Analysis of Steady-state Operation in Bipolar

Thyristor Circuits

Dr. Mahmoud S. Awwad

Faculty of Engineering Technology

Al-Balqa Applied University

Amman – Jordan

Abstract:- Thyristor regulators are among the most important parts of modern power distribution systems.

They help avoid big transformers or power consuming voltage dividers. One of the main disadvantages of bipolar thyristor regulators is the reactive power, generated or consumed by the network. The present paper shows how to calculate the reactive power. The Fourier analysis helps understand the origin of the reactive power and the ways of decreasing it.

Practical measures for reactive power compensation are proposed.

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1 Introduction

Single phase thyristor regulators are nowadays widely spread. They are used for active power regulation in electric lighting devices, home appliances and other equipment, consuming relatively high power from the electric network. Thus, the analysis of energy propagation processes in circuits like the one shown in Fig.1 is of practical interest.

Assuming thyristors T1 and T2 to be ideal ones and the source to be sinusoidal and with zero internal persistence, we can represent the non-sinusoidal current (Fig. 2a) in the circuit in the form of a Fourier series.

(1)

where An, Bnare the amplitudes of cosine components (quadrature) and sine components (in phase) for the nth harmonic; andis the initial phase of the nth harmonic; is the cyclic frequency of the source.

Amplitudes of the cosine and sine components can be found using the known formulae which have the form for the first (n=1) and higher (n2) harmonics.

where Em is the maximum value of the source voltage; R is the active load resistance;α is the cutoff angle (control angle) of the thyristor.Therefore, the expression (1) can be rewritten as

where I1m and Inm are the maxima of the first and higher harmonics for the current, while

The non-zero initial phasein the first harmonic of the current expansion in terms of Fourier components results in the inductive character of the load together with the power regulator. Consequently, the circuit consumes reactive power from the source where:

(2)

The minus sign in expression (2) shows that the consumption of the reactive power corresponds to the positive , while the reactive power generation corresponds to the negative values of .

While defining the power balance in the circuit under consideration, it is reasonable to present the voltage drop on the thyristors in the form of a Fourier series

where are the amplitudes of the consine and the sine components

is the initial phase of the nth harmonic, while

Comparison of the expressions for and shows, that higher harmonics of the thyristor current have an opposite phase to the phase of thyristor voltage harmonics.

Nonlinear elements are known to be the higher harmonics generators; consuming the first harmonic of the active power from the source, they transform it into the higher harmonics of the active power. Starting from this fact, we can write the power balance in the circuit under consideration as:

Where P is the average active power generated by the source, PT1 is the average active power of the first harmonic transformed by the thyristors, PTn is the average active power of the higher harmonics on the thyristors, PR1 and PRn represent respectively the average active power consumed by the load at the first and at the higher harmonics. It is easy to see that higher harmonics of the thyristors’ power and those of the load power are equal and have the form

Taking into account the fact, that the active power consumed by the load, is equal to:

(3)

where the average active power of the source at the first harmonic P is equal to:

Here is the first harmonic value of the current at any moment of time.

In the following table, the active power of the source and that of the load are presented at various control angles of the thyristors. The results satisfy equation (3).

Analysis of the curves showing the instantaneous values of the current and voltage (see Fig. 2a) confirms the fact that the current values of the active power for the source and for the consumer are coincident (Fig. 2b).

It is obvious from Fig.3c that at this region the function (P) has multiplicity, that is three different values of  gives the same active power P. Numerical analysis shows that bifurcation points are 1=0.85 and 2=1.85, while the minimum point is 3=1.06 and the maximum point is 4=/2 . Three values of  correspond to three different values of the reactive power Q. As one can see from Fig.3b, the minimum value of  gives the minimum reactive power. This fact poses the problem of firing angle optimization. If you decrease the active power increasing the firing angle, you reach =3 and then you need a sudden change in  jumping from 3 to 2. If you increase the active power and you reach 2 , you need to make a jump to 3. It helps to keep a low level of the reactive power Q[6].

Reactive power at the first harmonic is the result of the phase shift caused by the thyristor switches, which change the current values of the circuit resistance. That reactive power is a useless excessive load on the network, it requires an extra full power from the source. The power factor, usually defined as a ratio of the reactive power and the active power, measured at the first harmonic, decreases.

To decrease the losses caused by the reactive power, it is reasonable to connect a compensating capacitor C chosen from the condition of the best compensation of the average reactive power (average over the control angles)

Then

Analysis of the = f () curve (see Fig. 3) shows that with the constant capacitance C of the compensatory capacitor the circuit generates reactive power at 0 - 45o and =135-180o, while at =45-135o the circuit consumes the reactive power.

So it is reasonable to change the capacitance C together with the control angle according to the curve shown in Fig. 3b. It can help avoid reactive power generation or consumption.

The current value of the capacitance can be taken from the curve (Fig. 3b) or from expression (2)

Another solution is to switch the thyristor off not at the angle but at an angle to make the current in phase with the voltage, but it is difficult to implement this idea technically (see Fig. 2).

2 Conclusions

The analysis presented in the paper shows that one of the main problems in thyristor regulators’ application is the reactive power, it comes from the asymmetrical form of the current pulse. As a result, the current harmonics are not in phase with the voltage harmonics. Symmetrization of the current waveform requires thyristors with regulated switch-off moments. This is technically difficult, but it helps avoid the reactive power problem.

Another simple solution is the compensating capacitance. If it is constant, then the power is compensated for average control angles, if it is regulated together with the control angle, then compensation is full.

These simple but promising measures can help save a considerable amount of power in electric networks.

References:

[1]Kaudari, B., “Modeling and Analysis of a GTO-Based Multilevel Cascaded Inverter”. Proceedings of 4th Jordanian International Electrical and Electronic Engineering Conference”, Amman – Jordan, 16-18 April 2001.

[2]Palmer, P. R. and Johnson, C. M., “Measurement of the Redistribution of Current in GTO Thyristors During Turn-off”. 3rd European Conference on Power Electronics and Applications, pp. 1621-1625, Aachen, Oct. 1989.

[3]Silva, V. F., Silva, L. E. B., Cortez, J. A., Rosa, P. C. and Rezek, A. J. J., “Industrial Electronics”. EFEI, 1993.

[4]Touchan, E., “Improving the Effectiveness of Thyristor Controlled Rectifiers by Means of a Microprocessor”. Proceedings of Jordan International Electrical and Electronic Engineering Conference, 27-29 April 1998.

[5]Williams, B. W. and Palmer, P. R., “Switch-off Circuits for Transistors and Gate Turn-off Thyristors. British Patent No. 2142495, Jan. 1985, U. S. Patent #4602209, July 1986.

[6]William D. Rosehart, Member, IEEE, Claudio A. Caňizares, Senior Member, IEEE, and Victor H. Quintana, Fellow, IEEE, “Effect of Detailed Power System Models in Traditional and Voltage-Stability-Constrained Optimal Power-Flow Problems”, IEEE Transactions of Power Systems, Vol. 18, No. 1, Februaray 2003.

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Fig.1: Circuit diagram of a single-phase thyristor regulator of the active power.

Fig. 2: Temporal diagrams of the current, voltage and active power in the circuit.

Fig 3a

Fig 3a shows active power and Fig 3b presents the reactive power as functions of the

firing angle .

Fig. 3b

Fig. 3b: At Fig. 3c one can see the most interesting part of the curve from Fig. 3a, that is for 0.8<<2.

Fig.3c

Table showing values of the active power for the generator and the consumer

at various control angles .

30 / / / /
60 / / / /
80 / / / /

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