Chapter 2 Principles of Electrical Power Control

This chapter contains a review of the scientific works published till date in the field of power theory for systems with periodic non-sinusoidal waveforms. Nowadays, electrical energy belongs to goods indispensable in everyday life. Dynamic increase in the number of installed nonlinear loads, that are the source of higher harmonics in current and voltage waveforms, results in deterioration of electrical energy parameters. Higher harmonics make the electrical energy quality much worse. The number of power theories and papers concerning these issues give evidence about the importance of the problems of working condition optimisation in power systems. 2.1 Power Theory Power theory is a collection of information about the properties of propagation of energy in electrical circuits. It is the result of research and experience of many generations of scientists and electrical engineers. This concept is often used in phrases such as ‘‘Fryze power theory’’, ‘‘instantaneous pq theory’’, etc. In this context it means a way of interpreting the phenomena occurring in the electrical system proposed by the author’s ideas. The definition in this case was accompanied by the necessary formulas that permit the calculation of properties describing M. Pasko (&) M. Macią _ zek Silesian University of Technology, 2 Akademicka Street, 44-100, Gliwice, Poland e-mail: marian.pasko@polsl.pl M. Macią _ zek e-mail: marcin.maciazek@polsl.pl G. Benysek and M. Pasko (eds.), Power Theories for Improved Power Quality, Power Systems, DOI: 10.1007/978-1-4471-2786-4_2, Springer-Verlag London 2012 13 the electric circuit. Power theories are also used to optimise the operating point of electrical systems. They allow to minimise losses and thereby reduce operating. Every year, dozens of articles have been published on this subject, in one way or another trying to solve the problem of power quality. Why? The solution is purely economic, electricity is a commodity. In the market the economy which wins is the one with the better quality merchandise at a price comparable to others. The second reason is additional operating costs of the power grid. These costs are caused by: • Increased losses in resistive elements; • Increased losses in engines; • Capacitor failures; • The need to increase the efficiency of power source; • Increased current in the neutral wire; • Resonance phenomena (caused by higher harmonics); • Production shutdowns caused by improper operation of protection systems. The methods and ways of describing energy and power-quality properties related to improvement of source and load effectiveness in non-sinusoidal circuits have not been standardised so far. This is proved by the fact that in the past several decades the International Electrotechnical Commission (IEC) has changed reactive power definition several times [1–4]. 2.1. 1 Critical Review of Classical Power Theory, Power in Sinusoidal-Type Waveforms Circuits The following sinusoidal waveforms are used for two-terminal networks as shown in Fig. 2.1: vðtÞ 1⁄4 ffiffiffi 2 p V j j cos xt þ a ð Þ ð2:1Þ iðtÞ 1⁄4 ffiffiffi 2 p I j j cos xt þ b ð Þ ð2:2Þ where |V|, |I|—RMS values of voltage v(t) and current i(t), respectively. The different powers used in discussion of power properties of this circuit are: • instantaneous power p(t) pðtÞ 1⁄4 vðtÞiðtÞ 1⁄4 jV jjIj cos u 1þ cos 2xt þ 2a ð Þ 1⁄2 þjVjjIj sin u sin 2xt þ 2a ð Þ 1⁄4 p1ðtÞ þ p2ðtÞ ð2:3Þ It may be expressed as: pðtÞ 1⁄4 P 1þ cos 2xt þ 2a ð Þ 1⁄2 þ Q sin 2xt þ 2a ð Þ ð2:4Þ 14 M. Pasko and M. Macią _ zek