Power Flow Studies for Radial and Mesh Distribution System

Transcription

1 Power Flow Studies for Radial and Mesh Distribution System Mr.Tanveer HusainShaikhFeroz Khatik #1, Mr.M. M. Khan #2, Mr. M.M. Ansari #3 #1 M.E (EPS) (Student), #2 M.E (EPS), #3 Assistant Professor, #123 Electrical Department of SSBT s COET Bambhori c/o Nisar Ahmad Abdul78/16 Aqsa Nagar, Master Colony, Mehrun, Jalgaon (MH), India Abstract This paper presents a new and efficient method for solving the load flow problem of a distribution system. It is mainly based on network topology, basic circuit laws and power summation technique. The main contribution of this paper is: (i) proposing a new and efficient load flow method for radial and weakly meshed distribution systems, (ii) evaluating the impact of load models, different X/R ratios, load growth and tolerance levels, (iii) analysis of impact of number of loops on weakly meshed distribution systems, (iv) comparison of radial and weakly meshed distribution system. The results are obtained for voltage profile, total power losses time of computation, and number of iterations. Computer program coded to implement this power flow solution scheme in MATLAB and successfully applied to several practical distribution networks with radial and weakly meshed structure. MATLAB is viewed by many users not only as a highperformance language for technical computing but also as a convenient environment for building graphical user interfaces (GUI). Data visualization and GUI design in MATLAB are based on the Handle Graphics System in which the objects organized in a Graphics Object Hierarchy can be manipulated by various high and low level commands. If using MATLAB7 the GUI design more flexible and versatile, they also increase the complexity of the Handle Graphics System and require some effort to adapt to. Keywords Power Flow, MATLAB, radial distribution system, mesh distribution system, load growth. I. INTRODUCTION Power flow analysis is the backbone of power system analysis and design. They are necessary for planning, operation, economic scheduling and exchange of power between utilities. Power flow analysis is required for many other analyses such as transient stability, optimal power flow and contingency studies. The principal information of power flow analysis is to find the magnitude and phase angle of voltage at each bus and the real and reactive power flowing in each transmission lines. Power flow analysis is an importance tool involving numerical analysis applied to a power system. In this analysis, iterative techniques are used due to there no known analytical method to solve the problem. This resulted nonlinear set of equations or called power flow equations are generated. To finish this analysis there are methods of mathematical calculations which consist plenty of step depend on the size of system. This process is difficult and takes much time to perform by hand. By develop a toolbox for power flow analysis surely will help the analysis become easier. Power flow analysis software can help users to calculate the power flow problem. Over the past decade, a few versions of educational software packages using 2 advanced programming languages, such as C, C++, Pascal, or FORTRAN have been developed for power engineering curriculums. These choose an integrated study platform with support of database and GUI functions. Power flow analysis software develops by the author use MATLAB software. MATLAB as a high-performance language for technical computation integrates calculation, visualization and programming in an easy-to-use environment, thus becomes a standard instructional tool for introductory and advanced courses in mathematics, engineering and science in the university environment. Most of the students are familiar with it. Some efficient algorithms for solving the load flow problem of a radial distribution networks have been reported in the literature. However, these algorithms are not suitable for a mesh network. Several load flow algorithms specially designed for meshed distribution systems have been reported in the literature. Based on the previous work, a modified compensation based method was developed in, which uses active and reactive power as flow variables rather than complex currents. The compensation based method for weakly meshed networks presented in, was modified from single-phase system to three-phase system. The mesh network is converted into radial network by breaking the loops and the load flow has been carried out by calculating power injections at the loop break points by using a reduced order bus impedance matrix. In this paper, a simple load flow method is proposed based on network topology, basic circuit theory concepts and power summation technique. The power summation method is an iterative technique which includes two steps: (i) Calculation of the effective power at each node in backward propagation, (ii) then find the voltages at receiving end node and losses of each branch in forward propagation. First we ll calculate the effective power required by each node of the radial network. The effective power will be modified from radial network to mesh network by adding or subtracting the power required at each node to flow the same loop current in a loop and the loop current can be calculated by applying KVL in the loop. With the help of effective ISSN: Page 461

2 power at each node (considering the loop effect also), we ll carry out the load flow. Due to the distinctive solution techniques of the proposed method, the timeconsuming LU decomposition and forward/backward substitution of the Jacobian matrix or admittance matrix required in the traditional load flow methods and formation BIBC and BCBV matrices, tree labeling, breaking the loops and injecting power injections are not required. The convergence ability of the proposed load flow algorithm is tested on different IEEE systems under different scenarios. II. LITRATURE SURVEY This chapter discuss about literature review that been collected for this project. Author has refers through journals and paper especially from IEEE. This chapter consists of three parts. It is describe generally on power flow analysis problems and the solutions, Graphical User Interface in MATLAB and power system toolbox in market. A. Line Flow and Losses Calculation The power loss in line i j is the algebraic sum of the power flows determined from SL ij = S ij + S ji (05) The distribution systems usually fall into the category of ill-conditioned power systems for generic Newton-Raphson like methods with its special features i. Radial or Weakly Meshed Topologies: Most of the distribution systems are radial or weakly meshed types. The increase in requirements for reliability and outgoing distribution generation has made the structure of distribution systems more complex. Therefore, the power flow analysis in such distribution systems has become more difficult. ii. High R/X Ratio of the Distribution Lines: Transmission networks are composed mainly of overhead lines thus, the ratio is usually lower than 0.5. In distribution networks where both overhead lines and cables are used, the R/X ratio is high ranging from 0.5 to as high as 7, where high ratio values are typically for low voltage networks. iii. Unbalanced Operation: Three-phase unbalanced orientation greatly increases the complexity of the network model, since phase quantities have to be considered including mutual couplings. Fig. 1 Transmission line model for calculating line flows i j = is given by iv. Loading Conditions: Most of the load flow methods were developed assuming a static load model. But, a practical load model is required for getting reliable results. I ij = I l + I io = y ij (V i - V j ) + y io V i (01) Similarly, the line current I ij measured at bus j and defined positive in the direction j i is given by I ij = - I l + I io = y ij (V j -V i ) + y jo V j (02) The complex power S ij from bus I to j and S ji from bus j to i are S ij = V i I* ij (03) S ji = V j *I ji (04) v. Dispersed Generation: Distributed generation is being increasingly used to meet the fast load increase in the deregulation era. The utilities have to analyze the operating conditions of the radial-type systems with distributed sources. vi. Non-linear Load Models: Widespread use of non-linear loads such as, rectifiers in distribution system distorts the current drawn from the source. Usually the commercial SCADA/DMS systems treat these distribution systems as independent parts, i.e., HVAC (high voltage a.c.) loop and MVAC (medium voltage a.c.) or LVAC (low voltage a.c.) radial systems. Such rough equivalence will cause inaccuracies in the power flow solutions. ISSN: Page 462

3 III. SYSTEM DESIGN Fig. 2 A typical bus of the power system A. Proposed Load Flow Approach in Distribution Systems: An efficient and simple load flow method is proposed for analysis of the radial and weakly meshed network based on network topology and basic circuit laws (KCL and KVL). Radial distribution systems have poorest service reliability. In radial distribution systems customers at far end of the substation suffers from major voltage drops and distributor near to substation gets heavily loaded. To improve reliability and provide better voltage regulation meshed distribution networks are used by closing the tie line switches. Some distribution feeders serving high density load areas contain loops created by closing tie line switches. Referring to the above figure, power flow equations are formulated in polar form for the n-bus system in terms of bus admittance matrix Y as: B. Simple Radial Distribution System: I i = Y ij V j (06) where, i,j are to denote ith and jth bus Expressing in polar form: I i = Y ij V j θ ij + δ j (07) The current can be expressed in terms of the active and the reactive power at bus i as: I i = (08) Substituting for I i from eqn.(08) in eqn.(07) P i j Q i = V i δ i Y ij V j θ ij + δ j (09) Separating the real and imaginary parts Pi = Vi Vj Vij (10) Qi = Vi Vj Vij (11) Fig. 3Simple radial Distribution System The simple radial distribution system is shown in Fig. 3. The voltages can be calculated by knowing effective powers at each node as obtained. For example, the loads of six bus radial network are shown in Fig. 3. The effective powers at each node P(1)+jQ(1), P(2)+jQ(2), P(3)+jQ(3), P(4)+jQ(4), P(5)+jQ(5), P(6)+jQ(6). P(1)+jQ(1) = PL2 + jql2 + PL3 + jql3 + PL4 + jql4 + PL5 + jql5 + PL6 + jql6 + ploss(b1) + jqloss(b1) + ploss(b2) + jqloss(b2) + ploss(b3) + jqloss(b3)+ ploss(b4) + jqloss(b4) + ploss(b5) + jqloss(b5) (12) P(2)+jQ(2) = PL2 + jql2 + PL3 + jql3 + PL4 + jql4 + PL5 + jql5 + PL6 + jql6 + ploss(b2) + jqloss(b2) + ploss(b3) + jqloss(b3) + ISSN: Page 463

4 ploss(b4) + jqloss(b4) + ploss(b5) + jqloss(b5) (13) P (3)+jQ(3) = PL3 + jql3 + PL4 + jql4 + PL5 + jql5 + PL6 + jql6 + ploss(b3) + jqloss(b3) + ploss(b4) + jqloss(b4) + ploss(b5) + jqloss(b5) (14) P (4)+jQ(4) = PL4 + jql4 + PL5 + jql5 + ploss(b4) + jqloss(b4) (15) P(5)+jQ(5) = PL5 + jql5 (16) P(6)+jQ(6) = PL6 + jql6 (17) In this seminar, a simple load flow method is proposed based on network topology, basic circuit theory concepts and power summation technique. The power summation method is an iterative technique which includes two steps: (i) Calculation of the effective power at each node in backward propagation, (ii) then find the voltages at receiving end node and losses of each branch in forward propagation. First we ll calculate the effective power required by each node of the radial network. The effective power will be modified from radial network to mesh network by adding or subtracting the power required at each node to flow the same loop current in a loop and the loop current can be calculated by applying KVL in the loop. With the help of effective power at each node (considering the loop effect also), we ll carry out the load flow. Due to the distinctive solution techniques of the proposed method, the time consuming LU decomposition and forward/backward substitution of the Jacobian matrix or admittance matrix required in the traditional load flow methods and formation BIBC and BCBV matrices tree labeling breaking the loops and injecting power injections are not required. The convergence ability of the proposed load flow algorithm is tested on different IEEE systems under different scenarios. Fig. 4Simple radial Distribution System The simple distribution system with three loops addition to make the network as a mesh network is shown in Fig. 4. The mathematical modeling for load flow analysis of weakly meshed distribution network is explained in detail as below. In the presence of tie lines, the current in the each branch from radial network to mesh network will be changed because of the tie line currents. From Fig. 4, let the current flowing in branch 2 in radial network is IB2. In Fig. 4 because of the loop-3, the modified current in branch 2 is IB2 Iloop-3. That means the effective power at receiving end node of each branch in the loops will be changed from radial network to mesh network. The modified effective power at all nodes in each loop will be decided by the receiving end node voltage of the branches in that loop. So modified effective power can be calculated by adding or subtracting the effective power (in radial) with power at the node which is multiplication of the loop current with the receiving end node voltage of each branch in the loop. P(1) + jq(1) = P(1)+jQ(1) (18) P(2) + jq(2) = P(2)+jQ(2) (19) P(3) + jq(3) = P(3)+jQ(3) { Iloop(3) * [V(3)]*}* (20) P(4) + jq(4) = P(4)+jQ(4) + { Iloop(1) * [V(4)]*}* { Iloop(2) * [V(4)]*}* (21) C. Simple Meshed Distribution System with Three Loops: P(5) + jq(5) = P(5)+jQ(5) + { Iloop(1) * [V(5)]*}* { Iloop(2) * [V(5)]*}* (22) P(6) + jq(6) = P(6)+jQ(6) { Iloop(1) * [V(6)]*}* { Iloop(3) * [V(6)]*}* (23) ISSN: Page 464

5 D. Model of Load Growth: For future expansion and planning of the distribution systems, it is desirable that a system engineer must know the future estimate of the system solutions for planning and expansion or the efficient operation of distribution systems. The load growth (LG) pattern is essential to know for future planning and expansion of the distribution systems. In this paperwork, load growth is modelled as Loadi = Load * (1 + r)m (24) Where, r = annual growth rate m = plan period up to which feeder can take the load In this paper work r=0.07 and m=5. The load growth is incorporated for all the systems to consider the impact of load growth on voltage profile, total real and reactive power losses, number of iterations and convergence time. i. Static Load Model: In conventional load flow studies, it is presumed that active and reactive power demands are specified constant values, regardless of the amplitude of voltages in the same bus. In actual power systems operation, different categories and types of loads such as residential, industrial, and commercial loads are present. The nature of these types of loads is such that their active and reactive powers are dependent on the voltage and frequency of the system. Moreover, load characteristics have significant effects on load flow solutions and convergence ability. Common static load models for active and reactive power are expressed in a polynomial or an exponential form. The characteristic of the exponential load models can be given as: P = P0 ( Q = Q0 ( (25) (26) )np )nq Where np and nq stand for load exponents, P0 and Q0 stand for the values of the active and reactive powers at the nominal voltages. V and V0 stand for load bus voltage and load nominal voltage, respectively. ii. Polynomial Load Model : In this paper, a realistic static load model is considered that represents the power-voltage relationship as a polynomial equation of voltage magnitude. It is usually referred to as the ZIP model, as it is made up of three different load models: constant impedance (CZ), constant current (CI) and constant power (CP). The real and reactive power characteristics of ZIP load model are given as: P = P0 [ ap ( )2 + bp ( ) + cp ] (27) Q = Q0 [ aq ( )2 + bq ( )+ cq ] (28) Where, the sum of the ZIP load coefficients for both P, and Q loads is equal to 1. ap +bp + cp = 1, aq +bq + cq = 1 In this seminar work ap = aq = 0.3, bp = bq = 0.2, cp = cq = 0.5. P0 and Q0 are the real and reactive power consumed at a reference voltage Vo. IV. CONCLUSION Conclusion: In this paper, a new and efficient method for solving the load flow problem of a distribution system is proposed. The proposed method is compared with existing methods and it has been shown to be superior in the number of iterations, computationally efficient, and the robustness of convergence while the solution accuracy is well maintained. The proposed load flow approach is in close agreement with the existing methods. The proposed load flow method has been tested on two IEEE benchmark distribution systems under different loading conditions, different R/X ratio, different static load models, and considering load growth also. Load flow problem under different load conditions and for various ratios R/X has been determined with the proposed to check its convergence. It can be observed that the proposed method converges with varying load conditions and R/X ratios. It has been found from the cases that the method has good and fast convergence characteristics. Because of distinctive solution techniques of the proposed method, the time intensiveness due to LU decomposition and forward/backward substitution of the Jacobian matrix or admittance matrix required in the traditional load flow methods and formation BIBC and BCBV matrices, tree labeling, breaking the loops and injecting power injections are not necessary. Test ISSN: Page 465

6 results show that the proposed method is faster and converges with load variations and different R/X ratios and is suitable for large-scale distribution systems. REFERENCES(SIZE 10 & BOLD) [1] Tinney W. G., and Hart C. E., Power flow solutions by Newton s method, IEEE Trans. Power Apparatus Syst., Vol. 86, pp , [2] Stott B., and Alsac O., Fast decoupled load flow, IEEE Trans. Power Apparatus Syst., Vol. 93, No. 3, pp , [3] [3] Das D., Kothari D. P., and Kalam A., Simple and efficient method for load flow solution of radial distribution networks, Elect. Power Energy Syst., vol. 17, no. 5, pp , [4] [4] Ghosh S., Das D., Method for load-flow solution of radial distribution networks, IEE Proc. Gen. Trans. Dist. Vol. 146, no. 6, pp , [5] Hamouda A., and Zehar K., Improved algorithm for radial distribution networks load flow solution Elect. Power Energy Syst., vol. 33, Issue 3, pp , [6] Thukaram D., Banda H. M. W., and Jerome J., A robust three-phase power flow algorithm for radial distribution systems, Elect. Power Syst. Res., Vol. 50, No. 3, pp , [7] Ranjan R., Venkatesh B., Chaturvedi A., and Das D., Power flow solution of three-phase unbalanced radial distribution network, Elect. Power Compon. Syst., Vol. 32, No. 4, pp , [8] Shirmohammadi D., and Hong H. W., Semlyen A., and Luo G. X., A compensation-based power flow method for weakly meshed distribution and transmission networks, IEEE Trans. Power Syst., Vol. 3, No. 2, pp , [9] Luo G. X., and Semlyen A., Efficient load flow for large weakly meshed networks, IEEE Trans. Power Syst., Vol. 5, no. 4, pp , [10] [10] Cheng C.S, and Shirmohammadi D, A three phase power flow method for real time distribution system analysis, IEEE Trans. Power Syst.,Vol.10, No.2, pp , [11] Haque M. H., Efficient load flow method flow distribution systems with radial or mesh configuration, IEE Proc. Generat. Transm.Distrib., Vol. 143, No. 1, pp , [12] Haque M. H., A general load flow method for distribution systems, Elect. Power Syst. Res., vol. 54, pp , [13] Chang G., Chu S. Y., Hsu M. F., Chuang C. S., and Wang H. L., An efficient power flow algorithm for weakly meshed distribution system Elect. Power Syst. Res., vol. 84, issue. 1, pp , [14] Teng J. H., A Direct Approach for Distribution System Load Flow Solutions, IEEE Trans. on Power delivery, vol. 18, no. 3, pp , [15] Lin W. M., and Teng J. H., Phase-decoupled load flow method for radial and weakly-meshed distribution networks IEE Proc. Generat. Transm.Distrib., Vol. 143, No. 1, pp , [16] [16] Eminoglu U., Hocaoglu M. H., A new power flow method for radial distribution systems including voltage dependent load models, Elect. Power Syst. Res., vol. 76,no. 2, pp , [17] Kashem M. A., Ganapathy V., Jasmon G. B., and Buhari M. I., A Novel Method for Loss Minimization in Distribution Networks IEEE DRPT, pp , [18] Sivanagaraju S., Visali N., Sankar V., And Ramana T., Enhancing Voltage Stability of Radial Distribution Systems by Network Reconfiguration, Elect. Power Comp. and Syst., Vol. 33, No. 5, pp , ISSN: Page 466