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Transcript

ECE 8830 - Electric Drives Topic 9: Current-Fed Inverters Spring 2004 Introduction Current-fed inverters requires a “stiff” constant current source input - thus are sometimes referred to as CSI (current source inverters or current stiff inverters). A large inductance can be used to change a variable voltage input to a variable current input. VSI-inverters and CSI-inverters are dual to each other. Introduction (cont’d) Power semiconductor devices used in CSI inverters must be able to withstand large reverse voltages. Therefore, power MOSFETs, BJTs, IGBTs, MCTs, IGCTs and GTOs. Symmetric blocking GTOs and thyristors can be used in CSI inverters. Generally CSI inverters are now used in very high power applications. General Operation of a 6-Step Thyristor Inverter General Schematic of Thyristor Inverter General Operation of a 6-Step Thyristor Inverter (cont’d) Initially, ignore commutation considerations. Induction motor load is modeled by back emf generator and leakage inductance in each phase of the winding. The constant dc current Id is switched through the thyristors to create a 3 6-step symmetrical line current waves as shown on the next slide. General Operation of a 6-Step Thyristor Inverter (cont’d) General Operation of a 6-Step Thyristor Inverter (cont’d) The load or line current may be expressed by a Fourier series as: 1 1 ia I d cos t cos 5 t cos 7 t ... 5 7 2 3 where the peak value of the fundamental component is2 given / 3 2 3I d / . Each thyristor conducts for radians. At any instant one upper thyristor and one lower thyristor conduct. General Operation of a 6-Step Thyristor Inverter (cont’d) The dc link is considered harmonic-free and the commutation effect between thyristors is ignored. At steady state the voltage output from the rectifier block = input voltage of inverter. For a variable speed drive the inverter can be operated at variable frequency and variable dc current Id. General Operation of a 6-Step Thyristor Inverter (cont’d) If thyristor firing angle > 0, inverter behavior. If thyristor firing angle =0, rectifier behavior. Max. power transfer occurs when =. Inverter Operation Modes Two inverter operation modes are established depending on the thyristor firing angle: 1) Load-commutated inverter Applies when /2<<. 2) Force-commutated inverter Applies when <<3/2. Load-Commutated Inverter Mode Consider =3/4. In this case vca < 0 => thyristor Q5 is turned off by the load. This requires load to operate at leading power factor => motoring mode of a synchronous machine operating in over-excitation. Vd=-Vd0cos Force-Commutated Inverter Mode Consider =5/4. In this case vca> 0 and so thyristor Q5 is not turned off by the load. Thus some type of forced commutation is required in this case. Lagging VAR is consumed by the load => motoring mode of an induction motor. Vd=-Vd0cos Force-Commutated Inverters For driving an induction machine, a force-commutated inverter is required because of the phase lag characteristic of the induction motor. The topology of a 3 bridge inverter with an auto-sequential method of forced commutation is shown on the next slide. Force-Commutated Inverters (cont’d) Ref: D.W. Novotny and T.A. Lipo, “Vector Control and Dynamics of AC Drives” Force-Commutated Inverters (cont’d) The current is switched sequentially into one of the motor phases by the top half of the inverter and returns to the dc link from another of the phases via the bottom half of the inverter. By switching every 2/3 radians, a 6-step current waveform can be applied to the motor. The series diodes and delta-connected capacitors force the commutation of the thyristors. The capacitors store a charge with the correct polarity for commutation and the diodes isolate them from the load. Force-Commutated Inverters (cont’d) Since current is constant, voltage drop across stator windings = 0 and voltage drop across winding resistances = constant. Thus the motor terminal voltage is set by the motor not by the inverter. Since the motor is wound with sinusoidally distributed windings, the voltages at the motor terminals are nearly sinusoidal. Force-Commutated Inverters (cont’d) The current ideally follows a six-step waveform. However, current cannot change instantaneously through the winding inductances and so the current transitions have a finite slope. During these transitions the current transfers from one thyristor to the next via one of the six commutating capacitors. Force-Commutated Inverters (cont’d) Example: Commutation from Q2 to Q4 Force-Commutated Inverters (cont’d) When Q4 is fired, Q2 is impressed with a reverse voltage across the capacitor bank. => Q2 turns off almost instantaneously. Id flows through Q3 and D3, phases b and c, D2, the capacitor bank and Q4. The capacitor bank charges linearly with Id. During this time D4 is reverse-biased. When the capacitor bank voltage equals the line voltage, diode D4 turns on and the current Id flows through D4 and terminates the commutation process. Force-Commutated Inverters (cont’d) Ref: D.W. Novotny and T.A. Lipo, “Vector Control and Dynamics of AC Drives” Force-Commutated Inverters (cont’d) Note the large voltage spikes (Ldi/dt). These can be suppressed either by designing the motor with small leakage inductance or by using a diode bridge at the motor terminal with a zener diode load. Force-Commutated Inverters (cont’d) Two positive features of CSI inverters compared to VSI inverters: 1) CSI inverters are able to ride through a commutation failure and return naturally to normal operation; costly preventive measures used for VSI inverters. 2) CSI inverters can be switched to regenerative mode simply by reversing the polarity of the dc rectifier output voltage. This is automatically accomplished when an induction motor operates in a negative slip mode. In the VSI inverter, the current flow must be reversed - much harder. Force-Commutated Inverters (cont’d) On the other hand, CSI drives cannot be operated in open loop operation as can VSI drives. The torque-speed characteristics of an induction motor driven by a voltage source and a current source are shown below: Ref: D.W. Novotny and T.A. Lipo, “Vector Control and Dynamics of AC Drives” Force-Commutated Inverters (cont’d) A distinct “peaking” occurs in the current source case. Two possible operating points: 1) One on the stable, negatively sloped region, and 2) one above breakdown torque on the positively sloped region where operation is generally unstable (depending on load torque vs. speed characteristics). Force-Commutated Inverters (cont’d) On the stable side, the working flux in the machine is is high => saturated operation and excessive magnetizing current and iron losses. Thus, continuous operation is not feasible on this side. On the unstable side, the flux in the machine is near its rated value and losses are reasonable. However, being on the unstable side, feedback control must be used to maintain the operating point. Force-Commutated Inverters (cont’d) One system uses a motor voltage control loop (see next slide) which regulates the motor voltage by controlling the input phase controlled rectifier. Also, an internal current control loop is used with the voltage error serving as a reference signal for the current regulator. Some IR drop compensation is often added as are additional compensating circuits to improve system dynamics. Force-Commutated Inverters (cont’d) Ref: D.W. Novotny and T.A. Lipo, “Vector Control and Dynamics of AC Drives” Force-Commutated Inverters (cont’d) ASCI inverter-fed induction motor drives for medium to high power applications were popular. However, the size and cost of the commutating capacitors and the dc link inductor are the major disadvantages of this type of inverter. ASCI inverters are being replaced with inverters using self-controlled devices (e.g. GTOs). Six-Step CSI with Self-Commutated Devices Self-controlled symmetric blocking devices, e.g. GTO’s can be turned on and off by gate current pulses. This allows the 6-step waveform to be directly controlled. Six-Step CSI with Self-Commutated Devices (cont’d) In this circuit, the capacitors are freed from their commutating requirement and are simply placed across the terminals of the induction motor. These capacitors are much smaller and serve two roles: 1) primarily, to allow commutation from the outgoing GTO to the incoming GTO, 2) secondarily, to load filter higher harmonics Six-Step CSI with Self-Commutated Devices (cont’d) Example: Commutation from Q1 to Q3. Six-Step CSI with Self-Commutated Devices (cont’d) Initially current flows through Q1, phase a, phase c, and Q2. The equivalent capacitance Ceq and polarity of vba are as shown. Next, Q3 is turned on at time A. But because of voltage across Ceq, Q1 does not automatically turn off. Next, Q1 is turned off.The current Id transfers to Q3 and through Ceq. Ceq charges up overcoming the motor back emf b/w phases a and b. Gradually the current transfers to phase b. Commutation is completed when ib=Id. Six-Step CSI with Self-Commutated Devices (cont’d) Total commutation time is tc. Once commutation is complete, current can be commutated back to Q1. This back and forth current commutation can be used to create a PWM current wave and with suitable selection of notch angles, can be used to suppress higher harmonics (just as in the VSI inverter). Six-Step CSI with SelfCommutated Devices (cont’d) A major disadvantage of this scheme is the potential for resonance between the capacitors and the motor inductance. Care must be taken to avoid impressing current harmonics into the motor/capacitor network which will excite one of the system resonance frequencies. This can be avoided by careful use of PWM. However, since the motor parameters must be known to implement such an approach, this drive is not popular for generalpurpose applications. PWM Inverters The six-step CSI inverter has several disadvantages primarily associated with harmonics in the current waves. Pulse width modulation can be used to reduce the harmonic content of the current waves. The PWM methods are somewhat different from those for the voltage-fed inverters. Trapezoidal PWM Similar to the sinusoidal PWM method for voltage-fed converter. This method is shown below: Trapezoidal PWM Trapezoidal wave has max. amplitude of B and is compared to a triangle wave of amplitude A. For the first /3 radians both waves are compared. For the next /3 radians no triangular wave is applied. For the final /3 radians both waves are compared again. Two variables: 1) modulation index m=B/A 2) pulse number M in halfcycle of inverter operation. Trapezoidal PWM (cont’d) For M=21, harmonics vs. m is as shown below: At m=0.82, 5th harmonic =0, 7th harmonic=4%, 11th harmonic=1% and 13th harmonic=2%. Trapezoidal PWM (cont’d) The output current waves for these conditions is shown below: Trapezoidal PWM (cont’d) To limit switching losses it is necessary to control the device switching frequency, irrespective of the fundamental frequency of the current waveform. This can be achieved by making the parameter M constant in many segments of the fundamental frequency (see next slide for switching frequency 1kHz). Note: In multi-MW GTO inverters the switching frequency generally does not exceed a few hundred Hz. Trapezoidal PWM (cont’d) Trapezoidal PWM can reduce harmonic components up to order n=1.5(M+1) for M > 9 but does produce a pair of harmonics of order 3(M-1)1. Selected Harmonic Elimination PWM SHE-PWM can both lower the harmonic content of the output current and, more importantly, remove the resonant harmonic. Unlike SHE-PWM for voltage-fed inverters, several restrictions apply for application of SHE-PWM to current-fed inverters. Consider the 3 current waveforms for M=5 shown in the next slide. Selected Harmonic Elimination PWM (cont’d) Selected Harmonic Elimination PWM (cont’d) Angles 1 and 2 are the variables and all the other switching angles are in terms of these two variables. With two variables, two switching harmonics (e.g. 5th and 7th) can be eliminated. The fundamental is controlled by the dc link current frequency. The general relation between # of harmonics removed (K) and # of pulses per half cycle (M) is given by: K=(M-1)/2 Both K and M are odd numbers. Selected Harmonic Elimination PWM (cont’d) For M=3, only one harmonic (e.g. 5th) can be eliminated and for M=7, three harmonics (e.g. 5th, 7th and 11th) can be eliminated. Selected Harmonic Elimination PWM (cont’d) Double-Sided CSI Converter As mentioned earlier, the CSI converter can easily be used to send power back into the rectifier when the machine acts as a generator. In this case the load-side converter acts as a rectifier and the lineside converter acts as an inverter. Duality of Current-Fed and Voltage-Fed Inverters Ref: D.W. Novotny and T.A. Lipo, “Vector Control and Dynamics of AC Drives” Current-Fed vs. Voltage-Fed Inverters Current-Fed Inverters Voltage-Fed Inverters 1. More interactive with the load and hence require a close match to the machine. 2. Inherent 4-quadrant operation. 3. Robust through load short circuits/inverter misfirings. Not so interactive with machine and can thus be designed to be more general purpose. Requires additional circuitry to operate in all 4 quadrants. Shoot-through faults need to be avoided (use freewheel diodes). Current-Fed vs. Voltage-Fed Inverters Current-Fed Inverters Voltage-Fed Inverters 4. Devices must be symmetric blocking. 5. Multi-machine or multi-inverter system inverter system very difficult to implement. 6. Relatively sluggish response. Devices must be assymmetric blocking. Normally used for multi-machine or multiinverter system applications. PWM inverters can demonstrate relatively fast dynamic response. Current-Fed vs. Voltage-Fed Inverters Current-Fed Inverters Voltage-Fed Inverters 7. Cannot be operated open-loop. Can be operated openloop. 8. Minimum load required. Can operate at no-load. Based on these differences, PWM voltage-fed inverters are most widely used for motor drives. However, current-fed inverters are used for high-power applications, particularly loadcommutated synchronous motor drives. d,q Model for CSI Inverter The duality of VSI and CSI systems implies that the switching function models for CSI systems should be the duals of those for the VSI systems. The exact dual of a VSI feeding a Y connected load is a CSI feeding a connected load. However, since we generally want to consider Y connected loads, the model for the CSI inverter will not be the exact dual of the VSI inverter (but it will be close). d,q Model for CSI Inverter (cont’d) The d,q equations for each switching mode for the CSI inverter are obtained in the same way as for the VSI inverter. The six switching modes for the CSI inverter are shown on the next slide. d,q Model for CSI Inverter (cont’d) Ref: D.W. Novotny and T.A. Lipo, “Vector Control and Dynamics of AC Drives” d,q Model for CSI Inverter (cont’d) The d,q equations, in the stationary stator reference frame, can be written in terms of CSI inverter switching functions, h as: i s qs 2 3 h i ; i s qs i s ds 2 3 s ds i h i ; vi 3 3 (vqss hqss vdss hdss ) where the switching functions (shown on the next slide) can be expressed as Fourier series by: 1 1 h cos et cos 5 et cos 7 et ... 5 7 1 1 hdss sin et sin 5 et sin 7 et ... 5 7 s qs d,q Model for CSI Inverter (cont’d) Ref: D.W. Novotny and T.A. Lipo, “Vector Control and Dynamics of AC Drives” d,q Model for CSI Inverter (cont’d) These equations can be written in complex form as: i s qds 2 3 vi where h s qds ii (h jh ) s qs 3 3 e j et s ds s s 2 3 s ii h qds † Re[v qds h qds ] 1 5 jet 1 7 jet e e ... 5 7 Note that these are very similar to the VSI equations. In particular, only the signs in hqdss are altered. d,q Model for CSI Inverter (cont’d) As before we observe that the complex vector current is constant in each mode and simply shifts by 60 at each mode transition. We can write: i s qds 2 ii e j[ / 6( k 1)( / 3)] 3 for k=1, 2, 3, 4, 5, and 6. The six vectors corresponding to the switching of a CSI inverter are shown in the next slide. d,q Model for CSI Inverter (cont’d) Ref: D.W. Novotny and T.A. Lipo, “Vector Control and Dynamics of AC Drives” d,q Model for CSI Inverter (cont’d) See handout for d,q model for CSI inverter in stationary reference frame.