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Interactive Power Electronics

Thảo luận trong 'ĐT Cơ Bản-Mạch tương tự' bắt đầu bởi small ant, 11 Tháng tư 2011.

  1. small ant Well-Known Member

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    Chapter 1

    Introduction to Power Electronics

    Definition

    Power electronics refers to control and conversion of electrical power by power semiconductor devices wherein these devices operate as switches. Advent of silicon-controlled rectifiers, abbreviated as SCRs, led to the development of a new area of application called the power electronics. Prior to the introduction of SCRs, mercury-arc rectifiers were used for controlling electrical power, but such rectifier circuits were part of industrial electronics and the scope for applications of mercury-arc rectifiers was limited. Once the SCRs were available, the application area spread to many fields such as drives, power supplies, aviation electronics, high frequency inverters and power electronics originated.



    Main Task of Power Electronics

    Power electronics has applications that span the whole field of electrical power systems, with the power range of these applications extending from a few VA/Watts to several MVA / MW.
    The main task of power electronics is to control and convert electrical power from one form to another. The four main forms of conversion are:

    • Rectification referring to conversion of ac voltage to dc voltage,
    • DC-to-AC conversion,
    • DC-to DC conversion and
    • AC-to-AC conversion.
    "Electronic power converter" is the term that is used to refer to a power electronic circuit that converts voltage and current from one form to another. These converters can be classified as:

    • Rectifier converting an ac voltage to a dc voltage,
    • Inverter converting a dc voltage to an ac voltage,
    • Chopper or a switch-mode power supply that converts a dc voltage to another dc voltage, and
    • Cycloconverter and cycloinverter converting an ac voltage to another ac voltage.
    In addition, SCRs and other power semiconductor devices are used as static switches


    Rectification

    Rectifiers can be classified as uncontrolled and controlled rectifiers, and the controlled rectifiers can be further divided into semi-controlled and fully-controlled rectifiers. Uncontrolled rectifier circuits are built with diodes, and fully-controlled rectifier circuits are built with SCRs. Both diodes and SCRs are used in semi-controlled rectifier circuits.
    There are several rectifier circuits rectifier configurations. The popular rectifier configurations are listed below.

    • Single-phase semi-controlled bridge rectifier,
    • Single-phase fully-controlled bridge rectifier,
    • Three-phase three-pulse, star-connected rectifier,
    • Double three-phase, three-pulse star-connected rectifiers with inter-phase transformer (IPT),
    • Three-phase semi-controlled bridge rectifier,
    • Three-phase fully-controlled bridge rectifier and
    • Double three-phase fully-controlled bridge rectifiers with IPT.
    Apart from the configurations listed above, there are series-connected and 12-pulse rectifiers for delivering high power output.
    Power rating of a single-phase rectifier tends to be lower than 10 kW. Three-phase bridge rectifiers are used for delivering higher power output, up to 500 kW at 500 V dc or even more. For low voltage, high current applications, a pair of three-phase, three-pulse rectifiers interconnected by an inter-phase transformer(IPT) is used. For a high current output, rectifiers with IPT are preferred to connecting devices directly in parallel. There are many applications for rectifiers. Some of them are:

    • Variable speed dc drives,
    • Battery chargers,
    • DC power supplies and Power supply for a specific application like electroplating

    DC - To - AC Conversion

    The converter that changes a dc voltage to an alternating voltage is called an inverter. Earlier inverters were built with SCRs. Since the circuitry required to turn the SCR off tends to be complex, other power semiconductor devices such as bipolar junction transistors, power MOSFETs, insulated gate bipolar transistors (IGBT) and MOS-controlled thyristors (MCTs) are used nowadays. Currently only the inverters with a high power rating, such as 500 kW or higher, are likely to be built with either SCRs or gate turn-off thyristors(GTOs). There are many inverter circuits and the techniques for controlling an inverter vary in complexity.
    Some of the applications of an inverter are listed below:

    • Emergency lighting systems,
    • AC variable speed drives,
    • Uninterrupted power supplies, and
    • Frequency converters.

    DC - To - DC Conversion

    When the SCR came into use, a dc-to-dc converter circuit was called a chopper. Nowadays, an SCR is rarely used in a dc-to-dc converter. Either a power BJT or a power MOSFET is normally used in such a converter and this converter is called a switch-mode power supply. A switch-mode power supply can be of one of the types listed below:

    • Step-down switch-mode power supply,
    • Step-up chopper,
    • Fly-back converter and
    • Resonant converter.
    The typical applications for a switch-mode power supply or a chopper are:

    • DC drive
    • Battery charger and
    • DC power supply.

    AC - To - AC Conversion

    A cycloconverter or a cycloinverter converts an ac voltage, such as the mains supply, to another ac voltage. The amplitude and the frequency of input voltage to a cycloconverter tend to be fixed values, whereas both the amplitude and the frequency of output voltage of a cycloconverter tend to be variable. On the other hand, the circuit that converts an ac voltage to another ac voltage at the same frequency is known as an ac-chopper.
    A typical application of a cycloconverter is to use it for controlling the speed of an ac traction motor and most of these cycloconverters have a high power output, of the order a few megawatts and SCRs are used in these circuits. In contrast, low cost, low power cycloconverters for low power ac motors are also in use and many of these circuit tend to use triacs in place of SCRs. Unlike an SCR which conducts in only one direction, a triac is capable of conducting in either direction and like an SCR, it is also a three terminal device. It may be noted that the use of a cycloconverter is not as common as that of an inverter and a cycloinverter is rarely used.



    Additional Insights into Power Electronics

    There are several striking features of power electronics, the foremost among them being the extensive use of inductors and capacitors. In many applications of power electronics, an inductor may carry a high current at a high frequency. The implications of operating an inductor in this manner are quite a few, such as necessitating the use of litz wire in place of single-stranded or multi-stranded copper wire at frequencies above 50 kHz, using a proper core to limit the losses in the core, and shielding the inductor properly so that the fringing that occurs at the air-gaps in the magnetic path does not lead to electromagnetic interference. Usually the capacitors used in a power electronic application are also stressed. It is typical for a capacitor to be operated at a high frequency with current surges passing through it periodically. This means that the current rating of the capacitor at the operating frequency should be checked before its use. In addition, it may be preferable if the capacitor has self-healing property. Hence an inductor or a capacitor has to be selected or designed with care, taking into account the operating conditions, before its use in a power electronic circuit.
    In many power electronic circuits, diodes play a crucial role. A normal power diode is usually designed to be operated at 400 Hz or less. Many of the inverter and switch-mode power supply circuits operate at a much higher frequency and these circuits need diodes that turn ON and OFF fast. In addition, it is also desired that the turning-off process of a diode should not create undesirable electrical transients in the circuit. Since there are several types of diodes available, selection of a proper diode is very important for reliable operation of a circuit.
    Analysis of power electronic circuits tends to be quite complicated, because these circuits rarely operate in steady-state. Traditionally steady-state response refers to the state of a circuit characterized by either a dc response or a sinusoidal response. Most of the power electronic circuits have a periodic response, but this response is not usually sinusoidal. Typically, the repetitive or the periodic response contains both a steady-state part due to the forcing function and a transient part due to the poles of the network. Since the responses are nonsinusoidal, harmonic analysis is often necessary. In order to obtain the time response, it may be necessary to resort to the use of a computer program.
    Power electronics is a subject of interdisciplinary nature. To design and build control circuitry of a power electronic application, one needs knowledge of several areas, which are listed below.

    • Design of analogue and digital electronic circuits, to build the control circuitry.
    • Microcontrollers and digital signal processors for use in sophisticated applications.
    • Many power electronic circuits have an electrical machine as their load. In ac variable speed drive, it may be a reluctance motor, an induction motor or a synchronous motor. In a dc variable speed drive, it is usually a dc shunt motor.
    • In a circuit such as an inverter, a transformer may be connected at its output and the transformer may have to operate with a nonsinusoidal waveform at its input.
    • A pulse transformer with a ferrite core is used commonly to transfer the gate signal to the power semiconductor device. A ferrite-cored transformer with a relatively higher power output is also used in an application such as a high frequency inverter.
    • Many power electronic systems are operated with negative feedback. A linear controller such as a PI controller is used in relatively simple applications, whereas a controller based on digital or state-variable feedback techniques is used in more sophisticated applications.
    • Computer simulation is often necessary to optimize the design of a power electronic system. In order to simulate, knowledge of software package such as MATLAB and the know-how to model nonlinear systems may be necessary.
    The study of power electronics is an exciting and a challenging experience. The scope for applying power electronics is growing at a fast pace. New devices keep coming into the market, sustaining development work in power electronics.



    Structure of this Online Text

    The text contains several chapters. Each chapter is divided into sections. Each section is presented as a separate page. Each page is on a separate topic or a separate circuit. Each circuit is described in detail and in addition, a sufficiently high level of mathematical analysis has also been presented. It has also been how the circuit can be simulated using Pspice, MathCad and Matlab. In addition, there would be an interactive Java applet to illustrate how the circuit operates.

    Chapter 2

    A Single Diode Circuit


    Circuit Operation

    [IMG]
    A circuit with a single diode and an RL load is shown above. The source vs is an alternating sinusoidal source. If vs = E * sin (wt), vs is positive when 0 < wt < p, and vs is negative when p < wt <2p. When vs starts becoming positive, the diode starts conducting and the positive source keeps the diode in conduction till wt reaches p radians. At that instant defined by wt = p radians, the current through the circuit is not zero and there is some energy stored in the inductor. The voltage across an inductor is positive when the current through it is increasing and it becomes negative when the current through it tends to fall. When the voltage across the inductor is negative, it is in such a direction as to forward-bias the diode. The polarity of voltage across the inductor is as shown in the sketches shown below.
    [IMG]
    [IMG]
    When vs changes from a positive to a negative value, there is current through the load at the instant wt = p radians and the diode continues to conduct till the energy stored in the inductor becomes zero. After that the current tends to flow in the reverse direction and the diode blocks conduction. The entire applied voltage now appears across the diode.

    Mathematical Analysis

    An expression for the current through the diode can be obtained as shown below. It is assumed that the current flows for 0 < wt < b, where b > p . When the diode conducts, the driving function for the differential equation is the sinusoidal function defining the source voltage. During the period defined by b < wt < 2p, the diode blocks current and acts as an open switch. For this period, there is no equation defining the behaviour of the circuit. For 0 < wt < b, the equation (1) defined below applies.
    [IMG]
    Given a linear differential equation, the solution is found out in two parts. The homogeneous equation is defined by equation (2). It is preferable to express the equation in terms of the angle q instead of 't'. Since q = wt, we get that dq = w.dt. Then equation (2) then gets converted to equation (3). Equation (4) shown above is the solution to this homogeneous equation and is called the complementary integral.
    The value of constant A in the complimentary solution is to be evaluated later.
    The particular solution is the steady-state response and equation (5) expresses the particular solution. The steady-state response is the current that would flow in steady-state in a circuit that contains only the source, the resistor and the inductor shown in the circuit above, the only element missing being the diode. This response can be obtained using the differential equation or the Laplace transform or the ac sinusoidal circuit analysis. The total solution is the sum of both the complimentary and the particular solution and it is shown as equation (6). The value of A is obtained using the initial condition. Since the diode starts conducting at wt = 0 and the current starts building up from zero, i(0) = 0. The value of A is expressed by equation (7).

    Once the value of A is known, the expression for current is known. After evaluating A, current can be evaluated at different values of wt, starting from wt = p. As wt increases, the current would keep decreasing. For some value of wt, say b , the current would be zero. If wt > b , the current would evaluate to a negative value. Since the diode blocks current in the reverse direction, the diode stops conducting when wt reaches b. Then an expression for the average output voltage can be obtained. Since the average voltage across the inductor has to be zero, the average voltage across the resistor and the average voltage at the cathode of the diode are the same. This average value can be obtained as shown in equation (8).
    [IMG]


    Interactive Simulation


    The operation of the circuit can be simulated as shown below. In order to simulate, the solution for current is presented in the following form, where t = (wL)/R. Then
    [IMG]
    Again it is preferable to normalize. Here E is set to unity and E/R is also set to unity. Then
    vs = sin (wt).
    vo = i for 0 < wt < b,
    vL = vs - i for 0 < wt < b
    To solve the expression, all we need to know is then the ratio t. The applet shown below simulates this circuit. You have to key-in the ratio t and then click on the button next to it. Do not key-in NaN.

    The next page presents the same circuit with an additional diode.


    PSPICE Simulation


    For simulation using Pspice, the circuit used is shown below. Here the nodes are numbered. The ac source is connected between nodes 1 and 0. The diode is connected between nodes 1 and 2 and the inductor links nodes 2 and 3. The resistor is connected from 3 to the reference node, that is, node 0.
    [IMG]
    The Pspice program is presented below.
    * First Chapter: Half-wave Rectifier with RL Load
    * A problem to find the diode current
    VIN 1 0 SIN(0 340V 50Hz)
    D1 1 2 DNAME
    L1 2 3 31.8MH
    R1 3 0 10
    .MODEL DNAME D(IS=10N N=1 BV=1200 IBV=10E-3 VJ=0.6)
    .TRAN 10US 60.0MS 20.0MS 10US
    .PROBE
    .OPTIONS(ABSTOL=1N RELTOL=.01 VNTOL=1MV)
    .END
    The diode is described using the MODEL statement. The TRAN statement simulates the transient operation for a period of 60 ms at an interval of 10 ms. The OPTIONS statement sets limits for tolerances. The output can be viewed on the screen because of the PROBE statement. A snapshot of output is presented below.

    [IMG]


    MATLAB Simulation

    The Matlab program used is re-produced below.
    % Program to simulate the half-wave rectifier circuit
    % Enter the peak voltage, frequency, inductance L in mH and resistor R
    disp('Typical value for peak voltage is 340 V')
    peakV=input('Enter Peak voltage in Volts>');
    disp('Typical value for line frequency is 50 Hz')
    freq=input('Enter line frequency in Hz>');
    disp('Typical value for Load inductance is 31.8 mH')
    L=input('Enter Load inductance in mH>');
    disp('Typical value for Load Resistance is 10.0 Ohms')
    R=input('Enter Load Resistance in Ohms>');

    w=2.0*pi*freq;
    X=w*L/1000.0;
    if (X<0.001) X=0.001; end;
    Z=sqrt(R*R+X*X);
    loadAng=atan(X/R);
    A=peakV/Z*sin(loadAng);
    tauInv=R/X;

    for n=1:360;
    theta=n/180.0*pi;
    X(n)=n;
    cur=peakV/Z*sin(theta-loadAng)+A*exp(-tauInv*theta);
    if (cur>0.0)
    Vind(n)=peakV*sin(theta)-R*cur;
    iLoad(n)=cur;
    Vout(n)=peakV*sin(theta);
    else
    Vind(n)=0;
    iLoad(n)=0;
    Vout(n)=0;
    end;
    end;

    plot(X,iLoad)
    title('The diode current')
    xlabel('degrees')
    ylabel('Amps')
    grid
    pause

    plot(X,Vout)
    title('Voltage at cathode')
    xlabel('degrees')
    ylabel('Volts')
    grid
    pause

    plot(X,Vind)
    title('Inductor Voltage')
    xlabel('degrees')
    ylabel('Volts')
    grid
    The plots obtained for the typical values mentioned are shown below.
    [IMG]
    [IMG]
    [IMG]
    It can be seen from the waveform of voltage across the inductor is that the area above the x-axis at 0 V is equal to its area below the x-axis. It can be seen that the matlab program is relatively simple.

    Chapter 3


    A Single SCR Circuit


    This chapter describes a circuit with a single SCR. It is similar to the single diode circuit, the difference being that an SCR is used in place of the diode. Most of the power electronic applications operate at a relative high voltage and in such cases, the voltage drop across the SCR tends to be small. It is quite often justifiable to assume that the conduction drop across the SCR is zero when the circuit is analysed. It is also justifiable to assume that the current through the SCR is zero when it is not conducting. It is known that the SCR can block conduction in either direction. The explanation and the analysis presented below is based on the ideal SCR model. It is also assumed that the reader knows how an SCR operates.
    The next chapter shows how the behaviour of this circuit can be changed by adding a free-wheeling diode.



    Circuit Operation

    [IMG]
    A circuit with a single SCR and an RL load is shown above. The source vs is an alternating sinusoidal source. If vs = E * sin (wt), vs is positive when 0 < wt < p, and vs is negative when p < wt <2p. When vs starts becoming positive, the SCR is forward-biased but remains in the blocking state till it is triggered. If the SCR is triggered at when wt = a, then a is called the firing angle. When the SCR is triggered in the forward-bias state, it starts conducting and the positive source keeps the SCR in conduction till wt reaches p radians. At that instant, the current through the circuit is not zero and there is some energy stored in the inductor at wt = p radians. The voltage across an inductor is positive when the current through it is increasing and it becomes negative when the current through the inductor tends to fall. When the voltage across the inductor is negative, it is in such a direction as to forward-bias the SCR.
    There is current through the load at the instant wt = p radians and the SCR continues to conduct till the energy stored in the inductor becomes zero. After that the current tends to flow in the reverse direction and the SCR blocks conduction. The entire applied voltage now appears across the diode.



    Mathematical Analysis

    An expression for the current through the SCR can be obtained as shown below. It is assumed that the current flows for a < wt < d, where d > p . When the SCR conducts, the driving function for the differential equation is the sinusoidal function defining the source voltage. Outside this period, the SCR blocks current and acts as an open switch. For this period, there is no equation defining the behaviour of the circuit. For a < wt < d , equation (1) applies. Given a linear differential equation, the solution is found out in two parts. The homogeneous equation is given by equation (2), where a is the firing angle. The value of constant A in the complimentary solution is to be evaluated later. The particular solution is the steady-state response and is diplayed as equation (3). The total solution is the sum of both the complimentary and the particular solution and is presented as equation (4). The value of A is obtained using the initial condition. Since the SCR starts conducting at wt = a and the current starts building up from zero, i(a) = 0. In the expression above t = wL/R. Then A can be expressed as in equation (5).
    Once the value of A is known, the expression for current is known. When the firing angle a and the extinction angle d are known, the average output voltage at the cathode of the SCR can be evaluated as shown in equation (6).
    [IMG]
    The average load current can be obtained by dividing the average load voltage by the load resistance, since the average voltage across the inductor is zero.


    Simulation

    The operation of the circuit can be simulated as shown below. In order to simulate, the solution for current is presented in the following form, wheret = (wL)/R. Then
    Again it is preferable to normalize. Here E is set to unity and E/R is also set to unity. Then
    vs = sin (wt).
    vo = vs - i for a < wt < d, and
    vL = vs - i for a < wt < d.
    To solve the expression, all we need to know is then the ratio t. The applet shown below simulates this circuit. You have to key-in the ratio t and then click on the button next to it. Do not key-in a NaN. Enter the ratio t in the left text-field to the left of the click button and the firing angle in degrees in the textfield to its right.

    The next page presents the same circuit with a free-wheeling diode.



    PSPICE Simulation

    The program below presents a PSPICE program. The circuit used is shown below. [IMG] The PSPICE program shown below presents the SCR as a subcircuit. This model of the SCR has been described in the book SPICE FOR POWER ELECTRONICS AND ELECTRIC POWER (Muhammed H.Rashid, Prentice-Hall , 1993, pages 148-160).
    * Half-wave Rectifier with RL Load * A problem to find the SCR current VIN 1 0 SIN(0 340V 50Hz) XT1 1 2 5 2 SCR VP 5 2 PULSE(0 10 1667U 1N 1N 100U 20M) L1 2 3 31.8MH R1 3 0 10 * Subcircuit for SCR .SUBCKT SCR 101 102 103 102 S1 101 105 106 102 SMOD RG 103 104 50 VX 104 102 DC 0 VY 105 107 DC 0 DT 107 102 DMOD RT 106 102 1 CT 106 102 10U F1 102 106 POLY(2) VX VY 0 50 11 .MODEL SMOD VSWITCH(RON=0.0105 ROFF=10E+5 VON=0.5 VOFF=0) .MODEL DMOD D((IS=2.2E-15 BV=1200 TT=0 CJO=0) .ENDS SCR .TRAN 10US 60.0MS 20.0MS 10US .PROBE .OPTIONS(ABSTOL=1N RELTOL=.01 VNTOL=1MV) .END The waveforms obtained are presented below.
    [IMG]
    The voltage waveform at the cathode of the SCR
    [IMG]
    The load current waveform
    [IMG]
    The inductor voltage waveform
    [IMG]
    The voltage waveform acros the SCR
    [IMG]
    The voltage waveform of the pulse source used for triggering the SCR


    MATLAB Simulation


    The Matlab program used for simulation is presented below.
    The waveforms obtained for the typical specified values are displayed now.
    [IMG]
    [IMG]
    [IMG]
    The output file containing the values of average load current and the RMS load current is presented below.
    Avg Load Cur= 8.481852e+000 RMS Load Cur= 12.878237

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