**2. Model of Low Voltage grid**

The power electronics based low voltage network model is obtained using the SimPowerSystems Toolbox of Matlab/Simulink. The models include the Medium/Low voltage (MV/LV) transformer, the distribution lines, the most significant electrical loads and the microgenerators connected to the grid.

#### **2.1 Distribution transformer**

It is assumed that the distribution MV/LV transformer is ΔYN, with the secondary neutral directly connected to ground. The transformer used in the simulations is fed by a 30kV voltage on MV (medium voltage) and, in LV (Low Voltage) the line/phase voltage is 400V / 230V. The magnetization and the primary and secondary windings reactance and resistance are calculated from the transformer manufacturer no-load, short-circuit and nominal load tests [Elgerd, 1985].

Fig. 1. Equivalent single phase model of a distribution transformer

From the no-load test, applying the nominal voltage *Un* to the secondary side of the transformer, and leaving the primary side open, it is possible to obtain the transformer magnetizing current *Im*. As the series impedance is much lower than the magnetizing impedance, it is assumed that the iron losses are nearly equal to the no-load losses *P*0. Then, from the nominal voltage *Un*, the magnetizing current *Im* and the no load losses *P*0, it is possible to determine the transformer magnetizing reactance and resistance. The magnetizing conductance is given by (1).

$$\mathbf{G}\_m = \frac{P\_0}{\mathbf{U}\_n^2} \tag{1}$$

The magnetizing resistance *Rm* (2) is obtained from the magnetizing conductance *Gm* (1).

$$R\_{sv} = \frac{1}{G\_{sv}}\tag{2}$$

From the magnetizing current *Im* and the magnetizing conductance *Rm* it is possible to determine the magnetizing susceptance *Bm* (3):

From the obtained results, active μG have the capability to guarantee an overall Power Quality improvement (voltage THD decrease and Power Factor increase) allowing a voltage THD decrease when compared to voltage THD values obtained with conventional μG.

The power electronics based low voltage network model is obtained using the SimPowerSystems Toolbox of Matlab/Simulink. The models include the Medium/Low voltage (MV/LV) transformer, the distribution lines, the most significant electrical loads and

It is assumed that the distribution MV/LV transformer is ΔYN, with the secondary neutral directly connected to ground. The transformer used in the simulations is fed by a 30kV voltage on MV (medium voltage) and, in LV (Low Voltage) the line/phase voltage is 400V / 230V. The magnetization and the primary and secondary windings reactance and resistance are calculated from the transformer manufacturer no-load, short-circuit and nominal load

*R1 X1 R2 X2*

From the no-load test, applying the nominal voltage *Un* to the secondary side of the transformer, and leaving the primary side open, it is possible to obtain the transformer magnetizing current *Im*. As the series impedance is much lower than the magnetizing impedance, it is assumed that the iron losses are nearly equal to the no-load losses *P*0. Then, from the nominal voltage *Un*, the magnetizing current *Im* and the no load losses *P*0, it is possible to determine the transformer magnetizing reactance and resistance. The

> 0 *m* 2 *n*

> > 1

*m*

= (1)

*G*= (2)

*<sup>P</sup> <sup>G</sup> U*

The magnetizing resistance *Rm* (2) is obtained from the magnetizing conductance *Gm* (1).

*m*

From the magnetizing current *Im* and the magnetizing conductance *Rm* it is possible to

*R*

*Bm Gm*

Fig. 1. Equivalent single phase model of a distribution transformer

**2. Model of Low Voltage grid** 

**2.1 Distribution transformer** 

tests [Elgerd, 1985].

the microgenerators connected to the grid.

magnetizing conductance is given by (1).

determine the magnetizing susceptance *Bm* (3):

$$B\_m = -\sqrt{\left(\frac{I\_m}{\mathcal{U}\_n}\right)^2 - G\_m^2} \tag{3}$$

The magnetizing reactance *Xm* is given by (4):

$$X\_m = \frac{1}{B\_m} \tag{4}$$

The magnetizing impedance is much higher than the series branch impedances (Fig. 1). Then, from the short-circuit test, it is possible to obtain the short-circuit impedance *Zcc* (5) and the total resistance *Rt* (6) from the transformer primary and secondary windings, knowing the short-circuit voltage *Ucc*, necessary to guarantee the current nominal value *In* and the short-circuit losses *Pcc*.

$$Z\_{cc} = \frac{\mathcal{U}\_{cc}}{I\_n} \tag{5}$$

$$R\_t = \frac{P\_{cc}}{I\_n^2} \tag{6}$$

Then, from (5) and (6) it is possible to determine the leakage reactance *Xt* (7):

$$X\_t = \sqrt{Z\_{cc}^2 - R\_t^2} \tag{7}$$

The resistance and leakage reactance from the primary and secondary windings may be assumed to be equal. Then:

$$R\_1 = R\_2 = \frac{R\_t}{2} \tag{8}$$

$$X\_1 = X\_2 = \frac{X\_t}{2} \tag{9}$$

In this work a 400kVA 30kV/400V distribution transformer (base values *Sb*=400kVA, *Ub*=30kV, /( 3 ) *bb b IS U* = ) is used. From the no-load test a magnetizing current *Im*=2.9% and no-load losses of *P0*=1450W are considered. From the short-circuit test it is assumed *Ucc*=4.5%, with nominal current *In* (1 pu) and short-circuit losses *Pcc*=8.8 kW.

#### **2.2 Distribution cables**

The distribution cables models are based on the π model (Fig. 2) and their section is chosen according to the current nominal values. The series resistance and inductance and the shunt admittance may be obtained from the manufacturers values depending on the cables section and length.

In LV distribution networks four-wire cables are used (three phase conductors and a neutral conductor insulated separately), all enclosed by an outer polyethylene insulation mantle. Usually the conductors are sector shaped. The shunt and series impedance are determined by the physical construction of the cable.

Design of a Virtual Lab to Evaluate and Mitigate

Power Quality Problems Introduced by Microgeneration 189

a)

Fundamental (50Hz) = 1.883 , THD= 1.66%

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>0</sup>

Harmonic order

Nonlinear loads are assumed to be mainly represented as diode rectifiers and are divided in

The first group includes low power electronic equipment as TV sets, DVD players or computers. Usually, these electronic apparatus have isolated DC supplies connected to the grid through single phase rectifiers and they can be modelled as their first stage converter: a

D1

D2

*Co*

D4 D3

Fig. 4. Grid voltage and current waveform obtained for a refrigerator: a) Measured with a Fluke 435, THDi=10.8% and PF=0.57; b) Obtained with the simulated model, considering

0.5

THDv=5%; c) Simulated current harmonics, THDi=1.66% and PF=0.57

single phase rectifier feeding a DC *Ro*//*Co* load (Fig. 5) [Mohan et all, 1995].

*L*

Fig. 5. Single phase rectifier as a model for the majority of electronic apparatus

1

Mag (% of Fundamental)

three groups depending on their rated power.

Grid

**2.4 Nonlinear loads** 

1.5

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

c)

*Ro*

*Vo*

b)

230V 10A

Fig. 2. π model of the distribution electrical network

Based on the single phase model of Fig.2, the model of a three phase distribution cable is obtained, Fig. 3 [Ciric et all 2003], [Ciric et all 2005].

Fig. 3. Modified π model of the distribution electrical network

The series resistance *R* (Ω/km) [Jensen et all, 2001] depends on the cable internal resistance, on the ground resistance (there is no screen and the current diverted to ground must be included in the model) and on the proximity effect resistance. The skin effect and the proximity effect result in the increase of the conductors resistance.

The cable apparent inductance *Ls* depends on the self inductance, on the mutual inductance and on the inductance due to non-ideal ground.

The cable shunt admittance depends on the capacitances between conductors and on the conductors to ground capacitances [Jensen et all, 2001].

In overhead lines only the series impedance is considered. The capacitance is usually negligible.

Both for underground cables and overhead lines, the length should be adequate to guarantee their protection, according to the manufacturer values, and to assure that despite the voltage drops, the compliance with RMS voltage standard values [EN 50160] is always guaranteed.

#### **2.3 Linear loads**

Linear loads are represented as simple resistances (R) and inductances (RL). Resistive loads may be used to simulate incandescent lamps or conventional heaters, whether inductive loads may be used to simulate refrigerators, according to the measurements performed with a FLUKE 435 and shown in figure 4.

*R L*

Fig. 2. π model of the distribution electrical network

obtained, Fig. 3 [Ciric et all 2003], [Ciric et all 2005].

*CA /2*

*A*

*B*

*C*

*N*

*G*

negligible.

guaranteed.

**2.3 Linear loads** 

a FLUKE 435 and shown in figure 4.

*CB /2*

and on the inductance due to non-ideal ground.

conductors to ground capacitances [Jensen et all, 2001].

*CC /2*

*CN /2*

Fig. 3. Modified π model of the distribution electrical network

proximity effect result in the increase of the conductors resistance.

*CC /2 CC /2*

Based on the single phase model of Fig.2, the model of a three phase distribution cable is

*RA LA*

*RB LB*

*CA /2*

*CB /2*

*CC /2*

*CN /2*

*RC LC*

*RN LN*

The series resistance *R* (Ω/km) [Jensen et all, 2001] depends on the cable internal resistance, on the ground resistance (there is no screen and the current diverted to ground must be included in the model) and on the proximity effect resistance. The skin effect and the

The cable apparent inductance *Ls* depends on the self inductance, on the mutual inductance

The cable shunt admittance depends on the capacitances between conductors and on the

In overhead lines only the series impedance is considered. The capacitance is usually

Both for underground cables and overhead lines, the length should be adequate to guarantee their protection, according to the manufacturer values, and to assure that despite the voltage drops, the compliance with RMS voltage standard values [EN 50160] is always

Linear loads are represented as simple resistances (R) and inductances (RL). Resistive loads may be used to simulate incandescent lamps or conventional heaters, whether inductive loads may be used to simulate refrigerators, according to the measurements performed with

Fig. 4. Grid voltage and current waveform obtained for a refrigerator: a) Measured with a Fluke 435, THDi=10.8% and PF=0.57; b) Obtained with the simulated model, considering THDv=5%; c) Simulated current harmonics, THDi=1.66% and PF=0.57

#### **2.4 Nonlinear loads**

Nonlinear loads are assumed to be mainly represented as diode rectifiers and are divided in three groups depending on their rated power.

The first group includes low power electronic equipment as TV sets, DVD players or computers. Usually, these electronic apparatus have isolated DC supplies connected to the grid through single phase rectifiers and they can be modelled as their first stage converter: a single phase rectifier feeding a DC *Ro*//*Co* load (Fig. 5) [Mohan et all, 1995].

Fig. 5. Single phase rectifier as a model for the majority of electronic apparatus

Design of a Virtual Lab to Evaluate and Mitigate

0.6 0.605 0.61 0.615 0.62 0.625 0.63 0.635 0.64

230V 10A

0.6 0.605 0.61 0.615 0.62 0.625 0.63 0.635 0.64

lower power equipment as TV sets.

Simulated current harmonics, THDi=45% and PF=0.5

230V 10A

Power Quality Problems Introduced by Microgeneration 191

c)

e)

Fig. 7. Grid voltage and current waveform obtained for a washing machine; a) b) Measured with a Fluke 435, THDi=46.7%; c) Obtained with the simulated model, considering voltage THDv=5%; d) Simulated current harmonics, THDi=47.85% and PF=0.76; e) Obtained with the simulated model, considering voltage THDv=5% and a saturated inductance; f)

To smooth the current absorbed from the LV network, the rectifier is connected to the grid through a filtering inductance, which is calculated as a percentage of the output load impedance (3), where *f* represents the grid frequency and *k* is a constant, usually *k*=0.03 for

> 2 *o*

*R k R <sup>L</sup> <sup>f</sup>* <sup>=</sup> <sup>π</sup>

10 20

10

20

Mag (% of Fundamental)

30

40

30 40 50

Mag (% of Fundamental)

a) b)

Fundamental (50Hz) = 5.712 , THD= 47.85%

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>0</sup>

Harmonic order

Fundamental (50Hz) = 4.933 , THD= 45.00%

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>0</sup>

Harmonic order

(12)

d)

f)

Fig. 6 shows the voltage and current measurements obtained for a TV set and the equivalent simulated waveforms.

Fig. 6. Grid voltage and current waveform obtained for a TV set; a) b) Measured with a Fluke 435, THDi=65.6% and PF=0.75; c) Obtained with the simulated model, considering voltage THDv=5%; d) Simulated current harmonics, THDi=69.9% and PF=0.76

Fig. 7 shows the voltage and current measurements obtained for a washing machine and the equivalent simulated waveforms.

The virtual lab models of these non linear loads are sized based on their rated power. Then, assuming an adequate DC voltage *Vo av*, the value of the equivalent output resistance *Ro* is obtained from (10). For the TV set an output voltage average value *Vo av*=300V is assumed.

$$R\_o = \frac{V\_{o\_w}^2}{P} \tag{10}$$

The capacitor *Co* is designed to limit the output voltage ripple Δ*Vo*. Also, it depends on the output voltage average value *Vo av*, on the equivalent output resistance *Ro*, and on the time interval when all the diodes are OFF (approximately equal to one half of the grid period Δ*t*=10ms). In the simulations, the ripple is assumed to be lower than Δ*Vo*=50V.

$$\mathbf{C}\_o = \frac{V\_{o\_w}}{R\_o} \frac{\Delta t}{\Delta V\_o} \tag{11}$$

Fig. 6 shows the voltage and current measurements obtained for a TV set and the equivalent

c)

Fig. 6. Grid voltage and current waveform obtained for a TV set; a) b) Measured with a Fluke 435, THDi=65.6% and PF=0.75; c) Obtained with the simulated model, considering

Fig. 7 shows the voltage and current measurements obtained for a washing machine and the

The virtual lab models of these non linear loads are sized based on their rated power. Then,

*o V*

The capacitor *Co* is designed to limit the output voltage ripple Δ*Vo*. Also, it depends on the

interval when all the diodes are OFF (approximately equal to one half of the grid period

*av o*

*<sup>V</sup> <sup>t</sup> <sup>C</sup> R V*

*o o*

*R*

Δ*t*=10ms). In the simulations, the ripple is assumed to be lower than Δ*Vo*=50V.

*o*

2 *av o*

voltage THDv=5%; d) Simulated current harmonics, THDi=69.9% and PF=0.76

obtained from (10). For the TV set an output voltage average value *Vo*

Mag (% of Fundamental)

a) b)

Fundamental (50Hz) = 0.9027 , THD= 69.93%

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>0</sup>

Harmonic order

*av*, the value of the equivalent output resistance *Ro* is

*av*, on the equivalent output resistance *Ro*, and on the time

*<sup>P</sup>* <sup>≈</sup> (10)

<sup>Δ</sup> <sup>≈</sup> Δ (11)

*av*=300V is assumed.

d)

simulated waveforms.

0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1

equivalent simulated waveforms.

output voltage average value *Vo*

assuming an adequate DC voltage *Vo*

230V 5A

Fig. 7. Grid voltage and current waveform obtained for a washing machine; a) b) Measured with a Fluke 435, THDi=46.7%; c) Obtained with the simulated model, considering voltage THDv=5%; d) Simulated current harmonics, THDi=47.85% and PF=0.76; e) Obtained with the simulated model, considering voltage THDv=5% and a saturated inductance; f) Simulated current harmonics, THDi=45% and PF=0.5

To smooth the current absorbed from the LV network, the rectifier is connected to the grid through a filtering inductance, which is calculated as a percentage of the output load impedance (3), where *f* represents the grid frequency and *k* is a constant, usually *k*=0.03 for lower power equipment as TV sets.

$$L\_{\aleph} = \frac{k \, R\_{\circ}}{2 \pi \mathfrak{f}} \tag{12}$$

Design of a Virtual Lab to Evaluate and Mitigate

**2.5 Conventional single phase microgenerators** 

 Boost stage + MPPT

Fig. 10. Block diagram of a conventional μG

a DC voltage source *UDC* (Fig. 11).

S1

S2

Fig. 11. Model of the single phase microgenerator

Photovoltaic Panel

UDC

unitary power factor.

*Vo*

Power Quality Problems Introduced by Microgeneration 193

In this model the equivalent output load may be calculated from (1) assuming *P*=6kW and

Microgenerators are connected to the LV grid through single phase VSI (voltage source inverters) (Fig. 10) [Pogaku et all, 2007] and they are designed to guarantee the compliance with international standards (as EN 50438) and to have characteristics similar to the authorized equipment (maximum rated power, current THD and input power factor).

For simplicity reasons and minimization of simulation times, the microgenerators are simulated considering only the grid connection stage, as current controlled inverters fed by

It is assumed that the VSI is connected to the grid through a filtering inductance designed to guarantee a current ripple lower than Δ*Igrid*. To minimize filtering, a three level PWM is used. Then, the inductance *LL* (Fig. 11) is calculated according to (13), where *UDC* is the DC

4

*<sup>U</sup> <sup>L</sup>*

*L*

S4

The VSI is controlled using a linear control approach, assuming that the maximum power is supplied to the grid and guaranteeing that the current injected in LV grid has a nearly

*v*PWM

S3

*DC*

*s grid*

*RL*

link voltage, *fs* is the switching frequency and Δ*Igrid* is the current ripple.

Voltage Source Inverter

UDC vPWM Vgrid

AC Filter

*<sup>f</sup> <sup>I</sup>* <sup>=</sup> <sup>Δ</sup> (13)

*LL*

*i grid* Grid

*Vgrid*

9 shows the voltage and current waveforms obtained with the designed model.

*av*=520V. The output filter capacitor is obtained from (2) considering Δ*t*=3.3ms (in a 6 pulse rectifier Δ*t=T*/6). The input filtering inductance is obtained from (3) considering *k*=0.03. Fig.

As an example, with the designed model it is possible to obtain current waveforms similar to those measured on a TV set (Fig. 6), using the previously calculated values of *Ro*, *Co* and *LR* and assuming *P*=150W.

For other higher power household appliances as modern washing or dishwashing machines, a similar model may be used but the average rated power *P* should be higher, as well as the input filtering inductance. The voltage and current measurements obtained for a washing machine are shown in Fig. 7 a) b) and the equivalent simulated waveforms are shown in figures 7 c) d) where *P*=1kW, and the filtering inductance is obtained from (12) assuming *k*=0.1. Comparing figures 7 b) and 7 d) the measured and simulated currents THD as well as the harmonic contents are similar. Still, the current waveforms of Fig. 7 a) c) present some differences. To obtain similar current waveforms, the saturation effect of the input inductance should be considered, as shown in Fig. 7 c) d).

Even though the majority of LV grid connected loads are single phase, there may be a few three phase loads, as welding machines or three phase drives in small industries. Again, this equipment may be represented as their first stage converter, usually a three phase diode rectifier feeding an equivalent *Ro3*//*Co3* load (Fig. 8).

Fig. 8. Three phase rectifier as a model for an electronic equipment of a small industry

Fig. 9. a) Grid voltage and current waveform obtained for a three phase rectifier obtained with the simulated model, considering voltage THDv=5%; b) Current harmonics and THDi=34.86%, PF=0.91

As an example, with the designed model it is possible to obtain current waveforms similar to those measured on a TV set (Fig. 6), using the previously calculated values of *Ro*, *Co* and

For other higher power household appliances as modern washing or dishwashing machines, a similar model may be used but the average rated power *P* should be higher, as well as the input filtering inductance. The voltage and current measurements obtained for a washing machine are shown in Fig. 7 a) b) and the equivalent simulated waveforms are shown in figures 7 c) d) where *P*=1kW, and the filtering inductance is obtained from (12) assuming *k*=0.1. Comparing figures 7 b) and 7 d) the measured and simulated currents THD as well as the harmonic contents are similar. Still, the current waveforms of Fig. 7 a) c) present some differences. To obtain similar current waveforms, the saturation effect of the input

Even though the majority of LV grid connected loads are single phase, there may be a few three phase loads, as welding machines or three phase drives in small industries. Again, this equipment may be represented as their first stage converter, usually a three phase diode

D3

D6

D1

D4

Fig. 8. Three phase rectifier as a model for an electronic equipment of a small industry

a)

Fig. 9. a) Grid voltage and current waveform obtained for a three phase rectifier obtained with the simulated model, considering voltage THDv=5%; b) Current harmonics and

Mag (% of Fundamental)

*Ro3*

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>0</sup>

Fundamental (50Hz) = 12.96 , THD= 34.86%

Harmonic order

b)

*Vo3*

*Co3*

D2

D5

*LR* and assuming *P*=150W.

inductance should be considered, as shown in Fig. 7 c) d).

*L*

*L*

*L*

rectifier feeding an equivalent *Ro3*//*Co3* load (Fig. 8).

*Vgrid1*

*Vgrid2*

*Vgrid3*

0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1

THDi=34.86%, PF=0.91

230V 20A

In this model the equivalent output load may be calculated from (1) assuming *P*=6kW and *Vo av*=520V. The output filter capacitor is obtained from (2) considering Δ*t*=3.3ms (in a 6 pulse rectifier Δ*t=T*/6). The input filtering inductance is obtained from (3) considering *k*=0.03. Fig. 9 shows the voltage and current waveforms obtained with the designed model.

#### **2.5 Conventional single phase microgenerators**

Microgenerators are connected to the LV grid through single phase VSI (voltage source inverters) (Fig. 10) [Pogaku et all, 2007] and they are designed to guarantee the compliance with international standards (as EN 50438) and to have characteristics similar to the authorized equipment (maximum rated power, current THD and input power factor).

Fig. 10. Block diagram of a conventional μG

For simplicity reasons and minimization of simulation times, the microgenerators are simulated considering only the grid connection stage, as current controlled inverters fed by a DC voltage source *UDC* (Fig. 11).

It is assumed that the VSI is connected to the grid through a filtering inductance designed to guarantee a current ripple lower than Δ*Igrid*. To minimize filtering, a three level PWM is used. Then, the inductance *LL* (Fig. 11) is calculated according to (13), where *UDC* is the DC link voltage, *fs* is the switching frequency and Δ*Igrid* is the current ripple.

$$L\_{\rm L} = \frac{\mathcal{U}\_{\rm DC}}{\mathbf{4} \, f\_s \, \Delta I\_{g\rm rld}} \tag{13}$$

Fig. 11. Model of the single phase microgenerator

The VSI is controlled using a linear control approach, assuming that the maximum power is supplied to the grid and guaranteeing that the current injected in LV grid has a nearly unitary power factor.

Generally, the association of the modulator and the power converter may be represented as a first order model (14), with a gain *KD* and a dominant pole dependent on the average delay time *Td* (usually one half of the switching period *Td*=*Ts*/2) [Rashid, 2007].

$$\mathbf{G}\_{\circ}(\mathbf{s}) = \frac{\upsilon\_{\text{PWM}\_{w}}(\mathbf{s})}{\mu\_{\text{c}}(\mathbf{s})} = \frac{K\_{\text{D}}}{sT\_{d} + 1} \tag{14}$$

The incremental gain *KD* (15) depends on *UDC* voltage and on the maximum value max *uc* of the triangular modulator voltage.

$$K\_D = \frac{\mathcal{U}\_{DC}}{\mu\_{c\_{\text{max}}}} \tag{15}$$

Design of a Virtual Lab to Evaluate and Mitigate

0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1

10kHz and Δ*Igrid*<0.1 *Igrid*.

a non-linear load.

model; b) Current harmonics and THDi=2.33%, PF=-0.999

guaranteeing the compliance with international standards.

μG

Fig. 14. Example of a small LV grid with a μG and a non-linear load

230V 25A

(18).

Power Quality Problems Introduced by Microgeneration 195

From (16) and (17), assuming a damping factor ξ = 2 2 , the value of *Tp* is obtained from

*K T <sup>T</sup> R*

*p*

a)

2 *D id*

0

Fig. 13. a) Current and voltage waveforms of a single phase VSI obtained with the simulated

Figure 13 shows the results obtained for the proposed μG model, assuming that the μG apparent power is *S*=3450VA, the DC voltage is *UDC*=400V, the switching frequency is near

The μG power factor is negative, even though nearly unitary as the displacement factor between the voltage and the current is 180º. The current THD is lower than 3%. However, considering only the first 50 harmonics, as in most power quality meters, the current THD decreases to THDi=0.35% These results are according to the manufacturers values,

Even though these microgenerators are designed to present high power quality parameters (high power factor and low current THD), still they are not usually exploited to their full extent as in general, they are sized and the controllers are designed only to minimize the

As an example, consider a small LV grid, as the one represented in figure 14, with a μG and

*i grid i* μ*G*

Vgrid

Grid

Inductive + Non-linear load

impact on the LV grid. The mitigation of Power Quality issues is not considered.

*i nl* 0.5

1

Mag (% of Fundamental)

1.5

2

<sup>α</sup> <sup>=</sup> (18)

Fundamental (50Hz) = 21.23 , THD= 2.32%

0 5000 10000 15000 20000

b)

Frequency (Hz)

To control the current injected in the LV grid it is usual to choose a PI compensator (to guarantee fast response times and zero steady-state error to the step response). The block diagram of the current controller is then represented in Fig. 12, where α*<sup>i</sup>* represents the gain of the current sensor.

Fig. 12. Block diagram of the current controlled VSI

To design the current controller it is then necessary to obtain the closed loop transfer function of the whole system. To guarantee some insensitivity to the disturbance introduced by the grid voltage *Vgrid*, it is assumed that the disturbance is known (is the grid voltage). For simplicity in the controller design, it is considered that the μG sees an equivalent resistance *R0*=*Vgrid*/*igrid* connected to its terminals. From the controller point of view, this results in *R*=*RL*+*R0*. Then, making the compensator zero *Tz* coincident with the pole introduced by the input filter *T LR Z L* = , the second order transfer function of the current controlled VSI is obtained from (16).

$$\mathbf{G}\_{cl}(\mathbf{s}) = \frac{i\_{grid}\{\mathbf{s}\}}{i\_{grid\_{sq}}\{\mathbf{s}\}} = \frac{\frac{K\_D \,\mathbf{\alpha}\_i}{T\_p T\_d R}}{\mathbf{s}^2 + \frac{1}{T\_d}\mathbf{s} + \frac{K\_D \,\mathbf{\alpha}\_i}{T\_p T\_d R}}\tag{16}$$

The transfer function (16) is then compared to the second order transfer function (17) written in the canonical form.

$$\text{G}\_2(\text{s}) = \frac{\text{\textdegree\text{\textdegree\text{\textdegree}}}{\text{\textdegree\text{\textdegree}}^2 + 2\text{\textdegree\text{\textdegree\text{\textdegree}}}\text{\text{\textdegree\text{\textdegree}}}\text{\text{\textdegree}} + \text{\text{\textdegree}}^2}{\text{\text{\textdegree}}^2 + 2\text{\text{\textdegree\text{\textdegree}}}\text{\text{\textdegree}}\text{\text{\textdegree}} + \text{\text{\textdegree}}^2} \tag{17}$$

Generally, the association of the modulator and the power converter may be represented as a first order model (14), with a gain *KD* and a dominant pole dependent on the average delay

> ( ) ( ) () 1 *PWMav D*

The incremental gain *KD* (15) depends on *UDC* voltage and on the maximum value max *uc* of

*v s <sup>K</sup> G s*

*D*

*c d*

max *DC*

Modulator+VSI

+1 *<sup>d</sup> D sT K*

> α*i*

To design the current controller it is then necessary to obtain the closed loop transfer function of the whole system. To guarantee some insensitivity to the disturbance introduced by the grid voltage *Vgrid*, it is assumed that the disturbance is known (is the grid voltage). For simplicity in the controller design, it is considered that the μG sees an equivalent resistance *R0*=*Vgrid*/*igrid* connected to its terminals. From the controller point of view, this results in *R*=*RL*+*R0*. Then, making the compensator zero *Tz* coincident with the pole introduced by the input filter *T LR Z L* = , the second order transfer function of the current

2

= = <sup>α</sup>

*i s K s s*

*D i grid*

2

*grid p d*

The transfer function (16) is then compared to the second order transfer function (17) written

<sup>2</sup> 2 2 ( ) <sup>2</sup> *n n n*

*s s*

*i s TTR*

*D i*

α

*K*

+ +

*d pd*

*T TTR*

<sup>ω</sup> <sup>=</sup> <sup>+</sup> ξω +ω (17)

( ) ( ) ( ) <sup>1</sup> *ref*

*cl*

*G s*

*G s*

*c <sup>U</sup> <sup>K</sup>*

To control the current injected in the LV grid it is usual to choose a PI compensator (to guarantee fast response times and zero steady-state error to the step response). The block

*u s sT* = ≈ <sup>+</sup> (14)

*<sup>u</sup>* <sup>=</sup> (15)

*Vgrid*


+

α

Input Filter *i grid*

(16)

*<sup>i</sup>* represents the gain

time *Td* (usually one half of the switching period *Td*=*Ts*/2) [Rashid, 2007].

*C*

diagram of the current controller is then represented in Fig. 12, where

*uc <sup>V</sup> <sup>I</sup> PWMav grid\_ ref*

*z sT* 1+ *sT*

<sup>+</sup> -

Fig. 12. Block diagram of the current controlled VSI

*<sup>i</sup> <sup>p</sup>*

α

controlled VSI is obtained from (16).

in the canonical form.

the triangular modulator voltage.

of the current sensor.

From (16) and (17), assuming a damping factor ξ = 2 2 , the value of *Tp* is obtained from (18).

$$T\_p = \frac{2K\_D \,\alpha\_i \, T\_d}{R} \tag{18}$$

Fig. 13. a) Current and voltage waveforms of a single phase VSI obtained with the simulated model; b) Current harmonics and THDi=2.33%, PF=-0.999

Figure 13 shows the results obtained for the proposed μG model, assuming that the μG apparent power is *S*=3450VA, the DC voltage is *UDC*=400V, the switching frequency is near 10kHz and Δ*Igrid*<0.1 *Igrid*.

The μG power factor is negative, even though nearly unitary as the displacement factor between the voltage and the current is 180º. The current THD is lower than 3%. However, considering only the first 50 harmonics, as in most power quality meters, the current THD decreases to THDi=0.35% These results are according to the manufacturers values, guaranteeing the compliance with international standards.

Even though these microgenerators are designed to present high power quality parameters (high power factor and low current THD), still they are not usually exploited to their full extent as in general, they are sized and the controllers are designed only to minimize the impact on the LV grid. The mitigation of Power Quality issues is not considered.

As an example, consider a small LV grid, as the one represented in figure 14, with a μG and a non-linear load.

Fig. 14. Example of a small LV grid with a μG and a non-linear load

Design of a Virtual Lab to Evaluate and Mitigate

 Boost stage + MPPT

Fig. 17. Block diagram of an active μG

S1

*C*

*pv i*

*ic*

S2

Fig. 18. Model of the single phase active microgenerator

+ VSI <sup>+</sup> <sup>+</sup>

+ -

*i*μ*G ref*

*i pv i*

by the current *ipv* of the photovoltaic panel + boost stage.

unitary power factor).

Photovoltaic Panel

*i*

*Vc*

*Vcref*

+


*Vc*

Power Quality Problems Introduced by Microgeneration 197

power quality issues, as current THD, reducing the LV grid harmonic pollution (and near

VSI Active Power Filter

Based on the conventional μG model (Fig. 11), the proposed active μG is simulated according to Fig. 18, considering the DC link filtering stage and the disturbance introduced

S4

α*v*

*v*PWM

S3

VC vPWM Vgrid

AC Filter

*RL LL*

Non-linear load

*igrid*

Non-linear load

*i nl*

*VPWM av*


*ic*

+

*sC* 1

*i*

+ *i pv*

Filter

*i*μ*G*

+ +

 *inl*

*igrid*

Modulator

α*i*

*Cv*(*s*) *Ci* (*s*) Input

Fig. 19. Diagram block of the DC voltage controller and of the grid current controller to guarantee active filtering of the current harmonics introduced by the non-linear load

*i*μ*G*

*i nl*

*i grid i* μ*G*

Grid

*Vgrid*

Using the previously designed μG the current *i*μ*<sup>G</sup>* (Fig. 14) will be equal to the one obtained in Fig. 13. The non-linear load current *inl* is represented in Fig. 15 and is characterized by THDi=47.55%.

Fig. 15. a) Grid voltage *Vgrid* and current waveform *inl* obtained for the non-linear load; b) Current harmonics and THDi=47.55%, PF=0.15

The grid current *igrid* is represented in Fig. 16 and, as a result of the non-linear load THDi=18.79%.

Fig. 16. a) Waveforms of grid voltage *Vgrid* and current *igrid*; b) Current harmonics and THDi=18.79%

From this example it is possible to conclude that even though the μG injects nearly sinusoidal currents in the grid (Fig. 13), still it is not capable of guaranteeing sinusoidal currents when other nonlinear loads are connected to the grid.

#### **2.6 Active microgenerators**

To minimize some power quality problems as current and voltage THD, an active μG is included in this Lab (Fig. 17). Even though using the same power electronics converters as the conventional μG, with adequate control strategies and adequate filtering, it is possible to guarantee its operation as active power filter (APF), allowing the local mitigation of some

in Fig. 13. The non-linear load current *inl* is represented in Fig. 15 and is characterized by

a)

Fig. 15. a) Grid voltage *Vgrid* and current waveform *inl* obtained for the non-linear load;

a)

Fig. 16. a) Waveforms of grid voltage *Vgrid* and current *igrid*; b) Current harmonics and

currents when other nonlinear loads are connected to the grid.

0

From this example it is possible to conclude that even though the μG injects nearly sinusoidal currents in the grid (Fig. 13), still it is not capable of guaranteeing sinusoidal

To minimize some power quality problems as current and voltage THD, an active μG is included in this Lab (Fig. 17). Even though using the same power electronics converters as the conventional μG, with adequate control strategies and adequate filtering, it is possible to guarantee its operation as active power filter (APF), allowing the local mitigation of some

5

10

Mag (% of Fundamental)

15

The grid current *igrid* is represented in Fig. 16 and, as a result of the non-linear load

0

10

20

Mag (% of Fundamental)

30

40

μ

*<sup>G</sup>* (Fig. 14) will be equal to the one obtained

Fundamental (50Hz) = 6.072 , THD= 47.55%

0 500 1000 1500 2000

0 500 1000 1500 2000

Frequency (Hz)

b)

b)

Frequency (Hz)

Fundamental (50Hz) = 15.45 , THD= 18.79%

Using the previously designed μG the current *i*

1.9 1.905 1.91 1.915 1.92 1.925 1.93 1.935 1.94

1.9 1.905 1.91 1.915 1.92 1.925 1.93 1.935 1.94

**2.6 Active microgenerators** 

230V 25A

b) Current harmonics and THDi=47.55%, PF=0.15

230V 25A

THDi=47.55%.

THDi=18.79%.

THDi=18.79%

power quality issues, as current THD, reducing the LV grid harmonic pollution (and near unitary power factor).

Fig. 17. Block diagram of an active μG

Based on the conventional μG model (Fig. 11), the proposed active μG is simulated according to Fig. 18, considering the DC link filtering stage and the disturbance introduced by the current *ipv* of the photovoltaic panel + boost stage.

Fig. 18. Model of the single phase active microgenerator

Fig. 19. Diagram block of the DC voltage controller and of the grid current controller to guarantee active filtering of the current harmonics introduced by the non-linear load

Assuming that the *Vc* voltage dynamics in the DC link is considerably slower than the dynamics of the microgenerator AC current *i*μ*G*, then the active μG current *i*μ*<sup>G</sup>* and the voltage *Vc* may be controlled according to the diagram block of Fig. 19.

The active μG current controller design is equal to the design of the controller used for the conventional μG. Then, neglecting the high frequency poles, the current controlled system may be represented according to (19), where the controller gain *Gi* (20) is obtained from the input/output power constraint, where *Vmax* represents the amplitude of the grid voltage.

$$\frac{\text{i}\,\text{(s)}}{\text{i}\_{\mu G \,\text{ref}}\,\text{(s)}} = \frac{\frac{\text{G}\_i}{\text{\textdegree{}} \,\text{\textdegree{}} \,\text{\textdegree{}}}}{T\_{dv} \,\text{s} + \text{1}} \tag{19}$$

Design of a Virtual Lab to Evaluate and Mitigate

disturbances.

Then:

order polynomial (24).

microgenerator AC current *i*

grid period.

Power Quality Problems Introduced by Microgeneration 199

( ) 1 1 <sup>1</sup> 1 *cref*

*<sup>s</sup> T s sC* <sup>=</sup> <sup>=</sup> +α + α +

*i*

α

<sup>α</sup> <sup>=</sup> <sup>α</sup> <sup>α</sup> ++ +

*s Ts*

*pv vip vii <sup>v</sup>*

From the final value theorem (23), the response to the disturbance introduced by *ipv* current is zero, meaning that in steady-state, the PI controller guarantees the minimization of the

> ( ) lim <sup>0</sup> ( ) *cref*

*pv <sup>v</sup> v s i s* <sup>→</sup>

To determine the PI controller parameters, the denominator of (22) is compared to the third

*c*

0

<sup>1</sup> 1.75

2 0

 <sup>α</sup> ω = α

> 3 0

 <sup>α</sup> ω = α

2.15

 ω =

Solving (25), the proportional gain *Kp* and the integral gain *Ki* are obtained:

*p*

*i*

μ

*i s G K G K ss s T TC TC* <sup>=</sup>

1

*i dv*

( )

+

*dv*

*dv dv i dv i*

0

=

3 2 23

*dv v i p dv i*

*G K T C G K T C*

( )

*i*

1.75

2

3 2

*<sup>G</sup>*, then the pole *Tdv* is assumed to be 2 *T T dv* ≈ , where T is the

( ) ( )

*i*

1.75

Assuming that the dynamics of *Vc* voltage is considerably slower than the dynamics of the

Figures 22 to 24 show the results obtained for the proposed active μG model, assuming that the μG apparent power is *S*=3450VA, the DC voltage is controlled to be *Vc*=400V, the semiconductors switching frequency is near 10kHz and Δ*Igrid*<0.1 *Igrid*. The DC link capacitor

*v i dv*

*G T*

*T*

*vii dv i*

2.15

*v i dv*

*<sup>C</sup> <sup>K</sup> G T*

<sup>α</sup> <sup>=</sup>

*<sup>C</sup> <sup>K</sup>*

<sup>α</sup> <sup>α</sup> <sup>=</sup> <sup>α</sup>

1

α α

<sup>3</sup> 0 00 *Ps s s s* ( ) 1.75 2.15 = + ω + ω +ω (24)

(21)

(22)

= (23)

(25)

(26)

0

( ) 1 *cref*

*pv <sup>i</sup> <sup>i</sup> <sup>v</sup> <sup>v</sup> <sup>p</sup>*

Simplifying (21) it is possible to obtain the transfer function in the canonical form (22).

*v s sC i s <sup>K</sup> <sup>G</sup> <sup>K</sup>*

3 2 <sup>0</sup>

0

*s*

*c dv i*

*v s T C*

( )

*c*

( )

$$\mathbf{G}\_i(\mathbf{s}) = \frac{V\_{\text{max}}}{\mathbf{2}V\_{\varepsilon}} \tag{20}$$

Then, the current controlled system may be represented as a current source (19), as shown in Fig. 20.

Fig. 20. Simplified block diagram used to design the voltage controller

From Fig. 20, the block diagram of the DC voltage controller is obtained and represented in figure 21.

Fig. 21. Block diagram of DC stage voltage controller

From Fig. 21, the voltage response to the disturbance introduced by the photovoltaic panel is given by (21):

$$\left. \frac{v\_c(s)}{i\_{pv}(s)} \right|\_{v\_{is\_p} = 0} = \frac{\frac{1}{sC}}{1 + \alpha\_v \left( K\_p + \frac{K\_i}{s} \right) \frac{G\_i}{\alpha\_i} \frac{1}{T\_{ds}s + 1} \frac{1}{sC}} \tag{21}$$

Simplifying (21) it is possible to obtain the transfer function in the canonical form (22).

$$\left. \frac{\upsilon\_c(s)}{i\_{\upsilon v}(s)} \right|\_{v\_{i\_{\upsilon f}}=0} = \frac{s \frac{\alpha\_i}{T\_{dv} \mathbb{C} \alpha\_i} (T\_{dv} s + 1)}{s^3 + \frac{1}{T\_{dv}} s^2 + \frac{\alpha\_v \mathbb{G}\_i \mathbb{K}\_p}{T\_{dv} \mathbb{C} \alpha\_i} s + \frac{\alpha\_v \mathbb{G}\_i \mathbb{K}\_i}{T\_{dv} \mathbb{C} \alpha\_i}} \tag{22}$$

From the final value theorem (23), the response to the disturbance introduced by *ipv* current is zero, meaning that in steady-state, the PI controller guarantees the minimization of the disturbances.

$$\left. \lim\_{s \to 0} \frac{v\_{\boldsymbol{c}}(\boldsymbol{s})}{\dot{\boldsymbol{i}}\_{\boldsymbol{p}\boldsymbol{v}}(\boldsymbol{s})} \right|\_{\boldsymbol{v}\_{\boldsymbol{v}\_{\boldsymbol{q}\boldsymbol{f}}}=0} = 0 \tag{23}$$

To determine the PI controller parameters, the denominator of (22) is compared to the third order polynomial (24).

$$P\_3(\text{s}) = \text{s}^3 + 1.75\,\text{\textdegree{o}\_0}\,\text{s}^2 + 2.15\,\text{\textdegree{o}\_0}\,\text{s} + \text{o}\_0^3\tag{24}$$

Then:

198 Electrical Generation and Distribution Systems and Power Quality Disturbances

Assuming that the *Vc* voltage dynamics in the DC link is considerably slower than the

The active μG current controller design is equal to the design of the controller used for the conventional μG. Then, neglecting the high frequency poles, the current controlled system may be represented according to (19), where the controller gain *Gi* (20) is obtained from the input/output power constraint, where *Vmax* represents the amplitude of the grid voltage.

( )

*i*

*C*

Fig. 20. Simplified block diagram used to design the voltage controller

*i* μ*G ref*

*s <sup>K</sup> <sup>K</sup> <sup>i</sup> <sup>p</sup>* <sup>+</sup>

Fig. 21. Block diagram of DC stage voltage controller

*i c*

*i s*

*Gref dv*

( ) <sup>2</sup> *max*

Then, the current controlled system may be represented as a current source (19), as shown in

*pv* **)(** *si* **)(** *sT*

From Fig. 20, the block diagram of the DC voltage controller is obtained and represented in

*Vc ref Vc*

+1 α *sT G dv ii*

α*v*

From Fig. 21, the voltage response to the disturbance introduced by the photovoltaic panel is

*i*

+

+

 *ipv*

> *sC* 1

*<sup>V</sup> G s*

*i s Ts* <sup>μ</sup>

voltage *Vc* may be controlled according to the diagram block of Fig. 19.

μ

() 1

*i i*

*G*

*c*

*G*, then the active μG current *i*

<sup>α</sup> <sup>≈</sup> + (19)

*<sup>V</sup>* <sup>≈</sup> (20)

*<sup>G</sup> si Gref <sup>i</sup> dv i* <sup>μ</sup> +α <sup>≈</sup> <sup>1</sup> 1

μ

*<sup>G</sup>* and the

dynamics of the microgenerator AC current *i*

*VC i*

Fig. 20.

figure 21.

given by (21):

+ <sup>+</sup> -

$$\begin{cases} 1.75 \text{\color{red}{0}s\_0 = \frac{1}{T\_{\text{dv}}}}\\ 2.15 \text{\color{red}{0}s\_0^2 = \frac{\alpha\_v \text{ G}\_i \text{ K}\_p}{T\_{\text{dv}} \text{C} \alpha\_i}\\ \alpha\_0^3 = \frac{\alpha\_v \text{ G}\_i \text{ K}\_i}{T\_{\text{dv}} \text{C} \alpha\_i} \end{cases} \tag{25}$$

Solving (25), the proportional gain *Kp* and the integral gain *Ki* are obtained:

$$\begin{cases} K\_p = \frac{2.15 \text{ C} \,\alpha\_i}{\alpha\_v \text{ G}\_l \, T\_{dv} \left(1.75 \right)^2} \\ K\_i = \frac{\text{C} \,\alpha\_i}{\alpha\_v \text{ G}\_l \left(1.75 \right)^3 \left(T\_{dv} \right)^2} \end{cases} \tag{26}$$

Assuming that the dynamics of *Vc* voltage is considerably slower than the dynamics of the microgenerator AC current *i*μ*<sup>G</sup>*, then the pole *Tdv* is assumed to be 2 *T T dv* ≈ , where T is the grid period.

Figures 22 to 24 show the results obtained for the proposed active μG model, assuming that the μG apparent power is *S*=3450VA, the DC voltage is controlled to be *Vc*=400V, the semiconductors switching frequency is near 10kHz and Δ*Igrid*<0.1 *Igrid*. The DC link capacitor

Design of a Virtual Lab to Evaluate and Mitigate

Fig. 23.

THDi=13%

Power Quality Problems Introduced by Microgeneration 201

To guarantee nearly sinusoidal grid currents, the μG current will be the one presented in

230V 25A

1.9 1.905 1.91 1.915 1.92 1.925 1.93 1.935 1.94

Fundamental (50Hz) = 21.16 , THD= 13.00%

0 500 1000 1500 2000

Frequency (Hz)

1.9 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 <sup>2</sup> <sup>0</sup>

Fig. 23. a) Waveforms of grid voltage and μG current; b) μG current harmonics and

The proposed models will be further tested in a low voltage grid.

Fig. 24. Waveform of the DC link capacitor voltage

Mag (% of Fundamental)

a)

b)

The average value of the capacitor voltage is *Vc*=400V, as shown in Fig. 24.

is C=2.7mF, guaranteeing a voltage ripple lower than 5%. The results obtained for the nonlinear load are those presented in figure 15.

From Fig. 22 it is possible to conclude that the proposed active μG acts as an active power filter, guaranteeing nearly sinusoidal grid currents. Comparing the results of Fig. 22 and Fig. 16, there is a clear reduction of the grid current THD. This reduction will become more obvious for more complex grids and highly non-linear loads.

Fig. 22. a) Waveforms of grid voltage and current; b) Grid current harmonics and THDi=3.56%, PF=0.9999.; c) Grid current harmonics and THDi50=1.55% (considering only till the 50th order harmonic)

is C=2.7mF, guaranteeing a voltage ripple lower than 5%. The results obtained for the non-

From Fig. 22 it is possible to conclude that the proposed active μG acts as an active power filter, guaranteeing nearly sinusoidal grid currents. Comparing the results of Fig. 22 and Fig. 16, there is a clear reduction of the grid current THD. This reduction will become more

230V 25A

1.9 1.905 1.91 1.915 1.92 1.925 1.93 1.935 1.94

Fundamental (50Hz) = 15.24 , THD= 3.56%

0 5000 10000 15000 20000

0 500 1000 1500 2000

Frequency (Hz)

THDi=3.56%, PF=0.9999.; c) Grid current harmonics and THDi50=1.55% (considering only till

Fig. 22. a) Waveforms of grid voltage and current; b) Grid current harmonics and

Frequency (Hz)

Fundamental (50Hz) = 15.12 , THD= 1.55%

a)

b)

c)

linear load are those presented in figure 15.

obvious for more complex grids and highly non-linear loads.

0 0.5 1 1.5 2 2.5

0

0.5

Mag (% of Fundamental)

the 50th order harmonic)

1

1.5

Mag (% of Fundamental)

To guarantee nearly sinusoidal grid currents, the μG current will be the one presented in Fig. 23.

The average value of the capacitor voltage is *Vc*=400V, as shown in Fig. 24.

Fig. 23. a) Waveforms of grid voltage and μG current; b) μG current harmonics and THDi=13%

Fig. 24. Waveform of the DC link capacitor voltage

The proposed models will be further tested in a low voltage grid.

Design of a Virtual Lab to Evaluate and Mitigate

LV L1 L2

LV L1

L2

L3

L4

load distance increases, the voltage drop increases as well.

L5

L3 L4

L5

L6 a)

**Power Factor Voltage RMS value** 

L6 c) LV L1 L2

Fig. 26. Results obtained for 15 % and 85 % of the transformer rated power, without μG. Measurements carried out on the transformer LV side for each one of the groups of loads L1

Fig. 26 shows that the voltage THD increases more than 50% (as in load 6) from the no-load (15% SN) to the full load (85% SN) scenario. As the percentage of linear and non-linear loads is nearly equal for both scenarios, the current THD does not present significant changes (it even decreases slightly in the full load scenario). Also, the Power Factor results are similar for both scenarios, even though slightly lower for the no-load scenario. As for the load voltages RMS values, higher loads result in higher voltage drops. Also, as the transformer to

Figure 27 presents the results obtained with μG assuming that the transformer is at 15 % of its rated power SN (no load scenario). The measurements of phase voltages and currents are

carried out on the transformer LV side for each one of the groups of loads L1 to L6.

to L6: a) Voltage THD; b) Current THD; c) Power Factor; d) Value of RMS voltage

Power Quality Problems Introduced by Microgeneration 203

**Voltage THD Current THD** 

LV L1 L2 L3 L4 L5 L6

L3 L4 L5

b)

L6 d)

No load scenario (15% SN) – phase A No load scenario (15% SN) – phase B No load scenario (15% SN) – phase C Full load scenario (85% SN) - phase A Full load scenario (85% SN) - phase B Full load scenario (85% SN) - phase C
