Selective Modal Analysis …

Wirindi, dkk.

SELECTIVE MODAL ANALYSIS OF POWER FLOW OSCILLATION IN LARGE SCALE LONGITUDINAL POWER SYSTEMS

Warindi1, I Made Ari Nrartha1, Soedjatmiko2

  • 1)    Electrical Engineering Dept. University of Mataram, Mataram, Indonesia

  • 2)    Electrical Engineering Dept.Gadjah Mada University, Yogyakarta, Indonesia [email protected]

Abstract

Novel selective modal analysis for the determination of low frequency power flow oscillation behaviour based on eigenvalues with corresponding damping ratio, cumulative damping index, and participation factors is proposed. The power system being investigated consists of three large longitudinally interconnected areas with some weak tie lines. Different modes, such as exciter modes, inter area modes, and local modes of the dominant poles are fully studied to find out the significant level of system damping and other factors producing power flow instability. The nature of the energy exchange between area is determined and strategic power flow stability improvement is developed and tested.

Keywords: Power flow oscillation, longitudinal power systems, inter-area modes, eigenspectrum, stability improvement

  • 1.    INTRODUCTION

In large scale longitudinal power systems, large amounts of electric power are transmitted over very long transmission lines covering the entire power areas under consideration. This paper examines power flow oscillation characteristics of three large power areas which are interconnected longitudinally with weak tie lines causing several inter-area modes [1,2]. Power systems of this type have features quite different from radial power systems and commonly found in geographically long islands with relatively low or medium population densities. Power flow stability is a major issue in this kind of systems since any power disturbances may easily lead to sustained power flow oscillations or even power splits which are very detrimental to the goals of maximum power transfers. The effects of the oscillations should be minimized.

For achieving the system secure operation againts any disturbances or transient perturbation, appropriate damping of the power system oscillations between the interconnected power areas is very important. Preventive or corrective remedial actions are necessary to ensure that the systems remain dynamically secure. For example, large interconnected power areas with weak tie-lines or poorly damped are susceptible to low frequency oscillations. Types of remedial actions may include strengthening the tie-lines, and/or using strategic coordination of PSSs and FACTS devices [4, 6, 7]. Improper coordination may cause destabilizing interactions [2,9].

As briefly stated above, large power systems highly utilize available transmission-distribution networks and generators in power stations with large amounts of power interchanged among area control centers and geographical regions. In power system

operation and control, the modal properties of the systems can be explored through explicit knowledge of the whole eigen spectrum of the systems [10].

In this paper, the method of selective modal analysis is used where eigenvalues and participation factors computations of the systems are performed to determine the power flow characteristics and stability of the systems [8].

  • 2.    TEST SYSTEM AND STABILIZERS

Power System Model

A 54 machines, 118 bus system as shown in Fig. 1 is simulated in this research.


AREA


AREA B


AREA C


Figure 1. Three areas power system

The generators are represented by two axis model and static exciter model is used for the excitation control. The prime mover and governor dynamics are also taken into consideration.

The main characteristics and features of the test system are as follow:

  • •    Voltage levels: 138 kV and 345 kV

  • •    166 transmission lines at 138 kV

  • •    11 transmission lines at 345 kV

  • •    109 load buses

  • •    Total installed capacity of 44.5 GW and 315            corresponding participation factors of the system

MVAR.                                              generators. Case-4 refers to the application of

By means of selective modal analysis the test STATCOM which can improve the voltage profile at system is divided into 3 major areas with weak tie-        the connection point to the network by injecting or

lines where low frequency inter-area oscillations are        drawing reactive power to or from the network.

observed.

Series FACTS devices have been recognized as Case-1: Original system

economical and effective means to damp low            Eigenspectrum of the system is shown in Fig. 3

frequency power system oscillations. In this study, whereas the eigenvalues of the local, interarea, and besides PSS, a STATCOM is employed for damping exciter modes are indicated in Table 1, 2, and 3 the inter-area oscillations and maintaining voltage respectively.

stability. Coordinated applications of PSS, FACTS

Figure 2. Typical PSS Controller


It works through the excitation system generating additional damping torque proportional to speed change. The main components of the PSS structure are proportional or amplification block, a wash out block and lead lag blocks.

Flexible AC Transmission Systems (FACTS)

Basically series FACTS controller has similar structure as PSS controller. The output of the FACTS device is Vs which represents the controlled variable. In this simulation, a series FACTS controller is employed. By installing FACTS technology on the tie-lines and controlling it to effectively mitigate the inter-area oscillations, the power exchange between power areas can be maintained safely

  • 3.    SIMULATION RESULTS and DISCUSSIONS

In this study, the test system eigenspectrums are displayed for 4 different cases. Case-1 corresponds to the original system comprising longitudinally interconnected three power area. Note that in this operating mode, the system is not equipped with PSSs or other FACTS devices. Parallel tie-lines configuration is implemented in case-2 reducing the inter-area reactances. Case-3 considers placement of PSSs at dominant generating machines based on the

Table 1. Eigenvalue of Local Mode

Most associated state

Real

Imag

f (Hz)

delta_Syn_36, omega_Syn_36

-2.6668

±10.0732

1.6032

delta_Syn_21, omega_Syn_21

-1.5998

±10.1058

1.6084

delta_Syn_26, omega_Syn_26

-1.4558

±10.1196

1.6106

delta_Syn_46, omega_Syn_46

-2.0436

±10.2165

1.626

omega_Syn_21, delta_Syn_21

-1.5968

±10.4119

1.6571

delta_Syn_54, omega_Syn_54

-2.3496

±10.4317

1.6603


Table 2. Eigenvalue of Inter -Area Mode

Most associated state

Real

Imag

f (Hz)

delta_Syn_39, omega_Syn_39

-0.8547

±6.1922

0.98551

delta_Syn_14, omega_Syn_14

-0.80827

±6.3712

1.014

delta_Syn_3, omega_Syn_3

-0.10488

±6.912

1.1001

delta_Syn_49, omega_Syn_49

-1.2182

±6.941

1.1047

omega_Syn_27, delta_Syn_27

-0.57075

±6.9699

1.1093

Table 3. Eigenvalue of Exiter Mode

Most associated state

Real

Imag

f (Hz)

e1q_Syn_39, vf_Exc_39

-0.8760

±1.8524

0.29482

vf Exc 51, e1q Syn 51

-2.9945

±1.9724

0.31392

delta_Syn_11, omega_Syn_11

-0.0442

±2.3518

0.3743

omega Syn 27, delta Syn 27

-0.1902

±3.6723

0.58446

The interarea modes indicate very low damping with frequency of power flow oscillation around 1.1 Hz representing a poorly damped system. Pole placement approach is required to drag the complex conjugate poles away from the imaginary axis

Case-2: System With Parallel Tie-Lines

Fig. 4 indicates the eigenspectrum of the system with lower reactances of the inter-area lines. Various operational modes are shown in Table 4, 5, and 6.

Reducing the interarea reactances show some improvement. Left shiftings of some dominant poles are observed. Combination with series FACTS seems to be better.

Case-3: PSSs are installed at dominant generators

The eigenspectrum and the operational modes are shown in Fig. 5, Table 7, 8, and 9 respectively.

Figure 4. Eigenvalues of the system with tie-line strengthened


Figure 5. Eigen values of system with PSS


Tabel 4. Eigenvalues of Local Mode

Tabel 7. Eigenvalues of Local Mode

Most associated state

Real

Imag

f (Hz)

delta_Syn_28, omega_Syn_28

-1.3273

±10.556

1.68

omega_Syn_54, delta_Syn_54

-2.3498

±10.4166

1.6579

delta Syn 21, omega Syn 21

-1.5291

±10.2803

1.6362

delta Syn 46, omega Syn 46

-2.0436

±10.2168

1.626

delta_Syn_21, omega_Syn_21

-1.6398

±10.1892

1.6217

delta_Syn_36, omega_Syn_36

-2.6728

±10.0653

1.6019

Most associated state

Real

Imag

f (Hz)

omega_Syn_41, delta_Syn_41

-2

±10

1.5434

delta_Syn_6, omega_Syn_6

-2

±10

1.5248

omega_Syn_22, delta_Syn_22

-3

±10

1.5219

delta_Syn_16, omega_Syn_16

-3

±10

1.514

omega Syn 31, delta Syn 31

-3

±10

1.5133

omega Syn 43, delta Syn 43

-3

±9

1.5113

Tabel 5. Eigenvalues of Inter- Area Mode

Tabel 8. Eigenvalues of Inter- Area Mode

Most associated state

Real

Imag

f (Hz)

omega_Syn_11, delta_Syn_11

-0.1841

±4.9074

0.78103

delta Syn 40, omega Syn 40

-0.4451

±4.8469

0.7714

vf_Exc_30, e1q_Syn_30

-1.2459

±4.7209

0.75136

delta_Syn_11, omega_Syn_11

-0.2117

±3.8235

0.60853

Most associated state

Real

Imag

f (Hz)

delta_Syn_11, omega_Syn_11

0

±2.4128

0.38401

vf_Exc_51, e1q_Syn_51

-3

±1.9716

0.31379

e1q_Syn_39, vf_Exc_39

-1

±1.8525

0.29483

e1q_Syn_1, vf_Exc_1

-3

±1.7939

0.28551

Tabel 6. Eigenvalues of Exciter Mode

Tabel 9. Eigenvalues of Inter Mode

Most associated state

Real

Imag

f (Hz)

omega_Syn_11, delta_Syn_11

-0.1841

±4.9074

0.78103

delta_Syn_40, omega_Syn_40

-0.4451

±4.8469

0.7714

vf_Exc_30, e1q_Syn_30

-1.2459

±4.7209

0.75136

delta_Syn_11, omega_Syn_11

-0.2117

±3.8235

0.60853

omega Syn 11, delta Syn 11

-0.0562

±2.4873

0.39586

delta Syn 36, omega Syn 36

-2.6728

±10.0653

1.6019

Most associated state

Real

Imag

f (Hz)

vf_Exc_40, e1q_Syn_40

-1

±1.3922

0.22158

e1q_Syn_19, vf_Exc_19

-1

±1.3676

0.21766

e1q_Syn_44, vf_Exc_44

-1

±1.3597

0.2164

vf_Exc_21, e1d_Syn_21

-4

±1.3448

0.21403

Compared with other cases, case-3 has indicated quite different eigenspectrums, better power flow improvement is observed. Installations of PSSs at generators 21, 26, 36, 46, and 54 provide higher damping and lower frequency of oscillation (0.3 Hz).

Case-4: STATCOM is installed at bus 64 (tie-line end)

Simulation reveals that the eigenspectrum is practically unchanged (See Fig. 6). Installation of STATCOM does not show any significant effect on the power flow pattern, but improvement in voltage stability is observed.

Figure 6. Eigenvalues of system with 1 STATCOM at bus 64

  • 4.    CONCLUSIONS

A longitudinal multiarea system with weak tielines exhibits a highly oscillatory power flows in the forms of low frequency power flow oscillations as depicted in the eigenspectrum where large number of eigenvalues are concentrated in the region close to the imaginary axis.

Reducing the interarea reactances by connecting parallel tie-lines between power areas will bring the power areas closer and shifts some of the eigenvalues to the left, thus improving the power flow stability to some degree.

Proper installations of PSSs at the dominant machines based on the maximum participation factors of the generators have shown a noticeable improvement to the power flow stability indicating proper phase lag compensation between the exciter input and the generating unit electrical torque.

A STATCOM is basically a shunts FACTS device. In this study, simulation shows that the application of this device has little effects on the damping control but improves significantly the voltage profile and maintains the steady state voltage.

  • 5.    REFERENCES

  • [1]    V. Arcidiano, E. Ferrari, R. Marconato, J. Dosghali, and D. Grandez, “Evaluation and improvement of electromechanical oscillation damping by means of eigenvalue-eigenvector analysis. Practical results in the Central Peru power system,” IEEE Trans. On PAS-99, 1980.

  • [2]    L.J. Cai and I. Erlich, “Fuzzy coordination of FACTS controllers for damping power system oscillations,” Proc. International Sysmposium Wroclaw, 2002.

  • [3]    F.P. Demello, P.J. Nolan, T.F. Laskowski, and J.M. Undrill,” Coordinated application of stabilizers in multimachine power systems,” IEEE Trans. on PAS-99, 1980.

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  • [5]    C. Gama and R. Tenoris,” Improvements for Power System performace modelling , Anlysis and benefits of FACTSs,” Proc. IEEE/PES winter Meeting, Singapore, 2000.

  • [6]    X. Lei, D. Jiang. And D. Retzmann, “ Stability improvement in power systems with non-linear TCSC control strategies,” ETEP, Vol. 10, No. 6, 2000

  • [7]    X. Lei, E.N. Lerch, and D. Povh, “ Optimization and coordination of damping controls for improving system dynamic performance,” IEEE Trans. power systems, Vol. 16, 2001

  • [8]    I.J. Perez-Arriaga, G.C. Vergbese, and F.C. Schweppe,” Selective modal analysis with applications to electric power systems. Part 1: Heuristic introduction,” IEEE Trans. on PAS, Vol. 101, 1982.

  • [9]    P. Pourbeik and M.J. Gibbard,” Simultaneous coordination of power system stabilizers and FACTS device stabilizers in multimachine power system for enhancing dynamic performance,” IEEE Trans. power systems, Vol. 13, No. 2, 1998.

  • [10]    L.M. Silveira,” Model order reduction techniques for circuit simulation,” Ph.D. thesis. MIT, 1994.

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Vol. 8 No. 1 Januari - Juni 2009