Batch-11

ABSTRACT The first five-phase induction motor drive system was proposed in the late 1970s for adjustable speed drive applications. Since then, a considerable research effort has been in place to develop commercially feasible multiphase drive Systems .Multiphase (more than three phase) systems are the focus of research recently due to their inherent advantages compared to their three-phase counterparts. The multiphase motors are invariably supplied by ac/dc/ac converters. This is a special transformer connection scheme to obtain a balanced five-phase supply with the input as balanced three phases. The fixed voltage and fixed frequency available grid supply can be transformed to the fixed voltage and fixed frequency five-phase output supply. Since input is a three-phase system, the windings are connected in a usual fashion. Three separate cores are designed with each carrying one primary and three secondary coils, except in one core where only two secondary coils are used. Six terminals of primaries are connected in an appropriate manner resulting in star and/or delta connections and the 16 terminals of secondaries are connected in a different fashion resulting in star or polygon output. The connection scheme of secondary windings to obtain a star output. The turn ratios are different in each phase. The choice of turn ratio is the key in creating the requisite phase displacement in the output phases. The construction of output phases with requisite phase angles of 72 between each phase is obtained using appropriate turn ratios. The designed transformation turns ratio can be achieved by simply multiplying the gain factor in the turn ratios. A five-phase induction motor under a loaded condition is used to prove the viability of the transformation system. It is expected that the proposed connection scheme can be used in drives applications and may also be further explored to be utilized in multiphase power transmission systems.

I. INTRODUCTION

1

Multiphase (more than three phase) systems are the focus of research recently due to their inherent advantages compared to their three-phase counterparts. The applicability of multiphase systems is explored in electric power generation [2]–[8], transmission [9]–[15], and utilization [16]–[33]. The research on six-phase transmission system was initiated due to the rising cost of right of way for transmission corridors, environmental issues, and various stringent licensing laws. Six-phase transmission lines can provide the same power capacity with a lower phase-tophase voltage and smaller, more compact towers compared to a standard double-circuit threephase line. The geometry of the six-phase compact towers may also aid in the reduction of magnetic fields as well [12]. The research on multiphase generators has started recently and only a few references are available [2]–[8]. The present work on multiphase generation has investigated asymmetrical six-phase (two sets of stator windings with 30 phase displacement) induction generator configuration as the solution for use in renewable energy generation. As far as multiphase motor drives are concerned, the first proposal was given by Ward and Harrer way back in 1969 [1] and since then, the research was slow and steady until the end of the last century. The research on multiphase drive systems has gained momentum by the start of this century due to availability of cheap reliable semiconductor devices and digital signal processors. Detailed reviews on the state of the art in multiphase drive research are available in [18]–[22]. It is to be emphasized here that the multiphase motors are invariably supplied by ac/dc/ac converters. Thus, the focus of the research on the multiphase electric drive is limited to the modeling and control of the supply systems (i.e., the inverters [23]–[33]). Little effort is made to develop any static transformation system to change the phase number from three to -phase (where 3 and odd). The scenario has now changed with this paper, proposing a novel phase transformation system which converts an available three-phase supply to an output five-phase supply. Multiphase, especially a 6-phase and 12-phase system is found to produce less ripple with a higher frequency of ripple in an ac–dc rectifier system. Thus, 6- and 12-phase transformers are designed to feed a multi-pulse rectifier system and the technology has matured. Recently, a 24phase and 36-phase transformer system have been proposed for supplying a multi-pulse rectifier system [34]–[37]. The reason of choice for a 6-, 12-, or 24-phase system is that these numbers are multiples of three and designing this type of system is simple and straightforward. However, 2

increasing the number of phases certainly enhances the complexity of the system. None of these designs are available for an odd number of phases, such as 5, 7, 11, etc., as far as the authors know. The usual practice is to test the designed motor for a number of operating conditions with a pure sinusoidal supply to ascertain the desired performance of the motor [38]. Normally, a noload test, blocked rotor, and load tests are performed on a motor to determine its parameters. Although the supply used for a multiphase motor drive obtained from a multiphase inverter could have more current ripple, there are control methods available to lower the current distortion even below 1%, based on application and requirement. Hence, the machine parameters obtained by using the pulse width-modulated (PWM) supply may not provide the precise true value. Thus, a pure sinusoidal supply system available from the utility grid is required to feed the motor. This paper proposes a special transformer connection scheme to obtain a balanced five-phase supply with the input as balanced three phases. The block diagram of the proposed system is shown in Fig. The fixed voltage and fixed frequency available grid supply can be transformed to the fixed voltage and fixed frequency five-phase output supply. The output, however, may be made variable by inserting the autotransformer at the input side.

Fig. Block representation of the proposed system The input and output supply can be arranged in the following manner: 1) input star, output star; 2) input star, output polygon; 3) input delta, output star; 3

4) input delta, output polygon. Since input is a three-phase system, the windings are connected in a usual fashion. The output/secondary side connection is discussed in the following subsections.

THREE-PHASE ELECTRIC POWER Three-phase electric power is a common method of alternating current electric power transmission. It is a type of poly-phase system and is the most common method used by electric power distribution grids worldwide to distribute power. It is also used to power large motors and other large loads. A three-phase system is generally more economical than others because it uses less conductor material to transmit electric power than equivalent single-phase or twophase systems at the same voltage In a three-phase system, three circuit conductors carry three alternating currents (of the same frequency) which reach their instantaneous peak values at different times. Taking one conductor as the reference, the other two currents are delayed in time by one-third and two-thirds of one cycle of the electric current. This delay between phases has the effect of giving constant power transfer over each cycle of the current and also makes it possible to produce a rotating magnetic field in an electric motor. Three-phase systems may have a neutral wire. A neutral wire allows the three-phase system to use a higher voltage while still supporting lower-voltage single-phase appliances. In high-voltage distribution situations, it is common not to have a neutral wire as the loads can simply be connected between phases (phase-phase connection). Three-phase has properties that make it very desirable in electric power systems: 

The phase currents tend to cancel out one another, summing to zero in the case of a linear balanced load. This makes it possible to eliminate or reduce the size of the neutral conductor; all the phase conductors carry the same current and so can be the same size, for a balanced load.



Power transfer into a linear balanced load is constant, which helps to reduce generator and motor vibrations. 4



Three-phase systems can produce a magnetic field that rotates in a specified direction, which simplifies the design of electric motors.

Three is the lowest phase order to exhibit all of these properties. Most household loads are single-phase. In North America and some other countries, three-phase power generally does not enter homes. Even in areas where it does, it is typically split out at the main distribution board and the individual loads are fed from a single phase. Sometimes it is used to power electric cookers and electric clothes dryers.

TURNS RATIO Transformers are used in a wide array of electrical or electronic applications, providing functions that range from isolation and stepping up or stepping down voltage and current to noise rejection, signal measurement, regulation and a host of functions particular to specific applications. In order to test that a transformer will meet its design specification, a number of functions should be tested and one of the most commonly used tests is turns ratio. This technical note will review briefly the basic theory of turns ratio and then introduce some additional issues that should be considered when testing this critical transformer characteristic. BASIC THEORY The turns ratio of a transformer is defined as the number of turns on its secondary divided by the number of turns on its primary. The voltage ratio of an ideal transformer is directly related to the turns ratio:

The current ratio of an ideal transformer is inversely related to the turns ratio:

Where Vs = secondary voltage, Is = secondary current, Vp = primary voltage, Ip = primary current, Ns = number of turns in the secondary winding and Np = number of turns in the primary winding. 5

The turns ratio of a transformer therefore defines the transformer as step-up or step-down. A step-up transformer is one whose secondary voltage is greater than its primary voltage and a transformer that steps up voltage will step-down current. A step-down transformer is one whose secondary voltage is lower than its primary voltage and a transformer that steps down voltage will step-up current. VOLTAGE AND CURRENT TURNS RATIO DEFINITIONS

Factors Affecting Turns Ratio Measurements: With a theoretical, “ideal” transformer, the ratio of the physical turns on any winding could be established simply by measuring the rms output voltage on one winding, while applying a known rms input voltage of an appropriate frequency to another winding. Under these conditions, the ratio of the input to output voltages would be equal to the physical turns ratio of these windings. Unfortunately, however, “real” transformers include a number of electrical properties that result in a voltage or current ratio that may be not equal to the physical turns ratio. The following schematic diagram illustrates the electrical properties of a real transformer, with the ideal transformer component shown in the center, plus the electrical components that represent various additional properties of the transformer.

6



L1, L2 and L3 represent the primary and secondary leakage inductance caused by incomplete magnetic coupling between the windings.



R1, R2 and R3 represent the resistance (or copper loss) of the primary and secondary windings.



C1, C2, and C3 represent the interwinding capacitance.



Lp represents the magnetizing inductance core loss.



Rc represents the core loss of which three areas contribute, eddy current loss (increases with frequency), hysteresis loss (increases with flux density) and residual loss (partially due to resonance). FIVE-PHASE SYSTEM Variable speed electric drives predominately utilise three-phase machines. However,

since the variable speed ac drives require a power electronic converter for their supply (in vast majority of cases an inverter with a dc link), the number of machine phases is essentially not limited. This has led to an increase in the interest in multi-phase ac drive applications, since multi-phase machines offer some inherent advantages over their three-phase counterpart. Interesting research results have been published over the years on multi-phase drives and detailed review is available in Singh (2002), Jones and Levi (2002), Bojoi et al. (2006), Levi et 7

al. (2007), Levi (2008a) and Levi (2008b). Major advantages of using a multi-phase machine instead of a three-phase machine are higher torque density, greater efficiency, reduced torque pulsations, greater fault tolerance, and reduction in the required rating per inverter leg (and therefore simpler and more reliable power conditioning equipment). Noise characteristics of multi-phase drives are better when compared three-phase drive as demonstrated by Hodge et al. (2002) and Golubev and Ignatenko (2000). Higher Phase number yield smoother torque due to the simultaneous increase of the frequency of the torque pulsation and reduction of the torque ripple magnitude, as presented by Williamson and Smith (2006) and Apsley (2006). Higher torque density in a multi-phase machine is possible because fundamental spatial field harmonic and space harmonic fields can be used to enhance total torque as presented by Xu et al. (2001a) and Xu et al. (2001b), Shi et al. (2001), Lyra and Lipo (2002), Duran et al. (2008) and Arahal and Duran (2009). This advantage of enhanced torque production stems from the fact that vector control of the machine’s flux and torque, produced by the interaction of the fundamental field component and the fundamental stator current component, requires only two stator currents (d-q current components). In a multi-phase machine, with at least five phases or more, there are therefore additional degrees of freedom, which can be utilised to enhance the torque production through injection of higher order current harmonics. The stability analysis of five-phase drive system for harmonic injection scheme is carried out by Duran et al. (2008) for both concentrated winding and distributed winding machines. It was concluded that the 3rd harmonic injection not only enhances the torque production but also offers a more stable control structure. The studies on multi-phase drive system carried out so far is for high performance variable speed applications. Multi-phase drive is seen as a serious contender for niche applications such as ship propulsion, traction, electric vehicles and in safety critical applications requiring high degree of redundancy. However, general purpose drive applications using multi-phase machines are not yet investigated in detail. This paper advocates the use of a five-phase drive system for general purpose applications such as water pumping in remote and weak grid locations where the power quality is not adequate for operating sophisticated microprocessor based controllers due to their stringent power quality requirements. Further, the costs of such high performance drive systems are too high to be borne by poor farmers in remote locations. The question then arises why five-phase drive is at all required not conventional three-phase drive. The answer lies in the fault tolerant 8

characteristic, reliable and higher efficiency of five-phase drive compared to three-phase drive (detailed by Apsley et al. (2006), Arhal and Duran (2008)). The power electronic converters supplying multi-phase drives are controlled using advanced digital signal processors (DSP) and Field programmable Gate Arrays (FPGA). Many modulation techniques implemented using DSPs and FPGAs are proposed in the literature for controlling the multi-phase power electronic converters, Iqbal and Levi (2005). In contrast this paper proposes simple, reliable and cheap controller circuit using analogue components and square wave operation of a five-phase voltage source inverter (VSI). In environment of weak grid with poor power quality, stepped operation of voltage source inverter may be considered as more viable solution in comparison to PWM mode. FIVE-PHASE DRIVE STRUCTURE A simple open-loop five-phase drive structure is elaborated in Figure. The dc link voltage is adjusted from the controlled rectifier by varying the conduction angles of the thyristors. The frequency of the fundamental output is controlled from the IGBT based voltage source inverter. The inverter is operating in the quasi square wave mode instead of more complex PWM mode. Thus the overall control scheme is similar to a three-phase drive system. Since the inverter is operating in square wave mode the analogue circuit based controller is much simpler and cheaper compared to more sophisticated digital signal processor based control schemes. This type of solution is very cheap and convenient for use in coarse applications such as water pumping. These types of applications do not require fast dynamic response of drive systems and thus the need of high performance control schemes do not arise. The power quality of the remote locations in developing countries such as Indian subcontinents are not adequate for reliable and durable operation of sensitive microprocessors/microcontrollers/digital signal processors based controllers. It is thus intended to develop cheap and robust controller based on simple, and reliable analogue circuit components for such locations. The subsequent section describes the implantation issues of control of a five-phase voltage source inverter. The motivation behind choosing this structure lies in the fault tolerant nature of a five-phase drive system (Apsley et al., 2006).

9

THREE-PHASE DRIVE The predominant harmonics in a three-phase induction motor drive are 5th and 7th, with 5th being backward rotating and 7th being forward rotating both leading to 6th harmonic pulsating torques, Bose (2002) and Krishnan (2001). The expression for the sixth harmonic pulsating torque is given as;

An expression is derived for the sixth harmonic pulsating torque in terms of fundamental voltage and equivalent circuit parameter and is obtained as;

Where

and y mk is the peak of kth harmonic mutual flux, V1 is the

fundamental applied voltage, Xeq is the equivalent leakage reactance and P is the number of poles of induction machine.

FIVE-PHASE DRIVE

10

The predominant harmonics in a five-phase machine are 9th and 11th, with 9th being backward rotating and 11th being forward rotating both leading to 10th harmonic torques, Iqbal et al. (2008). The tenth harmonic pulsating torque for 180° conduction mode is obtained as;

The tenth harmonic pulsating torque for 144° conduction mode is obtained as;

An expression is derived for the tenth harmonic pulsating torque in terms of fundamental voltage and equivalent circuit parameter and is obtained as;

where

Thus the ratio of pulsating torques for a typical motor in two conduction modes is obtained as;

11

The relations show, there is reduction in torque ripples in five phase motor at 144° conduction mode by 10% (approx) when compared with 180° conduction mode of five phase motor, 700% when compared with 180° conduction modes of five phase motors, and 778% when compared with 180° conduction mode of three phase motor and 144° conduction mode of five phase motor. COMPARISON OF OUTPUT PERFORMANCE To provide a basis for comparing the output current of the 3-, 5- and 6-phase machines, it is convenient to represent the coupling of the rotor to stator windings through back-emf, which is shown on each of the stator windings. The average output current of the rectifier is a function of the back-emf on the stator windings, the commutating inductance (labeled LJ, and the battery voltage.

12

In general, winding harmonics, coupled with permeance harmonics due to stator slots and rotor saliency lead to a back-emf with significant harmonic content. Although important for evaluating acoustic noise, to compare the output of the machined rectifiers it is convenient to neglect harmonics and assume each of the machines has a phase-o back-emf of the form

where the amplitude e is a function of field flux linkage and rotor speed. As conduction begins, the switching of each of the rectifiers is a function of the back-emf waveforms and is consistent with the numbering of the diodes. If one assumes equal back-emf amplitudes for the three machines, the cut4 speed where conduction begins (the line-to line emf exceeds the battery voltage) is lower for the 5-phase machine. Specifically, the 6-phase machine is constructed as two 3-phase machines offset by 30 electrical degrees. Therefore, the line-line emf of the 3- and &phase machines is found from the vector sum of two phases displaced by I20 degrees, which is equal to

. The line-line emf of the 5-phase machine, in contrast is found

Gom the vector sum of two phases displaced by 144 degrees, which is equal to 1.902ee. Thus, for a given speed, one would expect a line-to-line emf that is roughly 10% higher for the 5-phase machine compared to the 3- and 6-phase machines. In theory, this leads to a cut in speed that is roughly 10% lower for the 5-phase machine. However, the influence of slotting and saturation both play a role in the respective cut-in speeds. For a given number of rotor poles and stator slot/pole/phase, 5-phase and 6-phase machines will have 513 and twice the number of slots as the 3-phase machine, respectively. When evaluating the impact of this on stators to rotor flux linkage. Carter's coefficient provides a starting point. For the geometry studied, the resultant Carter coefficients are shown in Table.

13

Table: Carter’s coefficients for 3, 5 and 6 phase machines

These values were calculated assuming similar slot openings and stator inner diameters for each of the designs. Comparing values, the impact of the additional slots is clear; the flux linkage for the 5- and 6-phase machines will be reduced compared to the 3-phase machine. However, it is noted that in typical automotive applications, the machine operates over a wide range of magnetic operating points. At lower speeds, the magnetic circuit is highly saturated, while at higher speeds it is much less so. The assumptions used to derive Carter's coefficient are weakened as the iron operates further in saturation. As the rotor speed increases above cut-in, the effect of the source inductance is significant. To illustrate, the modes of the 5-phase machine converter with a battery load are shown in Fig.

Fig. Operational modes of 5-phase machine/converter From the figure it can be seen that between rotor speeds of 1060-6000 rpm there are 8 distinct conduction patterns of the rectifier. At speeds between 1060 and 1076 rpm, a sequence of 0-2 diodes are conducting (mode 1): at speeds between 1076 and 1079 rpm a sequence of 0-2-3-2 14

diodes are conducting (mode 2). These modes are not shown due to their short durations. As the rotor speed increases more diodes conduct and above 2563 rpm, 5 diodes are always conducting. The effect of the source inductance on the 3- and 6-phase machine/converters is similar, although they each have distinct modes of conduction. Analytically deriving closed-form expressions for the output current of the respective systems in each of the conduction modes is very challenging. Average-value models of a 3-phase source rectifier with a battery load have been derived assuming the stator phase currents are continuous. Average-value models of 3- and &phase machine/converters with current-source loads have been derived for a single mode of operation. In lieu of average-value expressions, the results of a detailed-simulation are used to consider system behavior. For the simulation a somewhat simplified model of the machines is used. Specifically, to derive the model of the 3-phase machine, it is assumed that the stator is wound using concentrated windings (1 slot/poly phase). To derive the self and mutualinductances only the fundamental component of the air gap flux density is used, the effects of MMF and stator slot harmonics are neglected. The stator winding' leakage inductance is calculated Gom the slot geometry of the machine. The effect of d-axis saturation is included in the model using a compensation factor to adjust values of magnetizing inductance. To model the 5- and 6-phase machines, the back-emf and magnetizing inductance obtained from the model of the 3- phase machine at each operating point are used. Specifically, the values from the 3-phase machine are multiplied by the ratio of Carter's coefficient of the 3phase machine to that of the 5- and 6-phase machine to generate the respective 5- and 6-phase machine parameters. The stator leakage inductance for each machine is calculated from the respective slot geometry. It is recognized that the 5- and 6-phase machines have distinct saturation curves. The purpose of using the 3-phase data to generate 5- and 6-phase machine parameters is to assess the accuracy of using the ratio of Caner's coefficient to compare the performance of the three machines. The simulated performance of the simplified machine models are shown in Fig.

15

Fig. Simulated response using simplified machine models It is seen that the simulations predict the 5- phase machine will have a higher output current than the 6-phase machine over a majority of the sped range. In addition, at speeds below 3000 rpm, the 5-phase machine is predicted to have a lower output current compared to the 3- phase machine. It is also noted that the 5-phase machine has a lower cut-in speed compared to the 6phase machine, hut slightly higher compared to the 3-phase machine. To observe the behavior of the actual machines, the measured output current of the three systems is shown in Fig.

Fig. Measured output current as a function of rotor speed far 3-, 5- and 6-phase machines.

16

It is shown that the 5-phase machine does have a lower cut-in speed relative to the 3-, and 6phase machines. In addition, the 5-phase machine provides increased output current over a majority of the speed range. Comparing simulated and measured results it is shown that the 3phase measured/simulated responses are in very good agreement over the entire speed range. In contrast, neither the 5- nor 6- phase measured results compare favorably to simulated results at lower speeds. They agree more favorably at higher speeds. This is due to the effective air gap used in the models. At low speeds, where the machines operate in heavy saturation, using the ratio of the respective Carter coefficients to predict relative performance is not particularly accurate. At higher speeds, where a machine more closely approximates a linear magnetic system, the correlation of the models to test data is much closer. The results from the simplified models of the 5- and 6- phase machines indicate that predicting the output performance using lumped-parameter models requires operating-pointdependent parameters for each respective machine. Alternatively, numerical tools such as finite element or magnetic-equivalent may be used. COMPARISON OF COST In comparing the 5- and 6-phase machines, the 5-phase concept offers some advantages in terms of product performance as well as manufacturability that translate to lower cost. For one, the 5-phase is comprised of fewer slots. This helps not only the cost but also the machine performance. A 5-phase machine, wound with one slot/poly phase requires five stator slots per pole whereas a 6-phase machine with one slot/pole/phase requires six slots per pole. For machines of an equal pole count, a &phase machine has 20% more coils and stator slots. This equates back to manufacturing cost in that more coils must be wound for the 6- phase machine, adding labor over the 5-phase machine baseline for the insertion of additional slot liners, winding and inserting of the additional coils, termination of the additional coils, testing of the additional phase, and added complexity of tracking an additional set of leads through the manufacturing process until lead termination. From the product side, any additional part or operation offers the possibility of impacted reliability in that the additional part can fail or the process can be faulty. The additional manufacturing operations addressed reduce the product reliability as do the two additional diodes required for the 6-phase system. The added slots of the 6-phase also present possible performance drawbacks. As shown in the previous section, the flux will drop as a result of the larger effective air gap. An additional 17

concern of the added slot count is the increase in eddy current losses on the unlaminated rotor pole pieces. While complex to accurately calculate, these are attributable to permeance variations in the stator surface resulting in a flux ripple at the stator slot frequency. Given the 17% higher slot frequency of the 6-phase machine, one can expect the rotor surface losses to increase by 2037% depending upon the depth of penetration of the slot harmonic flux. If a continuous assortment of diode current ratings were available, one could select a diode for the 6-phase with 5/6th the current rating of the 5-phase generator. In practice, this is not the case, and one is usually forced to use diodes of the same rating for each machine, given the current requirements vary by only 20%.

MATLAB Matlab is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation. Typical uses include Math and computation Algorithm development Data acquisition Modeling, simulation, and prototyping Data analysis, exploration, and visualization Scientific and engineering graphics Application development, including graphical user interface building. Matlab is an interactive system whose basic data element is an array that does not require dimensioning. This allows you to solve many technical computing problems, especially those with matrix and vector formulations, in a fraction of the time it would take to write a program in a scalar no interactive language such as C or Fortran. The name matlab stands for matrix laboratory. Matlab was originally written to provide easy access to matrix software developed by the linpack and eispack projects. Today, matlab engines incorporate the lapack and blas libraries, embedding the state of the art in software for matrix computation.

18

Matlab has evolved over a period of years with input from many users. In university environments, it is the standard instructional tool for introductory and advanced courses in mathematics, engineering, and science. In industry, matlab is the tool of choice for highproductivity research, development, and analysis. Matlab features a family of add-on application-specific solutions called toolboxes. Very important to most users of matlab, toolboxes allow you to learn and apply specialized technology. Toolboxes are comprehensive collections of matlab functions (M-files) that extend the matlab environment to solve particular classes of problems. Areas in which toolboxes are available include signal processing, control systems, neural networks, fuzzy logic, wavelets, simulation, and many others.

The matlab system consists of five main parts: Development Environment. This is the set of tools and facilities that help you use matlab functions and files. Many of these tools are graphical user interfaces. It includes the matlab desktop and Command Window, a command history, an editor and debugger, and browsers for viewing help, the workspace, files, and the search path. The matlab Mathematical Function Library.

This is a vast collection of computational

algorithms ranging from elementary functions, like sum, sine, cosine, and complex arithmetic, to more sophisticated functions like matrix inverse, matrix eigenvalues, Bessel functions, and fast Fourier transforms. The matlab Language.

This is a high-level matrix/array language with

control flow statements, functions, data structures, input/output, and object-oriented programming features. It allows both "programming in the small" to rapidly create quick and dirty throw-away programs, and "programming in the large" to create large and complex application programs. Matlab has extensive facilities for displaying vectors and matrices as graphs, as well as annotating and printing these graphs. It includes high-level functions for two-dimensional and three-dimensional data visualization, image processing, animation, and presentation graphics. It 19

also includes low-level functions that allow you to fully customize the appearance of graphics as well as to build complete graphical user interfaces on your matlab applications. The matlab Application Program Interface (API).

This is a library that allows you to

write C and Fortran programs that interact with matlab. It includes facilities for calling routines from matlab (dynamic linking), calling matlab as a computational engine, and for reading and writing MAT-files.

SIMULINK: Introduction: Simulink is a software add-on to matlab which is a mathematical tool developed by The Math works,(http://www.mathworks.com) a company based in Natick. Matlab is powered by extensive numerical analysis capability. Simulink is a tool used to visually program a dynamic system (those governed by Differential equations) and look at results. Any logic circuit, or control system for a dynamic system can be built by using standard building blocks available in Simulink Libraries. Various toolboxes for different techniques, such as Fuzzy Logic, Neural Networks, dsp, Statistics etc. are available with Simulink, which enhance the processing power of the tool. The main advantage is the availability of templates / building blocks, which avoid the necessity of typing code for small mathematical processes. Concept of signal and logic flow: In Simulink, data/information from various blocks are sent to another block by lines connecting the relevant blocks. Signals can be generated and fed into blocks dynamic / static).Data can be fed into functions. Data can then be dumped into sinks, which could be 20

scopes, displays or could be saved to a file. Data can be connected from one block to another, can be branched, multiplexed etc. In simulation, data is processed and transferred only at Discrete times, since all computers are discrete systems. Thus, a simulation time step (otherwise called an integration time step) is essential, and the selection of that step is determined by the fastest dynamics in the simulated system.

Fig 4.1 Simulink library browser

21

Connecting blocks:

fig 4.2 Connecting blocks To connect blocks, left-click and drag the mouse from the output of one block to the input of another block. Sources and sinks: 22

The sources library contains the sources of data/signals that one would use in a dynamic system simulation. One may want to use a constant input, a sinusoidal wave, a step, a repeating sequence such as a pulse train, a ramp etc. One may want to test disturbance effects, and can use the random signal generator to simulate noise. The clock may be used to create a time index for plotting purposes. The ground could be used to connect to any unused port, to avoid warning messages indicating unconnected ports The sinks are blocks where signals are terminated or ultimately used. In most cases, we would want to store the resulting data in a file, or a matrix of variables. The data could be displayed or even stored to a file. the stop block could be used to stop the simulation if the input to that block (the signal being sunk) is non-zero. Figure 3 shows the available blocks in the sources and sinks libraries. Unused signals must be terminated, to prevent warnings about unconnected signals.

23

fig 4.3 Sources and sinks Continuous and discrete systems: All dynamic systems can be analyzed as continuous or discrete time systems. Simulink allows you to represent these systems using transfer functions, integration blocks, delay blocks etc.

24

fig 4.4 continous and descrete systems Non-linear operators: A main advantage of using tools such as Simulink is the ability to simulate non-linear systems and arrive at results without having to solve analytically. It is very difficult to arrive at an analytical solution for a system having non-linearities such as saturation, signup function, 25

limited slew rates etc. In Simulation, since systems are analyzed using iterations, non-linearities are not a hindrance. One such could be a saturation block, to indicate a physical limitation on a parameter, such as a voltage signal to a motor etc. Manual switches are useful when trying simulations with different cases. Switches are the logical equivalent of if-then statements in programming.

fig 4.5 simulink blocks Mathematical operations: Mathematical operators such as products, sum, logical operations such as and, or, etc. .can be programmed along with the signal flow. Matrix multiplication becomes easy with the matrix gain block. Trigonometric functions such as sin or tan inverse (at an) are also available. Relational operators such as ‘equal to’, ‘greater than’ etc. can also be used in logic circuits

26

fig 4.6 Simulink math blocks SIGNALS & DATA TRANSFER: In complicated block diagrams, there may arise the need to transfer data from one portion to another portion of the block. They may be in different subsystems. That signal could be dumped into a goto block, which is used to send signals from one subsystem to another. Multiplexing helps us remove clutter due to excessive connectors, and makes matrix(column/row) visualization easier.

27

fig 4.7 signals and systems Making subsystems Drag a subsystem from the Simulink Library Browser and place it in the parent block where you would like to hide the code. The type of subsystem depends on the purpose of the block. In general one will use the standard subsystem but other subsystems can be chosen. For instance, the subsystem can be a triggered block, which is enabled only when a trigger signal is received. Open (double click) the subsystem and create input / output PORTS, which transfer signals into and out of the subsystem. The input and output ports are created by dragging them from the Sources and Sinks directories respectively. When ports are created in the subsystem,

28

they automatically create ports on the external (parent) block. This allows for connecting the appropriate signals from the parent block to the subsystem. Setting simulation parameters: Running a simulation in the computer always requires a numerical technique to solve a differential equation. The system can be simulated as a continuous system or a discrete system based on the blocks inside. The simulation start and stop time can be specified. In case of variable step size, the smallest and largest step size can be specified. A Fixed step size is recommended and it allows for indexing time to a precise number of points, thus controlling the size of the data vector. Simulation step size must be decided based on the dynamics of the system. A thermal process may warrant a step size of a few seconds, but a DC motor in the system may be quite fast and may require a step size of a few milliseconds.

29

II.WINDING ARRANGEMENT FOR FIVE-PHASE STAR OUTPUT Three separate cores are designed with each carrying one primary and three secondary coils, except in one core where only two secondary coils are used. Six terminals of primaries are connected in an appropriate manner resulting in star and/or delta connections and the 16 terminals of secondaries are connected in a different fashion resulting in star or polygon output. The connection scheme of secondary windings to obtain a star output is illustrated in Fig. and the corresponding phasor diagram is illustrated in Fig.

30

Fig. (a) Proposed transformer winding arrangements (star-star). (b) Proposed transformer winding connection (star).

Fig. Phasor diagram of the proposed transformer connection (star-star). The construction of output phases with requisite phase angles of 72 between each phase is obtained using appropriate turn ratios, and the governing phasor equations are illustrated 31

below. The turn ratios are different in each phase. The choice of turn ratio is the key in creating the requisite phase displacement in the output phases. The input phases are designated with letters “X” “Y”, and “Z” and the output are designated with letters “A”, “B”, “C”, “D”, and “E”. As illustrated in Fig., the output phase “A” is along the input phase “X”. The output phase “B” results from the phasor sum of winding voltage “c6c5” and “ b1b2”, the output phase “C” is obtained by the phasor sum of winding voltages “a3a4 ” and “ b3b4”. The output phase “D” is obtained by the phasor addition of winding voltages “ a3a4” and “ c1c2” and similarly output phase “E” results from the phasor sum of the winding voltages “c3c4 ” and “b6b5 ”. In this way, five phases are obtained. The transformation from three to five and vice-versa is further obtained by using the relation given below

32

III. SIMULATION RESULTS The designed transformer is at first simulated by using “simpower system” block sets of the Matlab/Simulink software. The inbuilt transformer blocks are used to simulate the conceptual design. The appropriate turn ratios are set in the dialog box and the simulation is run. Turn ratios are shown in Table. Standard wire gauge SWG) is shown in Table. TABLE: DESIGN OF THE PROPOSED TRANSFORMER

A brief design description for the turn ratio, wire gauge, and the geometry of the transformers are shown in the Appendix. The simulation model is depicted in first fig and the resulting input and output voltage waveforms are illustrated in second fig.

33

Fig. (a) Geometry of the transformer. (b) Matlab/Simulink model of the three- to five-phase transformation.

It is balanced three-phase input. Individual output phases are, also, shown along with their respective input voltages. The phase Va is not shown because Va=Vx (i.e., the input and the output phases are the same). There was no earth current flowing when both sides neutrals were earthed. The input and output currents with earth current waveforms are also shown in Fig. From this, we can say that the transformer, connected to the X input line, carries 16.77% (19.5/16.7) more current than that of the other two transformers (or two phases). Due to this efficiency,

34

clearly seen that the output is a balanced five-phase supply for a the overall transformer set is slightly lower than the conventional three-phase transformer.

35

Fig. (a) Input Vy and Vz phases and output Vb phase voltage waveforms. (b) Input Vy and Vx phases and output Vc phase voltage waveforms. (c) Input Vz and Vx phases and output Vd phase voltage waveforms

IV. EXPERIMENTAL RESULTS This section elaborates the experimental setup and the results obtained by using the designed three- to five-phase transformation system. The designed transformation system has a 1:1 input:output ratio, hence, the output voltage is equal to the input voltage. Nevertheless, this ratio can be altered to suit the step up or step down requirements. This can be achieved by simply multiplying the gain factor in the turn ratios. In the present scheme for experimental purposes, three single phase autotransformers are used to supply input phases of the transformer connections. The output voltages can be adjusted by simply varying the taps of the autotransformer. For balanced output, the input must have balanced voltages. Any unbalancing in the input is directly reflected in the output phases. The input and output voltage waveforms under no-load steady-state conditions are recorded. The input and output voltage waveforms clearly show the successful implementation of the designed transformer. Since the input-power quality is poor, the same is reflected in the output as well. The output trace shows the no-load output voltages. Only four traces are shown due to the limited capability of the oscilloscope. Further tests are conducted under load conditions on the designed transformation system by feeding a five-phase induction motor.

36

Fig. Circuit diagram for a direct-online start of the five-phase motor Direct online starting is done for a five-phase induction motor which is loaded by using an eddy-current load system. DC current of 0.5A is applied as the eddy-current load on the fivephase induction machine. The resulting input (three-phase) waveforms and the output (fivephase) waveforms (voltages and currents) under steady state. The applied voltage to the input side is 446 V (peak to peak) , the power factor is 0.3971, and the steady-state current is seen as 7.6 A (peak-to-peak). The corresponding waveforms of the same phase “A” are equal to the input side voltage of 446 (peak-topeak), since the transformer winding has a 1:1 ratio. The power factor is now reduced in the secondary side and is equal to 0.324 and the steady-state current reduces to 3.3 A (peak-to-peak). The reduction in steady-state current is due to the increase in the number of output phases. Thus, once again, it is proved that the deigned transformation systems work satisfactorily. The transient performance of the three- to five-phase transformer is evaluated by recording the transient current when sup- plying the five-phase induction motor load. The maximum peak transient current is recorded as 7.04 A which is reduced to 4.32A in the steadystate condition. The settling time is recorded to be equal to 438.4 ms.

37

V. CONCLUSION This paper proposes a new transformer connection scheme to transform the three-phase grid power to a five-phase output supply. The connection scheme and the phasor diagram along with the turn ratios are illustrated. The successful implementation of the proposed connection scheme is elaborated by using simulation and experimentation. A five-phase induction motor under a loaded condition is used to prove the viability of the transformation system. It is expected that the proposed connection scheme can be used in drives applications and may also be further explored to be utilized in multiphase power transmission systems.

APPENDIX DESIGN OF THE TRANSFORMER 1)The volt per turn

2) Standard core size of No. 8 of E and I was used whose central limb width is 2*2.54=5.08cm =50.8mm. 3) Standard size of Bakelite bobbin for 8 no. core of 3*2.54=7.62cm=76.2 mm was taken which will give core area of 38.7096cm . 4) Turns of primary windings of all three single-phase transformers are equal and the enamelled wire gauge is 15 SWG. The VA rating of each transformer is 2000. Wire gauge was chosen at a current density of 4 A/mm because enamelled wire was of the grade which can withstand the temperature up to 180. The winding has 15 SWG wire because it carries the sum of two currents (i.e.,

times the 5-phase rated current). 38

REFERENCES [1] E. E. Ward and H. Harer, “Preliminary investigation of an inverter-fed 5-phase induction motor,” Proc. Inst. Elect. Eng., vol. 116, no. 6, 1969. [2] D. Basic, J. G. Zhu, and G. Boardman, “Transient performance study of brushless doubly fed twin stator generator,” IEEE Trans. Energy Convers., vol. 18, no. 3, pp. 400–408, Jul. 2003. [3] G. K. Singh, “Self excited induction generator research- a survey,” Elect. Power Syst. Res., vol. 69, pp. 107–114, 2004. [4] O. Ojo and I. E. Davidson, “PWM-VSI inverter-assisted stand-alone dual stator winding induction generator,” IEEE Trans Ind. Appl., vol. 36, no. 6, pp. 1604–1611, Nov./Dec. 2000. [5] G. K. Singh, K. B. Yadav, and R. P. Saini, “Modelling and analysis of multiphase (six-phase) self-excited induction generator,” in Proc. Eight Int. Conf. on Electric Machines and Systems, China, 2005, pp. 1922–1927. [6] G. K. Singh, K. B. Yadav, and R. P. Sani, “Analysis of saturated multiphase (six-phase) self excited induction generator,” Int. J. Emerging Elect. Power Syst., Article 5, vol. 7, no. 2, Sep. 2006. [7] G. K. Singh, K. B. Yadav, and R. P. Sani, “Capacitive self-excitation in six-phase induction generator for small hydro power-an experimental investigation,” presented at the IEEE Conf. Power Electronics, Drives and Energy Systems for Industrial Growth—2006 (PEDES-2006) PaperA-20. (CD-ROM), New Delhi, India, Dec. 12–15, 2006.

39

[8] G. K. Singh, “Modelling and experimental analysis of a self excited six-phase induction generator for stand alone renewable energy generation,” Renew. Energy, vol. 33, no. 7, pp. 1605–162, Jul. 2008. [9] J. R. Stewart and D. D.Wilson, “High phase order transmission- a feasibility analysis Part-ISteady state considerations,” IEEE Trans. Power App. Syst., vol. PAS-97, no. 6, pp. 2300–2307, Nov. 1978. [10] J. R. Stewart and D. D. Wilson, “High phase order transmission- a feasibility analysis PartII-Over voltages and insulation requirements,” IEEE Trans. Power App. Syst., vol. PAS-97, no. 6, pp. 2308–2317, Nov. 1978. [11] J. R. Stewart, E. Kallaur, and J. S. Grant, “Economics of EHV high phase order transmission,” IEEE Trans. Power App. Syst., vol. PAS-103, no. 11, pp. 3386–3392, Nov. 1984. [12] S. N. Tewari, G. K. Singh, and A. B. Saroor, “Multiphase power transmission research-a survey,” Elect. Power Syst. Res., vol. 24, pp. 207–215, 1992. [13] C. M. Portela and M. C. Tavares, “Six-phase transmission line-propagation characteristics and new three-phase representation,” IEEE Trans. Power Del., vol. 18, no. 3, pp. 1470–1483, Jul. 1993. [14] T. L. Landers, R. J. Richeda, E. Krizanskas, J. R. Stewart, and R. A. Brown, “High phase order economics: Constructing a new transmission line,” IEEE Trans. Power Del., vol. 13, no. 4, pp. 1521–1526, Oct. 1998. [15] J. M. Arroyo and A. J. Conejo, “Optimal response of power generators to energy, AGC, and reserve pool based markets,” IEEE Power Eng. Rev., vol. 22, no. 4, pp. 76–77, Apr. 2002. [16] M. A. Abbas, R. Chirsten, and T. M. Jahns, “Six-phase voltage source inverter driven induction motor,” IEEE Trans. Ind. Appl., vol. IA-20, no. 5, pp. 1251–1259, Sep./Oct. 1984.

40

[17] K. N. Pavithran, R. Parimelalagan, and M. R. Krsihnamurthy, “Studies on inverter fed fivephase induction motor drive,” IEEE Trans. Power Electron., vol. 3, no. 2, pp. 224–235, Apr. 1988. [18] G. K. Singh, “Multi-phase induction machine drive research—a survey,” Elect. Power Syst. Res., vol. 61, pp. 139–147, 2002. [19] M. Jones and E. Levi, “A literature survey of the state-of-the-art in multi-phase ac drives,” in Proc. Int. UPEC, Stafford, U.K., 2002, pp. 505–510. [20] R. Bojoi, F. Farina, F. Profumo, and A. Tenconi, “Dual-three phase induction machine drives control—A survey,” Inst. Elect. Eng. Jpn. Trans. Ind. Appl., vol. 126, no. 4, pp. 420–429, 2006. [21] E. Levi, R. Bojoi, F. Profumo, H. A. Toliyat, and S.Williamson, “Multiphase induction motor drives-A technology status review,” Inst. Eng. Technol. Electr. Power Appl., vol. 1, no. 4, pp. 489–516, Jul. 2007. [22] E. Levi, “Multiphase electric machines for variable-speed applications,” IEEE Trans Ind. Electron., vol. 55, no. 5, pp. 1893–1909, May 2008. [23] A. Iqbal and E. Levi, “Space vector PWM techniques for sinusoidal output voltage generation with a five-phase voltage source inverter,” Elect. Power Components Syst., vol. 34, no. 2, 2006. [24] A. Iqbal and E. Levi, “Space vector modulation schemes for a fivephase voltage source inverter,” presented at the Eur. Power Electron. Conf. EPE (CD-ROM.pdf), Dresden, Germany, 2005. [25] M. Jones, “A novel concept of a multi-phase multi-motor vector controlled drive system,” Ph.D. dissertation, Liverpool John Moores Univ., Liverpool, U.K., 2005.

41

[26] A. Iqbal, “Modelling and control of series-connected five-phase and six-phase two-motor drive,” Ph.D. dissertation, Liverpool John Moores Univ., Liverpool, U.K., 2006. [27] H. M. Ryu, J. H. Kim, and S. K. Sul, “Analysis of multi-phase space vector pulse width modulation based on multiple d-q spaces concept,” presented at the Int. Conf. Power Electronics and Motion Control IPEMC (CD-ROM Paper 2183.pdf.), Xian, China, 2004. [28] O. Ojo and G. Dong, “Generalized discontinuous carrier-based PWM modulation scheme for multi-phase converter-machine systems,” presented at the IEEE Ind. Appl. Soc. Annu. Meet. IAS (CD-ROM Paper no. 38P3), Hong Kong, China, 2005. [29] D. Dujic, M. Jones, and E. Levi, “Generalised space vector PWM for sinusoidal output voltage generation with multiphase voltage source inverter,” Int. J. Ind. Elect. Drives, vol. 1, no. 1, pp. 1–13, 2009. [30] M. J. Duran, F. Salas, and M. R. Arahal, “Bifurcation analysis of five-phase induction motor drives with third harmonic injection,” IEEE Trans. Ind. Electron., vol. 55, no. 5, pp. 2006–2014, May 2008. [31] M. R. Arahal and M. J. Duran, “Pi tuning of five-phase drives with third harmonic injection,” Control Eng. Practice, vol. 17, pp. 787–797, Feb. 2009. [32] D. Dujic, M. Jones, and E. Levi, “Analysis of output current ripple rms in multiphase drives using space vector approach,” IEEE Trans. Power Electron., vol. 24, no. 8, pp. 1926–1938, Aug. 2009. [33] M. Correa, C. R. da Silva, H. Razik, C. B. Jacobina, and E. da Silva, “Independent voltage control for series-connected six-and three-phase induction machines,” IEEE Trans. Ind. Appl., vol. 45, no. 4, pp. 1286–1293, Jul./Aug. 2009.

42

[34] S. Choi, B. S. Lee, and P. N. Enjeti, “New 24-pulse diode rectifier systems for utility interface of high power ac motor drives,” IEEE Trans. Ind. Appl., vol. 33, no. 2, pp. 531–541, Mar./Apr. 1997. [35] V. Garg, B. Singh, and G. Bhuvaneswari, “A tapped star connected autotransformer based 24-Pulse AC-DC converter for power quality improvement in induction motor drives,” Int. J. Emerging Electric Power Syst. Article 2, vol. 7, no. 4, 2006. [36] V. Garg, B. Singh, and G. Bhuvaneswari, “A 24 pulseAC-DC converter employing a pulse doubling technique for vector controlled induction motor drives,” Inst. Electron. Telecommun. Eng. J. Res., vol. 54, no. 4, pp. 314–322, 2008. [37] B. Singh and S. Gairola, “An autotransformer based 36 pulse controlled AC-DC converter,” Inst. Electron. Telecommun. Eng. J. Res., vol. 54, no. 4, pp. 255–262, 2008. [38] P. C. Krause, Analysis of. Electric Machinery. New York: McGraw- Hill, 1986.

43