**1. Introduction**

The presence of non-linear loads and the increasing number of distributed generation power systems (DGPS) in electrical grids contribute to change the characteristics of voltage and current waveforms in power systems, which differ from pure sinusoidal constant amplitude signals. Under these conditions advanced signal processing techniques are required for accurate measurement of electrical power quantities. The impact of non-linear loads in electrical power systems has been increasing during the last decades. Such electrical loads, which introduce non-sinusoidal current consumption patterns (current harmonics), can be found in rectification front-ends in motor drives, electronic ballasts for discharge lamps, personal computers or electrical appliances. Harmonics in power systems mean the existence of signals, superimposed on the fundamental signal, whose frequencies are integer numbers of the fundamental frequency. The electric utility companies should supply their customers with a supply having a constant frequency equal to the fundamental frequency, 50/60 Hz, and having a constant magnitude. The presence of harmonics in the voltage or current waveform leads to a distorted signal for voltage or current, and the signal becomes non-sinusoidal signal which it should not be. Thus the study of power system harmonics is an important subject for power engineers.

The power system harmonics problem is not a new problem; it has been noticed since the establishment of the ac generators, where distorted voltage and current waveforms were observed in the thirtieth of 20th century [2].

Concern for waveform distortion should be shared by all electrical engineers in order to establish the right balance between exercising control by distortion and keeping distortion under control. There is a need for early co-ordination of decisions between the interested parties, in order to achieve acceptable economical solutions and should be discussed between manufacturers, power supply and communication authorities [1].

Electricity supply authorities normally abrogate responsibility on harmonic matters by introducing standards or recommendations for the limitation of voltage harmonic levels at the points of common coupling between consumers.

Electric Power Systems Harmonics - Identification and Measurements 5

2. Interference with ripple control and power line carrier systems, causing mis-operation

4. Over voltages and excessive currents on the system from resonance to harmonic

5. Dielectric breakdown of insulated cables resulting from harmonic over voltages on the

8. Signal interference and relay malfunction, particularly in solid-state and

9. Interference with large motor controllers and power plant excitation systems. (Reported

11. Unstable operation of firing circuits based on zero voltage crossing detection or

These effects depend, of course, on the harmonic source, its location on the power system,

In this model, it is assumed that the waveform under consideration consists of a fundamental frequency component and harmonic components with order of integral multiples of the fundamental frequency. It is also assumed that the frequency is known and constant during the estimation period. Consider a non-sinusoidal voltage given by a

<sup>0</sup>

( ) ( cos sin sin cos )

*vt V t V t* 

cos *nn n x V*

*n n nn*

*n n*

 0 0

 

(2)

(3a)

(1)

sin

0

*n vt V n t*

0

*n*

*N*

*N*

1. Capacitor bank failure from dielectric breakdown or reactive power overload.

of systems which accomplish remote switching, load control, and metering. 3. Excessive losses in – and heating of – induction and synchronous machines.

voltages or currents on the network.

microprocessor-controlled systems.

*v*(*t*) is the instantaneous voltage at time *t (s.) Vn* is the voltage amplitude of harmonic *n*

*<sup>n</sup>* is the phase angle of harmonic *n*

0 is the fundamental frequency

*N* total number of harmonics Equation (1) can be written as

*n* order of harmonic

7. Errors in induction kWh meters.

6. Inductive interference with telecommunications systems.

to cause motor problems as well as non-uniform output.) 10. Mechanical oscillations of induction and synchronous machines.

and the network characteristics that promote propagation of harmonics.

**3. Estimation of harmonics and sub-harmonics; the static case** 

system.

latching.

**3.1 Time domain model [3]** 

Fourier-type equation:

where

Define
