**Comparison of Multi-Line Power Flow **

**Control using Unified power flow controller **

**(UPFC) and Interline **

**Power Flow Controller (IPFC) in Power **

**Transmission Systems **

SUNIL KUMAR JILLEDI M.Tech

Sri Venkateswara University College of Engineering Sri venkateswara University, Tirupathi, Chitoor,

Andhra Pradesh, India.

**Abstract—The Unified power flow controller (UPFC) and Interline power flow controller (IPFC) are two **
**latest generation flexible AC transmission systems (FACTS) controller used to control power flows of **
**multiple transmission lines. This paper presents a mathematical model of UPFC and IPFC, termed as **
**power injection model (PIM). This model is incorporated in Newton- Raphson (NR) power flow algorithm **
**to study the power flow control in transmission lines in which UPFC and IPFC is placed and power flows **
**are compared. A program in MATLAB has been written in order to extend conventional NR algorithm **
**based on this model. Numerical results are carried out on a standard 2 machine 5 bus system. The results **
**are seen with our incoperation of any FACTS device and it has been compared with incorporation of **
**UPFC and IPFC are compared in terms of voltages, active and reactive power flows to demonstrate the **
**performance of the IPFC model. **

**Keywords- flexible AC transmission systems (FACTS), Unified power flow controller (UPFC), interline *** power flow controller (IPFC), power flow control*.

**I. Introduction **

As a result of the Flexible AC Transmission System (FACTS) initiative, considerable effort has been spent in recent years on the development of power electronics-based power flow controllers. From a technical approach standpoint, these controllers either use thyristor-switched capacitors and reactors to provide reactive shunt and series compensation, or employ self-commutated inverters as synchronous voltage sources [I] to modify the prevailing transmission line voltage and thereby control power flow. The latter approach has two inherent advantages over the more conventional switched capacitor- and reactor-based compensators. Firstly, the power electronics-based voltage sources can internally generate and absorb reactive power without the use of ac capacitors or reactors. Secondly, they can facilitate both reactive and real power compensation and thereby can provide independent control for real and reactive power flow. The family of compensators and power flow controllers based on synchronous voltage sources, which are relevant to this paper, are the Static Synchronous (shunt) Compensator (STATCOM) [ 11], the Static Synchronous Series Compensator (SSSC) [ 1,2] and the Unified Power Flow Controller (UPFC) [l, 3,4]. Whereas the STATCOM and SSSC are usually employed as reactive compensators, the UPFC could be considered as a comprehensive real and reactive power compensator capable of in dependently controlling both the real and reactive power flow in the line. This capability of the UPFC is facilitated by its power circuit which is basically an ac to ac power converter, usually implemented by two, back-to-back dc to ac inverters with a common dc voltage link. The output of one inverter is Coupled in series while the output of the other is in shunt with the transmission line With this arrangement, the UPFC can inject a fully controllable voltage (magnitude and angle) in series with the line and support the resulting generalized real and reactive compensation by supplying the real power required by the series inverter through the shunt-connected inverter from the ac bus. (Recall that both the series and shunt dc to ac inverters used in the UPFC implementation can internally generate, without ac capacitors or reactors, the reactive power they exchange at their ac terminals.).

**II. Operating principles of UPFC and IPFC **

**A.** **Principles of UPFC **

The UPFC can provide simultaneous control of transmission voltage, impedance and phase angle of transmission line. It consists of two switching converters as shown in fig1. These converters are operated from a common d.c link provided by a d.c storage capacitor. Converter 2 provides the power flow control of UPFC by injecting an ac voltage with controllable magnitude and phase angle in series with the transmission line via a series transformer. Converter one is to absorb or supply the real power demand by the converter 2 at the common d.c link. It can also absorb or generate controllable reactive power and provide shunt reactive power compensation

Fig.1 Implementation of the UPFC by back-to-back voltage source converters.

The UPFC concept provides a powerful tool for cost effective utilization of individual transmission lines by facilitating the independent control of both the real and reactive power flow and thus the maximization of real power transfer at minimum

losses in the line.

**B.Operating Principle of IPFC **

In its general form the inter line power flow controller employs a number of dc-to-ac converters each providing series compensation for a different line. In other words, the IPFC comprises a number of Static Synchronous Series Compensators (SSSC). The simplest IPFC consist of two back-to-back dc-to-ac converters, which are connected in series with two transmission lines through series coupling transformers and the dc terminals of the converters are connected together via a common dc link as shown in Fig.1.With this IPFC, in addition to providing series reactive compensation, any converter can be controlled to supply real power to the common dc link from its own transmission line

[11].

Fig.2 Schematic diagram of two converter IPFC

**III. Mathematical modeling **

A. Power injection model of UPFC:

transformer impedance are assumed to be constant. No power loss is considered with the UPFC. However the proposed model and algorithm will give the solution of optimal power flow in the transmission lines

Fig.3. Two Voltage source model of UPFC

In this paper the load flow problems are solved by using N-R method in polar co-ordinate form is an iterative method which approximates the set of linear simultaneous equations using Taylor’s series expansion and the terms are limited to first approximation. In the power flow of the transmission line the complex power injected at the ith bus with respect to ground system is

Si= Pi+ j Qi …. (3.1) =Vi I*i …. (3.2) Where i=1, 2, 3………..n.

Where Vi is the voltage at the Ith bus with respect to ground and I*i is the source current injected into the bus.

Pi+ j Qi= ejδ1 I*i …. (3.3) Substituting for

Ii = …. (3.4)

Equating real and imaginary parts

=Real V*i …. (3.5)

=-imag V*i …. (3.6)

Vi =| Vi |ejδ1 …. (3.7) =| | ejδ1k …. (3.8) Real power reactive power can now be expressed as

Pi (Real power) =

|Vi | |cos(θik+δk-δi) …... (3.9) Qi (Reactive power) =

|Vi | |sin (θik+δk-δi) ………..(3.10) i=1, 2, 3,

4………..n-;i slack bus

**B.Mathematical Model of IPFC **

In this section, a mathematical model for IPFC which will be referred to as power injection model is derived. This model is helpful in understanding the impact of the IPFC on the power system in the steady state. Furthermore, the IPFC model can asily be incorporated in the power flow model. Usually, in the steady state analysis of power systems, the VSC may be represented as a synchronous voltage source injecting an almost sinusoidal voltage with controllable magnitude and angle. Based on this, the equivalent circuit of IPFC is shown in Fig.4

In Fig.4, i V , j V and k V are the complex bus voltages at the buses i,jand k respectively, defined as x x x V = V ∠θ (x=i, j and k ) . in Vse is the complex controllable series injected voltage source, defined as in in in Vse = Vse ∠θse (n=j,k ) and in Zse (n=j,k ) is the series coupling transformer impedance. The active and reactive power injections at each bus can be easily calculated by representing IPFC as current source. For the sake of simplicity, the resistance of the transmission lines and the series coupling transformers are neglected. The power injections at buses are summarized as

Pinj,i =∑ _{,} I Vsein binsin( − in)……….. (3.11)
Qinj,i =- ∑ _{,} I Vsein bincos( − in)……… (3.12)
Pinj,i = Vsein binsin( − in) …………. (3.13)
Qinj,i =I Vsein bincos( − in) ………….. (3.14)
Where n=j, k.

Fig.5 Power injection model of two converter IPFC

The equivalent power injection model of an IPFC is shown in Fig.5.As IPFC neither absorbs nor injects active power with respect to the ac system, the active power exchange between

the converters via the dc link is zero, i.e.

Re(VseijI*ji+ VseikI*ki) = 0 …………..(3.15)

Where the superscript * denotes the conjugate of a complex number. If the resistances of series transformers are neglected, (5) can be written as

∑ , , inj,m=0 …………(3.16)

Normally in the steady state operation, the IPFC is used to control the active and reactive power flows in the transmission

lines in which it is placed. The active and reactive power flow control constraints are Pni-Pspecni =0 ……….(3.17)

Qni-Qspecni =0 ……….(3.18) Thus, the power balance equations are as follows

Pgm+Pinj,m-Plm-Pline,m=0 ……….(3.19) Qgm+Qinj,m-Qlm-Qline,m=0 ……….(3.20)

Where gm P and gm Q are generation active and reactive powers, lm P and lm Q are load active and reactive powers. line m P , and line m Q , are conventional transmitted active and reactive powers at the bus m=i, j and k.

**IV Optimal power flow Algorithm: **

In this paper Optimal power flow algorithm is adopted as it offers a number of advantages that is to detect the distance between the desired operating point and the closest unfeasible point. Thus it provides a measure of degree of controllability and it can provide computational efficiency with out destroying the advantages of the conventional power flow when used error feedback adjustment to implement UPFC model. The proposed model and algorithm as follows.

1. Assume bus voltage except at slack bus i.e. p=1, 2, 3……….n; p s Where n is the number of buses.

2. Form Y-bus matrix. 3. Set iteration count k=0. 4. Set the convergence criterion,

5. Calculate the real and reactive power and at each bus where p=1, 2, 3…….n; p s.

6. Evaluate = - and = - at each bus where p=1, 2, 3…….n; p s.

7. Compare each and every residue with and if all of them are then go to step 13. 8. Calculate the elements of Jacobian matrix.

9. Calculate increments in phase angles and voltages.

10. Calculate new bus voltages and respective phase angles = + and = +

11. Replace by and by where p=1, 2, 3…….n; p s. 12. Set k=k+1 and go to step 5.

13. Print the final values of voltage magnitudes and corresponding phase angles.

**V. SOLUTION METHODOLOGY **

The overall solution procedure for Newton-Raphson method with UPFC andIPFC model can be summarized as follows.

1) Read the load flow data and UPFC and IPFC data. 2) Assume flat voltage profile and set iteration count K=0 3) Compute active and reactive power mismatch. Also, the Jacobian matrix using NR method equations [12].

4) Modify power mismatch and jacobian using UPFC and IPFC mathematical model (1) - (12).

5) If the maximal absolute mismatch is less than a given tolerance, it results in output. Otherwise, go to step 6 6) Solve the NR equations; obtain the voltage angle and magnitude correction vector dx.

7) Update the NR solution by x=x+ dx. 8) Set K=K+1, go to step 3.

**VI. CASE STUDY AND RESULTS **

In this section, numerical results are carried out on a standard 2-machine 5-bus system [13] to show the robust performance and capabilities of IPFC model. The test system without FACT device and with incorporation of UPFC and IPFC is shown in below figures.Bus 1 is considered as slack bus, while bus 2 as generator bus and other buses are load buses. For all the cases, the convergence tolerance is 1e-5 p.u. System base MVA is 100.

A. Voltage profile without FACTS devices.

voltage profile has been calculated in the standard IEEE 5 bus system without incorporation of and FACTS device.

B. Active and Reactive powers and losses with out FACTS devies

Power flows has been calculated in the standard IEEE 5 bus system, active power and reactive power and Losses has been calculated without incorporation of FACTS .

.

Bus code

Real power (p.u)

Reactive power(p.u)

Loss(p.u)

1-2 61.5899 85.8253 0.020914

1-3 27.9573 19.0009 0.008952

2-3 15.7541 2.8911 0.001500

2-4 15.3222 1.5307 0.001415

2-5 48.4222 5.3322 0.009603

3-4 40.0464 1.9989 0.000951

4-5 12.6755 0.2453 0.001375

Bus code Voltage(p.u) Angle(deg)

1 1.060000 0.000000

2 0.992621 -1.946578

3 0.981487 -4.584891

4 0.977982 -4.903633

C. Voltage profile with UPFC devices

Bus code Voltage(p.u) Angle(deg)

1 1.060000 0.000000

2 0.998054 -1.035270

3 0.990627 -2.710086

4 0.988389 -2.621289

5 0.972024 -4.307549

D. Active and Reactive powers and losses with UPFC device in the power system. Bus

code

Real power(p.u)

Reactive power(p.u)

Loss(p.u)

1-2 89.6246 86.8027 0.028772 1-3 42.0055 19.2529 0.016028

2-3 24.4368 -3.4026 0.003649

2-4 27.6769 -2.4054 0.004666

2-5 54.6338 5.3060 0.012304

3-4 19.4745 4.0617 0.000420

4-5 06.6428 0.9338 0.000462

E. Voltage profile with IPFC

F. Active and Reactive powers and losses with IPFC device in the power system

Bus code

Real power (p.u)

Reactive power(p.u)

Loss(p.u)

1-2 87.714 74.471 0.010014

1-3 42.945 16.982 0.006952

2-3 26.435 -2.508 0.000500

2-4 29.867 -1.435 0.000415

2-5 48.964 3.950 0.005603

3-4 22.369 2.625 0.000451

4-5 12.140 1.579 0.000275

**VII.CONCLUSION **

A power injection model of theUnified power flow controller (UPFC), Iinter line power flowcontroller (IPFC) and its implementation in Newton-Raphson power flow method has been presented. In this model, the complex impedance of the series coupling transformer and the line charging susceptance are included. Numerical results on the test system have shown the convergence and the effectiveness of the UPFC and IPFC model.A comparative results has been shown on the standard IEEE 5 bus system here voltage profile has been compared without incorporation of FACTS devices and incorporation of UPFC and IPFC has been made. And a comparative Real and Reactive power flow and Losses has been calculated in the IEEE 5 bus standard system. And comparison has been made without incorporation of FACTS devices and incorporation of UPFC and IPFC. With these results the IPFC is very effective FACTS device in the modern power system network.

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