min permanent magnet generator-3 phase full wave rectifier load system, Figure(1). The resulting model was used to study the generator-load system ...
machine parameters obtained from magnetic field solutions. Thus, the inherent nonlinearities and space harmonics in the flux linkages, inductances, as well as induced emfs are fully accounted for in this modeling and analysis approach. This method was applied to a two-pole, 75 kVA, 208 V, 24000 r/ min permanent magnet generator-3 phase full wave rectifier load system, Figure (1). The resulting model was used to study the generator-load system performance. Details of developing this model are given in the paper. Accordingly, by using generalized concepts of network graph theory in conjunction with hybrid matrix formulation of nonlinear networks, see references [51 and [91 in the paper, the state equations associated with this system were automatically formulated and continuously updated in a computer-aided network solution program. One of the major advantages of this modeling approach is the ability to reconstruct individual damper bar currents from the equivalent damping currents resulting from the simulations, including effects of the various inherent space harmonics associated with the machine's winding and magnetic circuit configurations. For example, from this model the current in a sample damper bar was determined, see Figure (2). Figure (2) demonstrates that the damper bars have a sustained (steady state) current of nonzero value, as expected. This is due to the continuous switching of the diodes in the rectifier load, which results in a continuous relative motion between the armature mmf and the rotor mounted damper bars, leading to perpetually induced currents in these bars. Furthermore, the model was used in studying rotor damping design options and the impact of incorporation of the damping effects on the overall generator-load system power. Here, three rotor damping design options were studied. Results of some performance characteristics are given in Table (1). Examination of the predicted performance results of rotor design options #1 through #3, Table (1), reveals that the existence of two sets of damping windings on the rotor in option #1 as compared to the lack of rotor damping windings in option #3 leads to a rise in the system's output power capability of about 4.3%. More details are given in the paper. Furthermore, the effects of electronic component failure in the associated rectifier bridge on the generator-rectifier load system performance, were studied. The type of fault simulated involves that of a diode failure leading to a short followed by an open circuit caused by fusing action. This resulted in a phase unbalance resulting from opening one of the three armature phases. The effect of this unbalanced operating condition is seen here by the higher current swings in the above mentioned sample damper bar current profile, Figure (3). These current swings are attributed to the "negative sequence like" nature of the phase unbalance resulting from opening one of the three armature phases, which leads to a strengthened relative motion between the rotor's damper bars and the field created by the unbalanced armature currents. Additional results from this investigation are given in the paper.
D1
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Fig. 2. Sample Damper Bar Current.
#1: #2: #3:
TABLE 1 Effect of Damping Circuits on System Performance PM Generator-Rectifier Load System Performance Phase Current DC Current Load Power (Peak) (Average) (Average) 179.3 A 160.6 A 62.14 kW Cage + Collar 176.3 A 158.9 A 60.74 kW Cage No Damping 175.8 A 157.3 A 59.52 kW
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Fig. 1. Permanent Magnet Generator-Rectifier-Load System Schematic Diagram.
IEEE Power Engineering Review, September 1989
89 WM 247-8 September 1989
Voltage Compensation of an Induction Generator with Long-Shunt Connection E. Bim, J. Szajner, and Y. Burian Faculdade de Engenharia El6trica-UNICAMP Caixa Postal 6101-13081 -Campinas, SP-Brasil For an induction generator, initial studies of the voltage vs. speed relationship and stability analysis of the generated voltage are presented. Voltage compensation of the self-excited induction generator is described and applied to a prototype machine. From expressions that relate angular speed and parameters of the equivalent circuit of the induction generator (at no-load'and loaded), qualitative voltage vs. speed curves are obtained. Laboratory tests are used to confirm these results. In the prototype machine, an unstable region for the generated
53
voltage is verified in the self-excited induction generator. From Loeb's criterion, the stability condition is obtained. In order to keep a constant terminal voltage in the induction generator, at a given speed, the fixed capacitor-thyristor controlled reactor type of static compensation has been used. In this paper, the reactive compensation technique (series-parallel ferro-resonance or two-capacitor method), applicable to saturable reactors, is used. The basic circuit used to implement the long-shunt connection of the capacitors is shown in Figure 1.a and 1.b, where the machine is represented by means of a saturable magnetizing inductance Lm. The value of the series and parallel capacitors are obtained from the saturation curve of the machine. The maximum voltage drop was about 4%, for the full-load induction generator. R S T
6
Cs
vr,l6C
Cs
c
8
c
:V
(a)(
Fig. 3. Long-shunt connection of the machine. (a) Generator-capacitors connection. (b) Per-phase equivalent circuit.
the subtransient reactances are less distinct. The commutating reactance will inevitably be a function of duration of commutation due to the skin effect produced by eddy currents within the solid pole iron. Also, the position of the rotor will influence the effective reactance the stator windings will see, so the commutating reactance will also be a function of rotor angle. The motor power factor will reduce as as
commutation time increases, and therefore a precise method of calculating x, is desirable especially for solid salient pole motors. A magnetic circuit method, based on the work of C. J. Carpenter, models a machine cross section which is linked to the stator electrical circuit making possible a direct coupling of the magnetic circuit with the inverter. The inter-linking of magnetic and electric circuits was achieved by the use of gyrators which fully satisfy the electromagnetic linkage equations. This method also allowed an exact representation of each stator phase-band distribution in the magnetic circuit. A layered structure of permeances regularly interspersed with "magnetic resistors" allowed for skin effects, associated with flux penetration in the solid rotor poles, magnetic resistances representing damping due to eddy currents in the solid iron. The circuits were solved using a numerical circuit solving routine S.P.I.C.E. Treating commutation as a line-to-line short circuit, initial studies were performed on a two pole pitch model neglecting motion. Commutation of a micro-alternator fitted with a solid rotor was measured and results compare well with those computed from the circuit approach. Motion has been considered by rotating stator conductors relative to a stationary stator and rotor. This effectively means the linkages between the electric and magnetic circuits become a function of time. The flux cutting rule is implemented within the magnetic circuit model to allow for the change of flux pattern due to motion. A field circuit linked to the rotor magnetic circuit enables the generation of back emf at the stator terminals. A full representation of the synchro-inverter system is thus made possible with the simple addition of the inverter power electronics in the stator circuit.
89 WM 242-9 September 1989
Circuit Representation of Inverter-Fed Synchronous Motors
89 WM 245-2 September 1989
M. J. Carpenter, Non-member Brush Electrical Machines Loughborough England D. C. Macdonald, Member Imperial College London SW7 2BT England
Speed Control of a DC Series Motor Using a Modulated Phase-Angle Controlled Single Triac N. H. Fetih, G. A. Girgis, and G. M. Abdel-Raheem Electrical Engineering Dept., Assiut. Univ., Assiut, Egypt
Inverter-fed synchronous motors are in use as variable speed drives, the thyristor inverters being naturally commutated by machine voltage. To achieve commutation the machine phase current has to be commutated before line-to-line voltage drops to zero, that is the machine has to run over-excited. Power factor can be kept nearest unity (and machine size minimized) by keeping the firing angle of the inverter to a minimal value. The firing angle should be of sufficient value to allow for commutation time u, plus a safety angle, the safety angle being necessary to ensure the thyristor recovers its blocking capability. Commutation time depends on: i) ii) iii) iv)
load current magnitude voltage magnitude inverter firing angle machine response to commutation, usually expressed mutating reactance, x,.
as com-
The first three factors are known for a specific operating point. Commutation reactance is often taken as the average of the d and q axis subtransient reactances, which is likely to be a good approximation if there is a complete damper cage present and the subtransient reactances are approximately equal. There remains the question of whether this yields the correct reactance, although it is thought to be a good approximation for laminated rotor machines. Solid salient-pole machines present a substantially different picture
54
The speed control of a dc series motor using the integral-cycle control method of thyristors (or triacs) triggering has some advantages over that using the phase-angle one. However, the integralcycle controlled motor suffers from the relatively high speed ripples, especially at low ratios of the ON/OFF motor applied supply cycles. In this paper the method of controlling the speed of a dc series motor using a modulated phase-angle controlled single triac is introduced. The suggested method has reduced the motor speed ripple to a prescribed value. A single triac is connected in series with ac supply lines. The triac is connected to the motor through a rectifier bridge to unify the motor current. The validity of the proposed new method of speed control is approved theoretically and experimentally. A microcomputer based measuring circuit is also used. The experimental results agree with the theoretical predictions. Curves for the performance characteristics of a dc series motor rated 1.25 kW using the modulated phaseangle controlled single triac are presented. Fig. 1 shows the experimental set-up of this speed control method using the mentioned technique. The motor speed is controlled by applying a number (N) of complete supply cycles followed by another (T N) phase-controlled supply cycles. In other words the triac has to be triggered for the first N cycles of the control period Tat the zerocrossings of the supply voltage and for the remainder (T N) cycles at a defined phase-angle, a, w.r.t. the zero crossing points of the supply voltage. Differential equations governing the motor-operation modes are written. The motor operates in one of the modes: triac conduction -
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IEEE Power Engineering Review, September 1989
