Nicolò Antonante Kristian Bergaplass Mumba Collins
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1 Norwegian University of Science and Technology TET4190 Power Electronics for Renewable Energy Mini-project 19 Power Electronics in Motor Drive Application Nicolò Antonante Kristian Bergaplass Mumba Collins October 28,
2 Contents 1 introduction 1 2 Theory Three-phase Full-bridge Rectifier Three-phase Transistor Based Inverter Asynchronous AC Motors Digital PWM Generation The TMS320F2812 DSP Assembly Code Triangular Wave Generation Sine Wave Generation Triangular - Sine Comparison PWM Generation for Three-legs Inverter Output PWM Waveform Energy Saving by Using Adjustable Speed Drives Introduction Fans Control Flow Control in Pumps Conclusions 17 6 References 18 2
3 List of Figures 1 Three-phase diode rectifier Waveforms for the circuit in figure Three-phase inverter (a) Three-phase PWM waveforms (b) V LL1 (rms)/v d as a function of ma A typical torque-speed characteristic; V s and f are constant at their rated values Package and Pin Assignment of a TMS320F The Main section of the Assembly code The time between two interrupts is the time between the min and max value of the triangular wave The PWM modulation for the upper transistor Zoom no the PWM wave Complementary PWM signal for both the upper transistor (channel1) and the bottom transistor (channel2) Dead band between the two complementary PWM signals Dead band in the up/down transition Illustration of a fan system driven by a constant speed motor, a dumper is used to reduce the airflow Illustration of a fan system driven by adjustable speed motor Illustration of a pump system driven by constant speed motor, a throttle valve is used to control the liquid flow Illustration of a pump system driven by an adjustable speed motor
4 1 introduction The first intention of this project was to build and investigate a variable speed motor drive based on a 3-phase IGBT-based inverter. However, due to unavailability of inverter boards at NTNU, this project will focus on the theoretical aspects of rectifiers, inverters, motors and digital Pulse-width modulation (PWM) generation. Practical applications for adjustable speed drives will also be presented. PWM is a very efficient way of providing intermediate amounts of electrical power between fully on and fully off. PWM can be used to control several kinds of signals and applications. This report will focus on power delivery, and specifically speed regulation for electric motors. Regulating the speed using PWM dramatically increases efficiency, and the technology is relatively simple and inexpensive. This makes PWM a popular speed-controlling technology. High frequency PWM power control systems are easily realizable with semiconductor switches. The major advantage of this kind of control system is that the switches are either off (no current conduction) or on (ideally no voltage drop across the switches). The main theoretical focus on this report will be the PWM, but the other parts of an adjustable speed drive (Three-phase full bridge rectifier, Three-phase transistor based inverter, asynchronous ac motor) will also be described briefly in the report. The focus on energy saving is increasing constantly worldwide. The last part of the report will discuss various practical applications for PWMcontrolled variable speed drives, and will focus on energy saving in such applications. 2 Theory 2.1 Three-phase Full-bridge Rectifier In industrial applications where three-phase ac voltages are available, it is preferable to use three-phase rectifier circuits, because of lower ripple and higher power-handling capability. A practical three-phase rectifier circuit contains inductances on the ac side. For a more ideal approach we assume these inductances (L s ) to be zero, and replace the load on the dc side with a constant current, I d (Figure1). In the top group of diodes (D1, D3, D5), the diode with the highest potential will conduct, while the other two become reversed biased. Similar 1
5 Figure 1: Three-phase diode rectifier in the lower group (D2, D4, D6), the diode with the lowest potential will conduct, while the other two will become reversed biased. The waveform for this idealized circuit is shown in figure 2. Figure 2b shows the output voltage V d, and the average output voltage can be calculated by using equation 1, V d0 = 1 π/3 π/6 ˆ π/6 2VLL cos(ωt)d(ωt) = 3 π 2VLL = 1.35V LL (1) where V LL is the is the rms value of the line-to-line voltages. In a practical three-phase diode rectifier where inductances (L s ) and a capacitor is included it is important to consider the current commutation process, distortion in the line-current waveform, harmonics, ripple and other practical issues. Many of these values can be calculated using tools as Fourier analysis, but computer simulation tools like PSpice are recommended to get more accurate results. 2
6 Figure 2: Waveforms for the circuit in figure Three-phase Transistor Based Inverter In this project we want to control the speed of a 3-phase motor drive. For this application, a three-phase inverter is most commonly used. The most frequently used inverter circuit is shown in figure 3. In an idealized circuit, the output of each leg (A, B, C) depends only on V d and the switch status; the output voltage is independent of the output load current since one of the two switches in a leg is always on at any instant. Figure 3: Three-phase inverter The objective in PWM three-phase inverters is to shape and control the 3
7 three-phase output voltages in magnitude and frequency with an essential constant input voltage V d. A triangular voltage waveform is compared with three sinusoidal control voltages to obtain balanced three-phase output voltages (Figure 4). Figure 4: (a) Three-phase PWM waveforms (b) V LL1 (rms)/v d as a function of ma Harmonics can be a problem in three-phase inverters, and some considerations should be taken when designing and operating such an inverter. 2.3 Asynchronous AC Motors The induction motor is the means by which electrical energy is converted to the required mechanical energy that is useful to the process. The induction machine, especially the cage type is widely used because it is rugged, reliable, simple in construction and has low maintenance costs. When the stator terminals of an induction machine are supplied with a constant ac voltage, the magnetic field induced in the air gap rotates at a constant speed, P, called synchronous speed. This speed in rpm is given by: P = 120 f (2) p where f is the frequency of the applied voltage and p is the number of poles. 4
8 The rotor of the machine will rotate at a speed that is less than but related to the synchronous speed by a slip, s, given by The other relevant induction motor equations are: f sl = s P (3) V s k 1 φ ag f (4) T em = k 2 φ ag f sl (5) Figure 5: A typical torque-speed characteristic; V s and f are constant at their rated values. From the Figure 5 Induction Motor Torque - Speed characteristic and the two equations (4) and (5), it can be said that to control the speed of the induction motor the following should be varied: 1. Applied voltage magnitude 2. Applied voltage frequency 3. The ratio of V/f has be kept constant in order to operate in the constant torque region. Several methods of varying complexity and performance can be used to realize the above requirements such as: 5
9 4. PWM, pulse width modulation 5. CSI, current source inverter 6. VSI, voltage source inverter 7. FVD, flux vector control drive However, the converter described here will be limited to the first technique because of its simplicity. 3 Digital PWM Generation In order to generate the PWM signals to control the transistors of the inverter, we used a DSP. Therefore a digital implementation of the comparison between the triangular and the sine waves is needed. The DSP used in this project is the TMS320F2812 by Texas Instruments. The implementation of the PWM generation algorithm is written in Assembly. 3.1 The TMS320F2812 DSP This DSP by Texas Instruments is a quite advanced microprocessor with many features. The main characteristics are: ˆ ˆ ˆ ˆ 150Mhz core frequency 3.3V I/O 12-Bit ADC with 16 channels 12 PWM output pins In Figure 6 we can see the TMS320F2812 package and pin assignment. We can easily find the position of the pins we need to use. Since we only need 6 PWM, one for each switch, we used only one of the two PWM sets. This DSP can be programmed both in Assembly or C languages. The first one is a low level language that allow to program an hardware device in a very efficient way, but is not portable to other device families. The second one, instead, is an higher level language that can be compiled to work on different devices. In our project we used an Assembly implementation of 6
10 Figure 6: Package and Pin Assignment of a TMS320F2812 the algorithm because this language allows us to control all the registers and data in the DSP. This way we can better understand how the algorithm works inside the microprocessor. 3.2 Assembly Code The Code used in this project is composed by a main body and different subroutines. When we start the program, the Main is launched. As we can see from Figure 7, this part of the code calls the subroutine initialize and then enters in an infinite loop. During this loop the system is basically in a waiting status and it operates parts of the algorithm only during interrupt calls. The initialize subroutine sets all data registers to zero and defines the Input/Output properties. 7
11 In our case it configures the six PWM pins that we want to use as outputs. During this subroutines, values of variables and time counters are also initialized. Figure 7: The Main section of the Assembly code 3.3 Triangular Wave Generation In order to generate a digital triangular wave, a free running counter can be used. What we have to do is to fix a maximum and a minimum value, then we can compare the current value in the counter with the max and min value. The counter will increase his value until it reaches the max, than it will decrease to the min and so on. Therefore, to set the amplitude of the triangle is sufficient to define the min e max value, while to set the period we have to specify how many clock cycles the counter has to wait before being increased/decreased by one step. Considering for example the clock frequency equal to 150MHz, it means a clock period T ck = 6.66ns. If we assume that the max value of the triangular wave form is V T rimax = 1024 h, where h is for hexadecimal, and the minimum is V T rimin = 0, it means the counter needs 4132 steps to rise to the max value. If we sets a step each clock cycle, we find that the period of the triangular waveform is T T ri = 2(T ck 4132) = 55us. If we want to increase T T ri we can simply set T step = kt ck, where k is the number of clock cycles the counter has to wait before increasing/decreasing its value. What we get is the following equation: T T ri = 2(T step n steps ) (6) 8
12 In this section the methodology used to generate a digital triangular waveform has been described. 3.4 Sine Wave Generation The generation of a sine waveform is a bit more complicated than the triangular one. In Assembly is not possible to calculate the values of a sine function, at least not in a simple way, therefore we have to generate the needed values with an external program, such as Matlab or Excel, and place them into a look-up table (LUT). In this project we used 128 values of the sine function calculated from 0 to 360, that means a step of 360 = 2.8. All 128 the values are between -1 and 1, so a 1.15 format would be the most accurate. We decided to use a 4.12 format because other variables in the code are in this format. This means 4bits for the integer part and 12bits for the decimal part. In order to change the amplitude of the sine wave it s sufficient to multiply all the values stored in the LUT for a constant. To modify the frequency, the procedure is a little bit more elaborated. First of all, the wave is generated reading sequentially a value from the LUT every time we generate an interrupt. This means that, if we want f s = 50Hz, we have to generate 128 interrupts in T s = 20ms, while if we want, for example, f s = 25Hz we have to generate 128 interrupts in T s = 40ms and so on. In both cases what we want is that the time between two interrupts is T int = T s (7) 128 Let s now see how an interrupt can be generated and how it s possible to vary T int. We can use a triangular wave, obtained with the method described in section 4.3, and a comparator register. An interrupt is generated each time the value in the counter reach the fixed maximum or minimum values. Changing these values is therefore possible to change the time between two consecutive interrupt. This idea is shown in Figure 8 Therefore, assuming the minimum value of the triangular wave equal zero, we can express T int as follow: T int = tri max T ck (8) where tri max is the maximum value of the triangular wave. We assumed one step each clock cycle. From equation (7) and (8) we get T s = 128(tri max T ck ) (9) 9
13 Figure 8: The time between two interrupts is the time between the min and max value of the triangular wave To set a desired value of T s we can find the corresponding tri max as tri max = 3.5 Triangular - Sine Comparison T s 128T ck (10) The generation of the Pulse Wave Modulation is obtained comparing the triangular wave with the sine. In order to do this comparison we need three steps: 1. multiply the sine for an amplitude factor 2. shift the sine to the mean value of the triangular wave 3. do the comparison between the current value of the sine and the one of the triangle The first step consist just in multiply the value of the LUT for a constant in order to get the desired amplitude of the sine. The second step is also easy, we just need to sum at each element of the LUT the mean value of the triangular. This is because we assumed that the triangular wave is all positive. For the last step we load the current values of the sine and the triangle in a register that will make the comparison. The PWM for the upper IGBT of the first leg of the inverter is generated setting an high logic 10
14 value (3.3V) on the corresponding PWM pin, while the sine is below the triangle.to generate the complementary signal for the bottom transistor of the same leg, we can just invert the PWM described above. There may be a problem using this method for the generation of the two complementary PWM. In fact, if both the switches are on at the same time, we have a short circuit on the supply bus. This can cause damages to the board and affect the output of the system. To avoid the possibility that both the upper and the bottom transistors of the same leg are simultaneously on, a dead band is introduced. This is just a delay between the instant in which the upper PWM goes down an the instant in which the bottom goes up. We set this delay symmetrically for the up/down and down/up transition. The dead band register is a feature available on the DSP used, so we just needed to set the right value in the Assembly code to get the desired delay. In our project we used a dead band equal 1.5us. 3.6 PWM Generation for Three-legs Inverter Since we have to control a three-phase inverter, we need to generate complementary PWM signal for each of the three legs. To generate these signals we don t need to use three different implementations of the algorithm described above. We actually have two ways to do this: 1. three pointer method 2. two pointer method. In the first method we use three pointers, one for each phase, that points to sine values in the LUT 120 out of phase one from the other. In this way, every time we generate an interrupt, each pointer is moved by one position. Comparing the three value with the triangular wave we get the PWM modulation for all the three legs. The second way to generate these signals is less easy but more optimized. In fact, is possible to use just two pointers in the LUT 90 out of phase one from the other. By using a 2-phase to 3-phase transformation is possible to get the same information of the three pointer method with advantages in computational time and resources usage. In our code the second method is implemented. 3.7 Output PWM Waveform The following section shows some screenshots of the DSP output taken using an oscilloscope. 11
15 As we can see from Figure 9 we get a very well defined wave, as we expected from theory. Figure 9: The PWM modulation for the upper transistor. A zoom on the rectangular wave better shows the variation in the duration of high and low status. Figure 10: Zoom no the PWM wave. 12
16 The next screenshot shows both the PWM for the upper transistor (channel1) and the PWM for the bottom one (channel2). Figure 11: Complementary PWM signal for both the upper transistor (channel1) and the bottom transistor (channel2). In Figure 12 is possible to clearly see the dead band between the upper and bottom PWM signals. As expected from theory the delay is 1.5us. Figure 12: Dead band between the two complementary PWM signals. 13
17 The same delay is symmetrically present also in the up/down transition as shown in Figure 13. Figure 13: Dead band in the up/down transition. 4 Energy Saving by Using Adjustable Speed Drives 4.1 Introduction Nowadays reduction in power consumption and energy saving are two keywords in research and industrial development. Reduce energy used in a process results in fact in a lower environmental impact and in money saving. In many industrial application, adjustable speed can be used to achieve a significant reduction in power consumption. Fans and pumps are typical examples of how it s possible to save energy controlling the speed of the motor. In this section examples of speed control application are presented. 4.2 Fans Control Fans are widely used industry, for example in cooling systems and in air ventilation. When a fan is driven by a fixed speed motor, the airflow may sometimes be higher than the needed. In this case, a damper can be used to restrict the flow and reduce the airflow to the desired value. 14
18 Figure 14: Illustration of a fan system driven by a constant speed motor, a dumper is used to reduce the airflow. This is, of course, a not efficient way to control the airflow. It s clear how, in this system, an adaptive speed control could match dynamically the airflow requirement and eliminate the waist of energy. Figure 15: Illustration of a fan system driven by adjustable speed motor. 4.3 Flow Control in Pumps The same idea presented for fans can be applied to pumps. Consider a simple pump operating at a fixed value. Since the motor speed is constant, in order to reduce the liquid flow is possible to partially close a throttling valve placed on the outflow. This introduces necessarily a loss of energy across the control valve. 15
19 Figure 16: Illustration of a pump system driven by constant speed motor, a throttle valve is used to control the liquid flow. The waist of energy can be avoided by eliminating the throttling valve and using an adjustable speed control to maintain the requested flow rate. Figure 17: Illustration of a pump system driven by an adjustable speed motor. 16
20 5 Conclusions ˆ Reviewed the main concepts of sinusoidal PWM technique. ˆ ˆ ˆ Reviewed the use of DSP technology in implementing the PWM technique. Discussed the energy savings due to use of motor speed control using techniques such as PWM and power electronic converters Demonstrated how to shape and control the PWM signals to the inverter switches. 17
21 6 References 1. N. Mohan, T. M. Undeland, W. P. Robbins, Power Electronics. Converters, Application and Design, 2nd ed., Jhon Wiley & Sons 2. Figures number 14 and 16 from http : //en.wikipedia.org/wiki/adjustable speed drive 3. Assembly code by Anandarup Das 4. Data sheet of the TMS320F2812 DSP from Texas Instruments website ( 18
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