Performance Analysis of Some FACTS Devices Using Newton Raphson Load Flow Algorithm

Biswajeet Kr Medhi Electrical Engineering Department

Assam Engineering College Guwahati, India

biswa3009@gmail.com

Satyajit Bhuyan Electrical Engineering Department

Assam Engineering College Guwahati, India

satyajitbhuyan1962@gmail.com

Abstract—A comparative study and performance analysis is done for a number of FACTS devices in this paper. The models used are incorporated in an existing Newton Raphson Load Flow (NRLF) algorithm using standard IEEE 5 bus and 30 bus system. Problem of initialization for proper convergence of load flow is studied and findings are presented. Results are presented for comparison of performance analysis and evaluation of degree of suitability of selected FACTS devices.

Keywords— Newton-Raphson load flow, FACTS, TCSC, STATCOM, UPFC, Jacobian, MATLAB.

I. INTRODUCTION FLEXIBLE AC transmission system is “A power electronic based system and other static equipment that provide control of one or more AC transmission system parameters to enhance controllability and increase power transfer capability”. Its first concept was introduced by N.G Hingorani, in 1988 [1]. Now- a-days multiple and multi-type FACTS devices are becoming interesting areas for the researchers [2]. Flexible AC transmission systems, so-called FACTS devices, can help reduce power flow on overloaded lines, which would result in an increased load ability of the power system, fewer transmission line losses, improved stability and security and, ultimately, a more energy-efficient transmission system [3].The transmission facilities are being overused owing to the higher industrial demands and deregulation of the power supply industry. Thus there is a need for exploring new ways for maximizing the power transfer capability of existing transmission facilities while, at the same time, maintaining acceptable levels of network reliability and stability [4]. This scenario makes necessary the development of power electronic based devices for high performance control of the power network. The FACTS controllers provide the most useful means and thus are used in regulating the power flows, maintaining transmission voltages within limits and mitigate the dynamic disturbance. UPFC and STATCOM are effective and robust devices for power system stability [5]. Static models of three FACTS devices consisting of SVS model of Unified Power Flow Controller (UPFC), Thyristor Controlled Series Capacitor (TCSC) and STATCOM have been selected for the steady-state analysis [6]. To minimize the power transmission loss, reactive power compensation is used. Reactive power compensation is also

used to maintain power transmission capability and to maintain the supply voltage within the specified limits. Control of line impedance of the transmission line is known as series compensation. When the line impedance changes it means that either capacitive or inductive compensation can be obtained which in turn enables to control active power. TCSC (Thyristor Controlled Series Capacitor) connected in series with the transmission line provides means to change the impedance of the line thus providing an option to enhance the power transfer capability. Shunt connected compensators are used to increase steady state transmittable power and to control voltage profile. One such shunt connected compensator is the STATCOM (Static Compensator) that comes under FACTS device category. The Synchronous voltage source UPFC model [7] injects into the system a voltage of variable magnitude and angle in series with the line. These parameters adjust automatically so as to control the active and the reactive powers exchanged between the UPFC and the AC system. In this paper FACTS device models are incorporated in Newton Raphson Load Flow (NRLF) algorithm in order to investigate the control of power flow and improvement of voltage. All the equations are then combined in to one set of non-linear algebraic equations. A jacobian matrix is then formed which is non symmetric in nature.

II. MODEL OF FACTS DEVICES

A. Thyristor Controlled Series Compensator A TCSC can be defined as a capacitive reactance compensator which consists of a series capacitor bank shunted by a thyristor-controlled reactor in order to provide a smoothly variable series capacitive reactance [8]. In a practical TCSC implementation, several such basic compensators may be connected in series to obtain the desired voltage rating and operating characteristics. However, the basic idea behind the TCSC scheme is to provide a continuously variable capacitor by means of partially canceling the effective compensating capacitance. A TCSC is a series-controlled capacitive reactance that can provide continuous control of power on the ac line over a wide range. A simple understanding of TCSC functioning can be obtained by analyzing the behavior of a variable inductor connected in parallel with a Fixed Capacitor. The maximum voltage and current limits are design values for

which the thyristor valve, the reactor and capacitor banks are rated to meet specific application requirements.

Figure 1: General model of TCSC

B. Static Synchronous Compensator(STATCOM) STATCOM is a Static synchronous generator operated as a shunt-connected static VAR compensator whose capacitive or inductive output current can be controlled independent of the ac system voltage. STATCOM is one of the key FACTS Controllers. A STATCOM is a controlled reactive power source. It provides voltage support by generating or absorbing capacitors banks. It regulates the voltage at its terminals by compensating the amount of reactive power in or out from the power system [5]. When the system voltage is low the STATCOM injects the reactive power to and when the voltage is high it absorbs the reactive power. The reactive power is fed from the Voltage Source Converter (VSC) which is connecting on the secondary side of a coupling transformer as shown in the Fig 2. By varying the magnitude of the output voltage the reactive power exchange can be regulated between the convertor and AC system.

Figure 2: General Model of STATCOM

C. Synchronous Voltage Source UPFC model The SVS is the solid-state synchronous voltage source employing an appropriate DC to AC inverter with gate turn-off thyristor used for series compensation of transmission lines [7]. The series controller could be variable impedance, such as capacitor, reactor, etc., or a power electronic based variable source of main frequency, sub synchronous and harmonic frequencies to serve the desired need. They inject voltage in series with the line. As long as the voltage is in phase quadrature with the line current, the series controller only supplies or consumes variable reactive power. Any other phase relationship will involve handling of real power as well [7]. SVS is one such series controller.

III. IMPLEMENTATION The basic power flow equations are given by (1) (2) Where i=1, 2,…..n n is the number of buses. All other symbols carry their usual meaning. The Jacobian matrix gives the linearized relationship between small changes in ∆δi

k and voltage magnitude ∆Vik with the

small changes in real and reactive power ∆Pik and ∆Qi

k.

A. Implementation of TCSC in existing NRLF Algorithm The effect of TCSC on the network can be seen as a controllable reactance inserted in the related transmission line. The model of the network with TCSC is shown in Fig 3.

Figure 3: TCSC connected between bus i and j The controllable reactance, Xc, is directly used as the control variable to be implemented in the power flow equation. The power flow equations of the branch can be derived as follows. (3) (4) Where δij = δi – δj All symbols carry their usual meaning. Here, the only difference between normal line power flow equation and the TCSC line power flow equation is the controllable reactance Xc. The linearized Newton equations of the compensated transmission line are given in “(5)”, where the variable reactance of the TCSC is taken as the state variable.

(5)

B. Implementation of STATCOM in existing NRLF Algorithm The effect of STATCOM on the network can be seen as a controllable static synchronous generator operated as a static VAR compensator whose capacitive and inductive output currents are controlled to control the bus voltage with which it is connected. Fig 4. STATCOM connected at bus i. Let the STATCOM be connected at bus i as shown in the fig 4. The general power flow equation of the STATCOM connected bus will be At node i, Pi = Vi

2gii + ViVj(gijcos(δij)+bijsin(δij)) + Vi

2gsh – ViVsh(gshcos(δis)+bshsin(δis)) (6) Qi = -Vi

2bii + ViVj(gijsin(δij)-bijcos(δij)) – Vi

2bsh – ViVsh(gshsin(δis) – bshcos(δis)) (7)

The reactive power injected by STATCOM to the bus is given by Qstat = -Vi

2bsh + ViVsh(bshcosδish – gshsinδis) (8) Where δij = δi – δj

δish = δi – δsh

δsh is the voltage angle of STATCOM. The linearized Newton equations of the compensated bus are given in “(9)”, where the variable phase angle δsh, and the variable voltage magnitude of the STATCOM are taken as the state variables. (9)

C. Implementation of SVS UPFC model in existing NRLF Algorithm

The effect of SVS on the network can be seen as a controllable voltage source inserted in series with the related transmission line. The model of the network with TCSC is shown in Fig 5. Fig.5 SVS connected between i amd j bus The general power flow equation of the buses between which the SVS is connected will be. At node i, Pi = Vi

2gii + ViVj(gijcos(δij)+bijsin(δij)) – ViVs(giicos(δis)+biisin(δis)) (10)

Qi = -Vi2bii + ViVj(gijsin(δij) - bijcos(δij)) - ViVs(giicos(δis) - biisin(δis)) (11)

At node j, Pi = Vj

2gjj + ViVj(gjicos(δji)+bjisin(δji)) – VjVs(gjicos(δjs)+bjisin(δjs)) (12)

Qi = -Vj2bjj + ViVj(gjisin(δji) – bjicos(δji))

- VjVs(gjicos(δjs) – bjisin(δjs)) (13) The linearized Newton equations of the compensated transmission line are given in “(14)”, where the variable phase angle δs, and variable magnitude Vs are taken as the state variable. (14)

IV. SIMULATION AND RESULTS The load flow tests are done in a standard IEEE 5 bus as well as 30 bus systems.

Fig.6 IEEE 5 bus system

Fig.7 IEEE 30 bus system

The TCSC is connected between lake bus and main bus for IEEE 5 bus system to control real power flow at 21MW and between bus number 6 and 7 for IEEE 30 bus system to control real power flow at 42MW. The STATCOM is connected at lake bus in case of 5 bus systems and for 30 bus system it is connected to bus 30. The SVS is connected between lake bus and main bus for 5 bus system to control real power flow at 40MW and reactive power at 2MVAR whereas for 30 bus system the SVS is connected between bus number 6 and 8 to control the real power flow at 33MW and reactive power at 6MVAR from bus 8 to bus 6. The results as shown in tabular form have been obtained and are compared with the uncompensated system.

TABLE I. BUS VOLTAGE MAGNITUDE AND ANGLE COMPARISON FOR 5 BUS SYSTEM

Uncompensated system Voltage

Compensated system Voltage

With TCSC With STATCOM With SVS Magnitude (PU)

Angle (degrees)

Magnitude (PU)

Angle (degrees)

Magnitude (PU)

Angle (degrees)

Magnitude (PU)

Angle (degrees)

0.9872(Lake) -4.637 0.9870 -4.727 1.0000 -4.840 0.9790 -5.724

0.9841(Main) -4.957 0.9844 -4.811 0.9944 -5.109 0.9948 -3.181

TABLE II. BUS VOLTAGE MAGNITUDE AND ANGLE COMPARISON FOR 30 BUS SYSTEM

Uncompensated system Voltage

Compensated system Voltage

With TCSC With STATCOM With SVS Magnitude (PU)

Angle (degrees)

Magnitude (PU)

Angle (degrees)

Magnitude (PU)

Angle (degrees)

Magnitude (PU)

Angle (degrees)

1.1010(bus 6) -11.06 1.1013 -11.23 1.1010 -11.06 1.008 -11.04

1.0022(bus 7) -12.86 1.0007 -12.67 1.0023 -12.86 1.045 -12.85

1.0100 (bus 8) -11.82 1.0100 -11.97 1.0100 -11.82 1.0100 -11.41

0.9918(bus30 -17.63 1.0074 -10.04 1.000 -17.75 0.9900 -17.55

Bus voltage almost remains unaffected with inclusion of TCSC in both the system. Inclusion of STATCOM maintains

bus voltage at 1pu for the bus where STATCOM is connected. For both the systems there is a negligible voltage sag in the sending end of the line where SVS is connected.

TABLE III. BUS POWERS FOR 5 BUS SYSTEM

Bus

Generated power Uncompensated system With TCSC With

STATCOM With SVS

P Q P Q P Q P Q

North 131.1 90.8 131.1 90.9 131.

1 85.3 130.9 94.9

South 40 -61. 6 40 -61.

8 40 -77. 1 40 -66.7

TABLE IV. BUS POWERS FOR 30 BUS SYSTEM

Bus number

Generated power Uncompensated system With TCSC With

STATCOM With SVS

P Q P Q P Q P Q

1 2.61 -0.164 2.61 -0.164 2.61 -0.165 2.61 -0.160

2 0.40 0.498 0.40 0.488 0.40 0.496 0.4 0.511

5 0.00 0.371 0.00 0.385 0.00 0.370 0.0 0.378

8 0.00 0.379 0.00 0.369 0.00 0.372 0.00 0.343

11 0.00 0.169 0.00 0.168 0.00 0.167 0.00 0.173

13 0.00 0.109 0.00 0.108 0.00 0.107 0.00 0.113 P in MW

Q in MVAR Generation remain unaffected with the inclusion of TCSC. With the inclusion of STATCOM the slack generator reduces its reactive power generation by almost 6% compared to the base case for 5 bus system, whereas for 30 bus system all the generator reduces reactive power generation by a small amount. Inclusion of SVS results in generation of 4.5% more reactive power by slack bus for 5 bus systems and for 30 bus system reactive power generation increases in all the generator buses except for bus number 8.

A. Power flow comparison of TCSC

TABLE V. POWER FLOW COMPARISON OF TCSC WITH BASE CASE FOR 5 BUS SYSTEM

From To Power Flows

Without TCSC With TCSC bus Bus P(MW) Q(MVAR) P(MW) Q(MVAR)

Lake Main 19.4 2.9 21.0 2.5

TABLE VI. POWER FLOW COMPARISON OF TCSC WITH BASE CASE FOR 30 BUS SYSTEM

From To Power Flows

Without TCSC With TCSC bus Bus P(MW) Q(MVAR) P(MW) Q(MVAR)

6 7 38.1 -3.1 42.0 -5.5

The TCSC upholds the target value, which is achieved with 72% series capacitive compensation for Lake–Main line of 5 bus system and 61.34% series capacitive compensation of the

line 6-7 for 30 bus system. From the load flow results it is evident that TCSC controls only the real power flow through a line and reactive power is almost unaffected. Thus TCSC has its application only when there is a need to control real power flow and also to change power flow routes.

B. Power flow comparison of STATCOM The 5 bus network is modified to include one STATCOM connected at Lake bus, to maintain the nodal voltage magnitude at 1 p.u. The power flow result indicates that the STATCOM generates 20.5MVAR in order to keep the voltage magnitude at 1 p.u. at Lake bus.

TABLE VII. POWER FLOW COMPARISON OF STATCOM WITH BASE CASE FOR 5 BUS SYSTEM

From To Power Flows

Without STATCOM With STATCOM bus bus P(MW) Q(MVAR) P(MW) Q(MVAR)

North Lake 41.8 16.8 42.0 11.3

South Lake 24.5 -2.5 24.5 -9.5

Lake Main 19.4 2.9 19.6 11.2

The STATCOM parameters associated with this amount of reactive power generation are Vsh=1.0205 p.u. and δsh=4.83 degrees. Use of the STATCOM results in an improved network voltage profile, except at Elm, which is too far away from Lake to benefit from the influence of the STATCOM. The slack generator reduces its reactive power generation by almost 6% compared to the base case, and the reactive power exported from North to Lake reduces by more than 32.74 %.

TABLE VIII. POWER FLOW COMPARISON OF STATCOM WITH BASE CASE FOR 30 BUS SYSTEM

From To Power Flows

Without STATCOM With STATCOM bus bus P(MW) Q(MVAR) P(MW) Q(MVAR)

27 30 7.1 1.7 7.1 9

29 30 3.7 6.0 3.7 1

The STATCOM generates -1.20MVAR and parameter associated with this amount of reactive power generation are Vsh=1.0012 p.u. and δsh = -17.75 degrees. The reactive power transmitted from bus 27 to 30 and from 29 to 30 reduces to almost 50%

C. Power flow comparison of SVS

TABLE IX. POWER FLOW COMPARISON OF SVS WITH BASE CASE FOR 5 BUS SYSTEM

From To Power Flows

Without SVS With SVS bus bus P(MW) Q(MVAR) P(MW) Q(MVAR)

Lake Main 19.4 2.9 40.0 2.0

TABLE X. POWER FLOW COMPARISON OF SVS WITH BASE CASE FOR 5 BUS SYSTEM

From To Power Flows

Without SVS With SVS bus Bus P(MW) Q(MVAR) P(MW) Q(MVAR)

6 8 29.5 -8.7 33.0 -6.0

The most noticeable changes are as follows: there is 16.73% increase of active power flowing towards Lake through North–Lake line and 35.2% increase in active power flowing towards Lake through South–Lake line for 5 bus system. The increase is in response to the large amount of active power demanded by the series converter. The SVS parameters associated with this amount of real and reactive power flow control are Vs= 0.0595 p.u. and δs= -115.19 degrees. For 30 bus system the active power flow increases to 3 MW in 8-28 line from 0.6MW. The parameters associated with this amount of real and reactive power flow control are Vs= 0.0112 p.u. and δs= -116.62 degrees.

V. INITIALIZATION OF FACTS PARAMETERS To achieve a strong convergence of the NRLF algorithm proper initialization of FACTS parameters is very necessary. Without proper initialization the NRLF algorithm may sometimes diverge or take more iteration to converge.

A. Effect of initialization of TCSC parameters Simulation results shows that choosing initial TCSC reactance at around 50% of the line reactance gives faster convergence for both 5 and 30 bus system. It is to be noted that if TCSC initial reactance is chosen a low or high value then in some cases it might give faster convergence, whereas in some cases it take more number of iterations to converge depending upon the amount of real power flow to be controlled. Hence it will be a good practice if the initial TCSC reactance is chosen at 50% of the line reactance.

B. Effect of initialization of STATCOM parameters

TABLE XI. IMPACT OF STATCOM INITIALIZATION

Initial value of STATCOM parameters

Number of iterations required

Voltage Magnitude

( PU)

Angle (radian)

5 bus systems

30 bus systems

1 0 5 5

0.7 0 5 5

1.3 0 5 5

1 -1 7 7

1 1 7 7

1 -2 10 10

1 2 10 10

STATCOM are used to maintain the bus voltage within limits. It is a good practice to keep the STATCOM variable voltage

magnitude at an initial value same as that of the desired voltage magnitude of the bus to which it is connected. With regard to initial assumption of the STATCOM voltage angle the following conclusion is obtained. 0.7 1.3 Fig.8 Range if initialization of STATCOM variable voltage The range of initial variable voltage of STATCOM for quicker convergence of the load flow is 0.3 < Vs < 1.3 with angle fixed at 0 radians.

C. Effect of initialization of SVS UPFC model parameters Various initial assumptions of the SVS parameter have been made and the load flow converges quickly for a particular combination of the series variable voltage magnitude and angle. The following combination of voltage magnitude and angle has been simulated and findings have been presented.

TABLE XII. IMPACT OF SVS INITIALIZATION

Initial value of SVS parameters

Number of iterations required

Voltage Magnitude

( PU)

Angle (radian) fixed at

5 bus systems

30 bus systems

0.01 -2.25 12 11

0.03 -2.25 6 7

0.05 -2.25 5 9

0.07 -2.25 6 8

0.09 -2.25 6 7

Initial value of SVS parameters

Number of iterations required

Voltage Magnitude

fixed at 0.05pu

Angle (radian)

5 bus systems

30 bus systems

0.05 2.25 9 9

0.05 1.25 6 7

0.05 0.25 12 10

0.05 -1.25 6 7

0.05 -2.25 5 9

It is interesting to note that proper initialization takes a major part in the suitable convergence of load flow. For SVS model the range of variable voltage is taken as 0.01 < Vs < 0.09 pu for a fixed δs of -2.25 radian. Similarly for a fixed value of Vs of 0.05pu the range of angle is taken as -2.25< δs <2.25 radian. Best combination is obtained for 0.05pu magnitude of voltage and -1.25 radian of angle.

VI. CONCLUSION In this paper, models of some FACTS devices (TCSC, STATCOM, and SVS) have been incorporated in the existing NRLF algorithm to observe the impact of these devices on the system performance. The performance comparison of the devices is done and the findings are presented. The suitability of the device depends on the system parameter to be controlled. For active power flow control TCSC is much preferred to others. It also increases system stability [11]. STATCOM is suitable for application when system bus voltage is to be maintained within desired limit. For control of both active and reactive power flows, SVS is very much suitable. It is also observed that load flow convergence strongly depends on initial assumption of the FACTS parameter. Improper initialization takes more processing time and more number of iterations. Sometime this may even lead to divergence of the load flow. This problem of initialization of device variables has been investigated thoroughly in this paper and findings are presented. The simulation tool used is MATLAB 7.8.0 (R2009a).

References [1] Hingorani, N.G., “Flexible AC Transmission Systems’, IEEE Spectrum,

vol 30, issue 4, pp 41–48, April 1993. [2] Narayana Prasad Padhy, M.A. Abdel Moamen, “Power flow control and

solutions with multiple and multi-type FACTS devices” , Electric Power Systems Research 74 (2005) 341–351

[3] Ghahremani.E., Kamwa.I., “Optimal placement of multiple-type FACTS devices to maximize power system loadability using a generic graphical user interface”, Power Systems, IEEE Transactions on, Vol 28, Issue 2, May 2013.

[4] Ying Xiao, Y.H.Song and Chen-Ching Liu, “Available Transfer Capability Enhancement Using FACTS Devices”, IEEE Transactions On Power Systems, Vol. 18, No. 1, pp. 305-312, February 2003.

[5] Amara. S, Hsan. H.A, “Power system stability improvement by FACTS devices: A comparison between STATCOM, SSSC and UPFC”, Renewable Energies and Vehicular Technology (REVET), 2012 First International Conference on, ISBN: 978-1-4673-1168-7, page 360-365, 26-28 March 2012.

[6] Tiwari. R, Niazi. K.R, Gupta. V, “Optimal location of FACTS devices for improving performance of the power systems”, Power and Energy Society General Meeting, 2012 IEEE, ISSN :1944-9925, pp 1-8, 22-26 July 2012

[7] C. R. Foerte-Esquivel, and E. Acha, “Unified power flow controller: a critical comparison of Newton-Raphson UPFC algorithms in power flow studies”, IEE proceedings, vol. 144. No- 5, september 1997.

[8] N. G. Hingorani and L. Gyugyi, “Understanding FACTS Concepts and Technology of Flexible AC Transmission Systems”, IEEE Press. New York, 1999.

[9] Sunil Kumar Singh, Lobzang Phunchok and Y.R.Sood, �Voltage Profile and Power Flow Enhancement with FACTS Controllers”, International Journal Of Engineering Research & Technology, Vol. 1 Issue 5, July – 2012.

[10] C. R. Foerte-Esquivel, E. Acha, and H. Amhriz-Perez, “A Comprehensive Newton-Raphson UPFC Model for the Quadratic Power Flow Solution of Practical Power Networks,” IEEE transactions on power systems, vol. 15. no.1, february 2000

[11] Xia Jiang, Joe H. Chow, Abdel-Aty Edris, Bruce Fardanesh, and Edvina Uzunovic, “Transfer Path Stability Enhancement by Voltage-Sourced Converter-Based FACTS Controllers”, IEEE Transactions on Power Delivery, Vol. 25, No. 2, pp. 1019-1025, April 2010.