15th Indonesian Scientific Conference in Japan Proceedings. ISSN:1881-4034
Generator Angle Difference Monitoring System to Ensure Power
Transmission Steady State Stability Based on Neural Network
Adi Soeprijanto1, Ardyono Priyadi1,2, Riyan Danisaputra1, Naoto Yorino2, Yoshifumi Zoka2
1
Electrical Engineering Department, Sepuluh Nopember Institute of Technology, Keputih-Sukolilo,
Surabaya-60111
2
Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashihiroshima, 7398527 Japan
Abstract. Power angle difference between groups of generators is an important measure of steady
state stability in power system. Using neural network, a model to predict power angle difference
between groups of generators at Java-Bali 500 kV is established. Neural Network is built with system
loads as inputs and the average angles of group of generators as targets. This target data is provided
through calculation based on Center of Angles (COA) criterion. Instead of measurement, Newton
Raphson power flow solution result is used as initial values of COA criterion method. The 32 varied
load data were used for learning process of the model. Backpropagation with momentum method is
applied with input layers consist of 20 neurons representing real power of 20 buses, while hidden
layers consist of 10 neurons. Output layer consists of only one neuron is represented as difference of
average power angle between west group and east group.
Keywords. Power angle stability, COA criterion, and neural network.
1
Introduction
Steady state stability is the ability of synchronous machine of a power system to remain in
synchronism after a very minute disturbance. Small disturbances are always present in a
power system; for example there are gradual changes in load, manual or automatic changes of
excitation, irregularities in prime-mover input, and so forth. Obviously these small
disturbances cannot cause loss of synchronism unless the system is operating at, or very near,
its steady state stability limit. Continuous electricity supply is conducted if only certain
synchronous generators are ready to supply. Once the generator is out of synchronism,
significant voltage and current fluctuation is occurred. These could initiate trouble in
transmission system. Consequently, a monitoring system to ensure power transmission steady
state stability is required.
Power transmission steady state stability shows maximum transmitted power. Power
transmission capacity of a generator group depends on power angle difference with another
generator group. Neural Network is built with system loads as inputs and the average angles
of group of generators as targets. This target data is provided through calculation based on
COA criterion. Instead of measurement, Newton Raphson power flow solution result is used
as initial values of COA criterion method.
2
Theory
2.1
Newton Raphson Power Flow Solution
Power flow solution is necessary for planning, economic scheduling, and control of an
existing system as well as planning its future expansion. The problem consists of determining
88
15th Indonesian Scientific Conference in Japan Proceedings
the magnitudes and phase angle of voltages at each bus and active and reactive power flow in
each line.
N
Pi = ∑ ViVnYin cos (δ i − δ n − θ in )
(1)
n =1
N
Qi = ∑ ViVn Yin sin (δ i − δ n − θ in )
(2)
n =1
The procedure for power flow solution by the Newton Raphson method is as follows (Saadat
1999, Grainger and Stevenson 1994):
1. For load bus, where Pi sch and Qi sch are specified, voltage magnitude and phase angles are
set equal to the slack bus values, or 1.0 and 0.0. For voltage-regulated buses, where
voltage magnitude and Pi,calc are specified, phase angle are set equal to the slack bus angle,
or 0.
2. Pi(k) and Qi,(k) are calculated from equation (1) and (2)
3. Calculate ∆P in each buses
4. Calculate Jacobian matrix, through estimation value or partial differentiation equation
from equation (1) and (2)
5. Inverse the Jacobian matrix to calculate ∆δi and ∆│Vi │ in each buses
6. Calculate the new δi and ∆│Vi │by adding ∆δi and ∆│Vi │ to the latest value
7. The process is continued until residuals ∆P and ∆Q are less than the specified accuracy.
2.2
Two Machine System
The type of power system whose steady-state stability limit can be found most simply consists
of two synchronous machines, a generator and a motor, connected through a network of pure
reactance. Power angle curve is established based on equation below:
P=
E1 .E 2
. sin δ
x
(3)
where:
P : Power transmitted from machine 1 to machine 2, E1: Internal voltage of machine 1, E2:
Internal voltage of machine 1, x :Transfer reactance between the internal voltages, δ:Angle by
which E1 leads E2 .
Figure 1. Power Angle Curve
Generator is stable if only transmitted power is less than Pm (δ<900).
89
Indonesian Student Association in Japan
15th Indonesian Scientific Conference in Japan Proceedings
2.3
Generator Power Angle Calculation (δ)
Before initiating power angle difference between groups of generator, power angle of each
generator must be defined. Power angle of each generator (δ) is angle by which E1 leads E2
(Taylor 1994, Gross 1986, Kundur 1994). Equivalent circuit of generator connected through
infinite bus is shown below:
E1
I
E2
Xs
Figure 2. Equivalent Circuit of Generator-Infinite Bus
According to the circuit showed in figure 2., the value of E1 is initiated by:
E1 = E 2 + jX s .I
I=
(4)
S*
*
E2
(5)
where:
E1: Internal voltage of generator, E2: bus voltage, Xs: synchronous generator reactance, I:
current flows (from generator) through bus, S: Apparent Power flows in bus, * : conjugate
According to equation (4), phase diagram of voltage and current is established and the δ can
be calculated (Kimbark 1947).
Figure 3. Three Phase Diagram of Voltage and Current
2.4
Average Power Angle of Generator Groups
Based on COA criterion, average power angle of generator groups is initiated (Kimbark 1999).
The equations are as follow:
Ma =
∑M
l∈A
(6)
l
δ a = M a−1 ∑ M l δ l
(7)
l∈ A
where:
l : generator number (1,2,3…n), Ml: inertia moment of each generator, Ma :Totalinertia
moment of group ‘a’, δl : power angle of each generator, δa: average power angle of group ‘a’
Indonesian Student Association in Japan
90
15th Indonesian Scientific Conference in Japan Proceedings
2.5
Basic Concept of Neural Network
To build a model of Neural Network, several input-output data are needed as data couple.
Figure 4 shows a simple neural network (Momoh and El-Hawary 1999).
Input
Layer
Hidden
Layer
Output
layer
X1
Z1
Y1
X2
Z2
Y2
Xi
vij
Zj
weight
wij
Yk
weight
Figure 4. A Simple Neural Network
Learning process of Neural Network is a process to search the best weight by training the
network appropriated with the wanted performance, so that given input vectors produce aimed
output vectors. The training is built by applying input vectors scheme orderly, and also to
control network’s weight to search output vectors in line with a learning algorithm. While
learning process, weight is convergent smoothly to certain value. In addition, output scheme
produce aimed output vectors (Warwick et al. 1997, Kreshna and Srivastava 2006).
The 32 varied load data were used for learning process of the model. Backpropagation with
momentum method is applied with input layers consist of 20 neurons representing real power
of 20 buses, while hidden layers consist of 10 neurons. Output layer consist only 1 neuron
representing average power angle difference between west group and east group.
3
Simulation
3.1
Simulation
Simulation step of the steady state stability monitoring system in Java-Bali 500 kV
Transmission System is shown below:
Figure 5. Simulation Design
91
Indonesian Student Association in Japan
15th Indonesian Scientific Conference in Japan Proceedings
The step of monitoring system design is started by collecting secondary data of line. The bus
data as inputs for Newton Raphson power flow. The solution of the power flow is used –
instead of direct measurement - as inputs to COA method (Kimbark 1999) in calculating
power angle difference between generator groups of East Java and West Java. The additional
data needed in this step is inertia of the generators.
Neural Network based monitoring system then is trained using the variation of load data as
input and calculated steady state stability as target. This model assists steady state stability
monitoring whether is stable, critical stable or unstable.
As those data are included, the simulation is ready to start. Power Flow simulation is firstly
done to find out power flow in each buses of 500 kV Java-Bali System.
14
11
9
1
10
13
12
8
2
3
4
15
16
17
18
19
20
7
5
6
Figure 6. A 500 kV Java-Bali Transmission System
Indonesian Student Association in Japan
92
15th Indonesian Scientific Conference in Japan Proceedings
Table 1. Load in 500 kV Java-Bali System
Table 2. The 500 kV Java-Bali System Data
Table 3. Inertia Moment of West Java Generators
93
Indonesian Student Association in Japan
15th Indonesian Scientific Conference in Japan Proceedings
Table 4. Inertia Moment of East Java Generators
Newton Raphson Power Flow solution results power angle of each generator. Then, those are
processed to find power angle difference between West Java and East Java groups using the
COA method.
3.2
Power Angle Difference (∆δ)
According to table 1 until table 4, equation (6) and (7), average power angle of each generator
group (Peak Load, 2004) is found. In addition, Power Angle Difference (∆δ) between East
Group and West Group of generator is 22.430 – 3.6160 = 18.810.
3.3
Applying Neural Network
Equal calculation is applied to determine the 32 of power angles difference by varying the
load. The 32 varied load data which results 32 power angle difference data are prepared as
input and target data for learning process in Neural Network. Learning process is finished
when maximum error (10-4) or maximum epoch (9000 epochs) is reached. Learning process
after 9000 epochs is shown in figure 7.
Performance is 0.000127315, Goal is 0.0001
1
10
0
Training-Blue Goal-Black
10
-1
10
-2
10
-3
10
-4
10
0
1000
2000
3000
4000
5000
9000 Epochs
6000
7000
8000
9000
Figure 7. Learning Process (after 9000 epochs)
After learning process, the built neural network model is tested by 5 similar data. Then, the
output is benchmarked with the target. Table 5. shows error between neural network output
and the target.
Table 5. Error Percentage of Neural Network
Indonesian Student Association in Japan
94
15th Indonesian Scientific Conference in Japan Proceedings
4
Conclusion
1.
The 500 kV Java–Bali Transmission System is still in power transmission steady state
stability when peak load was reached in 2004 (∆δ = 18.81 degrees)
2.
If Western and Eastern Java Loads are significantly different, the 500 kV transmission
system is closing critical steady state stability
3.
Neural Network could be applied to monitor power angle difference between groups of
generator
References
[1]
Chapman, S.J. (1999). “Electric Machinery Fundamentals Third Edition”, McGraw-Hill
Inc.
[2]
Grainger, J.J. and Stevenson, W.D. (1994). “Power System Analysis”, McGraw Hill Inc.
[3]
Gross, C.A. (1986). “Power System Analysis Second Edition”, John Wiley & Sons.
[4]
Kimbark, E.W. (1947). “Power System Stability Volume I”, John Wiley & Sons.
[5]
Kimbark, E.W. (1948). “Power System Stability Volume III”, John Wiley & Sons,
[6]
Kreshna, J. and Srivastava, L. (2006). ”Counterpropagation Neural Network for Solving
Power Flow Problem”, International of Intelligent Technology Vol. 1, Number 1.
[7]
Kundur, P. (1994). “Power System Stability and Control”, McGraw Hill Inc.
[8]
Momoh, J.A. and El-Hawary, M.E. (1999). ”Electric Systems, Dynamics, and Stability
With Artificial Intelligence Applications”, Technology .
[9]
Pai, M.A. (1981). “Power System Stability Volume 3”, North-Holland Systems and
Control Series.
[10] Saadat, H. (1999). ”Power System Analysis”, McGraw Hill Inc.
[11] Semitekos, D. and Avouris, N. (2002). "Power Systems Contingency Analysis using
Artificial Neural Networks", semitekos-power.
[12] Taylor, C.W. (1994). “Power System Voltage Stability”, McGraw-Hill Inc.
[13] Warwick, K., Ekwue, A., and Aggarwal, B.L. (1997 ). ”Artificial Intelligence
Techniques in Power Systems”, Technology.
.
95
Indonesian Student Association in Japan