Chennai and Dr.MGR University Second International Conference on Sustainable Energy and Intelligent System (SEISCON 2011) , Dr. M.G.R. University, Maduravoyal, Chennai, Tamil Nadu, India. July. 20-22, 2011.

456

A Matlab/GUI based simulation tool to solve load fl ow program for standard test systems

S. Prabhakar Karthikeyan*, K. Sathish Kumar*, Harissh. A.S*, I. Jacob Raglend$, D.P. Kothari

*School Of Electrical Engineering, Vellore Institute Of Technology, Vellore, India, spk25in@yahoo.co.in$ Proffesor, NI University, Thakkalai, Nagercoil, TamilNadu, India, jacobraglend@rediffmail.com

† FNAE, FNASc, Fellow IEEE, Director General, Vindhya Group of Institutions, Indore, Madhya Pradesh, India, d.p.kothari@vit.ac.in

Keywords: Topology based load fl ow, Distribution systems, GUI, Bus-Injection to Branch-Current (BIBC) matrix, Branch-Current to Bus-Voltage (BCBV) matrix.

AbstractLoad fl ow or power fl ow is the solution for the normal balanced steady-state operating conditions of an electric power system. It be-came an essential prerequisite for power system studies as it is used to ensure that electrical power transfer from generators to consum-ers through the grid system is stable, reliable and economic. In this paper, the topology based load fl ow studies are made available in the MATLAB –Graphical User Interface (GUI) environment which will bring the load fl ow studies more user friendly. Using this tool, extensive graphical analysis has also been made. Standard IEEE test systems are taken as an input data and the results are plotted. This can also be extended for any analysis where load fl ow results are used as an input.

1 IntroductionDeveloping a computer program that meets the requirements of a power system engineer has been a concern for researchers since the early 1990s [2]. Many programs of real-time applications in the area of distribution automation (DA), such as network optimi-zation, reactive power planning, switching, state estimation, and so forth, require a robust and effi cient load fl ow method. Such a load fl ow method must be able to model the special features of distribution systems in suffi cient detail [4]. The well-known char-acteristics of an electric distribution system are radial or weakly meshed structure, multiphase and unbalanced operation, unbal-anced distributed load, extremely large number of branches and nodes, wide-ranging resistance and reactance values [12].

The above features of the radial distribution system make the traditional methods fail and so we need a new method. In India all the 11 kV rural distribution feeders are radial and too long. The voltages at the far end of many such feeders are very low with very high voltage regulation. Many of these practical rural distribution feeders have failed to converge while using Newton Raphson (NR) and Fast Decoupled Load Flow (FDLF) methods.

2 Formulation of Load fl ow problemIn the power fl ow problem, it is assumed that the real power

PD and reactive power QD at each Load Bus are known. For this reason, Load Buses are also known as PQ Buses. For Generator Buses, it is assumed that the real power generated (PG) and the voltage magnitude (|V|) is known. For the slack Bus, it is assumed that the voltage magnitude |V| and voltage phase are known. Therefore, for each load bus, the voltage magnitude and angle are unknown and must be found; for each generator bus, the voltage angle must be obtained; there are no variables that must be ob-tained for the slack Bus. In a system with N buses and R genera-tors, there are then 2(N 1) (R 1) unknowns. In order to solve for the 2(N 1) (R 1) unknowns, there must be 2(N 1) (R 1)equations that do not introduce any new unknown variables [13]. The power balance equations can be written for real and reactive power for each bus. The real power balance equation is given in equation (1).

(1)

where Pi is the net power injected into bus i, Gik is the real part of the element in the Ybus corresponding to the ith row and kth col-umn, Bik is the corresponding imaginary part and ik is the differ-ence in voltage angle between the ith and kth buses. The reactive power balance equation is given by equation (2).

(2)

where Qi is the net reactive power injected at bus i.Equations (1) & (2) are the real and reactive power balance

equations for each load bus and the real power balance equation for each generator bus. Only the real power balance equation is written for a generator bus because the net reactive power injected is assumed to be unknown and therefore including the reactive power balance equation would result in an additional unknown variable. For similar reasons, there are no equations written for the Slack Bus.

When compared with the traditional Newton Raphson and gauss implicit Z matrix algorithms, which need LU (lower and upper order matrix) decomposition and forward or backward sub-stitution of the jacobian matrix or the Y admittance matrix, the new formulation uses only the distribution load fl ow matrix (DLF matrix) as in Equation 18 to solve load fl ow problem [14, 15].

A MTLAB/GUI based simulation tool to solve load flow program for standard test systems

457

The time-consuming LU decomposition and forward/ backward substitution procedures are not needed. This considerably reduces the amount of computation resources needed and makes the pro-posed method suitable for on-line operation [1]. Also all the tra-ditional methods are formulated for transmission systems. Due to unique characteristics of the distribution systems like high R/X ratio the traditional methods fail. Such systems with high R/X ratios are termed as “ill-conditioned” systems and the traditional methods do not converge for such systems as they are formulated for transmission systems with the assumption that they have high reactance values than resistance values.

Generally the most effi cient of the traditional methods is the fast decoupled method, which is a modifi cation of the Newton-Raphson method [11,5,6]. In an electric power transmission sys-tem operating in steady state, the changes which occur in the bus active power due to small changes in bus voltage magnitude is very small as compared to their changes due to the small changes in bus voltage phase angle as shown in equation (3).

P = (EV/X) sin (3)

Therefore, all the elements of the sub-matrix J2 of the jacobian matrix can be neglected and taken as zero. The changes which occur in bus reactive power due to small changes in bus voltage phase angle are quite small as shown in equation (4).

Q = (V/X) (E – V) (4)

So, all the elements of J3 of the same jacobian matrix can also be neglected and taken as zero. This gives the following two sim-plifi ed decoupled equations: [13]

P = J1 (5)Q = J4 |V| (6)

This simplifi cation leads to the failure of this method in dis-tribution systems where the above assumptions do not apply to them. This calls for a new approach.

3 Topology based load fl ow formulationThe method is based on the two matrices, the bus-injection to branch-current matrix and branch-current to bus-voltage matrix, and on the equivalent current injection [18, 19 & 20]. For every bus i, the complex power Si is given by equation (7)

Si = ( Pi + Qi ) where i = 1,2… N (7)

And the corresponding equivalent current injection at the kth

iteration is shown in Equation (8).

(8)

where,Vk

i is the node voltage at the kth iteration Ik

i is the equivalent current injection at the kth iteration.

3.1 Bus Injection to branch-current matrix

The simple distribution system shown in Fig. 1 will be used as an example. The branch currents can be formulated as a func-tion of the equivalent current injections. For example, the branch

currents B5, B3 and B1 can be expressed as shown in equations below.

Figure 1: Sample system to explain the algorithm

B5 = I6 (9)

B3 = I4 + I5 (10)

B1 = I2 + I3 + I4 + I5 + I6 (11)

Furthermore, the bus-injection to branch-current (BIBC) ma-trix can be obtained as

[B] = [BIBC][I] (12)

3.2 Branch-Current to Bus-Voltage matrix

The relations between the branch currents and bus voltages are given by KVL. For example, the voltages of Bus 2, 3, and 4 are shown in the equations below.

V2 = V1 – B1Z12 (13)

V3 = V2 – B2 Z23 (14)

V4 = V3 – B3Z34 (15)

where Vi is the bus voltage of bus i, and Zij is the line impedance between bus i and bus j. Substituting for V2 and V3 in equation (15)

V4 = V1 – B1Z12 – B2 Z23 – B3Z34 (16)

From the above equation it can be seen that the bus voltage can be expressed as a function of the branch currents, line param-eters and substation voltage. Similar procedures can be utilized for other buses, and the branch-current to bus-voltage (BCBV) matrix can be derived as

[ V] = [BCBV][B] (17)

Chennai and Dr.MGR University Second International Conference on Sustainable Energy and Intelligent System

458

It can be seen that the building algorithms for the BIBC and BCBV matrices are similar. In fact, these two matrices were built in the same subroutine of our test program. Therefore, the amount of computation resources needed can be reduced. In addition, the building algorithms are based on the traditional bus-branch oriented data base, so the data preparation time of the proposed algorithm can be reduced and can be integrated into the existing Distribution Automated Systems (DAS).The BIBC and BCBV matrices were developed based on the topological structure of distribution systems [3]. The BIBC matrix is responsible for the relations between the bus current injections and branch currents. The corresponding variation of the branch currents, which is generated by the variation at the current injection buses, can be found directly by using the BIBC matrix. The BCBV matrix is responsible for the relations between the branch currents and bus voltages. The corresponding variation of the bus voltages, which is generated by the variation of the branch currents, can be found directly by using the BCBV matrix. Combining BIBC and BCBV equations, the relations between the bus current injections and bus voltages can be expressed as in equation (18).

[ V] = [BCBV] [BIBC] [I] = [DLF] [I] (18)

The solution for the DLF can be obtained by solving the fol-lowing equations.

(19)

[ Vk+1] = [DLF] [Ik] (20)

4 Algorithm1. Input data.2. Form the BIBC matrix.3. Form the BCBV matrix.4. Form the DLF matrix.5. Iteration k = 0.6. Iteration k = k + 1.7. Solve for the three-phase power fl ow and update voltages.8. If |Vk+1| - |V k| > tolerance, go to Step 6, else calculate the

active and reactive power losses and print the results.9. End.

4.1 Flowchart

5 Graphic User Interface (GUI)A Graphic User Interface (GUI) has been developed for the pro-posed algorithm. The GUI was developed in MATLAB 2008b us-ing GUIDE (Graphic User Interface Development Environment).It is user friendly and very simple to run. Lot of interactive fea-tures are included such as: dynamic loading of bus and branch data, entering the base KV and MVA values, tolerance values etc. An interactive 3-dimensional plot is also provided. Once the load fl ow is made to run, it automatically plots the voltage values from the load fl ow and if provided, standard values are also plotted. The user can feel the values in the plot using the data-cursor [17] provided. The user can also rotate the plot to check quickly if the results are matching. If any data is entered wrongly, the GUI is programmed so that it displays appropriate error dialog boxes. This avoids usage of command line for displaying errors and saves time of navigating from GUI to the MATLAB command line. For any help, all the required documentation can be accessed by a single button click on the GUI.

A MTLAB/GUI based simulation tool to solve load flow program for standard test systems

459

Screen shots of the GUI are shown below.

Figure 2: Initial state of GUI

Figure 3: After running the GUI with correct data

Figure 4: Figure showing an error dialog box when there is a mis-match between Bus and Line data

Figure 5: Figure showing an error dialog box when there is a non-numeric value is entered in place of base KV

6 Results and AnalysisThe algorithm has been tested on different standard Radial Distri-bution Systems. The systems and their Load fl ow analysis results are given below:

6.1 IEEE 69 bus system

Total Real Power line losses = 225.001190 KWTotal Reactive Power line losses = 102.198261 KVARNo. of iterations = 6Elapsed time for load fl ow = 0.007274 seconds

6.2 IEEE 33 bus system

Total Real Power line losses = 210.987448 KW Total Reactive Power line losses = 143.128308 KVARNo. of iteration = 5Elapsed time for load fl ow = 0.004177 seconds

7 Plots of the Load Flow ResultsThe following plots (Figures 6&7) are plotted with bus number against the corresponding voltage values (p.u) of different sys-tems in their converged state. The tolerance was taken as 10-5.

Fig 6 Final converged values of voltages at different buses of IEEE 33 bus system

Chennai and Dr.MGR University Second International Conference on Sustainable Energy and Intelligent System

460

Fig 7 Final converged values of voltages at different buses of IEEE 69 bus system

8 ConclusionsIn this paper, a Matlab/GUI based power system load fl ow simula-tion tool has been developed which is user friendly and very less time consuming. This helps the power system engineers to extend it for their real time studies. All the results shown above were found to be in agreement, i.e. The IEEE 69 bus system results are in agreement with the results given in [7] and IEEE 33 bus system with [8].

From the above results, the voltage profi le at each bus, the active and reactive losses of the lines are also obtained. A fl at start is assumed initially. All the simulations were run on an Intel Pentium IV 3.06GHZ processor with 512 MB RAM. In the GUI, the voltage magnitude vs. the bus number has been plotted. The plot can be compared with the standard results plot using Rotate 3d and Data cursor provided in the GUI itself. This GUI can be extended using similar plots/profi les. The time taken for running and initializing the GUI is also very less. It is also very interactive and user friendly. Detailed results can be viewed with a single click on a button.

9 AcknowledgementThe authors thank the management of VIT University, Vellore, Tamil Nadu, India for their continuous encouragement and sup-port rendered in carrying out this research work.

References1. Shipley.R.B, Introduction to Matrices and Power systems,

Wiley, New York, 1976.2. T.H.Chen, M.S.Chen, K.J.Hwang, P.Kotas, and E. A.Chebli,

“Distribution system power fl ow analysis - A rigid ap-proach,” IEEE Transactions on Power Delivery, volume 6, pp. 1146–1152, July 1991.

3. D.Shirmohammadi, H.W.Hong, A.Semlyen, and G. X. Luo, “A compensation- based power fl ow method for weakly meshed distribution and transmission networks,” IEEE Transactions on Power Systems, volume 3, pp. 753–762, May 1988.

4. G.X.Luo and A.Semlyen, “Effi cient load fl ow for large weakly meshed networks,” IEEE Transactions on Power Systems, volume 5, pp. 1309–1316, November 1990.

5. C.S.Cheng and D.Shirmohammadi, “A three-phase power fl ow method for real-time distribution system analysis,” IEEE Transactions on Power Systems, volume 10, pp. 671–679, May 1995.

6. R.D.Zimmerman and H.D.Chiang, “Fast decoupled power fl ow for unbalanced radial distribution systems,” IEEE Transactions on Power Systems, volume 10, pp. 2045–2052, November 1995.

7. S.Ghosh and D.Das “Method for load-fl ow solution of radi-al distribution networks”, IEE Proceedings on Generation, Transmission & Distribution, volume 146, issue 6, Novem-ber 1999.

8. Abdellatif Hamouda and Khaled zehar “Effi cient Load fl ow method for radial distribution feeders,” Journal of applied sciences, volume 6, issue 13.

9. D. Das, H.S. Nagi, D.P. Kothari “Novel method for solving radial distribution networks,” IEE Proceedings on Genera-tion, Transmission & Distribution, volume 141, issue 4, July 1994.

10. Ching Tzong Su and Chih Cheng Tsai “A new fuzzy-reason-ing approach to optimum capacitor allocation for primary distribution systems,” Proceedings of the IEEE Internation-al Conference on Industrial Technology, 1996.

11. K.Vinoth Kumar and M.P.Selvan “A Simplifi ed Approach for Load Flow Analysis of Radial Distribution Network with Embedded Generation,” TENCON 2008, IEEE Region 10 Conference.

12. Alexandra von Meier, “Electric Power Systems - A concep-tual introduction,” IEEE Press, Wiley Publications

13. Hadi Saadat, “Power System Analysis,” Mcgraw Hill High-er Education, 2nd revised edition 2004.

14. Leonard L. Grigsby, “Electric Power Engineering Hand-book,” Second Edition, CRC Press

15. B.Venkatesh and Rakesh Ranjan, “Optimal radial distribu-tion system reconfi guration using fuzzy adaptation of evo-lutionary programming”, ELSEVIER, Electrical Power and Energy Systems, volume 25, pp. 775–780, 2003

16. N.C.Sahoo and K. Prasad “A fuzzy genetic approach for network reconfi guration to enhance voltage stability in ra-dial distribution systems”, ELSEVIER, Energy Conversion and Management, volume 47, pp. 3288–3306, 2006

17. Matlab documentation for Graphic User Interface Develop-ment Environment (GUIDE), Mathworks.

18. Jen Hao Teng “A Direct Approach for Distribution System Load Flow Solutions” IEEE TRANSACTIONS on power delivery, volume 18, issue 3, July 2003

19. S.Sivanagaraju, J.Viswanatha Rao and M.Giridhar,“A loop based load fl ow method for weakly meshed distribution network”, ARPN Journal of Engineering and Applied Sci-ences, volume 3, issue 4, August 2008

20. M.H.Haque,“Effi cient load fl ow method for distribution systems with radial or mesh confi guration,” IEE Proceed-ings on Generation, Transmission & Distribution volume 143, issue 1, January 1996.

A MTLAB/GUI based simulation tool to solve load flow program for standard test systems

461

Biographies

S.Prabhakar Karthikeyan has completed his B.E (EEE) from University of Madras, Tamil Nadu (1997), M.E (Electrical Power Engineering) from The M.S. University of Baroda, Vadodara, Gu-jarat (1999) and presently pursuing his research at VIT Univer-sity, Vellore, Tamil Nadu, INDIA. Currently he is in the School of Electrical Engineering of the same University as Programme Manager(EEE) & Division Leader(Power Systems). His area of interest includes Deregulation and restructured Power systems, issues in distribution systems.

K.Sathish Kumar has completed his B.E (EEE) from Madurai Kamaraj University, Tamil Nadu (2001), M.Tech (High Voltage Engineering) from SASTRA University (2002) and presently pur-suing his research at VIT University, Vellore, Tamil Nadu. Cur-rently he is in the School of Electrical Engineering of the same University as Assistant Professor (Senior). His area of interests includes distribution system restoration and reconfi guration.

Harissh.A.S is an under graduate student in the School of Elec-trical Engineering at VIT University, Vellore. His areas of inter-est are energy markets, distributed generation systems and smart grids.

I.Jacob Raglend has completed his B.E (EEE) from Manonmani-yam Sundaranar University, Tamil Nadu (2000), M.E (Power Sys-tems) from Annamalai University (2001) and Ph.D from IIT Ro-orkee (2007). Currently he is in the Department of Electrical and Electronics Engineering, NI University, Thakkalai, Tamil Nadu as Professor . His area of interests includes Power systems optimisa-tion problems, power system operation and control.

D.P.Kothari has completed his under graduate, post graduate and doctoral degree from BITS, Pilani during the year 1967, 1969, & 1975 respectively. Currently, he is the Director General, Vindhya Group of Institutions, Indore, Madhya Pradesh. Prior to this as-signment, he was the Vice Chancellor of VIT University (2007-2010), Professor of Centre for Energy Studies, Indian Institute of Technology, New Delhi. He also served as Director i/c, IIT, Delhi (2005), Deputy Director (Administration), IIT Delhi (2003-06), Principal, Visvesvaryaya Regional Engineering College, Nagpur (1997-98), Head, Centre for Energy Studies, IIT, Delhi (1995-97). His area of interests includes Optimal Hydro-thermal Scheduling, Unit Commitment, Maintenance Scheduling, Energy Conserva-tion (loss minimization and voltage control), Power Quality and Energy Systems Planning and Modelling.