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Steady-State Analysis of Electronic Load Controller for Three Phase Alternator

Anurag Yadav Alternate Hydro Energy Centre

Indian Institute of Technology Roorkee,India Uttarakhand, India

email:anuragyadav.iitr@hotmail.com

Abstract— The present work is dedicated to the steady-state analysis of electronic load controller (ELC) for three phase alternator. In an alternator employed in micro-hydro applications, the voltage is controlled by Automatic Voltage Controller (AVR) so here electronic load controller conforms itself to the control of frequency. It does so by diverting the difference between the rated power and consumer demand to the dump/ballast load for dissipation. The paper presents the mathematical and simulink model of Electronic Load Controller for three phase alternator. The developed mathematical model is first checked for its stability by employing Routh-Hurwitz criterion and then designed in MATLAB/Simulink which is then analyzed for its behavior under steady-state conditions. The controller is being modeled for proportional, proportional plus integral and proportional plus integral plus derivative control and the results are being compared and discussed.

Keywords—ELC, Alternator, P, PI, PID controller, Routh-Hurwitz criterion, IGBT, PWM.

I. INTRODUCTION In the present epoch, electricity has become inevitable for

the survival and for the reasons best known to all. Dwindling fossil fuels have posed a formidable challenge before the researchers to meet the growing energy requirements. The major setbacks of the fossil fuels are their limited stocks, inability to meet peaking demands, growing prices, not being environment friendly etc. Fast growing economy and expansion of the energy provisions for the exploding population demands an increment in the share of energy production from renewable energy sources in the overall energy mix. Micro-hydro generation system is quite captivating alternative for remote, hilly areas, where there is facile availability of water resources. Power plant operation in such areas demands less operation and maintenance costs, robust construction, exemption from the requirement of state of the art expertise etc. Micro Hydro project can generate power in decentralized and distributed mode which has the advantages of production at consumption points and is exempted from land and environmental related issues. Therefore, a standalone autonomous unit to feed local consumers using micro hydro project is a preferred choice but this power generated is directly feed to the consumers. If there is a variation in the load, it will affect the generator/turbine and other equipments connected to

Appurva Appan Alternate Hydro Energy Centre

Indian Institute of Technology Roorkee,India Uttarakhand, India

email:appurvaappan.ee2013@gmail.com

them. To solve this problem, a number of sophisticated control systems are available in power applications but they are expensive and inappropriate for micro hydro. One solution concept which is widely adopted is electronic load controller. The idea of ELC (Electronic Load Controller) is to maintain constant load on the alternator, irrespective of the amount of load on the generator. It does so by automatically dissipating any surplus power produced by the generator in additional load known as ballast load/dump load.

II. MATHEMATICAL MODELING The mathematical model of the controller is represented by

Fig. 1.

Fig. 1. Mathematical model of electronic load controller

The mathematical model is based on the following

assumptions:

(i) Load frequency dependency is linear.

(ii) State variables are ∆f , ∆X1, ∆X2 and Pr.

(iii) The ELC is proportional type.

(iv) Rated Capacity: 50 kW.

(v) Normal Operating Load: 25 kW.

(vi) Inertia Constant, H: 7.75.

(vii) Nominal Load: 48%.

The input to the system is consumer demand Pc and output is change in frequency ∆f. The transfer function of the system

with ke as the proportional gain and assuming Pc as U(t) and ∆f as Y(t) can be written as

where Y(s) and U(s) represent Laplace transform of the output and input respectively.

III. STABILITY OF THE SYSTEM According to Routh-Hurwitz stability criterion- “For a

system to be stable, it is necessary and sufficient that each term of first column of Routh array of its characteristic equation be positive. If this condition is not met, the system is unstable and number of sign changes of the terms of the first column of the Routh array corresponds to the number of roots of the characteristic equation in the right half of the s-plane”. Equation 1 represents the characteristic equation of the system

(1)

The Routh array may be constructed as follows

Based on the above mentioned assumptions, the various parameters may be calculated as

(2)

(3)

(4)

(5)

Now for the constraints on various parameters for stability can be derived from the following relations and utilizing the values of the desired parameters from equation 2-5.

(6)

(7)

(8)

The maximum allowable tolerance for frequency is 3% which means that ELC must switch on the load of 50kW as soon as it senses 1.5Hz change in the frequency which means that ke = 33.33 kW/Hz and Te = 0.0002 s. After substituting the values of all the parameters the transfer function of the system can be written as

(9)

Now the transfer function of derivative, integral controller can be easily obtained by introducing s, 1/s respectively with the proportional controller.

IV. DESIGN OF THE SIMULINK MODEL The model of the system is being designed in

MATALAB/Simulink. The developed model is depicted by Fig. 2.

Fig. 2. Simulink model of electronic load controller for 50kVA

synchronous generator.

The input power is held constant at 50kW by the hydraulic turbine. However, the full load on the generator is the rated load i.e. 50kW. The circuit breakers are programmed to connect/disconnect the main load and the ballast/dump load. The specifications of the synchronous generator used in the Simulink model is- 50kW, 3-phase, star-connected, 415V, 1500 rpm. The capacitor filter at the output terminals of the rectifier is connected so as to filter out the ripples in the rectified voltage. For the simulation two cases have been considered for each type of controller viz. one in which consumer demand is 0 kW and the other in which consumer demand is 50 kW. The waveforms depict the effectiveness of various controllers in controlling the frequency. The control

Fig. 3. Variation in frequency for proportional controller

Fig. 6. Variation in frequency for proportional plus integral controller

circuit of ELC comprises of an uncontrolled rectifier in series with an IGBT based chopper switch and a purely resistive dump/ballast load. The design parameters of the control circuit are represented by equations 10-14.

(10)

(11)

(12)

(13)

(14)

where,

Vdc = Rectifier output voltage VLL = Line-line Voltage of alternator Rd = Dump load resistance Pd = Dump Power C = Filter capacitor f = Line frequency R.F = Ripple factor Rs = Snubber resistance Cs = Snubber Capacitance Ts = Sampling time Pn = Nominal power of the converter Vn = Nominal line-line AC voltage

The ripple factor is assumed to be 5% and sampling time as 0.00005 s. The parameters of the control circuit play a vital role for the dumping of power effectively and efficiently, so these are designed taking into consideration their tolerance levels.

V. WORKING OF THE MODEL The main agenda of the ELC developed here is the control of frequency as the voltage is controlled independently by the AVR. The difference between the reference and the actual/operating frequency is sensed and based on the difference between the two; the error signal is generated as depicted in the simulink model. This difference is then fed to the electronic load controller whose output is then fed to discrete PWM generator which generates the firing pulses for IGBT based on Pulse Width Modulation (PWM) scheme. The duty cycle of the pulses vary as the consumer load varies and thus the power to be dumped is controlled accordingly.

VI. RESULTS AND DISCUSSION

A. Proportional Controller with Consumer Demand= 0kW

Fig. 4. Variation of stator currents for proportional controller

Fig. 5. Variation of terminal voltage for proportional controller

When the system reaches steady state the frequency flickers from 50 Hz to 50.05 Hz as shown in Fig. 3 because when the frequency becomes 50 Hz the difference between the actual frequency and the reference frequency becomes zero as a result gate signal is lost but as soon as the frequency increases to 50.05 Hz the gating pulse is generated due to which the frequency again becomes 50 Hz. The peak current is slightly more than 1 p.u. as shown in Fig. 4 and the peak value of voltage is 370V in steady state as shown in Fig. 5 because the sudden application of the dump load increases the current in the stator due to which the terminal voltage reduces and due to the AVR action the excitation is increased. Now with the increased excitation and the frequency at 50Hz the gating signal to the IGBT is lost due to which there is a peak in voltage. In this case steady state is attained at 0.29s.

B. Proportional plus Integral Controller with Consumer Demand= 0kW

Fig. 10. Variation of stator currents for proportional plus integral plus derivative controller

Fig. 14. Variation of voltage for proportional controller

Fig. 7. Variation of stator currents for proportional plus integral controller

Fig. 8. Variation of terminal voltage for proportional plus integral controller

In this case the PI controller reduces the error at steady state in case of frequency but it continue to flicker at low amplitude when compared to proportional type ELC as shown in Fig. 6 The peak current is slightly more than 1 p.u. as shown in Fig. 7. The peak value of voltage is increasing up to 370V for phase A as shown in Fig. 8. In this case also the steady state is attained at 0.29s.

C. Proportional plus Integral plus Derivative Controller with Consumer Demand= 0kW

Fig. 9. Variation of frequency for proportional plus integral plus derivative

controller

Fig. 11. Variation of terminal voltage for proportional plus integral plus

derivative controller

PID controller reduces the variation in the frequency as compared to PI controlled ELC as shown in Fig. 9 because the derivative gains respond to the rate of change of frequency. The stator current in this case also increases slightly more at 1 p.u. as shown in Fig. 10, peak voltage in this case also is 370V as shown in Fig. 11. In this case the steady state is obtained at 0.26s as the derivative control can anticipate the actuating error and reaches steady state earlier.

D. Proportional Controller with Consumer Demand= 50kW

Fig. 12. Variation in Frequency for proportional controller

Fig. 13. Variation of stator currents for proportional controller

When the alternator is on full load at steady state, the frequency becomes constant at 0.25 s as shown in Fig. 12. The stator current is 1 p.u. as shown in Fig. 13. Generated voltage does not have sudden spikes at all (as the IGBT is not required to be triggerred) with peak voltage of 340V as shown in Fig. 14.

E. Proportional plus Integral Controller with Consumer Demand= 50kW

Fig. 15. Variation in Frequency for Proportional plus Integral Controller

Fig. 16. Variation in stator currents for Proportional plus Integral Controller

Fig. 17. Variation in terminal voltage for proportional plus integral controller

When the alternator controlled by a PI controller is at full load, the steady state frequency is attained at 0.25s as shown in Fig. 15 Current in this case also is maintained at 1p.u. as

shown in Fig. 16. There are no sudden spikes in generated voltage and the peak voltage is 340V as shown in Fig. 17.

F. Proportional plus Integral plus Derivative Controller with Consumer Demand= 50kW

Fig. 18. Variation in frequency for proportional plus integral plus derivative controller

Fig. 19. Variation in stator currents for Proportional plus Integral plus derivative Controller

Fig. 20. Variation in terminal voltage for proportional plus integral plus

derivative controller

When the alternator controlled by a PID controller is at full load at steady state the frequency becomes almost constant at 0.25s as shown in Fig. 18. Current in the stator is observed to

be at 1p.u. as shown in Fig. 19. The voltage in line A does not have any spikes and the peak voltage is 340V as rated as shown in Fig. 20. The results been discussed so far have been tabulated in Table I and Table II for a better insight.

TABLE I. RESULTS OF VARIOUS CONTROLLER CONFIGURATIONS FOR CONSUMER DEMAND = 0 KW

CONSUMER DEMAND = 0 kW

Type of Controller Results

P

-Perturbation in frequency is from 50-50.05 Hz in steady- state.

-Peak stator current is slightly above 1pu.

-Peak value of voltage is 370 Volts.

-Steady-state is attained in 0.29 sec.

PI

-Perturbation in frequency in steady-state is of relatively lower amplitude.

-Peak stator current is slightly above 1pu.

-Peak value of voltage is 370 Volts.

-Steady-state is attained in 0.29 sec.

PID

-Perturbation in frequency in steady-state is reduced further.

-Peak stator current is slightly more than 1pu.

-Peak value of voltage is 370 Volts.

-Steady-state is attained in 0.26 sec.

TABLE II. RESULTS OF VARIOUS CONTROLLER CONFIGURATIONS FOR CONSUMER DEMAND = 50 KW

CONSUMER DEMAND = 50 kW

Type of Controller Results

P

-Frequency is maintained at 50Hz in steady-state. -Stator current is maintained at 1pu. -Peak value of voltage is 340 Volts with no sudden spikes. -Steady-state is attained in

0.25 sec.

PI

- Frequency is maintained at 50Hz in steady-state. - Current is also maintained at 1pu. -Peak value of voltage is 340 Volts without any sudden spikes. -Steady-state is attained in 0.25 sec.

PID

- Frequency is maintained at 50Hz in steady-state. - Current is also maintained at 1pu. -Peak value of voltage is 340 Volts without any sudden spikes. -Steady-state is attained in 0.25 sec.

VII. CONCLUSION The work presents the steady-state analysis of electronic

load controller for three phase synchronous generator. The result is obtained based on the equation which assumes linear relationship of the consumer demand and frequency. It also assumes linear relation between change in frequency and the dump load connected. The PID based electronic controller is faster as compared to Proportional and PI controller. The ELC is achieving its objective to control the frequency but the per phase peak voltage is rising up-to 370V at no load due to AVR action and the stator current of the generator is exceeding 1p.u.

REFERENCES [1] Anurag Yadav, et al, “A Fuzzy Logic based Electronic Load Controller

for Three Phase Alternator”, International Journal of Emerging Technology and Advanced Engineering, Vol. 5, Issue 3, pp. 514-520, March 2015.

[2] Das Dibyendu, M.Tech dissertation Work On, “Steady-State analysis of Electronic Load Controller for Three Phase Alternator” , Alternate Hydro Energy Centre, Indian Institute of Technology Roorkee, 2011.

[3] Singh B., et al, “Analysis and design of ELC for SEIG”, IEEE Transactions on energy conversion, Vol. 21, No. 21, pp 285-293, March 2006.

[4] Murthy S.S., et al, “A novel digital control technique for ELC for SEIG based micro hydel power generation”, IEEE International Conference on Power Electronics, drives and energy systems, pp 1-5, 12-15 dec, 2006.

[5] Ramirez J.M, et al, “An electronic load controller for self-excited induction generator”, IEEE Transactions on energy conversion, Vol. 22, No. 2, pp 1-8, 2007

[6] Rajagopal V., et al, “Electronic load controller for isolated asynchronous generator in pico hydropower generation”, Conference paper, Department of Electrical Engineering, Indian Institute of Technology Roorkee, 2010.