Sunday, April 25, 2010

shortest path computation in a transmission line network

ABSTRACT

In this paper a generalized algorithm has been developed to find the shortest path in a transmission line network. The selected network or graph for the proposed algorithm has the ability to traverse a network or graph with any complex structures, with any number of nodes and with any number of paths this algorithm has been developed by considering the source node as the starting node and designation node as the end node.

Dijikstras’s algorithm is used to find the closest node from the source node. The proposed software is developed, tested and verified with an example. The problem of finding efficient routing algorithm has been a fundamental area, in the field of a transmission line network. Routing is the act of transform the power from source to destination.

INTRODUCTION

Routing in network involves two basic activities
• Determining optimal routing paths and
• Transporting power from through an inter network.

An ideal routing algorithm should strive to find the optimal path for power transmission within a least transmission cost so as to satisfy the customers demand for a fast service. The optimality attributes which usually implies an efficient use of the network resources so as to optimize a selected performance measures such as network through put.

This paper focuses on the minimum short path routing where the goal is to minimize the weight of the traveling path and reduces the investment cost on transmission line.

CONSTRUCTION OF TRANSMISSION LINES:

 Transfer of bulk power from the generating station/substation to the load centers.
 Power transmission at higher voltage and reduced current for the same quantum of energy there by reducing the line loss (I2R)
 Efficient, safe and reliable power supply.

AVAILABLE VOLTAGE LEVELS IN KV

AC HVDC

India 66 500
110
132 800
220
400

Other countries 66 600
275
370
735
1000
1100
CONSTRUCTION ACTIVITIES
 Survey
 Design manufactures
 Laying of foundation
 Erecting of superstructures
 Stringing of conductors
 Commissioning

TOWER
This is the most important items to support the power conductor and ground wires at the required distance above ground level maintaining an appropriate inter conductor spacing in all operating condition. This constitutes about 30 to 40% of the cost of the line.

FACTORS INFLUENCING THE TOWER
 Voltage level
 Limitation of row
 Audio and interference
 Electrostatic fields

TYPES OF TOWERS
 Narrow Based
 Square Base
 Rectangular Base
 Y or V shaped supported by external and internal guys.
STRUCTURES
 Mild steel
 Mild steel + High tensile steel
SHAPES
 Vertical
 Horizontal
 Delta
CROSSINGS
 River crossing
 Railway crossing
 Power line crossing
 Communication line crossing
 Aerodromes
 Rifle ranges (Military target areas)
LINE PLANNING
The basic parameters for selection of material and standards, once decided will help adopting sound construction practices estimation of material labour and transports facilities should have been assessed. The material should be made available at site, required working equipped with tools and tackles should be available as when required.

SURVEY OF THE PROPOSED ROUTE OF LINE
The first step to be taken prior to the design or construction of any line is to conduct proper survey of the area which the line is to be passed, toposheet map of the area which indicate town roads, streams, river shills, railway lines may be collected and the proposed line should be marked on it before finalizing the route the following parameters should be kept in mind.
 The shortest route practicable
 As closed as possible to the road for easy during the construction and maintenance.
 Right direction in which future load is anticipated.
 Angle points should be less.

AVOIDING THE FOLLOWING AREA
 Restricted and difficult country side
 Urban development area
 Restricted access for transport vehicles
 Abrupt changes in route
 Wide river and railway crossing
 Property to aerodromes
 Natural hazards, like stapes, valleys, hills, lakes, gardens, forest, play grounds.
MINIMUM LAND WIDTH REQUIRED FOR POWER LINE CONSTRUCTION.
11KV 7 meters
33KV 15 meters
66KV 18 meters
110KV 22meters
132KV 27 meters
220KV 35 meters
400KV 52 meters

PROBLEM STATEMENT

The main objective of the proposed algorithm is to find the minimum path in a transmission line network. Starting from the source node to the destination node, there may be several paths in a net work. The lengths of a each path are taken in to consideration and they are compared

with each other respectively. Now the path having the minimum length among all the paths from source to destination will be regarded as the minimum path of the network. This is the normal procedure for finding the shortest path or minimum path of a transmission network or graph.

Several algorithms have been discovered so far to compute the short path in a graph. For instance Dijikstra’s algorithm computes the shortest path from the source node to every other node in the network. Similarly Wars Hal’s algorithm computes the shortest path from the source node to destination node of a given network.

All this algorithms described so far, find the minimum path of a communication network or a graph, where the network or graph, where network or the graph has exactly only one minimum path here question arises. What will be the minimum path if a network or graph has more than two paths having the same length (eight), that too the minimum lengths? The solution for the above question has not been answered yet. But the proposed algorithm gives a precise solution for the question discussed above.

DESCRIPTION OF THE PROPOSED SYSTEM
The proposed gives an exact solution for the question that has been asked below.
What will be the minimum path if two or more paths have the same length of a given graph? (all those paths having the minimum length).This procedure is a precise one which exact shortest path of a given graph and also gives the solution for the question discussed above and is completely different from Dijikstra’s and Wars hall’s algorithm.
Dijikstra’s has analyzed the various paths from source to destination and has given the minimum path among the N given paths as the shortest path of the graph.Warshall has traversed the entire graph from the beginning to end and has given the minimum path from the Oth vertices to the Nth vertices. But this paper gives a perfect solution for the above query.
Let us consider a graph or a network G with N vertices (nodes)and P paths. irst the various paths from the source node to the destination node are taken not consideration.the second step is to find the length path has been found out . If two or more paths have the minimum length then the paths having the minimum lengths ate taken into consideration separately. The number of edges of these paths is noted. the path having the minimum lengths will be the shortest path of the given graph .even now if two paths has the sane number of edges and same weight then both the paths are the shortest paths from the source node to the destination node of the given graph.

PATH COMPUTATION ALGORTHIM
1. The number of vertices of the given Graph N is noted
2. The source node and the destination node are noted
3. The number of paths and the number edges of each path are got in the run of time of the current program.
4. The lengths of each path are found out by adding the weight of each edge in as separable variable.
5. By using the exchange sort procedure the lengths of each path has been sorted and store in a separate array.
6. Now the first element in the array will have the minimum length
7. The paths are also sorted simultaneously using the string comparison functions.
8. If two or more paths have the same length, that too the minimum lengths, then the paths having the same minimum lengths are sorted in a separate array
9. The numbers of edges of each path are got in run time of the program and the total numbers of edges of each path are stored in a separate array.
10. These elements are again stored using the exchange sort procedure and the sorted elements are stored in a separate array available.
11. The first element in the array will have the path with the minimum number of edges.
12. Finally the corresponding path of the first element is considered to be the shortest path of the given graph G with N vertices.

VERIFICATION WITH AN EXAMPLE

Graph with 7 Nodes and 7 Paths

FLOW CHART FOR PATH COMPUTATION ALOGRITHM

OUT PUT
THE PATHS ARE AS FOLLOWD
1. THE 1 PATH IS (ABDFG) AND IT’S
2. LENGTHIS 16
3. THE 2 PATH IS (ABB1DFG) AND IT’S LENGTH IS 17
4. THE 3 PATH IS (ABG) AND IT’S LENGTH IS 10
5. THE 4 PATH IS (ABB1 G) AND IT’S LENGTH IS 11
6. THE 5 PATH IS (AEG) AND IT’S LENGTH IS 8
7. THE 6 PATH IS (AG) AND IT’S LENGTH IS 8
8. THE 7 PATH IS (ACG) AND IT’S LENGTH IS 9
9. THE NUMBER OF EDGESOF PATH AEG:2
10. THE NUMBER OF EDGES OF PATH AG:1
11. THE SHORTEST PATH IS (AG) WITH LENGTH 8 AND 1 EDGE.
APPLICATIONS

 Industrial automation
 Telecommunication
 Electrical transmission lines
 Local area net works (LAN).
CONCLUSION
Hence the proposed algorithm is used to find the minimum path of a graph or a network with any complex structure. The generalized software is highly interactive and user friendly. The algorithm is coded in C and the results are verified with different net work configuration for various numbers of nodes. It can address any real world problem.
1. find the cheapest way to travel between two locations.
2. Finding the minimum path even if there are two paths with the same length that too the minimum length.
The major advantages of the system are fast and accurate information retrieval, ease of use and time saving.

REFERENCES
1. Data structures and algorithms by Scham’s series
2. Construction of Transmission Lines at power training centre at PSTI manual
3. Programming in ANSI C by BalaGuruswamy