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Fuzzy expert system application to under voltage load shedding.

Introduction

To achieve an intelligent load shedding it is important to keep track

(a) Voltage security level

(b) Load to be shed

(c) Location of load shedding.

Studies show that in a large inter connected power system it will be difficult to implement UVLS because of change in load demand pattern also due to different topology load duration curves will not help in a violated environment. So knowledge based intelligent tools like fuzzy--expert system will eventually helps to reduce errors in judgment for load shedding and also increases the speed of decision making as shown in figure (34). Using intelligent load shedding techniques, the task of decision making will be independent of human operator and will be based on rules and knowledge base. fig (35). Since the implementation of the under voltage load shedding is based on particular mode or characteristics of power system, the fuzzy-expert system approach is considered most appropriate for under voltage load shedding for large power systems to improve voltage security.

Several papers on UVLS schemes were proposed based on the under frequency load shedding methods [25]. The philosophy of UVLS for voltage security was first proposed by Taylor [1] in 1992. He laid the underline principles for applying load shedding for regulating voltage profile of a load center. We adopted his work as a basis of our load shedding scheme. But it took almost five years to demonstrate the application of UVLS for improvement of voltage security. A load shedding scheme against voltage collapse was presented by C.J.Parker et al [2] in 1997 using modal analysis and it presented an encouraging work for us for using modal techniques for our voltage induced load shedding. Shah et al. [3] in 1999 developed a expert system for transmission line management based on power flows which depend upon frequency and phase angle measurements. References [4, 5] outline how a UVLS scheme relying on field data based on actual disturbance was implemented in Saudi Arabian power system. A new load shedding scheme is outlined by [6] implemented in Hydro Quebec power systems. In reference [7] authors use power system component model for UVLS scheme. They also explain how to use different load models for UVLS implementation.. Most of the works on UVLS are based on power transfer, incoming and outgoing of power flow in a bus of area of interest, which will be a time consuming. Authors in ref [8] use heuristic control schemes to assist operators, but use only approximate calculations only. Another expert systems application was presented by Franco Croce et al [9] where it is applied to a industrial plant. C.Moors and D.Lefebyre, T.Van Cutsem [10] published a paper on applying load shedding for voltage stability in 2000. They discussed the importance of including of time delay during load shedding.

By going through archives of the load dispatch centers [11,12] it can be concluded, that only a local load correction covering a small load area will give a accurate results for voltage security recovery. If we are able to locate the exact candidate bus where if the load shedding is executed will result in recovery in voltage profile, then UVLS will yield maximum success.]. If bus A is a potential candidate for load shedding and it is identified calculating active participation factors then UVLS in this bus will improve the voltage level in that particular load area.

In our approach, a operator is required to periodically update a priority table of these candidate buses where load to be shed. This table has to be updated for all possible voltage violations and change in network topology should also be taken in to account. The advantage of this expert system approach is by creating a knowledge base of area or buses prone to over loading by conducting off line studies, which can be converted to rule base for load shedding. Another advantage of this approach is, the algorithm developed is based on data relevant to a particular over loaded bus or area for a particular mode. This would eliminate unnecessary load shedding in other areas or bus. The priority table is prepared by finding the active participation factors of the buses present in the load center.

Our main objective for implementing a load shedding scheme for voltage security are

* To find out the candidate buses for load shedding to reduce wrong load shedding schemes.

* To incorporate the time delay factor to load shedding to stop further voltage violations.

* To find the amount of load shedding using experience gathered from previous load shedding operations.

Determination of active participation factors

Determination of Reduced Jacobian Matrix [JR]:

The linearized equations for a general power system can be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)

In equation (59) [J.sub.P[theta]] represents for partial derivatives of the power equations in relation to phase angle to phase angle. [J.sub.PV] represents partial derivatives as the function of voltage level and [J.sub.Q[theta]] is the partial derivative as the function of phase angle. [J.sub.QV] is the partial derivative of voltage level.

These equations are solved to have the angular and voltage variations as functions of the active and reactive power variations. The angular variations can be isolated from (57) and we get,

[DELTA]Q = [J.sub.p[theta]]P - [J.sub.PQ.sup.-1] [J.sub.PV] [DELTA]V (4)

Substituting equation (59) in (58) and reordering we get,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)

Using the similar approach the voltage angle can be found by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (6)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (9)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (10)

[J.sub.Rp[theta]] is called reduced jacobian matrix. The inverse of the full Jacobian can be expressed as a function of reduced jacobian matrix as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (11)

[J.sub.Rp[theta]] represents the coupling between active power and load angle and voltage angle. When [DELTA]Q = 0. It offers more information for load characteristics since it contains entries for both generator (PV) and load (PQ) buses. The reduced jacobian matrix [J.sub.Rp[theta]] represents the sensitivities of the system with respect to active power or load incremental variations. Since [J.sub.Rp[theta]] reflects the coupling between active power and voltage angle, there is no need to perform eigen analysis on full jacobian matrix saving in time and results in good accuracy. Also the most important modal results are obtained at the singularity point, the use of the reduced Jacobian matrice [J.sub.RP[THETA]] for modal analysis is fully justifiable. Therefore the conclusion, is that the reduced [J.sub.RP[THETA]] contains all information of the full load flow Jacobian matrix.

If the [J.sub.RP[THETA]] matrix is singular then an incremental change active power at a candidate bus can trigger a voltage security violation chain. So maximum loading at a load area can also be found using [J.sub.RP[THETA]].

Singular Value decomposition (SVD) on Reduced jacobian matrix ([J.sub.RP[THETA]] )

As discussed in section () SVD is conducted to the [J.sub.Rp[theta]] yielding a eigen vector which contains information for reactive power controller locations and directions. The eigen vector of [J.sub.RP[THETA]] reveals those buses where active power changes are more dangerous to system voltage security. They do not behave in non- linearly close to voltage violation point. Elements of right and left eigen vectors are associated with critical eigen values of [J.sub.RP[theta]].

By performing SVD on the reduced Jacobian matrix yields

J = U [SIGMA] [V.SUP.T] (12)

U = [J.sub.RP[theta]] [J.sup.T.sub.RP[theta]] (13)

V = [J.sub.RP[theta]] [J.sub.RP[theta]] (14)

Where,

U--left Eigen vector

V--right Eigen vector

[SIGMA]--Diagonal Matrix

The singular value decomposition is an important and practically useful orthogonal decomposition method used for making computations. The minimum value of the power flow jacobian matrix has been used as a static voltage stability index, indicating the distance between the studied operating point and the steady state voltage security limit.

Active participation factor is defined as the element-by-element product of left eigen vector and right eigen vectors of [J.sub.RP[THETA]] matrix.

APF = [U.sub.i]*[V.sub.i] (15)

[U.sub.i]--Right eigen vector of ith eigen value of [J.sub.RP[THETA]]

[V.sub.i]--Left eigen vector of ith eigen value of [J.sub.RP[THETA]]

The candidate buses for load shedding will show high active participation factor and so do the neighboring buses of the generators. This APF indicates which generator should be motivated to inject more active and reactive power in to the system and where the load shedding would be more effective to improve the voltage security margin. It is also used to identify the load buses for a minimum load shedding strategy for alleviating the voltage levels.

Main advantages of using APF for load shedding

* Small amount of computation time is needed.

* It only requires the information available from an for power flow calculations.

* It fully utilizes the sparsity of the power flow jacobian matrix to enhance the memory requirements for the computation or low.

Development of fuzzy-expert System for under voltage load shedding

Computational algorithm development

The inference engine or rule base is based upon the knowledge bases which are collected and are framed in to rules so that the system behavior gets well represented. Establishing the most effective location to shed and practical consideration of amount load shedding and the associated time delay are the main knowledge base for an intelligent UVLS system. The rules are

* If the real power flow in a line is more than the line flow limit then the system is overloaded.

* If the active participation factor of a bus is high in ranking then, it is a candidate bus for load shedding.

* If the voltage drop in a bus is less than 10% and it prevails for 6 sec then shed 10% of load connected.

* If the voltage drop in a bus is less than 8% of normal voltage profile then shed 7% of load connected.

* If the voltage drop in a bus in a bus is 8% below the normal voltage profile and it prevails for 3 sec then shed 5% of load.

* If the voltage violation in the system is more than 5% of normal voltage profile and it prevails for 2 sec then recommend load shedding.

* If the voltage profile neither is nor reached the normal value then go to the second ranked bus and start load shedding.

* If the bus having transmission line of high active participation factors then it is the most effective bus for load shedding.

* If the bus having transmission lines of low active participation factors then it is the least effective bus for load shedding.

* If the bus selected is near to the highest APF bus then select next ranked bus, which is away from the first bus connected.

* If the bus does not have the required amount of load to shed then shed the amount of load that is available.

Fuzzy control has been most successfully used for control problems where the control objectives are difficult to quantify or where one has some heuristic knowledge that can improve control. The basic idea is that an observation of each physical process variable can be translated to a fuzzy variable, giving it a linguistic interpretation. This process is usually called fuzzification. A fuzzy variable has a value between 0 and 1 describing to what extent the observation has the property described by the fuzzy variable. The fuzzy variables can be manipulated with the fuzzy set operators (^ (intersection), _ (union), : (complement) etc.) so that combinations of fuzzy variables can be formed and used to determine the controller output. The mathematics involved in these manipulations are described in Jantzen [1991]. They are written as a set of rules on the form some action. Together with the rules define the rule-base of the controller and should express the heuristic knowledge one has of the desired controller. The process of evaluation of the rules is called inference. The output of the inference is a fuzzy variable for each control signal. These fuzzy variables have to be translated to physical controller outputs. This translation is called defuzzification. The entire process is a simple mapping from measurements to controller outputs. Therefore, the rule base and membership functions can be seen as an intuitive way of defining nonlinearities for use in feedback control.

In the conventional fuzzy system, the input value are normalized and converted to fuzzy representation. The membership function for state variable is defined. The membership function of the control output is constructed. The rule base is applied to produce a consequent fuzzy region for each solution variable.

"IF premise (antecedent), THEN conclusion (consequent)"

The above form is referred to as the IF-THEN rule based form that if the fact is known premise (antecedent), then, it can drive to another fact called conclusion (consequent). The control table is developed according to experience and summarized the define rule. The entries of table are control action. The consequent region are defuzzified by converting to crisp value to find the final solution. The process of obtaining the final solution or the overall conclusion for the individual consequent contributed by each rule-base is known as aggregation of rules. The propagation process of the antecedents or consequent is depending on whether the "and" or "or" connective respectively, is used between the antecedent or consequent in the rule.

The aim of this study is to design and analyze a fuzzy-expert system controller for the study system to control against peak load and voltage insecurity by calculating the optimum and the minimum ratio of load shedding as a control output as presented in fig [2].

[FIGURE 2 OMITTED]

Advantages of Fuzzy--Expert Systems for a UVLS

The approach is considered most appropriate for under voltage load shedding for large power systems. The advantage of expert system approach is creating a knowledge base of the area or buses prone to overloading by conducting a offline study which can be converted to a rule base.

The data will be from the experienced operators of power dispatch centers. Another advantage of expert system approach is, it is based on governing rules and a set of data relevant to a particular overloaded bus or area for a particular mode. This would eliminate unnecessary load shedding in other areas.

This work is primarily based on the calculation of active participation factor of entire system. Most of the earlier works based on local load or bus characteristics. Some works based on power transfer in incoming and outgoing of power flow at a particular bus of interest which will be time consuming.

Heuristic control schemes are developed to assist the operators and can take advantage of knowledge of specific zone in a complex power system accelerates the decision process. The basic limitation of such classical expert system is its restriction to the two values of true and false in reasoning.

Components of Fuzzy--Expert Systems

A fuzzy--expert system consists of three fundamental components shown in fig [1]. Knowledge base: This contains specific facts about application and rules that apply under various situation. Here the knowledge based system comprises of

* Steps for load shedding.

* Amount of load shedding.

* Timing of load shedding.

* Location of load shedding.

INFERENCE ENGINE: This controls the problem of solving by selecting and executing the rules and determining when the solution has been found.

USER INTERFACE: this provides a convenient format for entering additional data and for describing possible solution and scenarios.

The intelligent load shedding controller can learn off line from simulation and are used on line to classify new step using knowledge gained in off line studies. They are much faster than analytical methods.

Linguistic Rules and Extended Fuzzy-Expert Reasoning

Linguistic rules for reasoning

Let {[x.sub.1i], [x.sub.2i],[x.sub.3i],....,[x.sub.ni]} and {[y.sub.1i],[y.sub.2i],[y.sub.3i],[y.sub.ni]} be a set of linguistic variables state just after disturbance(JAD) corresponding to a load control bus i, where [x.sub.1i] [x.sub.2i],[x.sub.3i],.... [x.sub.ni] represents the voltage violation of bus i and [y.sub.1i],[y.sub.2i],[y.sub.3i],... [y.sub.ni] represent the time delay. Let each variable and the load shedding amount, z, be distinguished by three linguistic terms: LOW (L), MEDIUM (M), and HIGH (H). After analysis and from observation, the following linguistic rules describing the loadshedding amount at load bus i can be formed.

a. If [x.sub.1i] is H and [y.sub.1i] is MIN then z is L or

b. If [x.sub.1i] is M and [y.sub.1i] is INT then z is M or

c. If [x.sub.1i] is M and [y.sub.1i] is MAX then z is H or

d. If [x.sub.1i] is L and [y.sub.1i] is MIN then z is L or

e. If [x.sub.1i] is L and [y.sub.1i] is MAX then z is L.

Conjunctive System of Rules

The process of obtaining the overall consequent (conclusion) from the individual consequent contributed by each rule in the rule-base is known as aggregation of rules. In this case, the individual rules is connected by "and "connective. The aggregated output (consequent), y, is found by the fuzzy intersection of all individual rule consequents, y(i) where i = 1,2,3 ... r. The linguistic variables are presented in the table[ ].

Fuzzification of input and output variables and Fuzzy Parameter Setting

For simplicity, the frequently used triangular and Gaussian membership functions are adopted here for fuzzifying the voltage violation and time delay. For the purpose of choosing the fuzzy parameter settings, two descriptive sets are introduced for a selected state variable x at a load control bus i:

[S.sub.1]: set [S.sub.1] includes all the training cases where at least some amount of load shedding at load control bus i is necessary, on the basis of off-line simulation study, to prevent dynamic voltage instability;

[S.sub.2]: set [S.sub.2] includes all the training cases where load shedding at load control bus I is not necessary for maintaining dynamic voltage stability. The ranges of the three linguistic terms L, M, H are chosen as follows:

L: COVERS {X|X [member of] [S.sub.1] AND X [not member of] [S.sub.2]}

H:COVERS {X|X [member of] [S.sub.2] AND X [not member of] [S.sub.1]}

FOR M, THE CENTRE POSITIONS ARE EQUALLY SPACED BETWEEN H AND M. SOME TRIALS FOR THE RANGE FOR M ARE USUALLY NECESSARY TO GET THE DESIRED CONSISTENT MATCHING. THE OUTLINE OF THE WHOLE TRAINING PROCESS FOR LOAD SHEDDING CORRELATION IS SHOWN IN FIG[36].

The two state variables for this simulation will be the bus voltage violation; V and the time delay are used as inputs. The output will be the ratio of load shedding, output which will be applied to the formulated problems in the system to reduce peak loads. The input voltage violation increase will be defined by three linguistic variables, labeled Low (L), Medium (M), and High (H).

The input time delay (T) will be defined by three linguistic variables Minimum (MIN), Intermediate (INT), Maximum (MAX). It is assumed that, the universe of discourse for the two variables is

Voltage V: [0: 0. 1] p.u as shown in fig. [4]

Time delay T: [0: 1 5] sec as shown in fig. [5]

For output the amount of load to be shed, the control space is partitioned in to (output, LS) three membership functions will be constructed on its universe, which is LS: [0: 0.15]. The three linguistic variables are: High (H), Medium (M), and Low (L) as shown in fig [6]

The fuzzification of input and output variables are shown in fig [4,5].

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

Defuzzification of output

The defuzzified output of the intelligent controller is presented in the table [4]. Centriod method is used for de- fuzzification.Ten different cases of violations have been considered and the fuzzy expert system output is presented in fig [41 to 50] .The voltage violations are listed in the table [4] and corresponding time delay and the amount to be shed is also presented in table [4]. Referring to case 1 where, if voltage violation reduces the system stable voltage profile by 5%, then the intelligent controller recommends a 0.075 pu of connected load has to be shed with a time delay of 5 seconds. The output of the controller is presented in fig [6]

Implementation and discussion

The fuzzy--expert system controller designed is to act against voltage violations by calculating the optimum and minimum ratio of load shedding as a control output. For testing purpose an IEEE 14 bus system is used for implementation. The reason for selecting such a smaller test system is because; UVLS scheme will be accurate only when implemented in a sub--load dispatch centers for short time voltage planning. The main reason for failure of under frequency load shedding is, when trying to implement it to a large power system network, which leads to more violations. Any load shedding scheme for voltage security will be effective only when it is implemented in local load level like sub load dispatch centers. The proposed method is applied to analysis the effect of using the fuzzy--expert systems to improve voltage security.

The load shedding model is divided in to two parts. The first part deals with analysis of load center operating conditions by using APF. Based on the results for active power factor, a rank table of the buses where load to be shed for particular voltage violation is created. The second part is the fuzzy expert system which is used to be determining amount of load to be shed with the load center and with the particular time delay. The validation of the developed expert system is in terms of its optimality and its execution speed. The test system used in this study is IEEE-14 bus system. It contain 5 voltage controlled generator, 3 transformers and 11 load-buses. The proposed method is applied to analyze the effect of using the fuzzy technique to improve voltage security. The defined linguistic rules are given in table [2] which is called control table. The entire of table represent the control output action. The results obtained from using fuzzy technique are listed in table [4].This table summarizes the recommendations of the intelligent controller for finding out the amount of load shedding to be shed and the corresponding time delay for voltage violations from 0.05 pu maximum to 0.037 pu minimum of the normal voltage level in p.u. The corresponding output control in p.u. which represents the ratio of load shedding at each violation also shown in table [4]. For example to a violation of 0.05 pu the fuzzy expert system controller is recommending a load shedding of 0.0750 of connected load in the top ranked bus with a 5 second time delay. The relation between voltage violation, time delay and amount to be shed can be explained with a three dimensional relation shown in fig [7].

For testing the fuzzy expert system controller, the test system is stressed by decreasing reactive load by 1.6 pu in all buses which is equal to a 0.05 pu drop in normal voltage profile. For each load increase or mode, the participation factor for load buses is calculated using the algorithm discussed in section (2). Table [1] shows, the load bus 9 has a largest participation factor for this mode. A negative participation factor indicates, load shedding cannot be implemented without additional reactive power support. Also reactive power support cannot be supplied to these buses because reactive power sources may be depleted or located in electrically remote places. From table [1], it is clear that load buses 9 and 6 are critical buses and buses 11 and 13 are least effective for UVLS implementation. Also power redispatching should be avoided in these buses.

In the selected bus 9 which is the top ranked bus from the rank table [1], load shedding is implemented with three steps, each step with a maximum 5% of the connected load. The amount of load to be shed is always will be small as recommended by the fuzzy expert controller, since the load shedding is applied in the optimal direction given by the participation factors. It also means that this approach presents a smaller impact on system cost compared with entire adjustment of system generation. The percentage of load to be shed is combined with a time delay using the knowledge gathered by observing load-shedding operations in sub load dispatch centers. The expertise of operators who are experienced in under voltage operations are collected by distributing questionnaires to them. It is interesting to note that majority of them replied that most of the load shedding results in tripping of loads not connected with voltage security process. The number of steps for load shedding is depending upon the behavior of the particular sub-load dispatch center decided by studying incoming and outgoing power flows.

At each step real and reactive power of generator buses are monitored and tabulated as in table [4]. Time delay for load shedding is applied using the knowledge gained using offline data's of system load shedding. Optimal time delay is found as discussed in section (2). Presence of reactive power controllers are neglected since they have a limited role to play during load shedding because of their depleted reactive power source. Only reactive power generated from generators are monitored since any improvement of Q flow from them will improve the voltage profile of the system as all the other reactive power controllers reached their saturation. Loads are assumed as constant power loads because of security point of view. Take generator bus 1 as an example to illustrate the effectiveness of fuzzy expert system controller. The table [5] shows how reactive power profiles of generator bus 1 are improving after a step by step shedding of load in bus 9. At high ranked load bus 9, only 0.0750 of the connected load is shed which is recommended by the fuzzy expert controller. The pre load shed reactive power flow of this bus is 68.80 MVAR and post load shed reactive power is 70.74 MVAR UVLS is implemented in three steps on bus 9. The reactive power available in generator buses, 1, 2, 3, 4 and 5 and reactive power flows in transmission lines 1-2, 1-5, 2 -1, 3-2, 4 -3 shows improvement. Although there is only marginal improvement in generator buses, by allowing load shedding in three steps, we can achieve further improvement in the reactive flows in other buses and transmission lines, which will help to keep voltage profile with in security level. To achieve more improvement in reactive power flow, load shedding in executed in next ranked bus number 6.The reactive power flow is shown in table [5] shows there is further improvement in reactive power output from the five generator buses in the test system. Thus, by following the recommended amount of load to be shed from the fuzzy expert system controller, there is improvement in reactive power flow from the generators which validates the effectiveness of the intelligent controller. We are also achieving a definite time delay, which is very crucial for voltage recovery. This time delay also helps in improving the voltage security of the entire system, which is the main constraint of any load shedding schemes. By local voltage security improvement actions, the voltage security of entire power systems is improved. Above results show, that a knowledge based system when combined with a superior mathematical tool like modal participation factors can contribute an Intelligent UVLS scheme which is fast in identifying load shedding locations for improvement of voltage security.

Conclusion

This work on under voltage load shedding presented application of fuzzy--expert systems concept to voltage security monitoring and control.. A generalized rule-base has been formed for both monitoring and control stage and tested on a sample power system model. Given the key variable (load bus voltage, generator MVAR reserve and generator terminal voltage), the expert system arrives at global state without the need for complex computations. It is fast and cost effective than conventional voltage stability methods. This will be of great use to power system operators to steer the system away from possible voltage collapse. In this proposed fuzzy-expert the membership function of key variable and the rule base may be defined based on the system requirements and operator's experience. Thus, it offers flexibility. There is a considered interest among utilities in developing on-line voltage security tool which will enable the power systems to be operated at higher loads without risking voltage insecurity. The proposed method has the potential to be integrated for online implementation in energy management system to achieve the goals of secure power system operation. To meet the challenge of a deregulated, competitive environment, electric utilities must seek new and cost effective solution to give them an edge in market place. This work aims to meet the above objective and also has given a further insight into the challenging problem of voltage security analysis and control.

Even with so many operating problems the developed algorithm may help an operator in assisting to correct local voltage violations with a minimum time delay and test results confirm these objectives. Any how, any tools that accelerate the decision making process for UVLS will be a good supporting aid for local load center operators.

[FIGURE 7 OMITTED]

Appendix

IEEE 14 bus test system

[ILLUSTRATION OMITTED]
Table 14: bus parameters.

                                                                Load
Bus   Bilis         Phase     Generation   Generation   Load    Reac-
no.   voltage       Angle     rreal        Reactive     real    tive
      Magnitude   (degrees)   (p.u)        (p.u)        (p.u)   (p.u.)

1     1.05        0.0         0.0          --           0.0     0.0
2     1.045       0.0         0.8          0.0          0.434   0.127
3     1.01        0.0         0.0          0.0          1.884   0.19
4     1.04        0.0         0.0          0.0          0.224   0.075
5     1.045       0.0         0.0          0.0          0.0     0.0
6     0.8         0.0         0.0          0.0          0.956   0.078
7     0.9         0.0         0.0          0.0          0.152   0.032
8     0.8         0.0         0.0          0.0          0.0     0.0
9     0.8         0.0         0.0          0.0          0.590   0.332
10    0.8         0.0         0.0          0.0          0.180   0.116
11    0.8         0.0         0.0          0.0          0.070   0.036
12    0.7         0.0         0.0          0.0          0.122   0.033
13    0.7         0.0         0.0          0.0          0.270   0.116
14    0.7         0.0         0.0          0.0          0.298   0.100


References

[1] C.W. Taylor, Power System Voltage Stability, McGraw Hill, New York, 1993.

[2] S.Shah and S.Shahidehpour "A Heuristic approach to load shedding scheme", IEEE Transactions on Power systems, vol 4, October 1989.

[3] Carson Taylor, " Concepts Of Under Voltage Load Shedding For Voltage Stability" IEEE Transactions on Power Systems, vol 7, no.2, April 1992.

[4] C.J. Parker, "Simulation of load shedding as a corrective action against voltage collapse", proceedings of the 4th Inter National Conference in Power System Control and Management, Hong Kong, November 1997.

[5] Moors, D.Lefebvre and T.Van Cutsem " Load shedding controllers against voltage instability a comparison of designs "IEEE Power Tech Conference, Porto, Portugal, September 10,11 2001.

[6] B.Isais Lima Lopes and A.C.Zambroni de Souza "An approach for under voltage load shedding" IEEE, Power Tech Conference, Bologna, Italy, June 2003.

[7] Alessindrao B.Marques, Glauco N,Toronto, Djalma.M.Falcao." A supervisory knowledge based system for monitoring and control of regional voltage profile", 2001 Power tech conference. Porto, Spain, 10-13 September.

[8] Luis S. Vargas and Claudio A.Canizares, "Time dependence of controls to avoid voltage collapse", IEEE Transactions on Power Systems, vol 15,no 4, November 2000.

[9] J.Deuse and J.Dubois, "EWR Under voltage load shedding, scheme", IEEE Transactions on Power Systems, vol 12, no.4, November 1997.

[10] Shinichi Imai "Undervoltage load shedding improving security as reasonable measure for extreme contegencies'', IEEE Proceedings, 2005.

M. Rathina Kumar (1) and Mrs. R. Suganesh (2)

(1) Faculty of electrical and electronics engineering, SCSVMV University, Ennathur, Kanchipuram 631561, Tamil Nadu, India. E-mail: rathinamari@rediffmail.com,

(2) Faculty of Electronics and Communication Engineering, Thiagarajar College of Engineering, Madurai, India.
Table 1 ranking of Load Buses.

Input 1             Input 2        Output
Voltage violation   Time delay     Amount of load to be shed

HIGH                MINIMUM        LOW
MEDIUM              INTERMEDIATE   MEDIUM
MEDIUM              MAXIMUM        HIGH
LOW                 MINIMUM        LOW
LOW                 MAXIMUM        LOW

BUSNO.   RANK FOR LOAD SHEDDING

9        1

6        2
7        3
8        4
12       5
10       6
14       7
11       8
13       9

Table 3: Participation factors of load buses.

Bus No   Participation for load buses

9        180400357376.00
6        166984761344.0
7        163668705280..0
8        30746288128.00
12       481492576.00
10       306452800.00
14       25290754.00
11       -632520.382812
13       -81328384.00

Table 4: Defuzzified output of Fuzzy--Experts Systems.

Case no.   Voltage Violation   Time delay   load to be shed
           (P.U)               (sec)        (p.u)

1          0.05                5.0          0.0750
2          0.0385              6.67         0.0795
3          0.0698              2.42         0.0562
4          0.0915              1.08         0.0272
5          0.0915              9.23         0.102
6          0.0571              2.15         0.0701
7          0.075               2.81         0.054
8          0.0834              6.39         0.095
9          0.0938              8.98         0.0997
10         0.037               8.98         0.113

Table 5: Reactive power flow before and after load shedding due to a
voltage violation.

Bus no   Base case   Q flow during    Q flow (MVAR) DUE
           Q flow      Violation     to load shedding at
          (MVAR)        (MVAR)               bus 9

1         68.78          68.80               70.74
2        -91.42         -91.43              -92.89
3         26.65          26.65               26.70
4         56.83          47.61               43.23
5         20.42          13.51               11.71
6         -7.50          -5.9                -5.95
7          0.0            1.6                 1.69
8          0.0            1.6                 1.64
9        -16.6          -15.0               -15
10        -5.8           -4.2                -4.2
11        -1.8           -0.2                -0.2
12        -1.6            0.0                 0.0
13        -5.8           -4.2                -4.2
14        -5             -3.4                -3.4

Bus no     Q flow(MVAR) due
         to load shedding at
               bus 6

1         70.992
2        -93.020
3         26.707
4         43.105
5         11.306
6         -5.9
7          1.6
8          1.6
9        -15.0
10        -4.2
11        -0.2
12         0.0
13        -4.2
14        -3.4
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Article Details
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Author:Kumar, M. Rathina; Suganesh, R.
Publication:International Journal of Applied Engineering Research
Article Type:Report
Geographic Code:1USA
Date:Sep 1, 2009
Words:5892
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