**1. Introduction**

194 Power Quality Harmonics Analysis and Real Measurements Data

Qingzhu, W., Mingli, W., Jianye, C. & Guipping, Z. (2010). Optimal balancing of large

Qingzhu, W., Mingli, W., Jianye, C. & Guipping, Z. (2010). Model for optimal balancing

Sainz, L., Pedra, J. & Caro, M. (2007). Influence of the Steinmetz circuit capacitor failure on

Sainz, L., Pedra, J. & Caro, M. (2009). Background voltage distortion influence on the power

Sainz, L., Caro, M. & Caro, E. (2009). Analytical study on the series resonance in power

Sainz, L., Caro, M., Caro, E. (in press). Influence of Steinmetz Circuit Capacitor Degradation

Sainz, L. & Riera, S. (submitted for publication). Study of the Steinmetz circuit design. *Power* 

Task Force on Harmonics Modeling and Simulations. Modeling and simulation of the

Task Force on Harmonic Modeling and Simulation. Impact of aggregate linear load

*Energy Conversion Congress an Exposition (ECCE)*, pp. 1565-1569, 2010. Sainz, L., Caro, M. & Pedra, J. (2004). Study of electric system harmonic response. *IEEE Transactions on Power Delivery*, Vol. 19, No. 2, April 2004, pp. 868-874. Sainz, L., Pedra, J. & Caro, M. (2005). Steinmetz circuit influence on the electric system

*Systems (RTS 2010)*, pp. 1-6, 2010.

No. 2, April 2007, pp. 960-967.

4, October 2009, pp. 2090-2098.

(DOI: 10.1002/etep.514).

*Systems Research*.

1996, pp. 452–465.

*Research*, Vol. 79, No. 1, January 2009, pp. 161-169.

pp. 1143-1156.

single-phase traction load. *Proceedings of the IET Conference on Railway Traction* 

single-phase traction load based on the Steinmetz's method. *Proceedings of the IEEE* 

harmonic response. *IEEE Transactions on Power Delivery*, Vol. 20, No. 2, April 2005,

the electric system harmonic response. *IEEE Transactions on Power Delivery*, Vol. 22,

electric systems in the presence of the Steinmetz circuit. *Electric Power Systems* 

systems with the Steinmetz circuit. *IEEE Transactions on Power Delivery*, Vol. 24, No.

on Series Resonance of Networks. *European Transactions on Electrical Power*, in press

propagation of harmonics in electric power networks. Part I: Concepts, models and simulation techniques. *IEEE Transactions on Power Delivery*, Vol. 11, No. 1, January

modeling on harmonic analysis: A comparison of common practice and analytical models. *IEEE Transactions on Power Delivery*, Vol. 18, No. 2, April 2003, pp. 625-630.

Switch mode electronic devices including Compact Fluorescent Lamp (CFL) and personal computers introduce capacitive power factor and current harmonics to the power system. Since middle 80's and with the expanding use of nonlinear switch mode electronic loads, concerns arose about their effect on the power systems. In many IEEE documents, it is recommended to study the effect of electronic loads. Switch mode devices have a capacitive power factor between 55 and 93 percent (Allexperts), which can cause the increase of reactive power and power loss. The power loss in an office building wirings due to the current harmonics may be more than twice that of the linear load equipment (Key et al., 1996). Capacity of the transformers may be reduced more than 50 per cent in the presence of harmonic components (Schneider, 2009).

CFL is a more efficient and durable replacement of the traditional incandescent lamp. Replacing traditional light bulbs by CFLs has several advantages including energy saving, increase in the capacity of plants and distribution transformers, peak shaving, less carbon emission and customer costs. On average, 20 percent of the total use of electricity is consumed in lighting (Michalik et al., 1997), (Tavanir). However, the increase in the number of electronic devices especially the CFLs in power systems must be carefully planned. Replacing the incandescent light bulbs with CFLs means replacing the system's major Ohmic load with a capacitive load of high frequency harmonic components. In areas where lighting is a major use of electricity, e.g. places where natural gas or other fossil fuels are used for heating purposes, unplanned replacing of incandescent lamps with CFLs can introduce unexpected negative effects on the system. Also, in areas with a considerable number of other switch mode devices e.g. commercial areas with many office buildings it is important to plan the number of CFLs carefully. Most of the present studies on the effect of switch mode devices are based on tentative experiments and power factor measuring before and after using the devices in the power system (Gonos et al., 1999), and proposing a model for the network has been less discovered.

In order for studying such effects, it is better to classify the system equipment to the substation equipment and consumer side equipment. Dramatic changes in power quality indicators of the distribution systems may cause disorders or even damages in the consumer equipments. Such disorders are especially important for sensitive appliances such as medical and hospital devices.

Stochastic Analysis of the Effect of Using Harmonic Generators in Power Systems 197

the proper harmonic values. Equation 1 shows the mathematical model for a CFL when the

<sup>4</sup>

  (1)

2 1 21 21 2 1 0 0

cos 2 (2 1) cos 2 (2 1)

*CFL n n n n n n*

The more the number of harmonics is, the more accurate the model will be. In this study we use the first five odd harmonics (1, 3, 5, 7, and 9). A schematic of the model is shown in Fig. 4. The power factor of this circuit is 93%. In order for having a flexible model for different

Fig. 3. Sinusoidal voltage and resulting current waveshape for a sample CFL ballast circuit.

*i I n ft I n ft*

market suppliers, the power factor is chosen flexible in the simulation experiments.

voltage is assumed to be a cosine function.

*CFL*

Fig. 2. Simulation of a sample ballast circuit in SPICE.

cos 2

*v V ft*

In this chapter we review our novel approach for studying the effect of switch mode devices and present a novel stochastic modelling approach for analysing the behaviour of the power system in the presence of switch mode devices. We also study the major KPI of the power system and study how these KPI will be affected by adding the current harmonics. Section 2 presents how we obtain an accurate model for CFL based on circuit simulation. This section also defines a general circuit model for the harmonic generating devices. Section 3 presents our novel approach for stochastic modelling of the power system behaviour. In section 4 we summarize the major power system KPI on both substation and consumer sides. We also discuss how the switch mode devices may affect the devices on each side. Section 5 presents our approach for simulating the power system behaviour. Conclusion and discussion are presented in section 6.
