19-12-2010, 05:49 PM
VOLTAGE STABILITY ANALYSIS UNDER NORMAL AND CONTINGENCY CONDITIONS
MINI PROJECT REPORT
Presented by
AJISHA.S
DEPARTMENT OF ELECTRICAL ENGINEERING
COLLEGE OF ENGINEERING THIRUVANANTHAPURAM-16
MINI PROJECT REPORT
Presented by
AJISHA.S
DEPARTMENT OF ELECTRICAL ENGINEERING
COLLEGE OF ENGINEERING THIRUVANANTHAPURAM-16
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ABSTRACT
The load on a power system network is increasing day by day without much enhancements in transmission and or generation capability. This causes the system to operate under stressed condition, even a small disturbance can lead to system collapse when it is operating under stressed condition. Hence it becomes very important for power system planning and operating engineers to perform comprehensive voltage stability analysis of the system.
Many researchers have suggested various indices for voltage stability and voltage collapse prediction. While the different methods give a general picture of the proximity of the system voltage collapse, the L-index gives scalar no. to each load bus, which gives fairly consistent results. L-index varies between 0 and 1. L-index values away from 1 and close to zero indicate an improved voltage stability margin.
Objective of this mini project is to do the voltage stability analysis of a 30 bus system, under normal and contingency conditions and to rank the contingencies based on a composite criteria using L-index and voltage profile.
A software program is developed using MATLAB for performing load flow and to find L-index. Contingency analysis is done.
1. INTRODUCTION
Electric power system is the main source of industrial growth and welfare as well as socio- economic development. In developing countries like India there is always a shortage of generation as compared to the rapidly increasing load demand. Growing demand without matching expansion of generation and transmission facilities and more tightly inter connected power system contribute to the increased complexity of the system operation. Heavy loading of the system or tripping of any one of the grids causes the reduction of the receiving end voltage. The objective of this project is to do voltage stability analysis on a 30 bus system under normal and contingency conditions, and rank the contingencies using voltage stability index.
In power system planning, various types of studies are carried out, considering the various systems – operational scenarios. Intended or unintended switching operations are considered for very fast transient conditions and protective measures are planned for the purpose. Under dynamic conditions such as faults, line openings, generator tripping, load throw off etc.., protective systems are designed with more emphasis on protecting the equipment than concerned to system security and stability.
Paper [1] presents an approach for selection of unified-power-flow-controller suitable locations considering normal and network contingencies after evaluating the degree of severity of the contingencies. Most contingency-ranking methods rank the contingencies in an approximate order of severity with respect to a scalar performance index (PI), which quantifies the system stress [2-4]. It has been pointed out that two separate ranking lists are required for real power flow problems and voltage profile problems respectively, since the contingencies causing the line over loads do not necessarily cause bus voltage violations and vice versa. Thus two performance indexes, which give measures for line overloads and for bus voltage violations, respectively, are needed for real power –and voltage – contingency rankings. With increased loading of exciting power – transmission systems. The problem of voltage stability and voltage collapse has also become a major concern in power system planning and operation.
It has been observed that voltage magnitudes do not give a good indicator of proximity to a voltage stability limit and voltage collapse, therefore in network contingency ranking, it is necessary to consider voltage–stability indices at all the load bus as the post contingent quantities, in addition to bus-voltage violation for estimating the actual system stress under a contingency. Suitable measures/preventive control actions can then be planned to improve system security / stability.
Out of several methods for voltage stability and voltage collapse prediction, voltage stability index based prediction gives a scalar number for each load bus, called the L-index. This index value ranges from 0(no load on the system) to 1 (voltage collapse). The bus with highest the L-index value indicates most vulnerable bus in the system and hence this method helps in identifying the weak areas in the system needing critical reactive power support. Among the different indices for voltage stability and voltage collapse prediction, it is seen that the L-index gives fairly consistent results. Voltage collapse analysis involves both static and dynamic factors. From a system operator’s view point (heavily loaded). System has to be carefully monitored adequate control action taken when the operating point approaches the limit of voltage stability. The advantage of this method lies in the simplicity of the numerical calculations and expressiveness of the result. Here MATLAB software is used for performing load flow and to find L-index
2. LOAD FLOW ANALYSIS
Load flow study in power system is the steady state solution of the power system network. The main information obtained from load flow study is comprises the magnitudes and phase angles of load bus voltages, reactive power at generator buses, real and reactive flow on transmission lines, other variables being specified. This information is essential for the continuous monitoring of the current state of the system and for analyzing the effectiveness of the alternative plans for future system expansion to meet the increased load demand. There are different methods used for load flow analysis like Guass-Siedal method, Newton-Raphson method, Decoupled method etc.
2.1 Newton-Raphson method
Newton-Raphson (N-R) method is powerful iterative process for solving a set of simultaneous non linear equation with equal number of unknowns. The basic philosophy of N-R method of solution is that at each step of iteration process, the non linear problem is approximated by linear matrix equation.
In this mini project we use Newton-Raphson (N-R) method for the following advantages:
1. Simplicity
2. Give accurate method within less number of iterations.
3. Rate of convergence is much high.
2.2. Algorithm for solving the power flow problem using N-R method
1. The algorithm starts by reading all input data, forming the system admittance matrix and initializing the bus voltages and angles for all nodes.
2. The real and reactive power at each bus is calculated using the equation
3. Check whether the real and reactive power mismatches are within a specified tolerance
4. form the Jacobian Matrix
5. Obtain and solving the system Jacobian related vector matrix equation
6. Find new values of and
7. Using new values of and as starting values of next iteration and continue till the problem converges by maintaining change in bus powers within a given tolerance.
3. VOLTAGE STABILITY INDEX (L-INDEX)
It has observed that voltage magnitudes do not give a good indicator of proximity to a voltage stability limit and voltage collapse. Therefore in network contingency ranking it is necessary to consider voltage stability index at all the load buses as post contingent quantities, in addition to the bus voltage violations for estimating the actual system stress under a contingency. A suitable measures/preventive control actions can then be planned to improve system security. Voltage stability index is a scalar number for each load bus. The L-index value ranges from 0 to 1. The bus with highest L-index value indicates the most vulnerable bus in the system and hence this method helps in identifying the weak areas in the system needing critical reactive power support.
3.1. L-INDEX COMPUTATION
Consider a system where n is the total number of buses with 1, 2,.. g generator buses, and g+1…….. n remaining (n-g) buses. For a given system operating condition, using the load-flow (state-estimation) results, the voltage-stability L index is computed as
Where j=g+1,...n and all the terms within the sigma on the right-hand side of (1) are complex quantities. The values of Fji are complex and are obtained from the network Y-bus matrix. For a given operating condition,
Where IG, IL and VG, VL represent complex current and voltage vectors at the generator nodes and load nodes. [YGG], [YGL], [YLL] and [YLG] are corresponding partitioned portions of the network Y-bus matrix. Rearranging (15)
We obtain
Where
The equation for L-index at the jth node can be rewritten as:
Where
Where
For stability, the index Lj must not be violated (maximum limit=1) for any of the nodes j. Hence, the global indicator L describing the stability of the complete subsystem is given by L=maximum of Lj for all j (load buses). An L-index value away from 1 and close to 0 indicates improved system security. For an unloaded system with generator/load buses voltages 1.0 0, the L indices for load buses are close to zero, indicating that the system has maximum stability margin. For a given network, as the load/generation increases, the voltage magnitude and angles change near maximum-power-transfer condition and the voltage-stability index Lj values for load buses tend to close to unity, indicating that the system is close to voltage collapse. While the different methods give a general picture of the proximity of the system voltage collapse, the L index gives a scalar number to each load bus. Among the various indices for voltage-stability and voltage-collapse prediction, the L index gives fairly consistent results. The L indices for given load conditions are computed for all the load buses and the maximum of the L indices gives the proximity of the system to voltage collapse.
4. CONTINGENCY ANALYSIS AND RANKING
The objective of contingency analysis is to shortlist a specified set of contingencies from a list of contingencies and ranks them according to their severity.
Although computer technology has made almost all aspects in human activities to run smoothly some events are unpredictable and beyond our control. In power system operation unpredictable events are termed as contingencies. Contingencies can be divided into generator outages, load outages and line outages etc.
The selection of contingencies is needed to reduce the computation time of contingency analysis. Among the various contingencies only the line outages are considered in this project since they are the most common contingencies and for simplicity single line outages are considered .in contingency analysis a load flow analysis is done for each contingency and L-indices for load buses are calculated in each case. Severity index is calculated for each contingency based on a composite criterion. The contingency ranking is done using various criteria, such as bus voltage profiles and voltage stability indexes of load buses are carried out. The ranking is evaluated using the composite criteria.
Bus-Voltage Profiles
The post contingent bus-voltage profiles are divided into three categories: Low voltage (LV), below 0.9 p.u; normal voltage (NV),0.9-1.02 p.u; and over voltage (OV),above 1.02.
Range of voltage (pu) Type
Below 0.9 Low voltage (LV)
0.9 – 1.02 Normal voltage (LV)
Above 1.02 Over voltage (OV)
Voltage Stability Indices
The post contingent voltage stability indices are divided into five categories: very low Index (VLI),0-0.2;low index(LI),0.2-0.4;medium index(MI),0.4-0.6;gigh index(HI),0.6-0.8;and very high index(VHI),above 0.8.
stability indexes Type
0-0.2 Very Low Index (VLI)
0.2-0.4 Low Index (LI)
0.4-0.6 Medium Index (MI)
0.6-0.8 High Index (HI)
above 0.8 Very High Index (VHI)
After obtaining the severity indexes (SI) of all the bus voltage profiles and voltage stability indexes, over all severity indexes (OSI) for a particular line outage are obtained using the following expressions
WVP, WVSI weighting co- efficients for severity indices of voltage profile and voltage stability indices.
SIVP, SIVSI - severity indices for post contingent voltage profile and voltage stability indices.
5. CASE STUDY
5.1 SYSTEM DETAILS
An IEEE 30bus is considered for doing the voltage stability analysis using the methods described in previous chapter.
No of Generator buses-5
No of Load buses 24
Total Load-153.7pu
Total generation -151.1pu
5.2. BUS DATA
Table 5.2.1: IEEE 30 BUS DATA (1-15)
Bus Type Vsp Theta PGi QGi Pli QLi Qmin Qmax
1 1 1.06 0 0 0 0 0 -40 0
2 2 1.043 0 40 50.0 21.7 12.7 -40 50
3 2 1.01 0 0 37.0 94.2 19 -40 40
4 2 1.01 0 0 37.3 30.0 30 -6 40
5 2 1.082 0 0 16.2 0 0 -6 40
6 2 1.072 0 0 10.6 0 0 0 24
7 3 1.0 0 0 0 2.4 12 0 24
8 3 1.071 0 0 0 7.6 1.6 0 0
9 3 1.0 0 0 0 0 0 0 0
10 3 1.0 0 0 0 22.8 10.9 0 0
11 3 1.0 0 0 0 0 0 0 0
12 3 1.0 0 0 0 5.8 2.0 0 0
13 3 1.0 0 0 0 11.2 7.5 0 0
14 3 1.0 0 0 0 6.2 1.6 0 0
15 3 1.0 0 0 0 8.2 2.5 0 0
Table 5.2.2. IEEE 30 BUS DATA (16-17)
Bus Type Vsp Theta PGi QGi PLi QLi Qmin Qmax
16 3 1.06 0 0 0 3.5 01.8 0 0
17 3 1.0 0 0 0 9.0 5.8 0 0
18 3 1.0 0 0 0 3.2 0.9 0 0
19 3 1.0 0 0 0 9.5 3.4 0 0
20 3 1.0 0 0 0 2.2 0 .7 0 0
21 3 1.0 0 0 0 17.5 11.2 0 0
22 3 1.0 0 0 0 0 0 0 0
23 3 1.0 0 0 0 3.2 1.6 0 0
24 3 1.0 0 0 0 8.7 6.7 0 0
25 3 1.0 0 0 0 0 0 0 0
26 3 1.0 0 0 0 3.5 2.3 0 0
27 3 1.0 0 0 0 0 0 0 0
28 3 1.0 0 0 0 0 0 0 0
29 3 1.0 0 0 0 2.4 0 .9 0 0
30 3 1.0 0 0 0 10.6 1.9 0 0
5.3. Load flow result
Table.5.3.1 Load flow result
Bus No Voltage (pu) Angle (degree) P(pu) Q(pu)
1 1.0600 0.0000 2.6257 -0.2462
2 1.0530 -4.6127 0.1830 0.1268
3 1.0100 -10.0942 -0.9420 -0.2503
4 1.0200 -10.6789 -0.3000 0.5301
5 1.0720 -8.1240 -0.0000 0.2660
6 1.0310 -10.6961 -0.0000 0.5698
7 1.0468 -9.6550 -0.0240 -0.0120
8 1.0314 -10.8615 -0.0760 -0.0160
9 0.9955 -16.0952 -0.0000 0.0000
10 0.9683 -19.2007 -0.2280 -0.1090
11 0.9955 -16.0952 -0.0000 0.0000
12 1.0020 -18.2835 -0.0580 -0.0200
13 0.9913 -19.1880 -0.1120 -0.0750
14 0.9818 -19.3710 -0.0620 -0.0160
15 0.9721 -19.4614 -0.0820 -0.0250
Table 5.3.2. Load Flow Result (contd…..)
Bus No. Voltage (pu) Angle(Degree) P (pu) Q (pu)
16 0.9800 -18.9626 -0.0350 -0.0180
17 0.9661 -19.3827 -0.0900 -0.0580
18 0.9577 -20.1682 -0.0320 -0.0090
19 0.9525 -20.3724 -0.0950 -0.0340
20 0.9556 -20.1426 -0.0220 -0.0070
21 0.9487 -20.0254 -0.1750 -0.1120
22 0.9429 -20.3037 -0.0000 0.0000
23 0.9473 -20.1050 -0.0320 -0.0160
24 0.9082 -21.5521 -0.0870 -0.0670
25 0.8416 -24.8908 0.0000 0.0000
26 0.8201 -25.5092 -0.0350 -0.0230
27 0.8316 -26.9063 0.0000 0.0000
28 1.0352 -10.8004 0.0000 0.0000
29 0.7878 -28.8761 -0.0240 -0.0090
30 0.7729 -30.3185 -0.1060 -0.0190
5.3.1. Rank 1 Contingency (line outage 6-9)
Fig.5.3.1. L-indices for Rank 1 contingency
Fig. 5.3.2. L-indices for Rank 1 contingency
In this contingency, for a peak load condition, the minimum voltage is at bus 8 and the maximum voltage stability index Lmax 0.698 at bus 13
5.3.2. Rank 2 Contingency (line outage 9-10)
Fig.5.3.2.1 L-indices for Rank 2 contingency
Fig. 5.3.2.1 L-indices for Rank 2 contingency
In this contingency, for a peak load condition, the minimum voltage is at bus 11 and the maximum voltage stability index Lmax 0.699 at bus 13
5.3.3. Rank 3 Contingency (line outage 27-28)
Fig.5.3.3.1. L-indices for Rank 3 contingency
Fig. 5.3.3.2. L-indices for Rank 3 contingency
In this contingency, for a peak load condition, the minimum voltage is at bus 30 and the maximum voltage stability index Lmax 0.634 at bus 13
5.3.4. Rank 4 Contingency (line outage 6-10)
Fig.5.3.4.1. L-indices for Rank 4 contingency
Fig. 5.3.4.2. L-indices for Rank 4 contingency
In this contingency, for a peak load condition, the minimum voltage is at bus 30 and the maximum voltage stability index Lmax 0.674 at bus 13
5.3.5. Rank 5 Contingency (line outage 25-27)
Fig. 5.5.2. L-indices for Rank 5 contingency
Fig.5.5.1. L-indices for Rank 5 contingency
In this contingency, for a peak load condition, the minimum voltage is at bus 30 and the maximum voltage stability index Lmax 0.682 at bus 30 . From the contingency analysis the most vulnerable us was identified as bus no 13 since in Rank1,Rank2,Rank4,rank5 contingencies maximum value of L-index occur at this bus.
6. CONCLUSION
A detailed contingency analysis based on the voltage stability indices was done on a IEEE 30 bus system. Contingency ranking is based on a composite criterion, which takes into account the voltage profile and voltage stability indices. The most severe five contingency is presented here for illustration. From the contingency analysis the most vulnerable us was identified as bus no 13 since in Rank1,Rank2,Rank4,rank5 contingencies maximum value of L-index occur at this bus. The advantage of this method lies in the simplicity of the numerical calculations and the expressiveness of the result.
7. FUTURE SCOPE OF WORK
1. Improvement of system security with FACTS devices at suitable locations at
network contingency.
2. Contingency ranking can be done by considering other outages such as
generator outage and load outages.
3. Optimal location of FACTS devices
8. REFERENCES
[1] Bansilal, D Thukaram and K parthasarathy, “Improvement of system security with unified-power flow controller at suitable locations under network contingencies of interconnected systems", Electrical power and energy systems,volume.19.no.6,pp.385-392,1997
[2] Bansilal, Thukaram, D., and Parthasarathy K. “Optimal reactive power dispatch algorithm for voltage stability improvement”, Electrical Power Energy Systems, 1996, 18, (7), pp. 461–468
[3] Lof P.A, Anderson G, and Hill D J,” voltage stability indices of stressed power system” Transaction on power system volume 1.pp.326-335,1993
[4] D.P. Kothari,.I.J.Nagrath, “Modern Power system Analysis”. Tata McGraw Hill Publications
[5] Lof P.A, Anderson G, and Hill D J,” voltage stability indices of stressed power system” Transaction on power system volume 1.pp.326-335,1993