1) The document presents a steady-state analysis of an electronic load controller (ELC) for a three-phase alternator used in micro-hydro applications. Mathematical and Simulink models of the ELC are developed and analyzed for proportional, proportional-integral, and proportional-integral-derivative controllers. 2) Simulation results show that PID control reduces frequency variation most compared to P and PI control. With no consumer load, voltage spikes up to 370V but current remains slightly above rated. With full consumer load, all controllers maintain 50Hz frequency and rated voltage/current. 3) In conclusion, the PID ELC controls frequency faster than P and PI controllers but voltage rises too high at no load due to

1. 978-1-4673-6540-6/15/$31.00 ©2015 IEEE
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

2. 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

3. 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

4. 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

5. 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

6. 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.
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