratio integer multiple of 3. Point 4) implies that all the harmonics of frequency equal to or integer multiple of that of the carrier disappear from the phase-to-phase voltages. As these harmonics are the highest in amplitude in the phase voltages, the benefit produced by 4) in a three-phase system is consistent. Furthermore the use of only one carrier for modulating the references greatly simplifies the circuital implementation of the control. PWM inverter controllers In general a three-phase PWM inverter controller has two inputs and three outputs. The inputs command the amplitude and the frequency of the sinusoidal references. The output is the three-phase system of PWM signals used to activate the trigger circuits of the inverter devices. As the waveform of these signals is a low-power copy of the phase voltages of the inverter, their characteristics determine the inverter performance. The early PWM inverter controllers were entirely analog (Parasuram and Ramaswami, 1976). The advantage of these controllers is the excellent control performance, i.e. the continuous-amplitude control of the fundamental harmonics of the PWM signals and the very quick response to commands aimed to vary the reference. The disadvantages are that they need a large
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Signal Processor Controller
number of components, are not flexible and have a moderate electrical performance. This latter disadvantage is due to the degradation over time, temperature and noise of the analog components. A step in improving flexibility and electrical performance of the PWM inverter controllers is represented by the combined use of analog and conventional digital circuits (Grant and Barton, 1978). These controllers maintain excellent control performance, but appear to be involved and expensive. Top flexibility and electrical performance are gained with a microcomputer, but to the detriment of the control performance. The reason for this disadvantage is that a microcomputer is too slow to accomodate on-line processing of the signals involved in the control of a PWM inverter so that the only useable solution is data processing, the data being the pulse widths. The most straightforward implementation consists of storing the widths in the ROM memory of the controller and requiring of the microcomputer the timing of one of the PWM signals only. Bulky circuitry external to the microcomputer provides then to generate the other two PWM signals and carry out the frequency change (Brickwedde and others, 1981). Such an implementation gives the controller a negligible throughput delay, but makes the control of the fundamental harmonics with a reasonable amount of ROM memory practicable over a limited number of levels. Moreover, the hardware of the controller is very complex, including many devices in addition to the microcomputer. As an alternative to this implementation Bolognani and others (1983) have proposed a microcomputer-suited method to derive on-line both the widths and the three PWM signals for the actual amplitude and frequency commands. This method has been proved to be effective in avoiding the control and hardware drawback of the previous controller, but, in spite of its power, produces a throughput delay not acceptable in all the applications.
But the novel feature of a signal processor is the possibility of demanding of it the real time control of a PWM inverter by means of an on-line generation and comparison of reference and carrier signals as in an analog system. Giving up data in favour of high-speed signal processing is the key for improving the control performance of the conventional microcomputer controllers. The result, of course, will not be as good as in an analog controller because the support of the control remains a digital device, operating on a programmed basis.This calls inevitably for a sample data representation of the control signals, thus reproducing undesired effects on the control performance. Mainly due to the amplitude quantization of the references, the fundamental harmonics of the PWM signals is controlled again in a discrete range. The time quantization of the control signals, on the other hand, causes a delay in up-dating the output. As a signal processor keeps all these effects at a low level, the resulting control performance is very satisfactory. Last but not least merit following from a signal processor concerns the simplification of the hardware of the controller. Reduction of ROM memory and capability of processing a three-phase system of signals without needing external circuitry are the grounds for this merit. Intel 2920 signal processor The signal processor which will be used in this paper is the Intel 2920 (Intel Corporation, 1980). In comparison with the other available signal processors, the 2920 exhibits the extra feature of containing in a single chip the arithmetic-logic unit (ALU), ROM and RAM memory, and A/D, D/A, and I/O circuitry for inputting and outputting of analog signals. This makes the 2920 more than a digital signal processor, but a complete sampled data system adapted to the control of an analog plant. The hardware architecture depicted in Fig. 2. The
SIGNAL PROCESSOR APPROACH Using a signal processor for realizing a controller for a three-phase PWM inverter is attractive for a lot of reasons. Foremost, the microcomputer structure of a signal processor gives the controller the well-known merits peculiar to a digital, logic-programmed approach. Stability, reliability, predictability, and reproducibility of the electrical performance are inherent to the digital approach. Easy development, debug and modification of the controller are a conseguence of the software implementation of the control activities.
of the 2920 is analog circuitry
EPROMI
JE
21
31 ALU
MUXWHlf^A/Db^ ++
RAM
Ηΐ 0 / Α
Fig. 2. Block diagram of the 2920. includes 4 channels and multiplexer (MUX) at the input, and demultiplexer (DMUX) and 8 channels at the output for multivariable operation. The A/D and D/A converters have
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up to 9 bits of resolution (1 sign bit, 8 bits). The digital circuitry amplitude consists of an EPROM (or ROM) arranged in 192 words, each word corresponding to one instruction, and a RAM organized as 40 words of 25 bits each. Any variable in RAM has the binary point just to the right of the sign bit so that its range is between -1 and 1. The software of the 2920 is also specific. Each instruction is divided into two main fields, one directs the analog functions, the other the digital. Among the analog functions are selection of the input, A/D conversion, signal outputting, and selection of the output. Among the digital functions are addition, subtraction,scaling, limitation, absolute value, and OR. Conditional digital functions take both the analog and the digital field. The instruction set would appear to be limited and restrictive, especially for the digital functions. Nevertheless a judicious manipulation of the set and the parallel execution of one analog function with two digital functions, one of these having to be scaling, permits the implementation of fairly complex signal processing. The program is repeated indefinetively, a jump from the end of the program back to the beginning occurring automatically. One loop of program, termed program pass, is of fixed execution time since no internal program branches are provided. As the cycle period is the same for all the instructions (600 ns for the EPROM version), the execution time of the programm pass is the cycle period times the number of instructions. With a maximum program length of 192 instructions, this time is of 115.2 ys and coincides with the sampling period of a signal when a single sample is processed per program pass. The sampling rate can be increased by writing a shorter program or using multiple samples per program pass. The 2920 is supported by software packages useful in developing a program. The simulator is expecially of great help for a designer allowing the test of the implemented control entirely in software, without resorting to a hardwired prototype.
THREE-PHASE PWM INVERTER CONTROLLER A controller for a variable-voltage, 50Hz-frequency, three-phase PWM inverter based on the 2920 EPROM version is now presented. The voltage being the only command, the controller will have one input. The synchronous sinusoidal modulation with a frequency ratio of 9 is selected for implementation. As results from the above considerations, this modulation is highly recommendable for a three-phase PWM inverter employing thyristor devices.
Controller operation Under control of the program stored in ROM, the 2920 generates a three-phase system of sinusoidal references, r , r, , and r , and one triangular carrier, c, internally. The frequency of the references and the carrier are 50 and 450Hz., respectively, while the amplitude of all the signals is 1. The time-phase displacement between the triangle and one of the references is forced to zero. Given that the frequency ratio is an integer multiple of 3, the other two displacements are also zero. Moreover, the control program provides acquisition and conversion of the input, multiplication by the references and comparison of the result with the carrier. A three-phase system of PWM signals, v , v, , and v , is so obtained, with the fundamental harmonics of required amplitude . Outputting of the PWM signals closes the controller operation. Controller hardware The hardware structure of the controller is illustrated in Fig. 3. Its drastic
1 POWER
SUPPLY
REGULATOR Vr 2920
I- I I -
CLOCK
c
Fig. 3. Schematic of the hardware of the three-phase PWM inverter controller. simplicity is evident: besides the 2920, a sample capacitor, C, a reference voltage for the A/D and D/A conversion, V ,and a clock for timing purposes are the only requirements of the controller. The range of the input, v., is between 0 and V , while the outputs switch between -kV and kV , where k is the output gain of the 2920. In general, the reference voltage and the clock must be precise and stable to prevent inaccurate operation of the 2920. The case under consideration, however, is somewhat different. As the outputs are on-off signals, the reference voltage has no influence in determining the output accuracy. For the input, instead, this may be not true. Nevertheless, when v. is obtained from a potentiometer fed by the same reference voltage used for the controller, the converted input does not suffer inaccuracy and instability of V . As
Signal Processor Controller
a result, only the clock must be precise and stable, its variations affecting the accuracy on the frequency of the PWM signals. SOFTWARE DEVELOPMENT The functional analysis of the controller operation performed above is the starting-point for developing the software. Each function singled out in the analysis must now be translated into an algorithm executable by the 2920. Putting the algorithms in a proper sequence produces the required control program. Note the conceptual similarity of this procedure with the analog approach, whereby the difference is in the support of the functions which is software in the case under consideration, and hardware in the analog case. The algorithm for obtaining the three-phase system of sinusoidal refences begins with the generation of a 50 Hz sawtooth oscillator. The sawtooth is then processed by a waveform shaper, for instance a filter, to be trasformed in a sine of amplitude 1. This sine is r . Afterwards, r is shifted by ð/2, resulting in a cosine. Using the familiar relationship sin(x - 2TT/3) - 0.866cosx - 0.5sinx (1) r, is achieved, r
follows directly from
The sawtooth oscillator is generated by subtracting a constant, C , from a register at each programm pass, and adding 1 to this register everytime its contents becomes less than zero. By indicating the sampling period of the sawtooth with T , C has to be sr r selected according to C
- 50 T (3) r sr in order that the sawtooth frequency is 50 Hz. The absolute error on the sawtooth period is one half T , yielding to a percent accuracy on the sawtooth frequency and therefore on that of the references less than T å - 50 -ψ-
100
(4)
The algorithm for obtaining the triangular carrier recalls that used for the sawtooth. A constant, C , is added to a register at each program pass, shaping the ascending edge of the triangle. As soon as the register gets over 1, C is no longer added but subtracted from register, thus shaping the discending edge. When the register gets over -1, the cycle begins again. Being that the carrier frequency must
465
be 450 Hz, C C c where T carrier.
is given by
= 450 T sc is the sampling
(5) period
of the
The algorithm for synchronizing the carrier with one of the references operates by writing zero in the carrier register when the reference is zero. The synchronization of the two signals, imperative at the power-on, is also useful from this time on to prevent a possible lack of synchronization arising from the finite length implementation of the constants C and C . Further algorithms are then arranged for performing the remaining functions required by the controller. Before presenting the entire control program, some considerations on the accuracy of the PWM signals outputted by the controller become necessary. The 2920-innerly generated references have a resolution of up to 24 bits. After multiplication by the input, their resolution goes down to 8 bits, resulting in an accuracy of about 0.4%. Without time quantization, an accuracy of the same magnitude would be induced on the fundamental harmonics of the PWM signals. Unfortunately the time quantization worsens this result, as it gives rise to a non constant delay between each of the switchings of the actual PWM signals and the theoretical ones. Though these delays go from 0 to a maximum which does not exceed the sampling period of the PWM signals, T , the concurrent action of all the delays may alter the amplitude control accuracy appreciably. The effect depends on the two following variables: the term f T , where f is the triangle frequency, and the amplitude of the references. Intuitively, the greater f T and the smaller the amplitude, the greater is the effect. As a conclusion, it is convenient to keep T as short as possible from the point of viiw of the amplitude control accuracy. The flow-chart of the control program is illustrated in Fig. 4. Its stucture is aimed at reducing T . The aspects of the program devoted to end are i) two samplings of the PWM signals for program pass, but one creation of the constants, one synchronization, and one acquisition of the input, ii) alternating at the filtering the computation of the references by interpolation, this latter requiring less instructions, iii)deriving of r after multiplying r and r, by the input, when filtering is used. The program is 132 instructions in length and takes 79.2 ys to be executed. This time, indicated in the following with T , coincides with the sampling period of tne
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G. S. Buja and W. Zoccarato
references. Its substitution in (3) gives the constant C to be implemented for generating the references, while its substitution in (4) shows that the frequency accuracy is less than 0.2%. The sampling period of the carrier, instead, is one half T . Using this value in (5) yields to C . Tße sampling period of the PWM signals is
\ GENERATE r a
1
BY FILTERING
i
GENERATE r b
1 1
BY FILTERING
|
/
°"Pt1 va,vb,vc
1
r b WITH vi
* DERIVE r
♦ c
EXPERIMENTAL RESULTS After the controller has been built in accordance with the hardware and software structures presented above, its operation has been evaluated under various conditions. Foremost the harmonic contents of the three-phase system of PWM signals outputted by the controller have been measured by a
♦
MULTIPLY r a AND
GENERATE
From the design also emerges the limitation of the approach. When one desires to implement a high frequency carrier, he must reckon with the amplitude control accuracy. a worse accuracy or Only accepting restricting the range of accurate control, the carrier frequency may be increased. Indicatively, under the same T and accuracy of the application above, a carrier frequency of 900 Hz restricts the range at about 0.6 times the maximum.
|
ß
SYNCHRONIZE c WITH r 0
i
t GENERATE v a, v b, v c
♦
GENERATE r a, r b
1 I 1
' /
OUTPUT va,vb,vc
/
BY INTERPOLATION
* DERIVE r c
♦ GENERATE c
♦
1
GENERATE v a, v b, v c
' /ACQUIRE AND CONVERT vi
I
♦ CREATE CONSTANTS
Fig. 4. Flow-chart of controller.
the software of the
one half T as well. By introducing these data in a spectral analysis simulated on a digital computer an accuracy on the fundamental harmonics is predicted within 1%, provided this harmonics ranges from 0.4 times the maximum to the maximum. The analysis has also shown that the accuracy approaches the value of 0.4% induced by the references, as the fundamental harmonics nears the maximum. With regard to the throughput delay, it is a little less than twice T , the highest value occuring when the command is changed an instant after the 2920 has acquired the input. The control performance so obtained is very satisfactory and represents a first, designed-based confirmation of the advantages of the signal processor approach.
b) Fig. 5. Waveform a) and spectrum b) of the PWM signals with v.=0.8V . The controller under test has R=0.866 and V =1.5V. Time scale and amplitude scale of Fig. a) are: 5 ms/div; 1 V/div. Frequency scale and amplitude scale of Fig. b) are: 200 Hz/div; 200 mV/div.
Signal Processor Controller
spectrum analyzer with v. ranging from 0.4V to V . As an example, two of the outputs ana the spectrum of one of these signals with v. equal to 0.8V are shown in Fig. 5. The measures of the fundamental harmonics and the two most important harmonics introduced by the carrier are collected in Fig. 6 a) and b ) . The continuous lines show the behaviours gained from the theory. Fig. 6.a) indicates that the input-output linearity is well within 1% of full scale. Fig. 6.b) affirms the subharmonic nature of the PWM signals. Neither subharmonics nor harmonics of significant amplitude have been found apart from those predicted by the theory. The throughput delay has also been tested and the worst-case result is of about 140 ys as it was expected. Lastly, no frequency instability has been experimented unless in the relation with the clock.
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CONCLUSIONS Recent advances in integrated circuits have made it possible to develop PWM inverter controllers which meet objectives not obtainable previously. A new device, the signal processor, has proved to be effective in setting up a controller for a variable-voltage, fixed-frequency, three-phase PWM inverter with overall performance far superior to the existing controllers. The principle of the controller is simple, the hardware consisting of a handful of components, the software imitating the analog system on digital basis. The signal processor approach appears also to be sucessful in developing controllers for PWM inverters operating at variable frequency or in closed-loop schemes. Besides the merits, this approach exhibits a limit. As pointed out in the paper, the maximum carrier frequency implementable in a signal processor with a satisfactory amplitude control performance is about 900 Hz. This limit, however, restricts very little the area of the potential applications which includes all the thyristor and the low- and medium-speed transistor inverters.
REFERENCES
Fig. 6.
50, 350 and 450 Hz harmonics at the output of the controller as a function of the input.
Bolognani,S., G.S.Buja, and D.Longo (1983). Hardware and performance-effective microcomputer control of a three-phase PWM inverter. Proc. of 1983 International Power Electronics Conference, (in press). Brickwedde,A., D.Hean, and H.Graham (1981). Microprocessor controlled 50KVA PWM inverter motor drive. Proc. of 1981 IEEE Ind. Appl. Society Annual Meeting, pp. 666-670. Buja,G.S., and G.Indri (1975) Improvment of pulse width modulation techniques. Archiv für Elektrotechnik, 57, 281-289. Grant,T.L., and T.H.Barton (1978). A highly flexible controller for a pulse width modulation inverter. Proc. of 1978 IEEE Ind.Appl. Society Annnual Meeting, pp. 486-492. Intel Corporation (1980). The 2920 analog signal processor design handbook. Santa Clara. Parasuram,M.K., and B.Ramaswami (1976). A three-phase generator for thyristorized motor controllers. IEEE Trans. Ind. Electron. & Control Instrum., 23, 270-276. Schönung,A., and H.Stemmler (1964). Static frequency changers with subharmonic control in conjunction with reversible variable speed a.c. drives. Brown Boveri Review, 3, 666-673.
SIGNAL PROCESSOR CONTROLLER FOR A THREE-PHASE PWM INVERTER0 G. S. Buja and W. Zoccarato Istituto di Elettrotecnica
e di Elettronica,
Universitä di Padova, Padova, Italy
Abstract. A new approach to realizing a controller for a subharmonic pulse width modulation (PWM) three-phase inverter is presented, based on the use of a signal processor as a control unit. The approach has the merits of simplifying the implementation of high-quality, three-phase modulation techniques, combining almost all the advantages of the analog approach with the microcomputer, and reducing to a minimum the hardware. All these merits have been experimented by designing, building, and testing an Intel 2920-based controller for an application of interest. The hardware structure of the controller, the procedure of developing its software and the results of the most significant tests are provided. Keywords. Analog microcomputer applications; controllers; control; power inverter control; pulse width modulation.
industrial
INTRODUCTION Among the latest advances in LSI devices are the signal processors which can be considered as special-purpose microcomputers designed especially for digital signal processing. Unlike the conventional microcomputers developed for data rather than signal processing, the signal processors are able to create, alter or detect signals at high speed. As a result, digital, programmable devices with effective real-time signal processing capabilities are ready to be utilized in the control systems of many industrial plants.
Intel 2920, a three-phase, desiderably featured PWM technique, used to control a variable-voltage, fixed-frequency inverter. The utmost simplicity of the hardware of the controller is emphasized and the new fashion of arranging its software is detailed. Some experimental results obtained from the controller with various values of the voltage command are also given.
BASIC REVIEW Subharmonic PWM techniques
In the field of power converters, which is of interest to the authors, a signal processor has already been introduced in the control of a single-phase PWM inverter by Buja and De Nardi (1981). This paper intends to extend the argument, exploring the possibilities offered by these devices in three-phase PWM inverter applications. Inverters modulated with the subharmonic techniques are concerned, as these techniques accomplish the modulation by processing analog signals and therefore are suited to be implemented in a signal processor.
Pulse width modulation is a well-established method of controlling the amplitude and the frequency, and improving the waveform of the basic square-wave voltage at the output of an inverter operating from a fixed-dc supply. The means most used for accomplishing such a modulation are the subharmonic techniques because they afford an easy solution to the problem of synthesizing the widths of the pulses at the inverter output. According to these techniques, the widths result from an electronic comparison of properly shaped and controlled analog signals. Undoubtely, the sinusoidal subharmonic PWM technique proposed by Schönung and Stemmler (1964) is the most direct in conception, whereby a triangular carrier of fixed frequency and amplitude is compared with a sinusoidal reference of frequency and amplitude less than the triangle. Both objectives of a modulation are thus achieved, as the inverter output contains a predominant component of sinusoidal waveform, and the
The contents of the paper is organized as follows. After a review of the subharmonic PWM techniques and the existing controllers, general considerations about the convenience of a signal processor approach are presented. The approach is then illustrated by implementing in one such processor °This work was supported by Contract 12.2.2, from Ministry of Education of Italy.
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G. S. Buja and W. Zoccarato
amplitude and the frequency of this sine, termed fundamental harmonics, are determined by the reference. Fig. 1. illustrates this PWM technique for a single-phase, half-bridge inverter. Desiderable features for the PWM voltage, v , so obtained are 1? linear relationship between the amplitude of t*he reference and the fundamental harmonics of v , 2) no subharmonics, i. e. harmonics of frequency lower than the fundamental, 3) no harmonics of significant amplitude in a certain frequency band having the fundamental as lower limit.
Fig. 1. Sinusoidal subharmonic modulation technique. Feature 1) is useful in providing a direct control from the reference of the amplitude of the fundamental harmonics of v , in addition to that of frequency. Features 2) and 3) serve to generate a PWM waveform faithfully reproducing the sine even upon rough, low-pass filtering. The spectral analysis of v carried out by Schönung and Stemmler (1964; shows that the features 1 ) , 2) and 3) are satisfied by selecting the carrier to reference frequency ratio, respectively a) greater than 7, b) odd integer, c) as high as possible. Point a) gives feature 1) an accuracy better than 0.5%. Point b) assures the rigorous fulfilment of feature 2) . The condition of odd ratio provides to eliminate the dc harmonics from v ; furthermore it yields to the elimination of all the even harmonics Actually, point b) may be ignored for a frequency ratio greater than 11, whereby the subharmonics are so small in amplitude not to affect any load. Point c) aims at enlarging the frequency band defined in 3) . This result is a theoretical finding; in practice, inverter losses due to the inverter current commutations, working frequency of the turnoff circuits, and, mainly, turnoff time of the inverter devices restrain the possible ratio. According to
whether the inverter devices are thyristors or transistors, this ratio is about 9 or 20 and more, respectively, with a fundamental frequency of 50 Hz. When the frequency ratio is integer, that is the triangle is synchronous with the sine, it is usual to set to zero the time-phase displacement between the signals, as shown in Fig. 1. Features 1 ) , 2) and 3) are desiderable for the phase-to-phase voltages of a three-phase PWM inverter as well. As in the standard three-phase, half-bridge configuration these voltages result from the difference between two different phase voltages waveshaped as in Fig. 1., points a ) , b) and c) are again valid in satisfying the above features. Furthermore, one can utilize this difference to improve the quality of the phase-to-phase voltages. This can be achieved by satisfying the following feature, special for a three-phase system: d) in phase of some harmonics of the same order belonging to different phase voltages. Feature d) intends the suppression of certain harmonics from the phase-to-phase voltages. A performance analysis of these voltages as obtained from a three-phase system of sinusoidal references and various terns of triangular carriers (Buja and Indri, 1976) has shown that very good results are attained by selecting 4) the same carrier for all the three phases and the frequency ratio integer multiple of 3. Point 4) implies that all the harmonics of frequency equal to or integer multiple of that of the carrier disappear from the phase-to-phase voltages. As these harmonics are the highest in amplitude in the phase voltages, the benefit produced by 4) in a three-phase system is consistent. Furthermore the use of only one carrier for modulating the references greatly simplifies the circuital implementation of the control. PWM inverter controllers In general a three-phase PWM inverter controller has two inputs and three outputs. The inputs command the amplitude and the frequency of the sinusoidal references. The output is the three-phase system of PWM signals used to activate the trigger circuits of the inverter devices. As the waveform of these signals is a low-power copy of the phase voltages of the inverter, their characteristics determine the inverter performance. The early PWM inverter controllers were entirely analog (Parasuram and Ramaswami, 1976). The advantage of these controllers is the excellent control performance, i.e. the continuous-amplitude control of the fundamental harmonics of the PWM signals and the very quick response to commands aimed to vary the reference. The disadvantages are that they need a large
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Signal Processor Controller
number of components, are not flexible and have a moderate electrical performance. This latter disadvantage is due to the degradation over time, temperature and noise of the analog components. A step in improving flexibility and electrical performance of the PWM inverter controllers is represented by the combined use of analog and conventional digital circuits (Grant and Barton, 1978). These controllers maintain excellent control performance, but appear to be involved and expensive. Top flexibility and electrical performance are gained with a microcomputer, but to the detriment of the control performance. The reason for this disadvantage is that a microcomputer is too slow to accomodate on-line processing of the signals involved in the control of a PWM inverter so that the only useable solution is data processing, the data being the pulse widths. The most straightforward implementation consists of storing the widths in the ROM memory of the controller and requiring of the microcomputer the timing of one of the PWM signals only. Bulky circuitry external to the microcomputer provides then to generate the other two PWM signals and carry out the frequency change (Brickwedde and others, 1981). Such an implementation gives the controller a negligible throughput delay, but makes the control of the fundamental harmonics with a reasonable amount of ROM memory practicable over a limited number of levels. Moreover, the hardware of the controller is very complex, including many devices in addition to the microcomputer. As an alternative to this implementation Bolognani and others (1983) have proposed a microcomputer-suited method to derive on-line both the widths and the three PWM signals for the actual amplitude and frequency commands. This method has been proved to be effective in avoiding the control and hardware drawback of the previous controller, but, in spite of its power, produces a throughput delay not acceptable in all the applications.
But the novel feature of a signal processor is the possibility of demanding of it the real time control of a PWM inverter by means of an on-line generation and comparison of reference and carrier signals as in an analog system. Giving up data in favour of high-speed signal processing is the key for improving the control performance of the conventional microcomputer controllers. The result, of course, will not be as good as in an analog controller because the support of the control remains a digital device, operating on a programmed basis.This calls inevitably for a sample data representation of the control signals, thus reproducing undesired effects on the control performance. Mainly due to the amplitude quantization of the references, the fundamental harmonics of the PWM signals is controlled again in a discrete range. The time quantization of the control signals, on the other hand, causes a delay in up-dating the output. As a signal processor keeps all these effects at a low level, the resulting control performance is very satisfactory. Last but not least merit following from a signal processor concerns the simplification of the hardware of the controller. Reduction of ROM memory and capability of processing a three-phase system of signals without needing external circuitry are the grounds for this merit. Intel 2920 signal processor The signal processor which will be used in this paper is the Intel 2920 (Intel Corporation, 1980). In comparison with the other available signal processors, the 2920 exhibits the extra feature of containing in a single chip the arithmetic-logic unit (ALU), ROM and RAM memory, and A/D, D/A, and I/O circuitry for inputting and outputting of analog signals. This makes the 2920 more than a digital signal processor, but a complete sampled data system adapted to the control of an analog plant. The hardware architecture depicted in Fig. 2. The
SIGNAL PROCESSOR APPROACH Using a signal processor for realizing a controller for a three-phase PWM inverter is attractive for a lot of reasons. Foremost, the microcomputer structure of a signal processor gives the controller the well-known merits peculiar to a digital, logic-programmed approach. Stability, reliability, predictability, and reproducibility of the electrical performance are inherent to the digital approach. Easy development, debug and modification of the controller are a conseguence of the software implementation of the control activities.
of the 2920 is analog circuitry
EPROMI
JE
21
31 ALU
MUXWHlf^A/Db^ ++
RAM
Ηΐ 0 / Α
Fig. 2. Block diagram of the 2920. includes 4 channels and multiplexer (MUX) at the input, and demultiplexer (DMUX) and 8 channels at the output for multivariable operation. The A/D and D/A converters have
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up to 9 bits of resolution (1 sign bit, 8 bits). The digital circuitry amplitude consists of an EPROM (or ROM) arranged in 192 words, each word corresponding to one instruction, and a RAM organized as 40 words of 25 bits each. Any variable in RAM has the binary point just to the right of the sign bit so that its range is between -1 and 1. The software of the 2920 is also specific. Each instruction is divided into two main fields, one directs the analog functions, the other the digital. Among the analog functions are selection of the input, A/D conversion, signal outputting, and selection of the output. Among the digital functions are addition, subtraction,scaling, limitation, absolute value, and OR. Conditional digital functions take both the analog and the digital field. The instruction set would appear to be limited and restrictive, especially for the digital functions. Nevertheless a judicious manipulation of the set and the parallel execution of one analog function with two digital functions, one of these having to be scaling, permits the implementation of fairly complex signal processing. The program is repeated indefinetively, a jump from the end of the program back to the beginning occurring automatically. One loop of program, termed program pass, is of fixed execution time since no internal program branches are provided. As the cycle period is the same for all the instructions (600 ns for the EPROM version), the execution time of the programm pass is the cycle period times the number of instructions. With a maximum program length of 192 instructions, this time is of 115.2 ys and coincides with the sampling period of a signal when a single sample is processed per program pass. The sampling rate can be increased by writing a shorter program or using multiple samples per program pass. The 2920 is supported by software packages useful in developing a program. The simulator is expecially of great help for a designer allowing the test of the implemented control entirely in software, without resorting to a hardwired prototype.
THREE-PHASE PWM INVERTER CONTROLLER A controller for a variable-voltage, 50Hz-frequency, three-phase PWM inverter based on the 2920 EPROM version is now presented. The voltage being the only command, the controller will have one input. The synchronous sinusoidal modulation with a frequency ratio of 9 is selected for implementation. As results from the above considerations, this modulation is highly recommendable for a three-phase PWM inverter employing thyristor devices.
Controller operation Under control of the program stored in ROM, the 2920 generates a three-phase system of sinusoidal references, r , r, , and r , and one triangular carrier, c, internally. The frequency of the references and the carrier are 50 and 450Hz., respectively, while the amplitude of all the signals is 1. The time-phase displacement between the triangle and one of the references is forced to zero. Given that the frequency ratio is an integer multiple of 3, the other two displacements are also zero. Moreover, the control program provides acquisition and conversion of the input, multiplication by the references and comparison of the result with the carrier. A three-phase system of PWM signals, v , v, , and v , is so obtained, with the fundamental harmonics of required amplitude . Outputting of the PWM signals closes the controller operation. Controller hardware The hardware structure of the controller is illustrated in Fig. 3. Its drastic
1 POWER
SUPPLY
REGULATOR Vr 2920
I- I I -
CLOCK
c
Fig. 3. Schematic of the hardware of the three-phase PWM inverter controller. simplicity is evident: besides the 2920, a sample capacitor, C, a reference voltage for the A/D and D/A conversion, V ,and a clock for timing purposes are the only requirements of the controller. The range of the input, v., is between 0 and V , while the outputs switch between -kV and kV , where k is the output gain of the 2920. In general, the reference voltage and the clock must be precise and stable to prevent inaccurate operation of the 2920. The case under consideration, however, is somewhat different. As the outputs are on-off signals, the reference voltage has no influence in determining the output accuracy. For the input, instead, this may be not true. Nevertheless, when v. is obtained from a potentiometer fed by the same reference voltage used for the controller, the converted input does not suffer inaccuracy and instability of V . As
Signal Processor Controller
a result, only the clock must be precise and stable, its variations affecting the accuracy on the frequency of the PWM signals. SOFTWARE DEVELOPMENT The functional analysis of the controller operation performed above is the starting-point for developing the software. Each function singled out in the analysis must now be translated into an algorithm executable by the 2920. Putting the algorithms in a proper sequence produces the required control program. Note the conceptual similarity of this procedure with the analog approach, whereby the difference is in the support of the functions which is software in the case under consideration, and hardware in the analog case. The algorithm for obtaining the three-phase system of sinusoidal refences begins with the generation of a 50 Hz sawtooth oscillator. The sawtooth is then processed by a waveform shaper, for instance a filter, to be trasformed in a sine of amplitude 1. This sine is r . Afterwards, r is shifted by ð/2, resulting in a cosine. Using the familiar relationship sin(x - 2TT/3) - 0.866cosx - 0.5sinx (1) r, is achieved, r
follows directly from
The sawtooth oscillator is generated by subtracting a constant, C , from a register at each programm pass, and adding 1 to this register everytime its contents becomes less than zero. By indicating the sampling period of the sawtooth with T , C has to be sr r selected according to C
- 50 T (3) r sr in order that the sawtooth frequency is 50 Hz. The absolute error on the sawtooth period is one half T , yielding to a percent accuracy on the sawtooth frequency and therefore on that of the references less than T å - 50 -ψ-
100
(4)
The algorithm for obtaining the triangular carrier recalls that used for the sawtooth. A constant, C , is added to a register at each program pass, shaping the ascending edge of the triangle. As soon as the register gets over 1, C is no longer added but subtracted from register, thus shaping the discending edge. When the register gets over -1, the cycle begins again. Being that the carrier frequency must
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be 450 Hz, C C c where T carrier.
is given by
= 450 T sc is the sampling
(5) period
of the
The algorithm for synchronizing the carrier with one of the references operates by writing zero in the carrier register when the reference is zero. The synchronization of the two signals, imperative at the power-on, is also useful from this time on to prevent a possible lack of synchronization arising from the finite length implementation of the constants C and C . Further algorithms are then arranged for performing the remaining functions required by the controller. Before presenting the entire control program, some considerations on the accuracy of the PWM signals outputted by the controller become necessary. The 2920-innerly generated references have a resolution of up to 24 bits. After multiplication by the input, their resolution goes down to 8 bits, resulting in an accuracy of about 0.4%. Without time quantization, an accuracy of the same magnitude would be induced on the fundamental harmonics of the PWM signals. Unfortunately the time quantization worsens this result, as it gives rise to a non constant delay between each of the switchings of the actual PWM signals and the theoretical ones. Though these delays go from 0 to a maximum which does not exceed the sampling period of the PWM signals, T , the concurrent action of all the delays may alter the amplitude control accuracy appreciably. The effect depends on the two following variables: the term f T , where f is the triangle frequency, and the amplitude of the references. Intuitively, the greater f T and the smaller the amplitude, the greater is the effect. As a conclusion, it is convenient to keep T as short as possible from the point of viiw of the amplitude control accuracy. The flow-chart of the control program is illustrated in Fig. 4. Its stucture is aimed at reducing T . The aspects of the program devoted to end are i) two samplings of the PWM signals for program pass, but one creation of the constants, one synchronization, and one acquisition of the input, ii) alternating at the filtering the computation of the references by interpolation, this latter requiring less instructions, iii)deriving of r after multiplying r and r, by the input, when filtering is used. The program is 132 instructions in length and takes 79.2 ys to be executed. This time, indicated in the following with T , coincides with the sampling period of tne
466
G. S. Buja and W. Zoccarato
references. Its substitution in (3) gives the constant C to be implemented for generating the references, while its substitution in (4) shows that the frequency accuracy is less than 0.2%. The sampling period of the carrier, instead, is one half T . Using this value in (5) yields to C . Tße sampling period of the PWM signals is
\ GENERATE r a
1
BY FILTERING
i
GENERATE r b
1 1
BY FILTERING
|
/
°"Pt1 va,vb,vc
1
r b WITH vi
* DERIVE r
♦ c
EXPERIMENTAL RESULTS After the controller has been built in accordance with the hardware and software structures presented above, its operation has been evaluated under various conditions. Foremost the harmonic contents of the three-phase system of PWM signals outputted by the controller have been measured by a
♦
MULTIPLY r a AND
GENERATE
From the design also emerges the limitation of the approach. When one desires to implement a high frequency carrier, he must reckon with the amplitude control accuracy. a worse accuracy or Only accepting restricting the range of accurate control, the carrier frequency may be increased. Indicatively, under the same T and accuracy of the application above, a carrier frequency of 900 Hz restricts the range at about 0.6 times the maximum.
|
ß
SYNCHRONIZE c WITH r 0
i
t GENERATE v a, v b, v c
♦
GENERATE r a, r b
1 I 1
' /
OUTPUT va,vb,vc
/
BY INTERPOLATION
* DERIVE r c
♦ GENERATE c
♦
1
GENERATE v a, v b, v c
' /ACQUIRE AND CONVERT vi
I
♦ CREATE CONSTANTS
Fig. 4. Flow-chart of controller.
the software of the
one half T as well. By introducing these data in a spectral analysis simulated on a digital computer an accuracy on the fundamental harmonics is predicted within 1%, provided this harmonics ranges from 0.4 times the maximum to the maximum. The analysis has also shown that the accuracy approaches the value of 0.4% induced by the references, as the fundamental harmonics nears the maximum. With regard to the throughput delay, it is a little less than twice T , the highest value occuring when the command is changed an instant after the 2920 has acquired the input. The control performance so obtained is very satisfactory and represents a first, designed-based confirmation of the advantages of the signal processor approach.
b) Fig. 5. Waveform a) and spectrum b) of the PWM signals with v.=0.8V . The controller under test has R=0.866 and V =1.5V. Time scale and amplitude scale of Fig. a) are: 5 ms/div; 1 V/div. Frequency scale and amplitude scale of Fig. b) are: 200 Hz/div; 200 mV/div.
Signal Processor Controller
spectrum analyzer with v. ranging from 0.4V to V . As an example, two of the outputs ana the spectrum of one of these signals with v. equal to 0.8V are shown in Fig. 5. The measures of the fundamental harmonics and the two most important harmonics introduced by the carrier are collected in Fig. 6 a) and b ) . The continuous lines show the behaviours gained from the theory. Fig. 6.a) indicates that the input-output linearity is well within 1% of full scale. Fig. 6.b) affirms the subharmonic nature of the PWM signals. Neither subharmonics nor harmonics of significant amplitude have been found apart from those predicted by the theory. The throughput delay has also been tested and the worst-case result is of about 140 ys as it was expected. Lastly, no frequency instability has been experimented unless in the relation with the clock.
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CONCLUSIONS Recent advances in integrated circuits have made it possible to develop PWM inverter controllers which meet objectives not obtainable previously. A new device, the signal processor, has proved to be effective in setting up a controller for a variable-voltage, fixed-frequency, three-phase PWM inverter with overall performance far superior to the existing controllers. The principle of the controller is simple, the hardware consisting of a handful of components, the software imitating the analog system on digital basis. The signal processor approach appears also to be sucessful in developing controllers for PWM inverters operating at variable frequency or in closed-loop schemes. Besides the merits, this approach exhibits a limit. As pointed out in the paper, the maximum carrier frequency implementable in a signal processor with a satisfactory amplitude control performance is about 900 Hz. This limit, however, restricts very little the area of the potential applications which includes all the thyristor and the low- and medium-speed transistor inverters.
REFERENCES
Fig. 6.
50, 350 and 450 Hz harmonics at the output of the controller as a function of the input.
Bolognani,S., G.S.Buja, and D.Longo (1983). Hardware and performance-effective microcomputer control of a three-phase PWM inverter. Proc. of 1983 International Power Electronics Conference, (in press). Brickwedde,A., D.Hean, and H.Graham (1981). Microprocessor controlled 50KVA PWM inverter motor drive. Proc. of 1981 IEEE Ind. Appl. Society Annual Meeting, pp. 666-670. Buja,G.S., and G.Indri (1975) Improvment of pulse width modulation techniques. Archiv für Elektrotechnik, 57, 281-289. Grant,T.L., and T.H.Barton (1978). A highly flexible controller for a pulse width modulation inverter. Proc. of 1978 IEEE Ind.Appl. Society Annnual Meeting, pp. 486-492. Intel Corporation (1980). The 2920 analog signal processor design handbook. Santa Clara. Parasuram,M.K., and B.Ramaswami (1976). A three-phase generator for thyristorized motor controllers. IEEE Trans. Ind. Electron. & Control Instrum., 23, 270-276. Schönung,A., and H.Stemmler (1964). Static frequency changers with subharmonic control in conjunction with reversible variable speed a.c. drives. Brown Boveri Review, 3, 666-673.