2.1.1 Eigenvalue Analysis and Participation Factor

The power swing equations of generators in an n-machine power system can be represented by [9]:

(2.1)

where i = 1, 2,…, n; ω is the angular velocity; δ is the rotor angle; M is the inertia constant; D is the damping coefficient; P_m is the mechanical input to the generator; P_e is the electrical output; and ω_r is the rated angular velocity. When including the effect of other generators and controller dynamics, it is just assumed that their responses are sufficiently faster than the responses of dominant modes. Interarea oscillations are mainly caused by the swing dynamics with a large inertia represented by Equation (2.1). Now in this system suppose that a specific mode associated with power oscillation becomes unstable with variation of a parameter such as changing the loading condition. Here, consider a generator (e.g., number k) that significantly participates in the critical dominant oscillation mode. This generator can be easily selected by calculating the linear participation factor, which is defined in Reference [10].

The system dynamics is represented in general by the following equation:

(2.2)

Linearizing (2.2) around an equilibrium point x = x₁ gives

(2.3)

The right eigenvector u_i and the left eigenvector v_i of the matrix A are defined as follows:

(2.4)

where λ_i is the ith eigenvalue of the matrix A. It is noteworthy that the eigenvectors should be normalized to satisfy the following condition:

(2.5)

The participation factor (p_ki) represents a suitable tool to measure the participation of the kth machine state in the trajectory of the ith mode. It can be defined as

(2.6)

Oscillation characteristics could be explained using the participation factor [10] and the mode shape [11], which provide critical information for operational control actions. As an example, the swing characteristics of the western Japan 60 Hz system have been evaluated by calculating eigenvalues of a simulation model [2]. So far, the estimation of the participation weights has been developed based on a WAMS [12].

2.1.2 Oscillation Characteristics in an Interconnected Power System

Here, an example of the oscillation dynamics in a longitudinally interconnected power system based on the eigenvalue analysis is described. Figure 2.1 shows the West Japan 10-machine system model [13,14] that is considered in this study. The model represents a standard model for the western Japan 60 Hz power system, which was developed by the technical committee of the Institute of Electrical Engineers of Japan (IEEJ), used for the verification of simulation studies. Table 2.1 shows the system constants. Each generator is equipped with an automatic voltage regulator (AVR), which is shown in Fig. 2.2.

Generator: Park's 5th Model, 1000 MVA Base
xd = 1.70 (p.u.)	= 0.35 (p.u.)	= 0.25 (p.u.)
xq = 1.70 (p.u.)	= 0.25 (p.u.)	M = 7.00 (s)
= 1.00 (s)	= 0.03 (s)	= 0.03 (s)
Transmission System: 1000 MVA, 500 kV Base
Impedance: Z = 0.0042 + j0.126 (p.u.)/100 km
Electrical charge capacity: jY/2 = j0.061 (p.u.)/100 km
Transformer: xt = 0.14 (p.u.)
Interconnected line: 100 km, double circuit
Line to generator: 50 km (G8: 100 km), double circuit

In Fig. 2.2, V_t, V_ref, E_fd, and E_fd0 are generator terminal voltage, reference voltage, AVR excitation signal, and nominal excitation signal, respectively. The rated capacity and output of the generators are shown in Table 2.2. The x_d (x_q), , and are d-axis (q-axis) synchronous, transient, and subtransient reactance, respectively. The , and are d-axis (q-axis) transient, and subtransient open circuit time constants, respectively.

In such a longitudinally interconnected power system, the mode associating with the low-frequency oscillation between both end generators tends to become unstable when the interconnected line is heavily loaded. Here, the load of node 2 and the power of generator 1 are increased by 1600 MW to heavily load the line between nodes 1 and 2. This results in the destabilization of the quasi-dominant mode (mode 2) in addition to the dominant mode (mode 1).

Figures 2.3 and 2.4 show mode shapes and linear participation factors corresponding to the generator rotor angles, respectively. Figure 2.3 shows that the mode 1 oscillates in opposite phase between both end generators, while the mode 2 oscillates in opposite phase between both end group and the middle group of generators. Figure 2.4 shows that generators 1, 5, and 10 principally participate in modes 1 and 2. Therefore, it should be better to monitor both ends and the middle region of the power system to capture the characteristics of the dominant and the quasi-dominant modes.

2.2.1 Monitoring of the Japan Power Network

In Japan, the West Japan 60 Hz system can be divided into several groups of six major electric power companies. Each group is connected through a 500 kV transmission line over a wide area. Due to its longitudinal structure there are some significant low-frequency oscillation modes in the whole system. Independent load frequency control based on tie-line bias control is adopted in each generation company [15]. Also, some independent power producers (IPPs) or power producer and suppliers are participating in the power market. So far, some oscillatory characteristics have been measured in the local area or between the interconnected areas. Here, a joint research project among some universities in Japan to develop an online wide-area measurement of power system dynamics by using the synchronized phasor measurement technique [16] is presented.

To establish a real WAMS, several PMUs are installed in universities/institutes in different geographical locations of Japan. Figure 2.5 shows the installed location of campus PMUs. The type of PMUs was NCT2000, which was manufactured by Toshiba Corp. (Fig. 2.6) [16], and synchronized by the global positioning system (GPS) signal. The installation of the PMUs started in 2001 to develop a WAMS covering the whole power system in Japan as a collaborative research called Campus WAMS. At least one PMU has been installed within the service area of each power company. The PMUs measured voltage phasors of 100 V outlets, which is the standard voltage of the Japan wall outlets, in the monitoring location (laboratory) of each university campus over 24 h schedules. In practical applications, the PMUs are usually installed at substations of transmission lines.

In the developed system, the measurement interval is 2/60 s in the western 60 Hz area, and 2/50 s in the eastern 50 Hz area in order to observe the dynamic characteristics of the power swing including the local and interarea modes. Synchronized monitoring can be achieved by using the precise pulse per second (PPS) output of the GPS receiver even in the widely spread power system, and the measured remote data can be easily concentrated via a fast communication network.

Figure 2.7 shows the overall framework of the performed Campus WAMS. The measured PMU data are automatically collected by phasor data concentrators (PDCs) installed at Nagoya Institute of Technology and Kyushu Institute of Technology via the Science Information Network. Although the IEEE COMTRADE format is employed as the format of data stored in each PMU, collected data by PDCs are converted into the comma-separated value format for usability, and then converted data are stored in a network-attached storage with a large capacity.

Phasor voltage is computed using sinusoidal voltage measured at the wall outlets as follows:

(2.7)

From Equation (2.7), voltage amplitude and phase can be easily obtained

(2.8)

(2.9)

Calculating Equation (2.9) gives phase angle referred to the GPS time.

2.2.2 Monitoring of the Southeast Asia Power Network

The Thailand power system has a longitudinal configuration with an interconnection between central and southern areas by 115 and 230 kV tie-lines with an 800 km-long distance. This configuration causes the interarea low-frequency oscillations with poor damping characteristics. In Malaysia, the 500, 275, 132, and 66 kV transmission network of Tenaga Nasional Berhad (TNB) spans the whole of peninsular Malaysia, which is known as the national grid. The national grid links the electricity power producers, made up of TNB power stations and IPPs, to the TNB distribution network and some large power customers. The transmission system of Malaysia is interconnected with the Thailand system operated by the Electricity Generating Authority of Thailand in the north via a high-voltage direct current interconnection with a transmission capacity of 300 MW and a 132 kV high-voltage AC overhead line with a maximum transmission capacity of 90 MW. In the south, the Malaysia system is interconnected to the transmission system of Singapore Power at Senoko via two 230 kV submarine cables with a firm transmission capacity of 200 MW. In Singapore, the 400, 230, and 66 kV transmission network is operated by Singapore PowerGrid.

Figure 2.8 shows the developed WAMS for the power system dynamics in the Thailand, Malaysia, and Singapore power network by using the PMUs [17] (NCT2000 Type-A manufactured by Toshiba Corp. [18]). Each PMU is installed at the northern (Chiang Mai), central (Bangkok), and southern (Songkla) areas in Thailand, Kuala Lumpur, Malaysia, and Singapore. Measurement units are installed at domestic 220 V, 50 Hz outlets in the university campuses or company buildings. Measured phasors with time stamps synchronized with the GPS signal are collected via the Internet.

2.4.1 Electromechanical Modes Characteristics

Figure 2.10 shows phase differences between the monitoring stations located at the University of Miyazaki (Miyazaki, Japan) and Nagoya Institute of Technology (Nagoya, Japan), which are located at both ends of the 60 Hz Japan power system. Small-signal fluctuations caused by continuous small disturbances such as load variations are clearly observed in the measured PMU data. Many oscillation modes are superimposed; however, a few dominant modes should be important to investigate the power system dynamics. Figure 2.11 shows the results of spectrum analysis. Low-frequency oscillations with frequency of about 0.37 Hz are also detected distinctly by phase differences between Miyazaki and Nagoya. In addition, this mode can be detected by phase differences between Hiroshima and Osaka (Japan), in the middle part of the system, although the amplitude of the mode is comparatively small. On the other hand, another quasi-dominant mode can be detected from recorded data between Miyazaki and Tokushima, where are located in one end and the central region of the system, respectively.

Figure 2.12 shows waveforms of most and quasi-dominant modes extracted by FFT-based filtering. These waveforms are depicted by the recorded data from Tokushima (Japan), which is roughly located in the central region of the system, as a reference of the phase angle. Figure 2.12a shows the most dominant mode (mode 1) with the frequency of about 0.37 Hz. This mode oscillates over the whole system in opposite phase with respect to another node located around the central region of the system. On the other hand, Fig. 2.12b shows waveforms of the quasi-dominant mode (mode 2) with the frequency of about 0.56 Hz, which oscillates in the same phase. It means that this swing has two nodes, where both ends oscillate in opposite phase with respect to the central region of the system. Consequently, the quasi-dominant mode has been detected in Fig 2.11c, while it has not been detected in Fig. 2.11a and b, because the mode has disappeared by recording the difference of each phase. As already described, these characteristics could be explained by the participation factor and the mode shape.

2.4.2 Oscillation Characteristics Analyses in Southeast Asia Power Network

Figure 2.13 shows frequency deviations of each area for 20 min from 15:20 (JST) on September 25, 2007. The figure shows frequency deviations of the synchronized Malaysia and Singapore system, where the Singapore system is evidently interconnected with the Malaysia system by AC transmission lines. On the other hand, the AC interconnection between the Thailand and Malaysia systems cannot be observed.

Figure 2.14 shows the frequency characteristics for frequency deviations of each area following FFT analysis. As can be seen, oscillation with a frequency of about 0.5 Hz is dominant in the Thailand system, while in the Malaysia and Singapore system, 0.3 Hz is the dominant oscillation frequency.

It is noteworthy that the spectrum of the Singapore system is larger than the other two systems. This result implies that the Singapore system mainly participates in the low-frequency mode with relatively poor damping characteristics.

Figure 2.15 shows waveforms of low-frequency oscillations extracted by the FFT-based filter. Figure 2.15a shows that the frequency deviation of the low-frequency oscillation mode in the central area (Bangkok) is oscillating in the opposite phase of the southern area (Songkla) low-frequency oscillation mode. Northern and central areas of Thailand form a coherent group with a large inertia, while the southern area oscillates against the coherent area.

The impact of system inertia on the frequency response is well discussed in Reference [19]. The configuration of the Thailand network is analogous to that of a single machine (Songkla) and infinite bus (Bangkok and Chiang Mai) system.

On the other hand, Fig. 2.15b shows that frequency deviations of Malaysia and Singapore oscillate in the opposite phase with each other, that is, each area seems to make a coherent group. Interarea low-frequency oscillations between each group with a frequency of about 0.3 Hz can be clearly observed. Major power plants concentrate on large cities, particularly in Kuala Lumpur and Singapore, and since these areas are interconnected with weak tie-lines, the interarea low-frequency oscillations tend to put the system in an unstable condition.