Small Signal Stability Analysis. Small Signal Stability analysis of a 330kV Network: A case study of the Nigerian 330kV network. Ogonji^yigbe J. K , Gonoh B.A2. Department of Electrical/Electronic Engineering, Faculty of Engineering, University of Abuja. Department of Electrical Engineering, Faculty of Technology, Bayero University, Kano. Correspondence author:k [email protected]Abstract This paper, examines the stability of the existing 330kV Nigerian network system when subjected to small disturbance such as gradual load and generation increase. Modal analysis method is employed to carryout the analysis using the NEPLAN software. Various scalingfactors for load and generation rangingfrom 0.4 to 0.6 andfrom 0.6 to 2.0 respectively were used to test the stability ofthe system. The results showed that all the generating nodes have negative real parts ranging from -0.001 to -1.404 and damping ratio from 0.054 to 0.211 which falls within the acceptable value o f 0.3 and above with the exception positive eigenvalue to the negative side ofthe complex plane (S-plane). Keywords: Eigenvalues, eigenvectors, small signal stability. a. INTRODUCTION Small-signal (or small-disturbance) stability is the ability of the power system to maintain synchronism when subjected to small disturbances [1]. Such disturbances occur continually on the system because of small variations in loads and generation. The main problem of small disturbance stability is that of ensuring sufficient damping of system oscillations [1]. Since the stability of power system is very important in ensuring the reliability and security of power supply, this therefore, informs the need to examine the stability of the Nigerian 330 kV network in the presence of small disturbance, which is the main focus of this paper. Various methods have been employed by different authors such as Heffron Phillips method employed by [2], which was applied to the reduced 330kV Nigerian system. The method gave an insight into the causes of small disturbance instability phenomena of the longitudinal multimachine, isolated systems such as the Nigerian power systems. The system response to small signal disturbances is seen to depend on initial operating point, characteristics of transmission lines, and type of excitation controls employed. The critical eigenvalues computed for various operating points were found to exhibit low frequency oscillation modes for different load combinations and operating conditions. One or more of the system eigenvalues were located to the right half of the s~plane, indicating instability. The worst case was for 110% load condition with oscillatory frequency of 2.38Hz. Appropriate FACTs (Flexible AC Transmissions) devices and damping controllers were recommended to strengthen capacity, enhance steady-state and transient stability of the network and alleviate low frequency oscillation. Eigenvalues and eigenvectors method employed by [3], was applied to three machine nine bus network, using Matlab tools to analyze the effects of variations in Generator inputs for small disturbance. The analysis showed that generation input of a system does affect the stability of the network when experiencing a small disturbance. An increase of generation capacity can cause machine to lose synchronism with the network and affect the rotor angle. a. The Nigerian 330kv Network. The dynamic behavior of a power system is mostly influenced by the impedance of the circuits interconnecting the main sites of the power generation, namely the 330 kV, 132 kV and other transmission network [4]. For this reason, the analysis was limited to the 3 3 OkV transmission network connecting all the existing power stations. Most 330 kV use twin Bison (350 mm: Aluminium conductor, steel reinforced) conductors which under typical environmental conditions in Nigeria, have a continuous maximum current capacity of about 680Amps per conductor [5]. The system is radial with long transmission lines in the Northern section. The west is linked to the East Ogunjnyigbe J.K, Gonoh B.A. 18
Transcript
Small Signal Stability Analysis.
Small Signal Stability analysis of a 330kV Network: A case study of the Nigerian 330kV network.Ogonji^yigbe J. K , Gonoh B.A2.
Department of Electrical/Electronic Engineering, Faculty of Engineering,University of Abuja.
Department of Electrical Engineering, Faculty of Technology, Bayero University, Kano.Correspondence author:k [email protected]
AbstractThis paper, examines the stability o f the existing 330kV Nigerian network system when subjected to small disturbance such as gradual load and generation increase. Modal analysis method is employed to carryout the analysis using the NEPLAN software. Various scaling factors fo r load and generation ranging from 0.4 to 0.6 andfrom 0.6 to 2.0 respectively were used to test the stability ofthe system. The results showed that all the generating nodes have negative real parts ranging from -0.001 to -1.404 and damping ratio from 0.054 to 0.211 which falls within the acceptable value o f 0.3 and above with the exception positive eigenvalue to the negative side ofthe complex plane (S-plane).
Keywords: Eigenvalues, eigenvectors, small signal stability.
a. INTRODUCTIONSmall-signal (or small-disturbance) stability is the ability of the power system to maintain synchronism when subjected to small disturbances [1]. Such disturbances occur continually on the system because of small variations in loads and generation. The main problem of small disturbance stability is that of ensuring sufficient damping of system oscillations [1]. Since the stability of power system is very important in ensuring the reliability and security of power supply, this therefore, informs the need to examine the stability of the Nigerian 330 kV network in the presence of small disturbance, which is the main focus of this paper. Various methods have been employed by different authors such as Heffron Phillips method employed by [2], which was applied to the reduced 330kV Nigerian system. The method gave an insight into the causes of small disturbance instability phenomena of the longitudinal multimachine, isolated systems such as the Nigerian power systems. The system response to small signal disturbances is seen to depend on initial operating point, characteristics of transmission lines, and type of excitation controls employed. The critical eigenvalues computed for various operating points were found to exhibit low frequency oscillation modes for different load combinations and operating conditions. One or more of the system eigenvalues were located to the right half of the s~plane, indicating instability. The worst case was for 110% load condition with oscillatory frequency of 2.38Hz. Appropriate FACTs (Flexible AC Transmissions) devices and damping controllers were recommended to strengthen capacity, enhance steady-state and transient stability of the network and alleviate low frequency oscillation.
Eigenvalues and eigenvectors method employed by [3], was applied to three machine nine bus network, using Matlab tools to analyze the effects of variations in Generator inputs for small disturbance. The analysis showed that generation input of a system does affect the stability of the network when experiencing a small disturbance. An increase of generation capacity can cause machine to lose synchronism with the network and affect the rotor angle.
a. The Nigerian 330kv Network.The dynamic behavior of a power system is mostly influenced by the impedance of the circuits interconnecting the main sites of the power generation, namely the 330 kV, 132 kV and other transmission network [4]. For this reason, the analysis was limited to the 3 3 OkV transmission network connecting all the existing power stations. Most 330 kV use twin Bison (350 mm: Aluminium conductor, steel reinforced) conductors which under typical environmental conditions in Nigeria, have a continuous maximum current capacity of about 680Amps per conductor [5].The system is radial with long transmission lines in the Northern section. The west is linked to the East
through one transmission line from Osogbo to Benin and one double circuit line from Ikeja to Benin [6]. The 330kV Nigerian network is connected to eleven generating stations with total installed capacity of 5940MW while the availability varies between 3000MW and 4000MW[5]. Out of the eleven generating stations, three are hyro which is made up of 1900MW and the rest are thermal with the capacity of over 4000MW. The total length of330kV is roughly put at 3642km with forty one buses and eleven transformers[5].The system is radial with long transmission lines in the Northern section. The West is linked to the East through one transmission line from Osogbo to Benin and one double circuit line from Ikeja to Benin [6]. The 330kV Nigerian network is connected to eleven generating stations with total installed capacity of 5940MW while the availability varies between 3000MW and 4000MW [5]. Out of the eleven generating stations, three are hyro which is made up of 1900MW and the rest are thermal with the capacity of over 4000MW. The total length of330kV is roughly put at 3642km with forty one buses and eleven transformers [5].
b. MATERIALS AND METHODNEPLAN is the most user friendly and simulation tool for transmission, distribution, generation and industrial networks. NEPLAN covers all aspects of modem power system planning and analysis. NEPLAN Software was therefore, employed in this work to carry out a complete small signal stability analysis on the Nigerian 330kV grid system. The entire existing Nigerian 330kV network is modeled in NEPLAN environment [7] as shown below
Small Signal Stability Analysis Ogvnjnvigbe J. K, Gonoh B.A.
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I Eigenvalues and EigenvectorsAn Eigenvector of a square matrix A is a non-zero vector v that when multiplied by A. yields the original vector multiplied by a single number compatibility; that is Av = v. (1)The number is called the Eigenvalue of A corresponding to eigenvectors v( 1} [8]Eigenvalues method which is also known as modal method was employed to analyze small disturbance on Nigerian 330kV network. This is achieved by evaluating the eigenvectors of state matrix A as follows: [6].The linearized state space equation of a nonlinear system are [ 1 ].
Small Signal Stability Analysis..... Ogimjuyigbe J.K, Gonoh B.A.
A X = A ' A x - B - Au (2)
A y = C • Ax 1 D • Au (3)
The stability of the system is determine by solving for the eigenvalues of matrix A and their corresponding eigenvectors. For any eigenvalue k, there exists at least one non zero column vector v which satisfies the Characteristics equation (4).Av = v (4)Where are scalar values called the eigenvalues and v are the corresponding eigenvectors. To solve for the eigenvalues of matrix A, take the following determinant [A- ]=0 (5)To solve for the eigenvectors, add an additional term, and solve for v /A -/v = 0 (6)The eigenvalues may be real or complex values. Areal eigenvalues represent a non-oscillatory mode, while a complex pair of eigenvalues correspond to oscillatory mo de.The real part of complex eigenvalues provides the damping coefficient, while the imaginary part gives the oscillation frequency [ 1 ].
For a complex pair of eigenvalue l - o T jta the frequency of oscillation in Hz is given by
f =0>?.u
The damping ratio is given by(7)
(8)
II Criteria for DampingThe rate of decay of the amplitude of oscillations is best expressed in terms of the damping ratio. For a oscillatory mode represented by a complex eigenvalues A- o lj<a, the damping ratio is given by
The damping ratio ? determines the rate of decay of the amplitude of the oscillation.
A power system should be designed and operated so that the following criteria are satisfied for all expected system conditions, including post-fault conditions following design contingencies:
The damping ratio \ 1. of all system modes oscillation should not exceed a specified value. The minimum acceptable damping ratio is system dependent and is based on operating experience and /or sensitivity studies, is typically in the range 0.03-0.05.
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Small Signal Stability Analysis..... Ognnjnyigbe J.K, Gonoh B.A.
TABLE 1: EXISTING 330kV TRANSMISSION CIRCUITS
From To No. of Circuit
Construction Length (km)
1 Brinin Kebbi Kainji 1 SC 2 x Bison 310
2 Kainji Jebba 2 SC 2 x Bison 81
3 Jebba TS JebbaPS 2 DC 2 x Bison 8
4 Jebba TS Oshogbo oJ SC 2 x Bison 157
5 Jebba TS Shiroro 2 SC 2 x Bison 244
6 Shiroro Kaduna 2 SC 2 x Bison 96
7 Kaduna Kano 1 SC 2 x Bison? 230
8 Kaduna Jos 1 SC 2 x Bison 196
9 Jos Gombe 1 SC 2 x Bison 264
10 Oshogbo Aiyede 1 SC 2 x Bison 115
11 Aiyede Ikeja West 1 SC 2 x Bison 137
12 IkejaW -st Akangba 2 SC 2 x Bison 17
13 Ikeja West Benin 2 DC 2 x Bison 280
14 Ikeja West Egbin 2 DC 2 x Bison 62
15 Egbin Aja 2 DC 2 x Bison 16
16 Benin Ajaokuta 2 SC 2 x Bison 195
17 Benin Sapele 2 DC 2 x Bison 50
18 Benin Onitsha 1 SC 2 x Bison 137
19 Onitsha New Haven 1 SC 2 x Bison 96
20 Onitsha Alaoji 1 SC 2 x Bison 138
21 Alaoji Afam 2 DC 2 x Bison 25
22 Sapele Aladja 1 SC 2 x Bison 63
23 Sapele Sapele/Aladja Tee 1 SC 2 x Bison 44
24 Aladja Sapele/Aladja Tee 1 SC 2 x Bison 19
25 Sapele/Aladja Tee Delta 2 DC 2 x Bison 13
TABLE 2: 330kV and 132kV Line Parameters [5]
Line TypeInput data - R & X in ohms/km, B in pS/km
Small Signal Stability Analysis. Ognnjnvigbe J.K, GonohB.A.
Newton-Raphson method in Neplan [7] was employed to calculate the load flow because it converges faster than other methods such as Gauss-seidel. At six iteration the network converges. See the results in Table 3 and 4.The Newton-Raphson method proceeds from the error equation for the network node I [7]:nAS; = (Pj - j. Q J - U i . £ YiV U|i (10)
k=lThe complex voltages Uk are to be found such that the error AS( becomes zero.Pi and Qj are the predefined active and reactive power. Yik is an element of the Ymatrix of the i-th row and k-th column. The solution of the above error equation consists o f three steps:* Calculation of the power mismatch with the help of the voltages of every nodeAS'i = Svarr S h e (11)
* Calculation of the voltage variations for every node with the Jacobian-matrix JAU = 1 YAS (12)
* Calculation of the node voltagesUncu = Ualtj - «, AUj (13)
These three iteration steps starts with U=1.0pu or a predefined value (see “initialization file” in the dialog of load flow calculation parameters) and are done until the convergence criteria;
£ = £ |4 S j| (14)i = '
is reached
c. RESULT AND DISCUSSIONSFrom the load flow results shown in the summary table 3, the total power generated in Mega Watt is 3733.73MW, the total network loss on transmission is 30.93MW while the total network load is 3702.8MW. It should be noted that no loss on the transformers because only 330kV network was looked into and not 330kV/l 32kV network, therefore transformers were not included in the analysis.
TABLE 3: SUMMARY OF LOAD FLOW RESULTSummary of Load Flow Result
Total Power Generation Total Network Load Total Network Loss
P Gen (MW) P Load (MW) P Loss (MW)
3733.73 3702.8 30.93
Note: The total 30.93MW loss is attributed to losses on the 330kV transmission system, no loss on the transformers.
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Ogunjnyigbe J.K, Gonoh B.A.
Table 4 shows the established voltages on 330kV busbars in the load flows results. Table 4 Established Voltages on 330kV Bubars in the Load Flow Result
Small Signal Stability Analysis.
TABLE 4: LOAD FLOW RESULTS - 330KV VOLTAGES
Load Flow Results - 330kV VoltagesS/N Busbar Name U (kV) u (%) U ang(")
The stability of the network system is determined by the eigenvalues as follows:The eigenvalues of 33 OkV Nigerian Power Grid based on the transmission interconnections described i : eve and operating scenario of generation/system load as explained in the load flow result are : e - r e n te d on Table 6 Generally the system is stable as most of the eigenvalues (see Table 5) indicate r. n- scillatory mode (negative real values) and those with oscillations have good damping ratio.
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Small Signal Stability Analysis..... Ogunjuyigbe J.K, Gonoh B.A.
Table 5: Eigenvalue of Existing Nigerian Power Grid at 3733.7MW Generation
However there are some few instances which are explained below;I. Positive real values
Positive real value is normally an indication of a periodic instability but in this case, it is only Egbin generators that participate in this mode hence this can be attributed to the fact that Egbin unit is used as slack and also speed governor model was not represented in the simulation which result in Egbin generators experiencing instability. This does not post a threat to overall system stability as this problem was rectified by incorporating speed governor and AVR (Automatic Voltage Regulator). See Table 6,7 and the chat plot in fig. 1 a and b under appendices.
Small Signal Stability Analysis.....
Table 6 Positive Real Values before incorporating a speed governor..
S/N Eigenvalue Real Part Maximum Participated State Value
1 0.206 Egbin-Gen: Flux Linkage
2 0.046 Egbin-Gen: Rotor Speed
Table 7 Eigenvalues for Egbin Generators after including the speed governor in the simulation.S/N Eigenvalue Real Part Maximum Participated State
Value1 0.203 Egbin-Gen: Flux Linkage fd
2 0.008 Egbin-Gen: Rotor Angle
3 -0.008 Egbin-Gen: Rotor Speed
Table 7 shows Egbin eigenvalues being relocated to the negative side after incorporating speed governor and AVR (Automatic Voltage Regulator) in the simulation. See the graph plot in fig. 1 b
ii. Positive real and Negative imaginary values.Positive imaginary eigenvalue means sustained oscillation, however for all the participation state variable shown in Table. 8, the real part is negative which means the oscillations are damped and also the damping ratios are quite gppd enough for the system to be considered stable in this scenario.
Other results listed are presented in graphical form as shown in fig.2,3 identifying local and inter-area modes of oscillations.
I. Identified Local Area ModeThe identified local area Modes are shown on fig 2, they occurred at frequencies of 1.102 and 1.142 respectively with damping ratios of0.137and0.143.
ii. Identified Inter-Area ModeThe inter-area mode for this system happens at frequency o f 0.916Hz and a damping ratio o f0.054, In this mode the generators in the North (Kainji, Shiroro and Jebba) all hydro generating plants are found to be swigging against the generators in the southern part o f the network. This is illustrated on the plot in fig 3, again the damping ratio is good, hence the oscillation is expected to damp out a T = ^ r seconds [1].
ConclusionThe increase in load and generation affect the system stability. Egbin generator for instance experience instability with positive eigenvalues but this was rectified by incorporating an AVR controller into the network which relocated the eigenvalue to negative side of the s-plane Overloads were aslo experienced in the far North. But with the injection of AVR compensators, this problem was resolved. Generally, the system is stable with the eigenvalues ranging from -0.001 to -1.404 and damping ratio from 0.054 to 0.211.
Recommendation for future work.This paper only examined the small signal stability of the existing 3 3 OkV Nigerian network, therefore, further research work should include 132kV network and the newly commissioned generating stations connected to the grid system.
References[1] RKundur. “Power System Stability and Control” 1994 by McGraw-Hill, Inc. New York San
Francisco Washington, D.C. Aukland Bogota Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto. Pp 669 - 712.
[2] O. Komolafe, M. Omoigui, and A Momoh, “Reliability Investigation of the Nigeria Electric Power Authority Transmission Network in a Deregulated Environment” Proceedings of the IEEE Industry Application conference, 12-16 Oct. 2003, vol.2ppl328-1331
[3] [11] Hemalan N, Agileswari K, Au Mau, Syed K “Effects of Variations in Generator Imputs for Small Signal Stability Studies of a Three Machine Nine Bus network”. World Academy of Science, Engineering and technology 74.2011.
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[5] PHCN Documents, Abuja.
[6] Olusola K, Olorunfemi D “Improvement of the Voltage Profiler of the Nigeria Electric Power Network Using Power Flow Controller”. Dept, of Electronic and Electrical Engineering Obafemi Awolowo University, Ile-Ife, Nigeria.
