EMP 32(7) #11071
Electric Power Components and Systems, 32:691–700, 2004 c Taylor & Francis Inc. Copyright ISSN: 1532-5008 print/1532-5016 online DOI: 10.1080/15325000490461064
Performance of Grid-Connected Induction Generator under Naturally Commutated AC Voltage Controller A. F. ALMARSHOUD College of Technology Buraydah, Saudi Arabia
M. A. ABDEL-HALIM Elec. Power & Machines Dept. College of Engineering Cairo University Giza, Egypt
A. I. ALOLAH EE Dept.—College of Eng. King Saud University Riyadh, Saudi Arabia This article presents a complete analysis of an induction generator connected to a grid through ac voltage controller utilizing two anti-parallel thyristors. The performance characteristics regarding the harmonic contents, active power, reactive power, power factor, and efficiency have been computed. These characteristics have been determined with the help of a novel abc-dq circuit model. The model posses the advantages of both the dq and direct phase model. The validity of the model and results have been confirmed experimentally. Keywords
grid-connected induction generator, voltage control
1. Introduction Induction generators have two states of operation; they are either autonomous or grid-connected units. The power factor of the grid-connected induction generator is fixed by its slip and its equivalent circuit parameters and not affected by the load [1]. The quadrature component of the output current is nearly constant for any fixed terminal voltage and frequency and leads the voltage. It is necessary, therefore, to operate such generators in parallel with synchronous machines. These Manuscript received in final form on 21 April 2003. Address correspondence to A. F. Almarshoud, College of Technology, P.O. Box 3658, Buraydah, 81999, Saudi Arabia. E-mail:
[email protected]
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synchronous machines do not only supply the quadrature lagging current demanded by the load, but also supply sufficient quadrature lagging current to neutralize the quadrature leading component of the current delivered by the induction generator. Thus, the synchronous machines in parallel with an induction generator determine its voltage and frequency, while its output is fixed by its slip [1]. When driven by wind turbines, induction generators are liable to run near its synchronous speed when the wind speed is low. This results in operation at bad power factor and low efficiency. To improve the power factor and efficiency of the generator at such loads, it is recommended to lower its terminal voltage. Thus, an ac voltage controller used as an interface between the network and the generator is useful in this concern [2–4]. In a previous work, an ac voltage controller utilizing a set of two anti-parallel thyristors in each phase has been used to link the induction generator to the grid, but without experimental verification [5]. In the present article, a rather simple ac voltage controller is used to control the active and reactive power of an induction generator connected to the grid. The ac voltage controller utilizes a set of two anti-parallel thyristors in each phase. The performance of the induction generator is studied. The machine and ac voltage controller are modeled by a novel equivalent circuit in a pseudo-stationary abc-dq reference frame. Based on the circuit model, a state space mathematical model is developed. The model is capable of dealing with the nonlinearities introduced by the used electronic solid-state switches. The performance characteristics have been computed for a wide range of operating conditions through a simulating computer program. In addition to the simulation process, extensive laboratory experiments have been carried out to insure the validity of the proposed system and its model.
2. Proposed Control Circuit The proposed circuit is shown in Figure 1. Each stator phase has a control circuit that consists of a Triac or two anti-parallel thyristors. This control circuit links the induction generator to the grid. The terminal voltage of the generator is controlled by changing the triggering angle, α, of the thyristors. The current begins to flow at this angle, and the thyristor is naturally commutated when the current falls down to zero. By changing the triggering angle, the current, power factor, and active and reactive powers of the generator are controlled.
3. System Modelling The stator of the induction machine is modeled in the direct phase reference frame, abc, while its rotor is modeled as two pseudo-stationary coils in the dq reference frame (Figure 2). This new model has the following advantages: 1. There is no need to transform the stator voltage and current quantities, as the stator is modeled keeping its original physical arrangement. 2. Stator direct phase modeling allows unbalanced conditions and nonlinearities arising from the use of electronic switches and other reasons to be easily represented. 3. Using pseudo-stationary coils for the rotor results in time-independent mutual inductances between the stator and rotor coils, therefore the advantages of the dqo model are reserved.
Grid-Connected Induction Generator
Figure 1. System under study.
Figure 2. Circuit model of the induction generator.
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The five coil currents and the rotor speed are chosen to be the state variables. Based on the developed model, the voltage matrix equation of the machine could be formulated as follows: [v] = [R][i] + [x]p[i] + ωm [G][i]
(1)
where: [R].[i] is the resistive voltage drop matrix; [X].p[i] is the transformer voltage matrix; [G].[i] is the rotational voltage matrix; ωm is the rotor speed. The resistance matrix is given by R1 0 0 [R] = 0 0
0 R1 0
0 0 R1
0 0 0
0
0
2 R2 3
0
0
0
0 0 0
0 2 R2 3
where: R1 and R2 are the resistance of stator and rotor windings, respectively. If the rotor d-axis is chosen along the magnetic axis of the stator phase “a,” and neglecting the space harmonic fluxes and the saturation effects, the [X] and [G] matrices are given by: 2 2 −Xm −Xm 0 Xm 3 Xm + X1 3 3 3 √ Xm 2 −Xm −Xm −Xm Xm + X1 − 3 3 3 3 3 3 √ −X 2 −X X −X m m m m [X] = Xm + X1 3 3 3 3 3 3 −X 2 2 −X m m X (X + X ) 0 m m 2 3 3 3 3 √ Xm √ Xm 2 0 − 3 3 0 (Xm + X2 ) 3 3 3
0 0 0 [G] = 0 2 Xm 3
0 0 0
0 0 0
√ Xm 3 3 −Xm 3
√ Xm − 3 3 −Xm 3
0 0 0
0 0 0
2 0 − (Xm + X2 ) 3 2 0 (Xm + X2 ) 3
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where: X1 is the leakage reactance of stator; X2 is the leakage reactance of rotor; Xm is the magnetizing reactance. The voltage and current vectors are:
T [V ] = νa νb νc 0 0
T [i] = ia ib ic id iq Accordingly, the electromagnetic torque is given by: √ 3 2 (2 · ia − ib − ic ) (ib − ic ) · Xm · id + · Xm · iq Te = 3 2 3
(2) (3)
(4)
where: ia , ib , ic are the stator currents; Id , iq are the rotor currents. The thyristors are treated as ideal switches. They are represented by a series of resistance and inductance, which are set to zero when the thyristor is turned on. When the current of the thyristors falls to zero, the thyristor resistance and inductance are set to high values.
4. Results and Discussion A computer program has been developed to simulate the proposed system. Numerical integration using the forth order Runge-Kutta algorithm has been applied to compute the currents step by step in the time domain [6]. Standard numerical techniques have been applied to calculate the average developed torque, supply and stator-phase (rms) currents, harmonic factor, power factor, displacement angle, active and reactive powers, and the generator efficiency. A three-phase, 3 kW squirrel cage induction generator having the specifications and parameters given in Table 1 has been used for computations and experimental work. The performance characteristics have been computed at different speeds and triggering angles. Figure 3 shows the generator fundamental current. As the rotor speed increases, the generator fundamental current increases, but with increasing the triggering angle, the fundamental current decreases slowly for a certain range of triggering angle, then drops rapidly approaching the zero value. The measured current follows the same behavior of a calculated current. When the current starts dropping rapidly at α > 155◦ , the generator enters the infeasible operation region. In this region the generator is unstable, so the experimental readings at α > 155◦ cannot be measured. Figure 4 shows the generator harmonic factor. The harmonic factor increases as the triggering angle increases, and decreases by increasing the rotor speed. The phase shift angle between the fundamental current component and the phase voltage (displacement angle) is shown in Figure 5. The fundamental current component leads the phase voltage. The displacement angle remains nearly constant for a certain range of triggering angle, then increases rapidly approaching 90 degree, but
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A. F. Almarshoud et al. Table 1 Parameters of induction generator under investigation Vrated Irated f Rs Xsl XM Rr Xrl Vbase Ibase Zbase Pbase
380 V 6.9 A 60 HZ 0.065024 pu 0.06527 pu 1.07196 pu 0.036147 pu 0.06527 pu 219.4 V 4.558 A 48.136 Ω 3000 W
Figure 3. Variation of fundamental component of generator current versus firing angle.
the displacement angle decreases as the rotor speed increases. The average of input torque (Figure 6) behaves in a manner similar to that of the generator fundamental current. Figure 7 shows the variation of the delivered active power of generator against the firing angle under different speeds. The pattern of the active power variation is in general similar to those of the generator fundamental current and torque. As expected, the induction generator consumes reactive power (Figure 8). This reactive power slightly decreases as the triggering angle increases over a certain range, then it decreases rapidly approaching zero, as expected from the measured readings. The power factor (Figure 9) remains high and nearly constant for triggering angle less than 155◦ (i.e., in the feasible operation region). But in the infeasible
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Figure 4. Variation of harmonic factor of generator current versus firing angle.
Figure 5. Variation of displacement angle versus firing angle.
operation region (α > 155◦ ), the power factor decreases rapidly to zero and may go to negative values because at these high triggering angles, the generated power is not enough to cover the internal losses of the machine. Accordingly, the generator will absorb active power from the grid, which leads to negative power factor. The efficiency behaves in a manner similar to that of the power factor in both calculated and measured readings, as shown in Figure 10. For the machine under investigation, the control starts at α > 120◦ . Other machines may start at a different angle, but not less than 90◦ depending on the
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Figure 6. Variation of input torque versus firing angle.
Figure 7. Variation of active power versus firing angle.
load angle. Also, the current exceeds the rated current at rotor speed greater than 1.03 pu, so the maximum rotor speed for the machine under investigation is 1.03 pu.
5. Conclusions The article has presented a novel circuit and mathematical model capable of representing the steady state conditions of induction generator when electronic switches are connected to its stator lines. The model has been used to analyze an induction generator connected to the network through an ac voltage controller. The
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Figure 8. Variation of reactive power versus firing angle.
Figure 9. Variation of power factor versus firing angle.
use of solid-state devices as electronic switches enables the control of active power and reactive powers delivered by the induction generator to the network. From the computed and measured performance characteristics, the following is concluded: 1. The feasible operation region is the region where power factor and efficiency is high (α < 155◦ ). 2. By using the proposed method, it is possible to get constant output power for a certain range of rotor speed by varying the triggering angle.
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Figure 10. Variation of the efficiency versus firing angle.
3. It is also possible to avoid the inrush current at the instant of connection between the induction generator and power system by applying the voltage gradually. 4. The existence of solid-state devices is associated with existence of current harmonic contents. 5. Experimental measured results verify the validity of the proposed control scheme and its model.
References [1] S. J. Chapman, Electric Machinery Fundamentals, 2nd edition, New York: McGrawHill, 1991. [2] V. Subbiah and K. Geetha, “Certain investigations on a grid connected induction generator with voltage control,” Proc. of the IEEE International Conference on Power Electronics, Drives and Energy Systems, pp. 439–444, 1996. [3] S. Suresh Babu, G. J. Mariappan, and S. Palanichamy, “A novel grid interface for winddriven grid-connected induction generators,” Proc. of the IEEE/IAS International Conference on Industrial Automation and Control, pp. 373–376, 1995. [4] M. A. Abdel-Halim, “Solid state control of a grid connected induction generator,” Electric Power Components and Systems, Vol. 29, pp. 163–178, 2000. [5] M. A. Abdel-Halim, A. F. Almarshoud, and A. I. Alolah, “Control of grid connected induction generator using naturally commutated AC voltage controller,” Proc. of the IEEE Canadian Conference on Electrical and Computer Engineering, Toronto, Canada, May 2001. [6] B. Adkins and R. G. Harley, The General Theory of Alternating Current Machines: Application to Practical Problems, London: Chapman and Hall, 1975.
