**1. Introduction**

206 Electrical Generation and Distribution Systems and Power Quality Disturbances

Using the proposed models a small low voltage grid model with six clusters of loads is designed to evaluate the impact of conventional μG and active μG on Power Quality for a

From the results obtained with the virtual lab LV grid, it was possible to conclude that conventional μG slightly increases voltage THD, while active μG reduces voltage THD (up to 30% when compared to voltage THD values obtained with conventional μG),

Even though the μG total power never exceeds 25% of the transformer rated power SN, with a high percentage of non linear loads, as the one considered in the proposed virtual lab LV grid model (85% of the transformer rated power), the active μG presents promising results and it can be concluded that it may be a solution to mitigate some power quality problems.

Ciric, R. M.; Ochoa, L. F.; Padilla-Feltrin, A.; Nouri, H.; *Fault Analysis in Four Wire* 

Ciric, R. M.; Padilla-Feltrin, A.; Ochoa, L. F.; *Power Flow in Four-Wire Distribution Networks –* 

Elgerd, O.; *Electric Systems Theory: an Introduction*, 2nd ed., 1985, International Student

EN 50160, *Voltage Characteristics of Electricity Supplied by Public Distribution Networks*,

EN 50438, *Requirements for the Connection of Micro-Generators in Parallel with Public Low* 

Jensen, M. H.; Bak-Jensen, B.; *Series Impedance of the Four-Wire Distribution Cable with Sector-*

Jensen, M. H.; Bak-Jensen, B.; *Shunt Admittance of the Four-Wire Distribution Cable with Sector-*

Mohan, N.; Undeland, T.; Robbins, W.; *Power Electronics: Converters, Applications and Design*,

Pogaku, N.; Prodanovik, M.; Green, T.; Modeling, *Analysis and Testing of Autonomous* 

Rashid, M.; *Power Electronics Handbook*, 2nd edition, 2007, Academic Press, Elsevier, ISBN 13:

*Voltage Distribution Networks*, European Standard EN 50438, 2007.

Engineering Conference, Perth, Australia, September 2001.

978-0-12-088479-7, ISBN 10: 0-12-088479-8, USA.

2nd Edition, 1995, John Wiley and Sons, ISBN 0-471-58408-8, USA.

*Distribution Networks*; IEE Proceedings on Generation, Transmission and

*General Approach*; IEEE Transactions on Power Systems, Vol. 18, No 4, November

*Shaped Conductors*, Proc. of PPT 2001, IEEE Porto Power Tech Conference, Porto,

*Shaped Conductors*, Proc. of AUPEC'2001, Australasian University Power

*Operation of an Inverter Based Microgrid*, IEEE Transactions on Power Electronics,

guaranteeing an overall Power Quality improvement (Power Factor increase).

Distribution, Vol. 152, No 6, November 2005.

European Standard EN 50160, 2001.

Portugal, September 2001.

Vol. 22, No 2, March 2007.

Edition, Mc Graw Hill, ISBN 0-07-Y66273-8, Singapore.

no-load and a full load scenario.

**5. References** 

2003.

The electricity is invisible and the complexity of mathematical models deviate the graduate students attention from well understanding the underlying main concepts. Interactive educational power system software has become a fundamental teaching tool because it helps in particular the undergraduate students to assimilate theoretical issues and complex models analysis through flexible graphic visualization of data inputs and the results (Abur et al., 2000), (Milano, F., 2005). From the educational point of view software developed for educational purposes should be flexible and interactive, easy to use and reliable. In particular, software for power system education should contain a user interface not only to allow graduate student to analyse and understand the physical phenomena, but also to improve the existing models and algorithms (Mahdad, B., 2010 ).

Flexible AC Transmission Systems (FACTS) philosophy was first introduced by Hingorani (Hingorani N. G., and Gyugyi L, 1999) from the Electric power research institute (EPRI) in the USA in 1988, although the power electronic controlled devices had been used in the transmission network for many years before that. The objective of FACTS devices is to bring a system under control and to transmit power as ordered by the control centers, it also allows increasing the usable transmission capacity to its thermal limits. With FACTS devices we can control the phase angle, the voltage magnitude at chosen buses and/or line impedances.

The avantages of the graphical user interface tool proposed lie in the quick and the dynamic interpretation of the results and the interactive visual communication between users and computer solution processes. The physical and technical phenomena and data of the power flow, and the impact of different FACTS devices installed in a practical network can be easily understood if the results are displayed in the graphic windows rather than numerical tabular forms (Mahdad, 2010).

The application programs in this tool include power flow calculation based Newton-Raphson algorithm, integration and control of different FACTS devices, the economic dispatch based conventional methods and global optimization methods like Parallel Genetic Algorithm (PGA), and Particle Swarm Optimization (PSO). In the literature many educational Graphical tools for power system study and analysis developed for the purpose of the power system education and training (Milano et al., 2005).

Understanding Power Quality Based FACTS

**0**

Fig. 3. Power angle curve

respectively, as follows:

Similarly, for the sending end:

evolution of the active power delivered.

receiving ends as well as line impedance.

**0.5**

**1**

**1.5**

**Active Power (P)**

**2**

**2.5**

Using Interactive Educational GUI Matlab Package 209

**Pmax** 

**0 90 180**

Electrical Angle (δ) (degree)

Complex, active and reactive power flows in this transmission system are defined,

max sin sin *S R*

<sup>2</sup> cos *S R <sup>R</sup>*

max sin sin *S R*

<sup>2</sup> cos *S SR*

Where *VS* and *VR* are the magnitudes of sending and receiving end voltages, respectively, while δ is the phase-shift between sending and receiving end voltages. Fig. 3 shows the

It's clear from the demonstrated equations, that the active and reactive power in a transmission line depend on the voltage magnitudes and phase angles at the sending and

δ

*VV V <sup>Q</sup> <sup>X</sup>*

*V V P P <sup>X</sup>* = = δ

*V V P P <sup>X</sup>* = = δ

*R*

*S*

*R*

*S V VV <sup>Q</sup> <sup>X</sup>* −

\* *S P jQ V I RR RR* =+ = (1)

<sup>−</sup> <sup>=</sup> (3)

= (5)

(2)

(4)

 δ

 δ

δ

**Stable Unstable** 

*Communication : User/Matlab Package* 

Fig. 1. Strategy for understanding power quality based FACTS technology

To carry out comprehensive studies on FACTS devices, to understand the basic principle of FACTS devices, and to determine the role that FACTS technology may play in improving power quality, it is mandatory to have an interactive educational tool using graphic user interface based Matlab, this is the main object of this chapter. This chapter is limited to show how the simplified software package developed works by showing the effects of the introduction of different FACTS devices like shunt Controllers (SVC, STATCOM), series Controllers (TCSC, SSSC) and the hybrid Controllers (UPFC) on a practical network under normal and abnormal situation. Fig.1 shows the strategy for understanding power quality based FACTS technology using an interactive graphical user interface (GUI).

#### **2. Basic principles of power flow control**

To facilitate the understanding of the basic principle of power flow control and to introduce the basic ideas behind the different type of FACTS controllers, the simple model shown in Fig. 2 is used (Mahdad, B., 2010). The sending and receiving end voltages are assumed to be fixed. The sending and receiving ends are connected by an equivalent reactance, assuming that the resistance of high voltage transmission lines is very small. The receiving end is modeled as an infinite bus with a fixed angle of 0°.

Fig. 2. Model for calculation of real and reactive power flow control

*Emission Communication : User/Matlab Package* 

*Models/ Power* 

*User* 

**2. Basic principles of power flow control** 

modeled as an infinite bus with a fixed angle of 0°.

**~** 

*Reception Communication : User/Matlab Package* 

To carry out comprehensive studies on FACTS devices, to understand the basic principle of FACTS devices, and to determine the role that FACTS technology may play in improving power quality, it is mandatory to have an interactive educational tool using graphic user interface based Matlab, this is the main object of this chapter. This chapter is limited to show how the simplified software package developed works by showing the effects of the introduction of different FACTS devices like shunt Controllers (SVC, STATCOM), series Controllers (TCSC, SSSC) and the hybrid Controllers (UPFC) on a practical network under normal and abnormal situation. Fig.1 shows the strategy for understanding power quality

To facilitate the understanding of the basic principle of power flow control and to introduce the basic ideas behind the different type of FACTS controllers, the simple model shown in Fig. 2 is used (Mahdad, B., 2010). The sending and receiving end voltages are assumed to be fixed. The sending and receiving ends are connected by an equivalent reactance, assuming that the resistance of high voltage transmission lines is very small. The receiving end is

> *jX* <sup>∠</sup><sup>δ</sup> *Vs* <sup>∠</sup><sup>0</sup> *VR*

*i j <sup>s</sup> S <sup>R</sup> S*

*Transmission Line* 

Fig. 1. Strategy for understanding power quality based FACTS technology

based FACTS technology using an interactive graphical user interface (GUI).

*ij I*

Fig. 2. Model for calculation of real and reactive power flow control

*Flow, FACTS.. Access to Code* 

*Visual Results* 

*Source* 

*GUI* 

Fig. 3. Power angle curve

Complex, active and reactive power flows in this transmission system are defined, respectively, as follows:

$$S\_{\mathcal{R}} = P\_{\mathcal{R}} + jQ\_{\mathcal{R}} = V\_{\mathcal{R}}I^\* \tag{1}$$

$$P\_{\mathcal{R}} = \frac{V\_{\mathcal{S}} V\_{\mathcal{R}}}{X} \sin \mathcal{S} = P\_{\text{max}} \sin \mathcal{S} \tag{2}$$

$$Q\_{\aleph} = \frac{V\_S V\_{\aleph} \cos \delta - V\_R^2}{X} \tag{3}$$

Similarly, for the sending end:

$$P\_s = \frac{V\_S V\_R}{X} \sin \delta = P\_{\text{max}} \sin \delta \tag{4}$$

$$Q\_s = \frac{V\_s^2 - V\_S V\_k \cos \delta}{X} \tag{5}$$

Where *VS* and *VR* are the magnitudes of sending and receiving end voltages, respectively, while δ is the phase-shift between sending and receiving end voltages. Fig. 3 shows the evolution of the active power delivered.

It's clear from the demonstrated equations, that the active and reactive power in a transmission line depend on the voltage magnitudes and phase angles at the sending and receiving ends as well as line impedance.

Understanding Power Quality Based FACTS

1. Without line compensation, 2. With series compensation, 3. With shunt compensation, 4. and with phase angle control.

considered:

Using Interactive Educational GUI Matlab Package 211

shunt with the line at the midpoint. The four classical cases of power transmission are

The different operation mode can be obtained by appropriately specifying *Vpq* and *<sup>q</sup> I* in the

**Case 1** Power flow controller is off. Then the power transmitted between the sending and

2 <sup>1</sup> sin( ) *l*

**Case 2** Assume that 0 *<sup>q</sup> I* = and*V jkXI pq* = − , the voltage source acts at the fundamental frequency precisely as a series compensating capacitor. The degree of series compensation is

> 2 <sup>2</sup> sin( ) (1 )

**Case 3** The reactive current source acts like an ideal shunt compensator which segments the transmission lines into independent parts, each with an impedance of X/2, by generating the reactive power necessary to keep the mid-point voltage constant, independently of angle

2

<sup>0</sup> <sup>20</sup> <sup>40</sup> <sup>60</sup> <sup>80</sup> <sup>100</sup> <sup>120</sup> <sup>140</sup> <sup>160</sup> <sup>180</sup> <sup>0</sup>

1

normal shunt compensation serie compensation

3

Electrical Angle

<sup>2</sup> sin( ) <sup>2</sup>

δ

δ

δ

− (7)

= (8)

(6)

*<sup>V</sup> <sup>P</sup> X* =

Where δ is the angle between the sending and receiving-end voltage phasors.

defined by coefficient k ( 0 1 ≤ ≤ *k* ), the relationship between P and δ becomes:

*<sup>V</sup> <sup>P</sup> X k* <sup>=</sup>

3

*<sup>V</sup> <sup>P</sup> X*

2

generalized schematic power flow controller is shown in Fig. 5.

δ, for this case the relationship between P and δ becomes:

0.5 1 1.5 2 2.5 3 3.5 4

Fig. 6. Active power transit with different compensation types

Active Power Transit

receiving end generators can be expressed by:

## **2.1 Example of power flow control**

The concepts behind FACTS controller is to enable the control of three parameters which are:


Fig. 4. Three vector control structure (Voltage control -Active power control - Reactive power control) based FACTS technology

The ability to control power rapidly, within appropriately defined boundaries, can increase transient and dynamic stability as well as the damping of the system.

The following section illustrate the basic principle of the FACTS Controllers designed to be integrated in a practical network. Fif. 4 shows the three mode control related to FACTS compensators.

Fig. 5. Generalized schematic of power flow controller

The simplified genralized power flow controller consists of two controllable elements, a voltage source (*Vpq* ) inserted in series with the line, and a current source ( *<sup>q</sup> I* ), connected in shunt with the line at the midpoint. The four classical cases of power transmission are considered:


210 Electrical Generation and Distribution Systems and Power Quality Disturbances

The concepts behind FACTS controller is to enable the control of three parameters which

3. And transmission line reactance (*X*) in real-time and, thus vary the transmitted power

i j *Pij*

*Vm+Vp* 

*Iq* 

*Qij Qi*

ij <sup>−</sup><sup>P</sup>

*Vi*

ij <sup>⊕</sup><sup>Q</sup>

Fig. 4. Three vector control structure (Voltage control -Active power control - Reactive

transient and dynamic stability as well as the damping of the system.

Fig. 5. Generalized schematic of power flow controller

The ability to control power rapidly, within appropriately defined boundaries, can increase

The following section illustrate the basic principle of the FACTS Controllers designed to be integrated in a practical network. Fif. 4 shows the three mode control related to FACTS

*X/2 X/2* 

**~** 

*Vpq* 

~ **~ ~** 

Vm

The simplified genralized power flow controller consists of two controllable elements, a voltage source (*Vpq* ) inserted in series with the line, and a current source ( *<sup>q</sup> I* ), connected in

*Vs Vr* 

Iq

**2.1 Example of power flow control** 

according to system condition.

ij <sup>−</sup><sup>Q</sup>

ij <sup>⊕</sup><sup>P</sup>

power control) based FACTS technology

1. Voltage magnitude (V)

2. Phase angle (δ)

compensators.

are:


The different operation mode can be obtained by appropriately specifying *Vpq* and *<sup>q</sup> I* in the generalized schematic power flow controller is shown in Fig. 5.

**Case 1** Power flow controller is off. Then the power transmitted between the sending and receiving end generators can be expressed by:

$$P\_1 = \frac{V^2}{X\_1} \text{sin(\(\delta\))}\tag{6}$$

Where δ is the angle between the sending and receiving-end voltage phasors.

**Case 2** Assume that 0 *<sup>q</sup> I* = and*V jkXI pq* = − , the voltage source acts at the fundamental frequency precisely as a series compensating capacitor. The degree of series compensation is defined by coefficient k ( 0 1 ≤ ≤ *k* ), the relationship between P and δ becomes:

$$P\_z = \frac{V^2}{X(1-k)}\sin(\delta)\tag{7}$$

**Case 3** The reactive current source acts like an ideal shunt compensator which segments the transmission lines into independent parts, each with an impedance of X/2, by generating the reactive power necessary to keep the mid-point voltage constant, independently of angle δ, for this case the relationship between P and δ becomes:

$$P\_3 = \frac{2V^2}{X} \sin(\frac{\delta}{2})\tag{8}$$

Fig. 6. Active power transit with different compensation types

**Case 4** The basic idea behind the phase shifter is to keep the transmitted power at a desired level independently of angle δ in a predetermined operating range. Thus for example, the power can be kept at its peak value after angle δ exceeds π/2, by controlling the amplitude of quadrature voltage*Vpq* . Fig. 6 shows the evolution of active power transit based different compensation types.

$$P\_4 = \frac{V^2}{X}\sin(\delta + \alpha) \tag{9}$$

Understanding Power Quality Based FACTS

**Case 1: Capacitive Series Compensation at line 1-3** 

**G1** 

**G1** 

Xc=5.0081 Ω

*Series FACTS Controller*

Xc=6 Ω

*Series FACTS Controller*

active power flow with another degree of compensation ( 6 *XC* = Ω ).

1750 MW

Fig. 8. Load flow solution with consideration of dynamic compensators: Case1

1841.73 MW

Fig. 9. Load flow solution with consideration of dynamic compensators: Case1

92.09%

15.83%

87.50%

Using Interactive Educational GUI Matlab Package 213

If the dynamic series FACTS Controller (type capacitive)installed at line 1-3 adjusted to deliver a capacitive reactance, it decreases the line's impedance from 10Ω to 4.9919Ω, so that power flows through the lines 1-2, 1-3, and 2-3 will be 250 MW, and 1750 MW, respectively. Fig. 8 illustrates the per cent loading of lines. It is clear that if the series capacitor is adjustable, then other power flow levels may be realized in accordance with the ownership, contract, thermal limitations, transmission losses, and wide range of load and generation schedules. Fig. 8 shows clearly the effect of series capacitive compensation to control the

**1 2** 

250 MW

**G2** 25%

1250 MW

158.27 MW

**G2** 

1158.27MW

92.66%

100%

2000MW 1000MW

**3** 

Load 3000MW

**1 2** 

2000MW 1000MW

**3** 

Load 3000MW

#### **2.2 Role of FACTS devices in power system operation and control**

To further understand the strategy of FACTS devices in power system operation and control, consider a very simplified case in which generators at two different regions are sending power to a load centre through a network consisting of three lines.

Fig. 7 shows the topology of simple electrical network, suppose the lines 1-2, 1-3 and 2-3 have continuous ratings of 1000MW, 2000MW, and 1250MW, respectively, and have emergency ratings of twice those numbers for a sufficient length of time to allow rescheduling of power in case of loss of one of these lines (Hingorani, N. G., and Gyugyi L, 1999).

For the impedances shown, the maximum power flow for the three lines are 600, 1600, and 1400, respectively, as shown in Fig. 7, such a situation would overload line 2-3 (loaded 1600 MW for its continuous rating of 1250 MW), and there for generation would have to be decreased at unit 2, and increased at unit 1, in order to meet the load without overloading line 2-3. The following simplified studies cases demonstrate the main objective of integration of FACTS technology in a practical power system to enhance power system security.

Fig. 7. Topology of the electrical network 3-bus with technical characteristics without dynamic compensators

**Case 4** The basic idea behind the phase shifter is to keep the transmitted power at a desired level independently of angle δ in a predetermined operating range. Thus for example, the power can be kept at its peak value after angle δ exceeds π/2, by controlling the amplitude of quadrature voltage*Vpq* . Fig. 6 shows the evolution of active power transit based different

> 2 <sup>4</sup> sin( ) *<sup>V</sup> <sup>P</sup> X* = + δ α

To further understand the strategy of FACTS devices in power system operation and control, consider a very simplified case in which generators at two different regions are

Fig. 7 shows the topology of simple electrical network, suppose the lines 1-2, 1-3 and 2-3 have continuous ratings of 1000MW, 2000MW, and 1250MW, respectively, and have emergency ratings of twice those numbers for a sufficient length of time to allow rescheduling of power in case of loss of one of these lines (Hingorani, N. G., and Gyugyi L,

For the impedances shown, the maximum power flow for the three lines are 600, 1600, and 1400, respectively, as shown in Fig. 7, such a situation would overload line 2-3 (loaded 1600 MW for its continuous rating of 1250 MW), and there for generation would have to be decreased at unit 2, and increased at unit 1, in order to meet the load without overloading line 2-3. The following simplified studies cases demonstrate the main objective of integration of

> Load 3000MW

1600 MW

128%

1250 MW

**3** 

Fig. 7. Topology of the electrical network 3-bus with technical characteristics without

*10 Ω 5 Ω* 

2000 MW

**2.2 Role of FACTS devices in power system operation and control** 

sending power to a load centre through a network consisting of three lines.

FACTS technology in a practical power system to enhance power system security.

**1 2** 

**2000MW 1000MW**  600 MW

*10 Ω* 

60%

 1000 MW

(9)

**G2** 

*Overload at line 2-3* 

compensation types.

1999).

**G1** 

*Risk o f Black out* 

dynamic compensators

1400 MW

70%
