International Electrical Engineering Journal (IEEJ) Vol. 6 (2015) No.1, pp. 1711-1715 ISSN 2078-2365 http://www.ieejournal.com/
An Effective Technique for Load-Flow Solution of Radial Distribution Networks Krishna Murari ,Smarajit Ghosh, Nitin Singh EIED, Thapar university, Patiala-147004, India Email-
[email protected],
[email protected],
[email protected]
Abstract— A new method has been developed for load-flow solution of radial distribution systems using matrix method. The motive of this paper is to propose a technique to identify the nodes beyond each branch with less computational time. The formulated equations have been solved using matrix method. In order to find branch current, node voltage and power loss in the radial distribution network matrix method has been used. Efficacy of this method has been implemented on 33- bus radial distribution systems with constant power (CP), constant current (CC), constant impedance (CZ) composite and exponential load modelling. The suggested method converges well for constant power, constant current, constant impedance, composite and exponential load modeling. The advantages of proposed method have compared with several existing methods in terms of relative value CPU time and memory size. The proposed method requires much less time to converge and also require less memory size when compared with the several existing methods.
Index Terms— Constant Power Load, Distribution system, Load flow, Load Flow Equations, Radial Distribution systems.
I. INTRODUCTION The conventional methods of load flow are not applicable to the radial distribution network because the solution does not converge quickly due to high R/X ratio of radial network. Moreover, the radial or weakly meshed topology of radial distribution networks affects the variables of load flow analysis. The transmission system is usually meshed whereas the distribution system is generally radial and can be weakly meshed in some cases. The main objective in a radial distribution network load flow problem is to find branch currents, node voltages, phase angle and line losses. Table I Lists
of symbols
NB LN jj k
Total number of nodes Total number of Branches Branch number Node Number
N(jj)
Total number of nodes beyond Branch jj
R(jj) X(jj) V(k) LP(jj) LQ(jj) Z(jj) IL(k) DVMAX PL(k) QL(k) S(k)
Resistance of Branch jj Reactance of branch jj Voltage at node k Real power loss of branch jj Reactive power loss of branch jj Impedance of branch jj Load current at node k Maximum voltage difference Active power load at node k Reactive power load at node k Complex power load at node k
II. SOLUTION METHODOLOGY In the proposed method a matrix based approach has been used. The load flow equations have been presented in matrix form. The network is read through a program with the help of an examining technique devised in this method. The laterals, sub-laterals, main system and system beyond a node have been identified separately in this work. (1) Where k is set containing all the elements of set nb(jj). Where nb(jj) is set of all nodes beyond branch jj. The branch current in any branch (jj) is sum of all the load current beyond the branch ( jj). Once the branch current is evaluated, the voltage at each node can be evaluated easily by the use of equation given below V (k+1) = V (k) –I(jj)*Z(jj) (2) LP (jj) =
* R (jj)
(3)
QP (jj) =
* X (jj)
(4)
These equations are the main load flow equation. By the application of above equations in matrix form we can easily perform load flow calculation to evaluate the results. The use of matrix manipulation makes solution of load flow quite easier and very fast. The proposed method for load flow calculation is done in three steps1. Find number of nodes beyond each branch in radial distribution network. 2. Find current in each branch. 3. Find node voltage and phase angle 1711
Krishna Murari et. al.,
An Effective Technique for Load-Flow Solution of Radial Distribution Networks
International Electrical Engineering Journal (IEEJ) Vol. 6 (2015) No.1, pp. 1711-1715 ISSN 2078-2365 http://www.ieejournal.com/
S(k1) =
Fig. 1 Single line diagram of a radial distribution network
III. ALGORITHM FOR IDENTIFYING NODES BEYOND A BRANCH
1. Start 2. Read total no branches (LN) and total no of nodes (NB). 3. Read the set of all nodes , laterals and sub laterals. 4. C=1 5. Check the first element of main set of nodes M and first element of laterals and sub laterals. 6. If it does not match then remove the first elements of main set M and the reduced set is subset SB.Otherwise, remove the elements of set from the main set with which first element of that set matches and get subset SB. 7. M is replaced by SB in first iteration and in all other Iteration SB (old) is replaced by SB (new). 8. C=C+1 9. If C
