Power System Stability Control Based on the Characteristics of the Observed

Information via Excitation Control

Tomohiro Maeda, Masayuki Watanabe, Yasunori Mitani and Yaser Qudaih Kyushu Institute of Technology

Fukuoka, Japan

Abstract—This paper presents a method for tuning power system stabilizer (PSS) parameters to control low-frequency oscillations. The dynamics of the low-frequency oscillations can be identified by wide area phasor measurements. Hence, the theory builds a low-order model that reflects the dynamics of the full system, based on observation components that are included in the system oscillations. Since the model reflects the real structure of an excitation control such as PSS and Automatic Voltage Regulator (AVR), also it can tune AVR parameters at the same time. As a result, the PSS parameters tuning can effectively damp low-frequency oscillations.

Keywords-power system control; PSS; wide area phasor measurements; low-frequency oscillation; exciation control

I. INTRODUCTION Interconnections in power systems are intended to improve

the reliability and the economical efficiency, while operated in a wide area. Power system states are always changing according to its nature. At the same time the system characteristics are also changing. Therefore, real-time power system monitoring and control based on wide area data collection is considered to be necessary crucial. On the other hand, in the power system with long distance transmission such as west Japan, it occasionally causes the inter-area low-frequency oscillation with poor damping characteristics. PSS is effective against inter-area oscillations, it is able to stabilize the power system effectively by the appropriate design of each constant such as phase lead-lag compensation and gain [1].

However, since it is difficult to design PSS against a huge power system, this paper proposes an easier way to design PSS by building a low-order power system model that reflects the dynamics of the full system, especially focusing on the characteristics of the AVR, using phasor information obtained by Phasor Measurement Units (PMUs).

This paper focuses on the actual structure of an AVR. The voltage control of AVR operates to attempt keeping the generator voltage to the set value voltage. The synchronizing power is increased, but the damping force is reduced because the gain is set high in the quick response AVR. On the other hand, the control signal from PSS can make the damping force

increase. Thus, by using a combination of PSS and AVR, the characteristics can be improved. In addition, it is also possible to design at the same time. These devices are used in other papers [2], [3]. The input of the PMU is voltage; PMU has the ability to compute phasor (the calculation of the phase and amplitude) based on Global Positioning System (GPS) signal. The characteristics of this device is what the measurement of the voltage and phasor at different points can be synchronized correctly by receiving GPS signal from satellites (position and time data) using the antenna in each unit. By using GPS, the time for the sampled data can be synchronized on less than error of ±10 [μs]. By using the internet, it is easy to download the collected data and change various settings. Thus, by putting on PMU to multiple outlets in the same system, the oscillation analysis of power system, the characteristics analysis of power demand and the phasor measurement of the same time can be worked. This device is used in other papers [1], [4], [5].

Fourier transform is very useful to find the synchrony that exists in a steady state signal. By using Fourier transform, a signal in time domain can be transformed to a signal in frequency domain. The data obtained by a PMU are sampled data. Therefore, discrete Fourier transform is used when it is transformed to frequency domain. The process of the FFT filter is based on the following steps:

1) Compute the FFT of original data. 2) Set to zero those components of the FFT which are

beyond the designated frequency. 3) Compute the Inverse FFT of the measured data.

Thus, the extracted data only contain components within a

dominant mode. This technique is used in other papers [1], [6], [7].

In this paper, section 2 is talking about the construction of a low-order model which represents the characteristics of the full system. Section 3 is explaining about power system control with the low-order model, and section 4 ends with conclusion.

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II. CHARACTERISTICS OF THE FULL SYSTEM BASED ON A LOW-ORDER MODEL CONSTRUCTION

A. Extraction Oscillation Mode using Fast Fourier Transform (FFT) Analysis In a wide area measurement using PMU, there are not only

low-frequency oscillation components but also many components of various frequency bands such as local oscillation components which have about 1 second cycle. Therefore, a filtering can effectively extract dominant low-frequency oscillation components.

A signal in time domain can be transformed into a signal in frequency domain by using Fourier transform. When we transform a signal to frequency domain, we should use discrete Fourier transform, because data obtained by a PMU are sampled data. Fourier series expansion of discrete-time signal can be considered as transformation formula for time series data of finite number. Discrete Fourier transform for time series data x of finite number (N) is represented by the following form:

∑−

=

=1

0

][1][N

n

mnWnxN

mX (n, m = 0, 1, ･･･, N−1) (1)

where, )/2exp( NjW π−= . After the FFT analysis, by getting out the only part corresponding to the focused frequency, where X[m] corresponding to the unnecessary frequency band are all 0, and calculating inverse FFT to reconstruct time series data, the FFT filter can completely eliminate unnecessary signal and extract only the oscillation components in the frequency band of focused oscillation mode. The formula of inverse FFT is represented by the following form:

∑−

=

−=1

0][1][

N

m

mnWmxN

nx (2)

The process of the FFT filter is based on the following steps: Firstly, FFT is applied to the phase difference of both ends of system. Fig. 1 shows the result of FFT analysis. In the result, a dominant inter-area mode appears around 0.35 [Hz]. Therefore, the frequency band of FFT filter is set to 0.35 ± 0.09 [Hz]. Fig. 2 shows the phase difference of inter-area low-frequency oscillations extracted by the FFT filter. Thus, by extracting oscillations with a specific frequency band, the FFT filter can eliminate other oscillation components.

Figure 1. The result of FFT.

Figure 2. Filtered phase difference.

B. Oscillation Model Estimation Based on Phasor Measurement of the Two Locations Since low-frequency oscillations have a large contribution

on group of generators at the both ends of the system, it is easy to capture the characteristics of low-frequency oscillations by using information observed at both ends of the system. By considering that the data obtained from PMUs are phase angle, a swing equation can be represented by the following form:

⎥⎦

⎤⎢⎣

⎡ΔΔ

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

ΔΔ

ωδ

ωδ

21

10aa

(3)

where, Δδ is the deviations of the phase angle obtained by PMUs, in which data with the necessary frequency band are extracted by the FFT filter. The coefficients a1 and a2 can be determined by the least square method [8]. The characteristics of the extracted mode can be estimated by the eigenvalues of the coefficient matrix. By evaluating the positive or negative signs of real part of eigenvalues, it is possible to discriminate whether the system is stable or not. It can be also known the degree of stability by the magnitude. The low-order oscillation model of the interested mode is represented by the following form:

21

2

1)(asas

sG−−

= (4)

On the other hand, the output of the system is the phase difference information, which can be observed by synchronized phasor measurements. The system model is assumed as in Fig. 3 and then the input is estimated by multiplying the inverse of G(s) to the phase difference data shown in Fig. 2. Fig. 4 shows the estimated input.

C. Low-order Model Composition In this paper, a low-order model focusing on the

characteristics of the PSS and AVR is considered.

Figure 3. Simplified model representing low-frequency oscillations.

G(s)u Δδ

Phasor fluctuationsMeasured

Load fluctuationsEstimated

G(s)u ΔδPhasor fluctuations

MeasuredLoad fluctuations

Estimated

Figure 4. Estimated input signal.

Fig. 5 shows the low-order model in this paper. In Fig. 5, the oscillation model G(s) can be represented by a second order transfer function, which shows the characteristics of a low-frequency mode. F1(s) shows the model to connect the PSS and AVR, while F2(s) is the model that represents the feedback function of the applied voltage. Details are described in the next section.

The real structure of a Δω-type PSS that can damp inter-area oscillations is shown in Fig. 6. K is the gain, T1 ~ T4 are the time constants of the phase lead-lag compensator. In this study, the time laggings for the signal washout are T0 = 0.02 [sec], Tw = 5.0 [sec].

The real structure of an AVR used in this study is shown in Fig. 7. Since the internal impedance of the generator is large, the generator voltage swings when the load of the system changes. Therefore, the AVR automatically adjusts the fluctuations of the generator voltage by the internal voltage drop and serves to adjust the field voltage to keep the voltage setting (90R) [2].

D. Identification of the Model to Represent the Excitation Control System The output of PSS and AVR in a real system is connected

to an excitation system through a variety of compensation systems. Hence the output signal of AVR model does not work propriety if the output is connected directly to the feedback. Therefore, it is necessary to identify the model F1(s) for connecting the output of AVR to the oscillation model. Likewise, it is necessary to identify the model F2(s) that represents the function of the voltage feedback.

These models are identified by numerical algorithms for subspace state system identification (N4SID) [9] which is an identification method based on the subspace method, by using input-output data. The method is applied to IEEJ WEST 10-machine system model [10] shown in Fig. 8, which is showing the single line diagram of the whole original system. F1(s) and F2(s) are represented by a transfer function of 8th order and 3rd order as (5) and (6), respectively.

12

78

812

78

1 )(asasas

bsbsbsF

+++++++

= (5)

12

23

312

23

2 )(asasas

bsbsbsF+++

++= (6)

Figure 5. Low-order power system model considering the characteristics of an AVR.

Figure 6. The real structure of Δω -type PSS.

Figure 7. The real structure of AVR.

Figure 8. IEEJ WEST 10-machine system model (original system) [10].

III. POWER SYSTEM CONTROL WITH THE LOW-ORDER MODEL

A. PSS Tuning Based on Low-order Model PSS on generator 1 is designed by building a low-order

model for damping low-frequency oscillations. The PSS has been designed in order to stabilize enough all transfer functions of the model F(s), oscillation model G(s), PSS blocks and AVR blocks. PSS parameters are adjusted to increase the gain of around 2.2 [rad/sec] that is the center frequency of the oscillations which it should be stabilized. But it will be expected that PSS-loop will cause instability if the phase compensations are not appropriate. In this study, the width change of the parameter was decided to 5 % because of the changes may not be able to be represented correctly if the parameter changes is wide. Table I shows the parameters of the adjusted PSS, where Case 1 represents that there is no PSS, Cases 2 ~ 4 represent each transition of the PSS parameters with PSS design.

Disturbance G(s)

Oscillation model

Phase differences

PSS

AVR

F1(s)

F2(s)

GeneratorTerminalVoltage

++

+

-

-π120

sDisturbance G(s)

Oscillation model

Phase differences

PSS

AVR

F1(s)

F2(s)

GeneratorTerminalVoltage

++

+

-

-π120

s

ωΔsTsT

2

1

11

++

sTsT

W

W

+1pssV

sTsT

4

3

11

++

sT011

+KωΔsTsT

2

1

11

++

sTsT

W

W

+1pssV

sTsT

4

3

11

++

sT011

+K

G1

G2 G3 G4 G5 G6 G7 G8 G9

G10

21 1

2

12

22

3 4 5 6 7

13 14 15 16 17 18

23 24 25 26 27 28

9 30

8

29

19

＋ ＋

＋＋

＋

s1.010.1

+

ss2.01

05.0+

0.1tV 0.150 fdE

pssV

refV 0.1500fdE

－－

＋ ＋

＋＋

＋＋ ＋

＋＋

＋

s1.010.1

+

ss2.01

05.0+

0.1tV 0.150 fdE

pssV

refV 0.1500fdE

－－

B. Model Evaluation The Effect of the PSS tuning can be checked by observing

the response of speed deviations for the disturbance. A three- phase short circuit fault at the point between nodes 8 and 9 in Fig. 8 is assumed. The fault is eliminated at 4 cycle (0.067[sec]) after the fault occurred. Fig. 9 shows the result which illustrates that the low-frequency oscillation is damped effectively by the tuning. Table II shows the transition of the eigenvalues of each PSS tuning in Cases 1 to 4. Fig. 9 shows that the speed deviation responses faster to the disturbance. Moreover, Table II shows that the system becomes gradually stable. Thus, these results demonstrate the effectiveness of the proposed method based on wide area phasor measurements.

TABLE I. THE PARAMETERS BY PSS DESIGN

K T1 T2 T3 T4 Case 1 ― ― ― ― ― Case 2 1.93 3.63 0.26 1.41 4.51 Case 3 2.03 3.81 0.25 1.48 4.28 Case 4 2.13 3.99 0.24 1.55 4.05

Figure 9. Response of speed deviations for the disturbance of the original system.

TABLE II. TRANSITION OF EIGENVALUES WITH PSS TUNING

Original system Case 1 − 0.050 ± j 2.235 Case 2 − 0.086 ± j 2.209 Case 3 − 0.092 ± j 2.201 Case 4 − 0.098 ± j 2.192

IV. CONCLUSION In this study, a method for tuning PSS based on the wide

area phasor measurement was proposed. By focusing on the characteristics of the excitation control system, PSS and AVR, a low-order model was constructed to reflect the system state. PSS was designed by using the proposed model. The simulation results show that the PSS designed by using the low-order model can damp low-frequency oscillations effectively. The proposed model in this study is expected to improve the modeling problem that is difficult to capture the characteristics of oscillations in the process of the PSS tuning. In addition, the proposed model is also expected to have the advantage of the PSS design accuracy.

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