A PSO Based Cluster Formation Algorithm for Optimal PMU Placement in KPTC
A PSO Based Cluster Formation Algorithm for Optimal PMU Placement in KPTCL
First A. Writer,Appellation, Organization, Second B. Author, and Third C. Author, Jr. , Designation, Organization
Abstraction— Power system province appraisal with the sole deployment of synchronal phasor measurings demands that the system must be wholly discernible with PMUs merely. Direct measuring of stage angles of current and electromotive force phasors are now possible by Phasor Measurement Units ( PMUs ) . To hold lesser figure of PMUs, the arrangement job in any web is considered as an optimisation job. This paper presents a Particle Swarm Optimization ( PSO ) based bunch formation algorithm for optimum PMU arrangement. The proposed algorithm clusters the coachs into many sub groups and the maximal connectivity coach is selected as the heading coach. The PMU is placed on the heading coach to pull off the affiliated coachs for complete system observability. This paper analyses the proposed algorithm for the undermentioned three instances: 1. Without PMU loss, 2. With individual PMU loss, and 3. Zero Injection Bus. The simulation consequences for IEEE coach and the KPTCL coach systems are presented and compared with the bing attacks. The proposed consequences show that the method is simple to implement and supply the accurate PMU arrangement.
Index Terms— IEEE Bus, Karnataka Power Transmission Corporation Limited ( KPTCL ) , Optimal PMU Placement, Particle Swarm Optimization ( PSO ) , Phasor Measurement Units ( PMUs ) , and Power System State Estimation
Power public-service corporations are confronting legion menaces of security of operation due to the over stressed power web in the today’s competitory power market scenario. Phasor Measurement Unit ( PMU ) is an measuring device which is used to mensurate the current and electromotive force. It uses the Global Positioning System ( GPS ) pulsation to ease the synchronised measurings of existent clip phasors of currents and electromotive force. A power system is said to be recognizable when electromotive force phasors at all the coachs are known. Harmonizing to Ohm’s Law, if a PMU is placed at the coach, so the neighboring coachs besides become discernible. Obviously, when PMUs are placed at all the coachs of the web, and the measurings for all the PMUs are communicated to the control units, so the electromotive force phasors at all the coachs would be known. This attack can alter the traditional appraisal to province measuring. PMUs are already installed in several public-service corporations for assorted applications around the universe such as province appraisal, adaptative protection and system protection strategies. Other application Fieldss include stableness monitoring, Wide Area Monitoring and Control ( WAMC ) and efficient system use.
In the traditional power systems, the coachs are monitored utilizing the conventional measurings from electromotive force and current transformers and the informations are forwarded to the Energy Management System ( EMS ) through the Supervisory Control and Data Acquisition ( SCADA ) system. It collects the existent clip measurings from the Remote Terminal Units ( RTUs ) placed in substations. This attacks are non able to supervise all the measurings across a broad country power system because the informations are non time-synchronized [ 1 ] . PMUs are an indispensable portion of smart grids and therefore the rate of PMU installings are increasing. In the emerging engineering, the major issue demand to be addressed is the arrangement of PMUs, which is influenced by the awaited system applications. The major factor restricting the figure of PMU installings are their cost and the communicating installations. Hence, the cost and communicating restraints of PMUs have been motivated the research workers to place the minimum PMU installing for the awaited applications. Puting PMUs on all coachs of the power system consequences a complete observability of the system. Since, a coach is observed if a PMU is placed on it or some of its adjacent coachs, it is neither economical nor necessary to transport set such installings. As a effect, a job called Optimal PMU Placement ( OPP ) job has been occurs.
The purpose of this paper is to place the optimum figure of PMUs to do the KPTCL topologically discernible. Here, a PSO based Clustering Algorithm is proposed to constellate the coachs. The heading coach is selected based on the maximal connectivity among the coachs. The heading coach is placed with the PMU to supervise the other affiliated coachs. The PMU arrangement scheme confirms the system observability during the normal on the job conditions and besides the individual PMU failures. The proposed method is found to be simple, fast and accurate in calculation. The proposed method is applied on IEEE-6, IEEE-7, IEEE-9, IEEE-14, IEEE-30 coach systems and KPTCL power maps for 28 coach, 127 coach and 155 coach systems to verify the proposed algorithm public presentation.
The staying portion of the paper is organized as follows: Section II involves the plants related to the bing algorithms for optimum PMU arrangement job. Section III involves the description of the proposed PSO based bunch formation algorithm for optimum PMU arrangement. Section IV involves the public presentation analysis of the proposed work. The paper is concluded in Section V.
II. Related Plants
With the figure of PMUs estimated for installing in the close hereafter, both the public-service corporations and research workers are looking for the optimum solutions to their arrangement. The solutions for the optimum PMU arrangement job can be classified into two types: mathematical and heuristic algorithms. Some of the bing plants related to the optimum PMU arrangements are discussed. Integer scheduling is a mathematical scheduling attack for work outing an optimisation job holding whole number design variables.Singhintroduced an whole number programming based methodological analysis for the optimum arrangement of PMU. It reduces the cost of installing and ease the full power system observability. The zero injection coachs construct was used to further cut down the figure of PMUs. Integer programming helps to supply multiple consequences if the adjacent coachs to zero injection coachs were non handled decently. The best consequences was selected based on the [ 2 ] .Fan and Watsonproposed a multi-channel PMU arrangement job and their solution. Here, a close relationship among the PMU arrangement job and the authoritative combinatorial job were identified [ 3 ] .
Roy et Alproposed an optimum PMU arrangement attack for power system observability. Here, a three phase optimum PMU arrangement method was formulated based on web connectivity information. Phase 1 and present 2 of the algorithm iteratively estimate the less of import coach locations to extinguish the PMUs and estimates where the PMUs were retained. The last phase reduces the figure of PMUs utilizing the pruning operation. The optimum set of PMU locations were obtained for web observability [ 4 ] .Manousakis and Korresdesigned a leaden least squares algorithm for optimum PMU arrangement. A quadratic minimisation job with uninterrupted determination factors were formulated capable to the nonlinear observability restraints. The optimum solution was obtained by an unconstrained nonlinear weighted least squares method [ 5 ] .Mahari and Seyediproposed a Binary Imperialistic Competition Algorithm ( BICA ) for optimum PMU arrangement. The zero injection coach was considered for all probes to obtain the suited replies. In add-on to the traditional regulations, new regulation was besides generated. It helps to cut down the figure of PMUs arrangement [ 6 ] .
Tai et Alproposed a Random Component Outages ( RCO ) for optimum PMU arrangement for power system appraisal. The optimum locations were chosen to cut down the province appraisal and mistake covariance [ 7 ] .Sodhi et Alpresented an optimum PMU arrangement method for complete topological and numerical observability of power system. A two phase PMU arrangement attack was proposed. Phase 1 identifies the minimal figure of PMUs to do the system topologically discernible. Phase 2 was proposed to place if the resulted PMU arrangement outputs to a full graded measuring Jacobian. A consecutive riddance algorithm was proposed to place the optimum locations of extra PMUs [ 8 ] . An Exhaustive hunt is an optimisation technique which consistently enumerates all possible campaigners for the solution. It chosen the campaigner which satisfy the restraints at the optimal nonsubjective map value. It guaranteed the determination of the planetary optimum but it was non suited for big scale systems with immense hunt infinite.Azizi et Alproposed an optimum PMU arrangement by an tantamount additive preparation for thorough hunt. The province appraisal was implemented based on the complete additive arrangement [ 9 ] .
Fei et Al[ 10 ] discussed an optimum PMU arrangement based on the limited thorough attack. An about optimum PMU arrangement ( AOPP ) was established in order to place the seeking infinite. AOPP was deterministically retrieved by elaborate power system province observability analysis. The impression of coach neighbour was defined to deduce the seeking infinite of limited thorough attack. The heuristic algorithms applied for optimum arrangements are Familial algorithm, Tabu Search, Simulated Annealing, Differential Evolution, Particle Swarm Optimization ( PSO ) , Immune Algorithm, Iterated Local Search ( ILS ) , Crossing Tree Search ( STS ) , Greedy Algorithm, Recursive Security N Algorithm, Decision Tree and Practical Heuristic Algorithm.Hajian et Alintroduced an optimum PMUs arrangement to keep the web observability utilizing a modified BPSO algorithm. An optimum measuring set was estimated to obtain the full web observability during normal conditions. After any PMU loss or individual transmittal line outage, the derived strategy in normal status was modified. Observability analysis was carried out based on topological observability regulations. A new regulation was added to minimise the figure of PMUs for complete system observability. A modified BPSO algorithm was used as an optimisation tool to acquire the minimum figure of PMUs and their corresponding locations [ 11 ] .
Sharma and Tyagidesigned an optimum PMU arrangement attack based on Binary Particle Swarm Optimization ( BPSO ) with the conventional measurings. Quadratic scheduling was used in BPSO algorithm. A method for pseudo observability was introduced for deepness one and depth two with and without zero injection measurings. It was tested on IEEE-7, IEEE-14, IEEE-30 and IEEE-57 coach system utilizing BPSO technique [ 12 ] .Peng et Alformulated a multi nonsubjective optimum PMU arrangement utilizing a non-dominated sorting differential development algorithm. It is an organic integrating of Pareto non-dominated sorting operation and the differential development algorithm. It enhances the single crowding mechanism and common mechanism [ 13 ] .El-Zonkoly et Alproposed an Improved Tabu Search ( ITS ) for complete observability and out of measure anticipation. The system was based on numerical observability and unreal intelligence. ITS was used to place the optimum arrangement for the PMU to maintain the system wholly discernible. A Predictive Out of Step ( OOS ) algorithm was proposed based on the observation of the electromotive force stage difference among the substations [ 14 ] .Aminifar et Alformulated an optimum PMU arrangement based on probabilistic cost or benefit analysis. The decrease of system hazard cost was recognized as the benefit linked with the development of broad country measuring system [ 15 ] .
Das et Aldesigned a simulation of broad country measuring system with optimum phasor measuring unit location. These measurings were by and large taken for every 4 to 10 seconds offering a steady province position of the power system behaviour. It was implemented on IEEE six coach system [ 16 ] .Jamuna and Swarupproposed a multi-objective biogeography based optimisation for optimum PMU arrangement. Here, the coincident optimisation of the two conflicting aims like minimisation of the figure of PMUs and maximization of the measuring redundancy were performed. The Pareto optimum solution was obtained based on the non-dominated sorting and herding distance. The compromised solution was selected based on the fuzzy based mechanism from the Pareto optimum solution [ 17 ] .Ghosh et Almade a dependability analysis of GIS aided optimum PMU location for smart operation. It look into the impact of topological properties on commissioning PMUs. Reliability was ensured through assorted PMU connectivity constellation [ 18 ] .Peppanen et Alproposed an optimum PMU arrangement with binary PSO [ 19 ] .Abiri et Alintroduced an optimum PMU arrangement method for complete topological observability of power system. A revised preparation for the optimum arrangement job of the sorts of PMUs was presented [ 20 ] .
III. PSO Based Cluster Formation For Optimal PMU Placement
Power system observability is indispensable for placing the existent clip monitoring and province appraisal of the system. PMUs enable advanced solutions to bing public-service corporation jobs and supply power system engineers a whole scope of possible benefits:
- Accurate appraisal of the power system province can be obtained at frequent intervals,
- Permiting dynamic phenomena to be observed from a main location and suited control actions are taken.
Post perturbation analysis will be much improved for the PMU arrangement job, which is obtained with the precise images of the system states through GPS synchronism.
This subdivision proposed a PSO based Optimal PMU Placement in power systems. The aim of this method is to supply the optimum arrangement of PMUs, which can do the system discernible and to maximise the measurement redundancy of the system. Fig.1 shows the flow of the proposed method. Initially, the coach system is taken and each coach is considered as a node. Each node connectivity is updated in the binary tabular array. Here, we are sing the undermentioned three instances:
- Without PMU Loss
- With PMU Loss
- Zero Injections
A. Particle Swarm Optimization Based Cluster Formation for Optimal PMU Placement
PSO is an optimisation algorithm which facilitates a population based search process in which single are termed as atoms. Here, the PSO algorithm is used to constellate the coachs for optimum PMU arrangement. Each atom contains a PMU arrangement constellation for a power system. It represents that each atom is constructed by binary dimensions, such that each coach of the power system has a dimension which indicates the being of a PMU in that coach, it is equal to 1, otherwise 0.
Algorithm 1: PSO based Cluster Formation
Input signal:Connectivity inside informations of the given coach system
1: Create binary tabular array for the given coachs as
ForI = 1 to figure of coach
ForJ = 1 to figure of coach
Ifcoach ( I ) connect to bus ( J )
Matrix element represent as 1
Matrix element represent as 0
2: D= Sum ( degree Fahrenheit ( x ) )
3: L = soap ( vitamin D )
4: Calculate the coach connexion for LThursdaycoach and topographic point PMU on that coach
5: Update the binary tabular array by extinguishing the coach from binary tabular array
6: Initialize atoms
7: Position of atoms = ‘x’ and ‘y’ organizing points of coach location.
8: Speed = random ( figure of coachs )
9: Check fittingness for given place by utilizing nonsubjective map.
10: Minimum ( F_Position )
12: Position = Position + Velocity
13:ForK = 1 to loop
IfPresent_fitness & A ; lt ; Last_fitness
Update fittingness value
Update speed and place.
14: Find upper limit ( fitness_value ) , mf = soap ( fittingness )
15: Topographic point PMU on that coach.
16: Update double star tabular array by extinguishing the coach from binary tabular array.
17: Cringle to Step 6 until binary table gets empty.
18:Ifthe PMU placed at merely one coach,
Check the nearest coach and made connexion between them and update bunch.
The proposed algorithm is applied on the three instances for optimum PMU arrangement.
B. Case 1: Without PMU Loss
In this instance, the zero injection and the flow measuring are ignored. To explicate the restraint set, the binary connectivity matric is formed whose entries are defined in the undermentioned equation:
( 1 )
The matrix can be straight calculated from the coach entree matrix by change overing the entries in the binary signifier.
See the six coach system
The binary tabular array B is defined as
( 2 )
The restraints for this instance is,
( 3 )
From the binary tabular array, place the maximal connectivity among the coachs. The tabular array shows the maximal connectivity is occurred in coach 3. Hence, coach 2, 3, 4, 5, and 6 are eliminated from the binary tabular array.
Then, the binary tabular array can be updated as,
( 4 )
After executing the PSO based constellating algorithm, the PMU is placed on coach 1 and bus 3, which is shown in fig.3.
C. Case 2: With loss of PMU
It is considered as each coach is discernible by individual PMU and these PMUs are placed by the proposed bunch algorithm. Hence, the arrangement of PMUs are extremely dependable but, if any perturbation occurred in power system or due to maintenance purpose any of the PMUs topographic points is out from the system. If any of the PMU is disconnected, so some of the coachs are connected to that PMUs are non remain discernible. In order to get the better of such unexpected PMU failures, a scheme is considered for individual PMU loss. It can be achieved if all the coachs are observed by at least two PMUs. These are operated as two sets,
- Primary set
- Backup set
If suppose the PMU from primary set is non working decently, so the backup set will take the duty to detect the coachs. To obtain the twosome of PMUs, the restraint and nonsubjective map will stay same by merely modifying the alteration in matrix f. In this instance, the elements of degree Fahrenheit is equal to 2 alternatively of 1. It is defined as follows:
( 5 )
This instance place the PMU for supervising the individual coach by two PMUs. Other than the nonsubjective map, the stairss are same. The new restraint map can be constructed as follows:
( 6 )
D. Case 3: Zero Injection
Zero injection coachs are the coachs from that no current is passed into the system. Zero injection correspond to the reassigning nodes in the system. If zero injection coachs are besides designed in the PMU arrangement job, the full figure of PMUs are farther minimized. See the undermentioned illustration for zero injection on six coach system where coach 2 is considered as the zero injection coach.
Now, the restraint for zero injection coach can be written as follows,
( 7 )
From the above equation, it is identified that the coach 3 has maximum connectivity. Hence, PMU is placed on the coach for full system observability.
IV. Performance Analysis
To measure the public presentation of the proposed method, the optimum arrangement of PMU job is solved for IEEE criterion coach system and KPTCL 220 and 400 kV power systems. The KPTCL power coachs are shown in fig.6. The consequences of the proposed method for IEEE coach system is illustrated in table 2. Here, IEEE-6 coach, IEEE-7 coach, IEEE-9 coach, IEEE-14 coach, and IEEE-30 coach system are considered for rating. Table 2 provides consequences for the three instances of IEEE coach systems.
We collect the information from the KPTCL 220 and 400 kilovolt power system. Here, the PMU arrangement is obtained merely for the instance 1 ( without PMU loss ) . Hence, we proposed an algorithm to obtain the PMU arrangement, which suits for all the three instances ( with loss, without loss, zero injection coach ) . Table 3 provides the entire figure of PMU arrangement collected from the KPTCL. Whereas table 4 provides the proposed consequence for the given power system. The proposed method consequences for 28 coach, 127 coach and 155 coach system in all the three instances.
V. Conclusion and Future Work
In this paper, a PSO based bunch formation algorithm is proposed to work out the optimum PMU arrangement job.