LINE FLOW ANALYSIS OF IEEE BUS SYSTEM WITH THE LOAD SENSITIVITY FACTOR

LINE FLOW ANALYSIS OF IEEE BUS SYSTEM WITH THE LOAD SENSITIVITY FACTOR Puneet Sharma 1, Jyotsna Mehra 2, Virendra Kumar 3 1,2,3 M.Tech Research scholar, Galgotias University, Greater Noida, India Abstract In this paper, line flow analysis coding is been drawn by the help of Newton-Raphson (NR) algorithm for the IEEE 30 bus system. Further in IEEE 30 bus system load has been increased to 135% with an increment of 5% in each step. This change in load gives the node voltage load dependency factor (NVLDF) and line loss load dependency factor (LLLDF). By the help of NVLDF and LLLDF priority list has been made with respect to load sensitivity factor so that system performance index [1] in terms of voltage profile could be obtained. All the system performance study is made under steady- state condition. MATLAB R2013a has been used for calculation purpose. Keywords flow analysis, Newton-Raphson algorithm, Load sensitivity factor, System performance index, Voltage profile. I INTRODUCTION flow analysis (LFA) is used to mae sure that electrical power transfer from generator stations to consumers end through the grid system in reliable and economical form. Conventional techniques [2] for line flow analysis problem are iterative mathematical method lie the Newton-Raphson (NR) or the Gauss-Seidel (GS) methods. An engineer is always concerned about economical condition of the system operation. For the mighty interconnected grid system, the power shortage results continuous hie in prices. Thus, it is the priority of engineer to control this continuous hie. Another major problem is economic load dispatch in an optimized manner as it is directly related with load demands. For economically optimized operation of interconnected grid system modern system theory and optimization techniques are being applied with the optimized generation cost function. Through the line flow study, the voltage magnitude and angle at each bus under the steady state can be obtained. The steady state line flow in interconnected networ is represented in nonlinear algebraic equations [3]. And, for solving them iterative method is needed. For system to operate in stable condition the voltage has to be maintained within its voltage stability limit. In this paper, NR method is been used for solution of the line flow equations. By the help of voltage and angle at respective bus, the real and reactive power flow through each line can be computed. And further, the difference between each line flow from the sending end to receiving end is calculated which called as line losses. Furthermore, from increasing the load at each node to 140% with an increment of 5%, the system operation in over-load condition could be studied. Based upon, the over load system the priority list is been created which is very much beneficial to determine the most sensitive node and most sensitive line with respect to change of load. II LINE FLOW ANALYSIS flow analysis (LFA) is very important tool for analysis of power systems [4] which is used at operational as well as planning stages of the system, lie adding and installation of new generation station, load balancing in dynamic running condition and transmission lines site selection. The LFA gives the voltage and phase angle at each bus which is further used to determine the power injection at all the busses along with power flow through interconnected nodes. All these system parameter obtained values are needed for determining the optimal location as well as optimal capacity of proposed generation station, substation and new lines. In order to avoid the system unbalance condition, the voltage should be maintained within its tolerance limit with minimized line transmission losses. In this paper, firstly NR method and its application is been discussed. 2.1 BUS CLASSIFICATION: A bus [4][6] is the inter-connection point of the lines, loads and generators. These interconnected elements could be one or more. In electric power system each bus has 4 system variables, which are voltage magnitude, voltage phase angle, active power and reactive power in line flow 898

problem. For solving the line flow equation of the system, out of these four variables two are made constant and two are treated as variable. Bus categories are been made on the basis of the constant parameters. Step 5-Source current is determined between the nodes 1 to n. Step 6- Final node voltage equation: I Y * V bus bus bus 2.3 NR method and line flow analysis (LFA) [5][7]:- Step1: Assume, initial point p s, Vs= 1+j0.0. V p =1+j0.0 for p= 1, 2.n, Load bus: No generator is attached to the bus. The real and reactive power is specified at each node. Voltage and phase angle are the uncontrolled variable. It is required to specify only real power demand (Pd) and reactive power demand (Qd) at such bus as at a load bus voltage can be allowed to vary within the permissible values. Generator bus or voltage controlled bus: Here the voltage magnitude corresponding to the generator voltage and real power (Pg) corresponds to its rating are specified. Reactive power generation (Qg) and voltage phase angle are treated as uncontrolled variable for the line flow analysis. Slac (swing) bus: For the Slac Bus, it is assumed that the voltage magnitude V and voltage phase angle ( ) are nown, and real generated power (Pg) and reactive generated power (Qg) are treated as uncontrolled variable. 2.2 Bus Admittance Matrix Formation [7] Step1 Numbering of the buses is done from 1 to n. Bus 1 is the reference node (or ground node). Step2 -Replace all generators with equivalent current sources connected in parallel to the equivalent admittance. Step 3- Replace all lines, transformers and loads to equivalent admittances wherever possible. Step 4- Now by inspection: Yii (diagonal element) = sum of admittances connected to node, and Yij(off diagonal element) = Yji = -(sum of admittances connected from node i to node j ). Step 2: Predefined tolerance value till which the iteration process is followed for the convergence of the system equation. Step 3: Iteration count is set to K=0. Step 4: Bus count is set to p=1. Step 5: Case chec when p is slac bus, if yes sip to step 10. Step 6: Real power (Pp) and reactive powers (Qp) is measured from solving the power flow equations, n P { e ( e G f B ) f ( f G e B )} p p q pq p pq p q pq q pq q 1 n Q { f ( e G f B ) e ( f G e B )} p p q pq q pq p q pq q pq q 1 Step 7: Measure the active power correction factor P P P p sp p Step 8: Case when then bus is generator bus, then chec for reactive power limit. If Q Q set Qgen Qmax else if Q gen < Q min set, Q gen = Q min and otherwise, no change is made in Qp and voltage residue is evaluated as, then go to step 10. gen max 2 2 2 p p spec p V V V and Step 9: Measure the reactive power correction factor Q Q Q p sp p 899

Step 10: Bus count is incremented by 1, i.e. p=p+1 and chec if all buses have been accounted else, move bac to step 5. Step 11: Determine the largest of the absolute value of residue. load dependency factor (NVLDF). Also with the change of load results change in the line flows of the system, this termed as line loss load dependency factor (LLLDF). This NVLDF and LLLDF is used to determine the most sensitive node and sensitive line with in the power system on which the effect of change of load is observed to be most. Step 12: If the largest of the absolute value of the residue is less than tolerance then go to step 17. Step 13: Jacobian matrix elements are evaluated. Step 14: Voltage increment factor Δep and Δfp is calculated. Step 15: Calculate new bus voltages ep+1 = ep + Δep and Δfp= fp + Δfp. Evaluate cosine δ and sin δ for all voltages. In the second stage of this paper, load on each bus is been firstly increased to 140% of initial load with an increment of 5% of initial load so that system overloaded condition could be studied. III CASE STUDIES System data is obtained from [11-12] 3.1 GENERAL 5 BUS SYSTEM:- Step 16: Advance iteration count is K =K+1, then go to step 4. Step 17: Finally bus and line powers flow are evaluated and results printed. 2.4 Load and line flow analysis (LFA):- Load is the term used for the power sin [10], which consumes the power either in the form of active power or reactive power. For the stable operation [6] of the power system the load should be resistive in nature so that system s reactive component could be reduced. But in real world most of the loads either they are residential load, commercial load or industrial load is inductive in nature. It s a characteristic of the inductive load to consume the reactive power. And, with the increase of load demand the generation should also be increased in order to matchup the power demand. But in real world generation increment ass for huge investment and for engineers minimizing the cost function is the main objective. So in order to match up the generation to demand, engineer need to determine the effect of load change on the line flow of the power system on which this paper is based upon. This effect of load on the power system line flow is termed as load sensitivity factor. With the change in the load the node voltage also get change, this termed as node voltage 900 Fig. 2 connection diagram of general 5 bus system 3.3 IEEE 30 BUS SYSTEM:- Fig. 3 connection diagram of IEEE 30 bus system

GENERAL 5 BUS SYTEM TABLE III NVLDF FOR 5 BUS SYSTEM No. of lines No. of buses No. of Tolerance generator buses 7 5 1.0001 IEEE 30 BUS SYTEM No. of lines No. of buses No. of Tolerance generator buses 41 30 6.0001 TABLE I BUS CONNECTION DATA GENERAL 5 BUS SYTEM GENERAL 5 BUS SYTEM REACTIVE POWER LINE FLOW STUDY number from bus to bus Reactive power line loss load dependency factor 1 1 2-0.0239 2 1 3-0.0219 3 2 3-0.0050 4 2 4-0.0065 5 2 5-0.0179 shunt loss 0+j0 shunt loss 0 + j0 Slac bus power 1.2945- j0.074 Slac bus power 0.987- j0.074 generation load 1.695+j0.225 1.650+ j0.400 IEEE 30 BUS SYTEM generation load 2.888+j1.083 2.834+ j1.262 TABLE II NR LINE FLOW ANALYSIS RESULT GENERAL 5 BUS SYSTEM Bus number NODE VOLTAGE LOAD DEPENDENCY FACTOR(NVLDF) 1 0.000 2 0.000 3-0.008 4 0.008 5-0.009 System loss 0.046-j0.174 System loss 0.053+j0.059 6 3 4-0.0009 7 4 5-0.0014 TABLE IV REACTIVE LINE LOSS LOAD DEPENDENCY FACTOR FOR 5 BUS SYSTEM IEEE 30 BUS SYSTEM Bus number NODE VOLTAGE LOAD DEPENDENCY FACTOR(NVLDF) 1 0 2 0 3-0.004 4-0.005 5 0 6-0.0039 7-0.0042 8 0 9-0.0067 10-0.0147 11 2.220e-16 901

12-0.0071 5 2 5 2.5338 13 0 14-0.0107 15-0.0119 16-0.0104 17-0.0122 18-0.0144 19-0.0152 20-0.0144 21-0.0140 22-0.0139 23-0.0142 24-0.0164 25-0.0150 26-0.0190 27-0.0121 28-0.0046 29-0.0168 30-0.0195 number TABLE V NVLDF FOR IEEE 30 BUS SYSTEM IEEE 30 BUS SYTEM REACTIVE POWER LINE FLOW STUDY to Reactive power line loss from bus load dependency factor bus 1 1 2 3.3202 2 1 3 1.8712 3 2 4 0.7851 4 3 4 0.5004 6 2 6 1.3979 7 4 6 0.3477 8 5 7 0.1543 9 6 7 0.5081 10 6 8 0.0275 11 6 9 2.8063e-16 12 6 10 0 13 9 11-3.083e-16 14 9 10 2.4671e-15 15 4 12 1.2890e-15 16 12 13 6.1679e-16 17 12 14 0.1134 18 12 15 0.3314 19 12 16 0.0738 20 14 15 0.0097 21 16 17 0.0148 22 15 18 0.0547 23 18 19 0.0064 24 19 20 0.0275 25 10 20 0.1293 26 10 17 0.0238 902

27 10 21 0.1764 28 10 22 0.0850 29 21 22 0.0006 30 15 23 0.0056 31 22 24 0.0864 32 23 24 0.0150 33 24 25 0.0071 34 25 26 0.0689 35 25 27 0.0252 36 28 27 3.0839e-16 37 27 29 0.1338 38 27 30 0.2519 39 29 30 0.0521 40 8 28 0.0155 41 6 28 0.0464 TABLE VI REACTIVE LINE LOSS LOAD DEPENDENCY FACTOR FOR IEEE 30 BUS SYSTEM IV. RESULT By line flow analysis (LFA) of the 5 bus system and IEEE 30 bus system, the system parameters lie bus voltage, voltage phase angle, active power generation (Pg) and reactive power generation (Qg) for each type of system are obtained. Further for over-loaded condition study, in which the load is increased to 140% from 100% with an increment of 5% in each step, the NVLDF and the LLLDF is obtained. The NVLDF is the difference of the average incremental node voltage with standard voltage at 100% load. More is the value of NVLDF more is node sensitive to load increment. 903 The LLLDF is the difference of the average change in line power loss with the standard load. More is the value of LLLDF more is the line loss sensitive to the load increment. IV. CONCLUSION LFA of the general 5 bus system is been studied with IEEE 30 bus system. Along with the study of system parameter NVLDF and LLLDF is also obtained. By table III, most sensitive bus is 5 th. By table IV, most sensitive line is line number 1and 2. By table V, most sensitive bus is bus number 26 th and 30 th. By table VI, most sensitive line is line number 1 st, 2nd and 5 th line. For this paper, program is been designed in the MATLAB2013a environment. V. REFERENCES [1] A.E. Guile and W.D. Paterson, Electrical power systems, Vol. 2, (Pergamon Press, 2nd edition, 1977). [2] Carpentier Optimal Power Flows, Electrical Power and Energy Systems, Vol.1, April 1979, pp 959-972. [3] W.D. Stevenson Jr., Elements of power system analysis, (McGraw-Hill, 4th edition, 1982). [4] Hadi Saadat, Power System Analysis, Tata McGRAW-HILL Edition. [5] W. F. Tinney, C. E. Hart, "Power Flow Solution by Newton's Method, " IEEE Transactions on Power Apparatus and systems, Vol. PAS-86, pp. 1449-1460, November 1967. [6] A. J. Wood, B. F. Wollenberg. Power Generation Operation and Control. 2nd ed. John Willey & Sons Inc [7] Load flows, Chapter 18, Bus classification, Comparison of solution methods, N-R method Electrical Power system by C.L.WADHWA. [8] D.I.Sun, B.Ashley, B.Brewer, A.Hughes and W.F.Tinney, Optimal Power Flow by Newton Approach, IEEE Transactions on Power Apparatus and systems, vol.103, No.10, 1984, pp2864-2880. [9] T.K.A. Rahman and G.B. Jasmon, A new technique for voltage stability analysis in a power system and improved loadflow algorithm for distribution networ, Energy Management and Power Delivery Proceedings of EMPD '95; vol.2, pp.714 719, 1995. [10] P. Kundur, 1. Paserba, V. Ajjarapu, G. Anderson, A. Bose, C.A. Canizares, N. HatziargYfiou, D. Hill, A. Stanovic, C. Taylor, T. Van Cutsem, and V. Vittal, "Definition and Classification of Power System Instability," IEEE Trans. On Power Systems, Vol. 19, No.2, pp.1387-1401, May 2004 [11] A. Bergen and V. Vittal, Power Systems Analysis, second edition, Prentice Hall, Upper Saddle River, New Jersey, 2000 [12] J.Alsac, O. & Stott, B., "Optimal Load Flow with Steady State Security", IEEE Transactions on Power Apparatus and Systems, Vol. PAS 93, No. 3, 1974, pp. 745-751