Reliable Load Flow Solution for Controlling Power Network by FACTS Devices

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459,ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013)

739

Reliable Load Flow Solution for Controlling Power Network by

FACTS Devices

C. Sreenivasulu

1

, Dr. G. Madhusudhana Rao

2

, Dr.B.V.Sanker Ram

3

1_{S.S. Institute of Technology, JNTU, Hyderabad, INDIA.} 2

JJ Group of Institutions, Hyderabad, INDIA.

3_{Professor of EEE,JNTU, Hyderabad, INDIA.}

Abstract-- In this paper a new and efficient method for the reliable load flow solution of power network branches controlled by flexible AC transmission systems (FACTS) is presented. In the various methods proposed in past, the formulations was derived in which the Jacobian matrix is in UDUT form, where U is a constant upper triangular matrix depending solely on system topology and D is a block diagonal matrix. Now this paper is presenting a new technique consisting of embedded series Flexible AC Transmission System (FACTS) devices, facilitated by a formulation of power flow equations with bus voltage magnitudes and line flows as independent variables. Using IEEE standard systems, the line flow-based (LFB) formulation is shown to provide easy implementation with multiple series and shunt FACTS devices. The proposed method is very reliable with comparison to N-R method.

Keywords-- Distribution power flow analysis, flexible AC transmission system (FACTS), power system planning and modeling, voltage controls.

I. INTRODUCTION

Power flow is the most fundamental numerical algorithm for power system analysis. In 1967, Tinney and Hart developed the classical Newton based power flow solution method[l]. Later work by Stott and Alsac [2] made the fast decoupled Newton method as well as its various alternatives a kind of standard power flow method for EMS systems. Even though the fast decoupled Newton method works well for transmission systems, its convergence performance is poor for most distribution systems due to their high r/x ratio which deteriorates the diagonal dominance of the Jacobian matrix. For this reason, several non-Newton types of methods have been proposed [3-6].

Increased use of transmission facilities due to higher industrial output and deregulation of the Power Supply Industry have provided the momentum for exploring new ways of maximizing power transfers in existing transmission facilities while, at the same time, maintaining acceptable levels of network reliability and stability. In this environment, high performance control of the power network is mandatory. An in-depth analysis of the options available for achieving such objectives has pointed in the direction of power electronics.

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International Journal of Emerging Technology and Advanced Engineering

740 The main objective of this paper is to develop an LFB formulation of power balance equations for analyzing a radial distribution system that will efficiently incorporate embedded series and shunt FACTS devices. The LFB equations use bus voltage magnitudes and line power flows as independent variables and directly relate the FACTS device variables with system operating conditions. The line loss terms are the only nonlinear terms in the formulation. By adding them to bus power injections, the coefficient matrix of LFB equations is rendered linear. A preliminary Breadth-First-Search (BFS) ordering of the branches transforms the coefficient matrix structure to strictly upper/lower diagonal and leads to simple backward/forward substitution for calculating real and reactive line power in each branch and voltage at each bus. The FACTS device models are described first, and the development of LFB equations follows. Numerical examples, including multiple FACTS devices in the standard IEEE systems, illustrate the power of the new approach. The procedure exhibits good convergence characteristics, high reliability, and computational efficiency. A balanced distribution feeder modeled by the positive sequence impedance is used in the paper, since the aim of this paper is to demonstrate the advantages of the LFB formulation in handling the embedded FACTS devices. FACTS devices can be assumed to be cost-effective when deployed on the main distribution feeder.

II. BASIC CIRCUIT THEORY IN DISTRIBUTION SYSTEMS

For a linear, time-invariant RLC circuit with a sinusoidal voltage source, the basic circuit theory can be expressed as (see Appendix A for details):

Ohm's Law: ib = ybvb (1)

KCL: Ab=in (2)

KVL: Bib, =0 (3)

For fundamental frequency power flow calculations, a distribution system is always modeled as a linear, time invariant RLC circuit. Earth is always treated as a reference node. For a radial distribution system with n nodes and without shunt branches, the number of branches is n-1. Therefore, the dimension of matrix A is n x (n-1).

Figure.1Single line diagram for independent radial distribution system

The independent loop for radial distribution systems can always be formed by a branch with its two shunt branches. Since shunt branches are usually neglected in modeling distribution lines, a fictitious shunt branch can be placed with branch voltage to be the nodal voltage as shown in Figure 1can be written as:

Vb=A T

Vn (4)

Combining (l), (2), and (4), we have: AYbATVn=In (5)

By knowing the nodal voltage at one node, assuming it is the first node for convenience, and nodal current injections at the other n-1 nodes, (6) can be derived from (5) for solving the remaining n-1 unknown nodal voltages:

Where

Note matrix An-1 is a square matrix Since every branch

is always directed away from one node and towards the other node, we have:

Where en and en-1 are unity column vectors with

dimension n and n-1 respectively. Then (6) can be simplified as:

An-1YbATn-1 is the Nodal Admittance Matrix which

most power engineers are familiar with. In other words, for a radial system without shunt branches, the Nodal Admittance Matrix is formed as the product of three square matrices. It is interesting to note that the back forward sweep method proposed in [5] for a radial system is exactly the same as solving Vn-1from (8) if we

organize (8) as follows:

Solving IL from (8a) is equivalent to the 'Backward

Sweep', and solving Vn-1 from (8b) is equivalent to the

'Forward Sweep'. This observation is very important as it motivated us to derive a Jacobian matrix in UDUT form and a back/forward sweep algorithm for the Newton method.

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International Journal of Emerging Technology and Advanced Engineering

741 III. RADIAL SYSTEM

The radial distribution network graph has a tree structure with no loops as shown in Fig 2. The total number of lines equals the number of buses minus one. The pattern of incidence matrix depends on the order of lines and nodes, the incidence matrix of given distribution network is shown Fig.3 The Arbitrary order incidence matrix has a structure that depends on the order in which the lines are read from the data. Further, the incidence matrix is non square and singular. Any line oriented from a bus is given +1 and for towards node - 1 is assigned if the slack bus is excluded, the incidence matrix becomes square and non singular.

Fig.2 IEEE 13-node test feeder

Fig.3: Graph of IEEE 13-node feeder

Fig.4: Incidence matrix – with nodes in arbitrary order

IV. DECOUPLED LFB MODEL OF RADIAL DISTRIBUTION

SYSTEMS

The below matrix may be split into three “decoupled” equation sets and rewritten as follows:

With BFS ordered lines, the bus incidence matrix A and as (8) A1 and are upper triangle matrixes and AT1 is a

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International Journal of Emerging Technology and Advanced Engineering

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742 This model is called linear LFB. The other variations are the LFB model, including the loss term and the decoupled formulation (D-LFB). Calculations are carried out with a PC. For a convergence criterion of, all three iterative methods took four iterations in each case. Table I shows the computation time in the various cases. For comparing the accuracy of the results, the maximum absolute error and the mean square deviation of the bus voltage values are calculated in the new formulations using the Newton–Raphson results as accurate ones. Table II shows the results from the three variations for the various cases studied. The conclusion is that the proposed LFB formulation is computationally superior and acceptably accurate.

Fig.5: Bus Incidence matrix

V. ALGORITHM FOR DECOUPLED LFB

1. Read the system line data and bus data

A) System data: no of buses, no of lines, reference bus or slack bus

b) Line data: From bus, to bus, line resistance, line reactance

c) Bus data: bus no , P Load, Q load..

d) Read itermax , epsilon, epsilon, base KVA , base voltage

e) Read the initial voltage at all buses

2. using above BFS method to modify the system network.

3. From idegree , itagf , itagto , adjq , and adjL vectors. 4. Calculate effective load at each bus starting from the last bus P effective load, Q effective load.

5. Initialize sum of active power loss slp=0, sum of

reactive powerloss slq=0, Previous iteration active power loss pl=0, reactive

power loss ql=0

6. Start iteration count iter=1

7. Initialize total active power loss tploss [i]=0,total reactive power loss

tqloss[i] = 0 for i = 1 to n. 8. Assign slp=pl, slq= ql, pl=ql=0 9. Find effective losses at each bus 10. Calculate load at each bus with losses

11. Calculate the voltages and phse angles, equations (3.3)

12. ∆ploss = slp – pl& ∆ qloss= slq-ql then set ploss of (i) = qloss (i)=0 for 1 to n

13.If ∆ ploss <= epsilon and ∆qloss <= epsilon go to step 10

14. If iter <= itermax Then iter = iter + 1 go to step 9 15. Problem not converged and stops.

16. Problem converged and prints the results.

VI. TEST RESULTS

IEEE 13 Bus System Results (Decoupled LFB)

Table I

Line Data of load Pl and Ql at end buses of each line

L.No LP LQ R X Pl Ql

1 1 2 0.020 0.065 0 0

2 2 3 0.022 0.020 0.04 0.023

3 2 4 0.020 0.065 0.034 0.025

4 2 5 0.015 0.020 0.271 0.155

5 3 6 0.013 0.012 0 0

6 4 7 0.013 0.012 0.046 0.026

7 4 8 0.010 0.032 0 0

8 4 9 0 0 0 0

9 5 10 0 0 0.034 0.030

10 7 11 0.007 0.007 0.08 0.058

11 7 12 0.019 0.007 0.034 0.016

12 9 13 0.013 0.012 0.025 0.017

Table II NLCONT

BUSNO NLCOUNT

1 1

2 4

3 2

4 4

5 2

6 1

7 3

8 1

9 2

10 1

11 1

12 1

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International Journal of Emerging Technology and Advanced Engineering

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Table III ITAG Vector

Table IV

Real &Reactive Power at each Bus

Table V

Real &Reactive Power Loss at each line

Table VI

Voltage and Phase angle of each bus

BUSNO Voltage(v) Phase angle(deg)

1 1 0

2 0.942 -2.1729

3 0.939 -2.2039

4 0.9043 -4.0366

5 0.9394 -2.2206

6 0.938 -2.2175

7 0.9029 -4.0565

8 0.9043 -4.0366

9 0.9043 -4.0366

10 0.9394 -2.2206

11 0.9025 -4.066

12 0.9022 -4.0462

13 0.9005 -4.0946

Fig.6. Graph: Bus no Vs Voltage.

VII.CONCLUSIONS

FACTS devices offer a flexible and comprehensive solution to voltage profile control in distribution systems. Traditional methods such as voltage regulators, series, and parallel capacitor switching can be adapted to work more effectively with FACTS control. Methods of power flow analysis of distribution networks are generally different from the Newton–Raphson algorithm used in interconnected system analysis. This paper proposes a line flow-based formulation, which uses line power flows as variables instead of line currents. Since line reactive flows and bus voltage magnitudes are of interest in controlling voltage profiles, the line flow-based algorithm provides a direct and simple approach to handle single or multiple devices. This will enable easy determination of size and placement of such devices. The line flow-based equations have constant coefficient matrices and need no updating during the iterative procedure.

BUSNO ITAGF ITAGTO IDEGREE

1 1 1 1

2 2 5 4

3 6 7 2

4 8 11 4

5 12 13 2

6 14 14 1

7 15 17 3

8 18 18 1

9 19 20 2

10 21 21 1

11 22 22 1

12 23 23 1

13 24 24 1

BUSNO Peff Qeff

1 0.7332 0.4436

2 0.7332 0.4436

3 0.08 0.0514

4 0.5332 0.311

5 0.08 0.058

6 0.046 0.0264

7 0.0596 0.0332

8 0 0

9 0.2026 0.1226

10 0.08 0.058

11 0.034 0.016

12 0.0256 0.0172

13 0.1686 0.0924

LINE NO PLOSS QLOSS

1 0.0216 0.0694

2 0.0002 0.0002

3 0.0104 0.0333

4 0.0002 0.0002

5 0 0

6 0.0001 0.0001

7 0 0

8 0 0

9 0 0

10 0 0

11 0 0

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International Journal of Emerging Technology and Advanced Engineering

744 REFERENCES

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Compensation-Based Power Flow Method for Weekly Meshed Distribution Networks", IEEE Trans. on Power Systems, Vo1.3, No.2, May 1988, pp.753-762.

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AUTHORS PROFILE

Mr. C. Sreenivasulu, Associate Professor in S.S. Institute of Technology in the Department of Electrical and Electronics Engineering, AP, Hyderabad. He received his M.Tech & B.Tech from Sri Venkateswara University, Tirupati, AP, INDIA. Both in Electrical and Electronics Engineering. His research interests are power system opration and control, power system stability, FACTS and new type of A.C transmission system. Email: [email protected].

Dr. G. Madhusudhana Rao, Professor in JJ Group of Institutions, Hyderabad. Obtained his PhD from JNT University Hyderabad and completed M.Tech from JNT University-Hyderabad. He has Published 14 research papers in International Journals and more than 15 International conference papers and more than 10 national conference papers. His area of interest is Power Electronics and Drives with Expert Systems. E-mail: [email protected]