Electrical and Power Engineering Frontier
Sep. 2013, Vol. 2 Iss. 3, PP. 59-63
Application of a Stepper Motor tothe Frequency
Control of a Mini Hydropower Plant
Ayele Nigussie Legesse*1, Mengesha Mamo2
1
Department of Electrical and Computer Engineering, Institute of Technology, Haramaya University, Ethiopia
Department of Electrical and Computer Engineering, Addis Ababa Institute of Technology, Addis Ababa University, Ethiopia
*1
ayelenigussie@yahoo.com; 2mmamo2006@gmail.com
2
Abstract- This paper describes the application of a stepper motor in controlling the frequency of a standalone mini hydropower plant.
In Ethiopia, the frequencies of the existing mini hydropower plants are controlled by mechanical governors. Unfortunately, these
governors are expensive, complex and slow in response. Furthermore, the governors do not act fast enough during big load changes;
consequently, frequency spikes are created. In this research, a stepper motor which is cheap, fast, easy to control and less complexis
used to control the frequency of a mini hydropower plant.Thestepper motor is used to rotate aspear valve which in turn controls the
flow of water into the turbine of a mini hydropower plant. The position of the stepper motor is controlled by a controller. Thus,a
frequency control system usinga stepper motor is modeled, designed and simulated. Simulation results for mini hydropower plants
with different capacities demonstrate that transient and steady state performances are enhanced by replacing mechanical governors
with stepper motors. Moreover, frequency spikes are reduced.
Keywords- Stepper Motor; Mini Hydropower Plant; Frequency Control System; Spear Valve
I. INTRODUCTION
Hydropower plants whose capacities range from 100 to 1000 kW are classified as mini hydropower plants [1, 2]. Mini
hydropower plants are among the ideal renewable energy resources to electrify isolated rural communities, especially in
developing countries.
Like other developing countries, most of the rural part of Ethiopia is not yet electrified. Unfortunately, it is technically
feasible and cost wise to extend the national grid to isolated rural communities. As the current international trend in rural
electrification is to utilize renewable energy resources, mini hydropower plants have become paramount. Ethiopia has high
hydro potential which can be exploited for the development of mini hydropower plants. Nevertheless, this vast renewable
energy resource has not yet been exploited sufficiently for electric generation. More effort is required from the government as
well as the private sector to exploit this resource for rural electrification.
One of the challenges in developing mini hydropower plants is associated with the frequency control system. The
frequency control system is intended to be cost-effective so that isolated rural communities can afford to develop their own
mini hydropower plants [1].Moreover, the frequency control system is expected to be less complex and more reliable.
Conventionally, mechanical governors are used to control the frequency of standalone mini hydropower plants; however,
these governors are expensive, complex and slow in response. Furthermore, conventional governors are less reliable. Therefore,
the objective of this paper is to model, design and simulate a less expensive, less complex and fast frequency control system
for standalone mini hydropower plants using a stepper motor and a spear valve. Stepper motors are cheap and easy to control,
and they are also faster than mechanical governors. Thus, a robust controller, which controls the position of a stepper motor
that controls a spear valve, is designed to handle all ranges of mini hydropower plants and also different ranges of loadings. In
addition, the controller is capable of reducing frequency spikes.
II. MATHEMATICAL MODELING AND CONTROLLER DESIGN
The major components of the proposed frequency control system including the mini hydropower plant are shown in Fig. 1.
Before designing the frequency control system, the appropriate mathematical model for each component should be obtained.
Transfer functions are used to model the different components.
Spear valve
Turbine
Stepper motor
Generator
Controller
Load
Sensor
Fig.1 Block diagram of the proposed frequency control system
A. Turbine Model
The output mechanical power of a hydraulic turbine depends on the amount of water flowing into the turbine. In Fig.1, the
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Electrical and Power Engineering Frontier
Sep. 2013, Vol. 2 Iss. 3, PP. 59-63
amount of water flowing into the turbine is regulated by a spear valve. Consequently, the input mechanical power to the
synchronous generator is controlled by controlling the position of the spear valve.
In general, the transfer function model of a hydraulic turbine is given as [3]
Pm
1   ws

G 1  0.5 w s
(1)
where Pm is change in mechanical power, G is change in the position of the spear valve, and  w is water time constant [3, 4].
B. Generator and Load Model
The frequency of a synchronous generator is directly related to the balance between the mechanical power input to the
generator and the demand [3, 5]. Additionally,the frequency depends on the damping coefficients of the generator and the load
connected to it. The relationship between frequency deviation and change in power is modeled as [3]
f
1

Pm  PL 2 Hs  D
(2)
where f is frequency deviation, PL is change in per unit non-frequency sensitive load, H is per unit inertia of rotating parts,
and D is cumulative damping coefficient in the mini hydropower plant.
C. Controller Model
Different types of controllers can be used to control the position of the stepper motor, and consequently, the position of the
spear valve. However, for the sake of simplicity, a proportional-integral (PI) controller is proposed. The input to the PI
controller is the frequency deviation and the output is the input angle of the stepper motor. The mathematical model of the PI
controller is
i
f
 Kp 
KI
s
(3)
where  i is the input angle to the stepper motor, KP is the proportional constant and KI is the integral constant of the PI controller.
D. Stepper Motor Model
A permanent magnet stepper motor is used to control the spear valve of the mini hydropower plant. In Ref. [6], the transfer
function between the input and the output angle of a permanent magnet stepper motor is given as
Km I p Nr
o
 2
 i Js  s  K m I p N r
(4)
where  o is the output angle, J is the moment of inertia of the rotor, Km isthe torque constant, Ip is the phase current, Nr is
thenumber of rotor teeth, and  is the viscous friction coefficient of the permanent magnet stepper motor.
E. Frequency Sensor and Spear Valve Models
The frequency sensor is modeled to be a scalar multiplier whereas the model of the spear valve is a linear one with
minimum and maximum gate positions because the relationship between the output angle of the stepper motor and the position
of the spear valve is directly proportional. Thus, the sensor can be modeled by a scalar Ks and the spear valve by a limiter as
shown in Fig. 2.
 PL
G
1  ws
1  0.5 w s
 o
Km I p Nr
Js 2  s  K m I p N r
 i
Pm
KP 
1
2 Hs  D
KI
s
f
Ks
Fig. 2 The transfer function model of the proposed frequency control system
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Sep. 2013, Vol. 2 Iss. 3, PP. 59-63
F. Overall Model
All the different components of a mini hydropower plant have already been modeled in the previous sections. Now, putting
together all the transfer functions obtained results in the block diagram shown in Fig. 2. Therefore, any mini hydropower plant
can be modeled as shown in Fig. 2 for frequency control.
G. Design and Analysis
A 492 kW synchronous generator has been selected for the purpose of designingthe frequency control system of the
proposed model [7]. The different parameters of the generator model shown in Fig. 2 are determined. A stepper motor with the
specifications in [7] is also selected. The transfer function between the input and output angles of the permanent magnet
stepper motor is determined from the given specifications. The water time constant depends on the head of the mini
hydropower plant; thus, three different heads [5 m, 10 m and 15 m] are considered in the design.
After determining all the parameters of the mini hydropower plant, the PI controller has been tuned using different
techniques. And Ziegler-Nichols technique gives the best results (Kp = 1 and KI = 0.125). Fig. 3 shows all the
designedparameters for a mini hydropower plant with 1.0 sec water time constant.
 PL
G
1 s
1  0.5s
 o
200
0.0013s 2  0.5s  200
 i
Pm
1
1
10 s  1.5
f
1
0.125
s
Fig. 3Block diagram of a mini hydropower plant with frequency control for 1.0 sec water time constant
III. SIMULATION RESULTS AND DISCUSSION
The frequency deviation of the mini hydropower plant with and without the controller was simulated using MATLAB. Fig.
4 shows the step response of frequency deviation for a 3% load changein the plant with the designedfrequency control system
included. From the simulation result, it is observed that the frequency error is eliminated and the overshoot (or undershoot) is
0.981%. The settling time is 68.7 sec.
Fig. 4Simulation results of a low head, mini hydropower plant
The performances of this frequency control system are better than that of conventional governors. Table 1 presents the
comparison between the performances of the proposed frequency control system and that of a typicalconventional governor.
TABLE 1 COMPARISON OF PERFORMANCES OF PROPOSED AND CONVENTIONAL FREQUENCY CONTROL SYSTEMS
Performance
Proposed
Typical conventional
Overshoot
0.981%
5%
Settling time
68.7 sec
300 sec
The performances of the proposed control system depend on the head, capacity, and type of loading of the mini
hydropower plant. Therefore, the frequency control system is expected to be robust.
The block diagram in Fig. 3 was simulated for low, medium and high head mini hydropower plants by varying the water
time constant. The result is shown in Fig. 5. The frequency deviation step responses of the three types of mini hydropower
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Electrical and Power Engineering Frontier
Sep. 2013, Vol. 2 Iss. 3, PP. 59-63
plants for a 3% load change demonstrate that the proposed frequency control system can be applied for any range of heads of
mini hydropower plants.
Fig. 5 Frequency deviation step responses of low, medium and high head mini hydropower plant
The per unit inertia constant of a plant indicates its capacity; as the per unit inertia increases, the capacity of the plant also
increases. The proposed frequency control system was subjected to different capacities of mini hydropower plants and the
performances obtained are tabulated in Table 2.
TABLE 2 TRANSIENT PERFORMANCES FOR DIFFERENT CAPACITIES OF HIGH HEAD MINI HYDROPOWER PLANT
Inertia constant (H), D=1.5%, 3%
load change and high head
Settling time
Overshoot
(undershoot)
2.8 sec
54.9 sec
1.78%
4 sec
54.2 sec
1.52%
5 sec
52.0 sec
1.38%
7 sec
41.6 sec
1.21%
10 sec
76.6 sec
1.07%
Similar tests were done for low and medium head mini hydropower plants (see Table 3 and Table 4) and the results
demonstrate that the controller works efficiently. This indicates that the proposed control system is robust with regard to capacity.
TABLE 3 SETTLING TIME AND OVERSHOOT FOR DIFFERENT CAPACITIES OF MEDIUM HEAD MINI HYDROPOWER PLANT
Inertia constant (H), D=1.5%, 3%
load change and high head
Settling time
Overshoot
(undershoot)
2.8 sec
63.4 sec
1.41%
4 sec
62.4 sec
1.25%
5 sec
60.3 sec
1.15%
7 sec
52.7 sec
1.05%
10 sec
80 sec
0.95%
TABLE 4 SETTLING TIME AND OVERSHOOT FOR DIFFERENT CAPACITIES OF LOW HEAD MINI HYDROPOWER PLANT
Inertia constant (H), D=1.5%, 3%
load change and high head
Settling time
Overshoot
(undershoot)
2.8 sec
72.8 se
1.09%
4 sec
71 sec
1.02%
5 sec
68.7 sec
0.981%
7 sec
62.2 sec
0.92%
10 sec
77.3 sec
0.853%
The frequency controller was also subjected to different types of loadings. Table 5 shows the performances obtained for
different types of loadings of a mini hydropower plant for a 3% load change of the maximum load.
TABLE 5 SETTLING TIME AND OVERSHOOT FOR DIFFERENT TYPES OF LOADINGS OF A LOW HEAD, MINI HYDROPOWER PLANT
Load damping constant (D), H=5, 3%
load change and low head
Settling time
0.48%
58.7 sec
1.4%
0.8%
40 sec
1.24%
1.2%
56.3 sec
1.08%
1.5%
68.7 sec
0.981%
2%
87.1 sec
0.849%
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Overshoot
(undershoot)
Electrical and Power Engineering Frontier
Sep. 2013, Vol. 2 Iss. 3, PP. 59-63
Similar tests were done for medium and high head mini hydropower plants (see Table 6 and Table 7) and the results
demonstrate that the controller works efficiently. This indicates that the proposed control system is also robust with regard to
different types of loadings.
TABLE 6 SETTLING TIME AND OVERSHOOT FOR DIFFERENT TYPES OF LOADINGS OF
A MEDIUM HEAD, MINI HYDROPOWER PLANT
Load damping constant (D), H=5, 3%
load change and low head
Settling time
Overshoot
(undershoot)
0.48%
49.6 sec
1.75%
0.8%
46.6 sec
1.51%
1.2%
47.8 sec
1.29%
1.5%
60.3 sec
1.15%
2%
78.1 sec
0.986%
TABLE 7 SETTLING TIME AND OVERSHOOT FOR DIFFERENT TYPES OF
LOADINGS OF A HIGH HEAD, MINI HYDROPOWER PLANT
Load damping constant (D), H=5, 3%
load change and low head
Settling time
Overshoot
(undershoot)
0.48%
78.1 sec
2.23%
0.8%
52.2 sec
1.88%
1.2%
37.3 sec
1.56%
1.5%
52 sec
1.38%
2%
69.2 sec
1.16%
To put it in a nut shell, the simulation results show that the proposed frequency control system is applicable in the whole
ranges of mini hydropower plants with different types of loadings.
The controller has shown good transient and steady state performances for a range of mini hydropower plants. The average
overshoot/undershoot achieved in the simulations is 1.27% which is less than that of conventional governors. The average
settling time is 61.07 seconds which is by far less than 300 seconds.
IV. CONCLUSION AND RECOMMENDATION
A. Conclusion
In this paper, a frequency control system for a standalone mini hydropower plant has been modeled, designed and
simulated. Simulation results have demonstrated that the controller is applicable for different capacities, types of loadings and
heads of standalone, mini hydropower plants. Moreover, from simulation results it is observed that frequency spikes are very
low.
The cost of the designed controller is significantly lower than its counterpart to be imported resulting in foreign currency
saving. Therefore, this controller can play crucial role in the rural electrification program of Ethiopia.
B. Recommendation
In the future, the performances of the frequency controller with grid connected mini hydropower plants can be investigated.
In addition, the controller can be modified to engage artificial neural networks.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
NRC (A Buyer’s Guide), Micro-Hydropower Systems, Canada, 2004.
NRC, Introduction to Micro-Hydropower Systems, Canada, 2005.
P. Kundur, Power System Stability and Control, McGraw Hill, New York, 1994.
H. Sadat, Power System Analysis, McGraw Hill Companies, 2002.
A. Nigussie and M. Mammo, A Novel Scheme of Controlling the Frequency of a Standalone Micro Hydropower Plant, ESEE 4 th
Conference, 2010.
C. Erdal, Determination of the Optimum Parameter Tolerances for a Permanent Magnet -Step Motor : A Sensitivity Approach,
Department of Control and ComputerEngineering, Istanbul Technical University, Faculty of Electrical-ElectronicsEngineering, 80626
Maslak, Istanbul, Turkey, 2003.
Asia Commerce Import and Export Corporation, 1FC2 Brushless Three-Phase Synchronous Generators, Shangai, 2009
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