**6. Examples**

188 Power Quality Harmonics Analysis and Real Measurements Data

in the analytical location of the resonances, making a contribution to previous studies. This resistance, as well as damping the impedance values, shifts the resonance frequencies because it influences Steinmetz circuit design (i.e., the determination of the Steinmetz circuit

A sensitivity analysis of all variables involved in location of the parallel and series resonance is performed from (22). Thus, considering the range of the variables, Fig. 10 shows the contour plots of the harmonics where the parallel and series resonance is located. These

> τ<sup>1</sup> = 0.2

> > 9 11 13 15 17 19

τ<sup>1</sup> = 0.1

τ<sup>1</sup> = 0.025

21 25 <sup>27</sup>

τ

τ<sup>1</sup> = 0.4

τ<sup>1</sup> = 0.2

33 43 53 63 73

τ<sup>1</sup> = 0.05

31

21

*rL* (pu) 5 40 20 60 80 100

41

51 61 71

83

93 … λ*L*= 0.95

λ*L*= 1.0

λ*L*= 0.9

1 range is fixed from (4)

**5. Sensitivity analysis of power system harmonic response** 

harmonics are calculated from the expression of *kr*, a, (22), and the

*<sup>L</sup>* value. From Fig. 10, it can be noted that

3 5 7

reactances).

considering the

*dC* (%)

3

5

100

50

75

25

*dC* (%)

100

50

75

25

*dC* (%)

100

50

25

Fig. 10. Contour plots of *kr*, a.

λ

τ<sup>1</sup> = 0

7

τ<sup>1</sup> = 0

τ<sup>1</sup> = 0

<sup>9</sup> 1113 15 17 21 23 <sup>25</sup>

9

*rL* (pu)

5 40 20 60 80 100 100

9

13

17

27 29 …

> *rL* (pu) 5 40 20 60 80

31

29

41

51

For the sake of illustration, two different implementations of the *kr*, a expression, (22), are developed. In the first, the analytical study in Section 4 is validated from laboratory measurements. Several experimental tests were made to check the usefulness of the *kr*, a expression in locating the parallel and series resonance. In the second, this expression is applied to locate the harmonic resonance of several power systems with a Steinmetz circuit in the literature.
