Voltage Control of Unbalanced Distribution system with ... - IEEE Xplore

The 2nd IEEE Conference on Power Engineering and Renewable Energy (ICPERE) 2014

10A1-3

Voltage Control of Unbalanced Distribution system with Wind Energy Conversion System and High Photovoltaic Penetration Zakaria Ziadi

Mamdouh Abdel-Akher

Department of Electrical and Electronics Engineering, Faculty of Engineering, University of the Ryukyus Okinawa, Japan 903-0129. Email: [email protected]

Department of Electrical Engineering, Aswan Faculty of Engineering, South Valley University, 81542 Aswan, Egypt. Email: [email protected]

Abstract—This paper presents a voltage control method which is able to mitigate the voltage fluctuations caused by the integration of directly connected wind energy conversion system (WECS) based on induction generator (IG) into an unbalanced distribution system. Photovoltaic (PV) systems are widely spread in the distribution systems thus the proposed method takes into consideration high penetration of PV systems’ effect especially voltage deviations. The method is based on the use of the available reactive power in the inverters interfaced with PV systems for voltage control. However, in the connection point (CP) with the directly connected IG based WECS, the PV inverter will be used to control the voltage, compensate the reactive power needed by the WECS and smooth the fast voltage variation caused by the wind speed fluctuations. Since the distribution system is considered to be unbalanced, the directly connected IG based WECS three-phase model has been taken into account as well as the other components three-phase model and the powerflow solution method. Simulations have been conducted on a 14-bus system with high penetration and one IG based WECS to evaluate the proposed control method. Keywords – Unbalanced distribution system; induction generator based wind energy conversion system; Photovoltaic; Voltage control; Reactive power control.

I. I NTRODUCTION The integration of distributed energy resources (DERs) is increasing more and more in the past few decades. However, the high penetration of renewable energy based power can affect the actual distribution systems which were not constructed to host such intermittent sources of energy. One of the important challenges facing distribution systems is voltage control, as the voltage will raise depending on the penetration level and the fast voltage fluctuations will increase depending on the weather conditions. Controlling tap transformers is not enough to deal with the voltage problems because of their slow response. Thus, control of reactive power available in the inverters of the distributed generators (DGs) has been investigated in the literature as a promising solution to control the voltage [1,2], even sometimes at the expense of the active power as in [3]. In [4-6], the problem of voltage control is addressed as voltage reference scheduling and real time control exploiting

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the available reactive power in the inverters interfaced with DGs. The fact of the inherent unbalance nature was taken into consideration in the work. However, the DGs model was considered as a negative complex power load (PQ). That was acceptable since the DGs were assumed in that research to be PV systems connected through fully controlled inverters. In other words, even though the system voltage is unbalanced at the nodes where the DGs are connected, the DGs are not affected since they are interfaced with the grid using a fully controlled inverter which can deal with this problem and can inject the active and reactive power according to the control references. In this case, the three-phase unbalanced powerflow solutions can likely be obtained using a Newton-Raphson method or other solving method. The WECS considered in this research is supposed to be based on an IG and connected directly to the grid. In this case, more detailed modeling of the IG has to be considered since the voltage terminal at the CP is unbalanced. The WECS is also assumed to be connected in the same node with a PV system. This latter is controlling the voltage through its inverter by injecting the necessary reactive power. However, the reactive power load is very high at the concerned node since the IG consumes reactive power by nature. Also, the issue of smoothing the fast voltage fluctuations caused by the fast variations of the wind speed may be important for power quality point of view. A pitch angle control system is integrated into the WECS to smooth the output power when the wind speed is above the rated speed which will protect the IG, reduce the power output fluctuation and by consequence reduce the voltage variations [7-9]. Based on the aforementioned assumptions, a control method of a super-sized PV inverter at the CP is also proposed as a solution to control and smooth the node voltage as well as compensation of the reactive power consumed by the WECS. The super-sizing solution as well as other solution such as using two inverters or the use of one inverter aside to a capacitor bank will be investigated in the paper through numerical simulations. Different scenarios for the use and control of the inverters in an unbalanced distribution system

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The 2nd IEEE Conference on Power Engineering and Renewable Energy (ICPERE) 2014

10A1-3 Droop control Vref + -

1

V

n

Distribution network

using inverters which cannot control each phase by it self. Thus, the positive sequence of the three-phase voltage is used to be controlled as in [6].

P,Q Qref

dq abc

Inverter

Pref

Qmax Qmin

MPPT

Output range calculator

Fig. 1.

P PV

Proposed voltage droop characteristics control system.

are formulated to assess the proposed voltage control method. II. VOLTAGE C ONTROL OF P HOTOVOLTAIC S YSTEMS The voltage control system of the inverters interfaced with the PV panels is based on voltage droop control theory. The control system configuration is shown in Fig. 1. Droop control is a technique that decides the reactive power output based on the droop characteristics which are the voltage reference and slope. Applying droop control, the PV systems can respond to the voltage drop/rise according to their droop characteristics by increasing/decreasing their reactive power outputs simultaneously. The increase in active power output will counteract the reduction in frequency and the units will settle at active power outputs and frequency at a steady-state point on the droop characteristic. This will allow the different PV systems to settle at different reactive power levels and control the voltage to follow the references assigned to the different inverters. If the slope in droop characteristics is set to 𝑛 and a reference value is set to 𝑉𝑟𝑒𝑓 , voltage in distribution system 𝑉 and the relation of reactive power output variation Δ𝑄 will be defined by the following equation [10]: 1 (𝑉0 − 𝑉 ) (1) 𝑛 The droop characteristics may be adjusted to have better voltage control performance as in [5]. However, in this work the slope will be fixed and the voltage reference will follow a predecided schedule where the voltage reference will change every half an hour. In order to control the voltage without cutting or ”clipping” the PV active power generation, the reactive power output of the PV inverter has to be controlled within the inverter’s capacity limits. It is to notice that there are no restrictions on the power factor in this work since the main goal is to control the voltage. The PV inverter size has to be at least equal to the maximum PV maximum generation. Oversizing the inverters’ capacity is an option to ensure the availability of the reactive power even when the PV generation is maximum. The following formula determines the reactive power output margin: √ (2) 𝑄𝑚 = 𝑆 2 − 𝑃𝑃2 𝑉 Δ𝑄 =

Since the distribution system is inherently unbalanced it is not possible to control the unbalanced three-phase voltage

III. M ODELING OF THE W IND T URBINE G ENERATION S YSTEM The following section is concerned about the mathematical models adopted for the WECS’s parts which are the wind turbine, IG including the interfacing transformer. Since the IG is directly connected to the grid, the internal circuit of the generator will be fully investigated in the power-flow analysis [11-12]. Also, the IG model must take into account the unbalanced nature of the distribution system as the voltage across the generator terminals will be unbalanced. A. Wind turbine The mechanical power captured from wind by a wind turbine and transmitted to the IG can be formulated as follows: 𝑃𝑇 = 0.5𝐶𝑝 (𝜆, 𝛽)𝜌𝜋𝑅2 𝑉𝑤3

(3)

where 𝑉𝑤 is the wind speed, 𝜌 is the air density, 𝑅 is the radius of wind turbine, 𝐶𝑝 is the wind turbine power coefficient, 𝜆 = 𝜔𝑤 𝑅/𝑉𝑤 is the tip-speed ratio, 𝜔𝑤 is the angular rotor speed of wind turbine and 𝛽 is the pitch angle. 𝐶𝑝 is given by the following equations [9]: ) ( 12.5 116 𝐶𝑝 = 0.22 − 0.4𝛽 − 5 exp− Γ (4) Γ Γ=

1 −

1 𝜆+0.08𝛽

0.035 𝛽 3 +1

.

(5)

B. Induction Generator Sequence models in symmetrical component coordinates are used to derive the model of induction generator operating under unbalanced voltage conditions. The advantage of using this model is that the positive, negative, and zero-sequence networks are completely uncoupled due winding symmetry design [12]. The zero sequence network is not considered since the induction machine in wind power application is usually connected as delta or ungrounded Wye. Positive and negativesequence networks of the induction generator are shown in [11]. In this model, the negative sequence network presents the unbalanced operation of generator. The positive sequence and negative sequence equivalent voltages and currents at the machine terminals are: 𝑍𝑆 𝑟 𝑍𝑆 𝑍𝑅 𝑟 )𝑉𝑅 + (𝑍𝑆 + 𝑍𝑅 + )𝐼𝑅 (6) 𝑉𝑆𝑟 = (1 + 𝑍𝑚 𝑍𝑚 1 𝑍𝑅 𝑟 𝐼𝑆𝑟 = ( )𝑉𝑅𝑟 + (1 + )𝐼 (7) 𝑍𝑚 𝑍𝑚 𝑅 where 𝑟 is the sequence networks (= 1𝑜𝑟2), 𝑍𝑆 is the total stator impedance (= 𝑅𝑠 + 𝑗𝑋𝑠 ), 𝑍𝑅 is the total rotor impedance (= 𝑅𝑅 /𝑠 + 𝑗𝑋𝑅 ), and 𝑍𝑚 is the magnetizing branch impedance (= 𝑗𝑋𝑀 ). The total delivered power at the generator shaft can be calculated using the sequence networks

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The 2nd IEEE Conference on Power Engineering and Renewable Energy (ICPERE) 2014

10A1-3 Distribution system PCC Vpa

I pa

Vpb

Ip b

c

Vp

Transformer

Ipc

Vw

Induction generator Isa Vsc

-Isa

Isb V b s

-Isb

c

Is

Vs

c

Wind Turbine

Pw PM

of the generator model, ignoring the friction and winding losses, as follows: (8)

where 1−𝑠 )𝑅𝑅 𝑠 2 2 𝑠−1 )𝑅𝑅 𝑃𝑅2 = 3(𝐼𝑅 ) ( 2−𝑠

1 2 𝑃𝑅1 = 3(𝐼𝑅 ) (

(9) (10)

The calculated shaft power 𝑃𝑤 should be equal the delivered power by the turbine in equ. 3 hence the following power mismatch, Δ𝑃𝑠ℎ𝑎𝑓 𝑡 at the generator shaft can be defined as: Δ𝑃𝑠ℎ𝑎𝑓 𝑡 = 𝑃𝑇 − 𝑃𝑤

(11)

The above equation is function of the operating slip and sequence voltages at the generator terminals. The mismatch power equation at the generator shaft is nonlinear and can be solved numerically using Newton-Raphson method [25]. The sequence currents calculated using (4) are transformed to their counterparts in phase components as follows: 𝐼𝑎𝑏𝑐 = 𝐴𝐼012

(12)

where 𝐴 is the sequence transformation matrix. Then the updated voltages calculated by the three phase load flow method are converted to their counterparts in sequence components as follows: 𝑉012 = 𝐴−1 𝑉𝑎𝑏𝑐

(13)

The injected phase active and reactive powers at the PCC are calculated as follows: 𝑆𝑥𝑃 𝐶𝐶 = 𝑉𝑥𝑃 𝐶𝐶 (𝐼𝑥𝑃 𝐶𝐶 )∗

+ _

Pw N

Fig. 2. WECS based IG directly connected to the grid through the interface transformer.

𝑃𝑤 = 𝑃𝑅1 + 𝑃𝑅2

90

Wind power

-Isc

(14)

where x refers to phase a, b, or c. IV. VOLTAGE C ONTROL AT THE CP OF THE W IND E NERGY C ONVERSION S YSTEM In this section, the mitigation of the voltage fluctuations caused by WECS will be explored. That is ensured in this paper using two methods; by controlling the pitch angle and by controlling the reactive power injected at the CP.

0 Fig. 3.

+10 /s β(Pitch Angle)

PI -10 /s Rate limiter

Wind turbine pitch angle control system.

A. Pitch angle Control The main objective of controlling the pitch of the wind turbine is to protect it from high speed wind. Thus, the pitch angle control is active only when the wind speed is greater than the rated speed. Consequently, by controlling the blades’ pitch angle when the wind speed is above the rated speed the output power of the WECS will be smoothed to be equal to the nominal output power. This will mitigate the possible voltage fluctuations caused by the wind gusts. Pitch angle control method is intensively investigated in the literature [8-10]. The pitch angle control system used in this paper is shown in Fig. 3 where the maximum rate of the pitch angle change is ±10∘ /s. According to the wind speed, a selector will decide which value the pitch angle will be set to: ∙ if the wind speed is less than the rated speed, the pitch angle is set to zero. ∙ if the wind speed is between the rated speed and the cutout speed, a PI controller will determine the pitch angle reference. ∙ if the wind speed is greater than the cut-out speed, the pitch angle is set to 90∘ to protect the WECS. B. Reactive Power Control at the Connection Point The voltage control at the CP of the WECS is ensured by local injection of the right amount of reactive power. Since the WECS is directly connected to the grid, the reactive power has to be provided from a controlled a voltage source converter (VSC) based device e.g. STATCOM and static VAR compensator (SVC). In this paper, the proposed way to get this necessary reactive power is to control a fully controlled inverter existing at the CP rather than investing in a new SVC based device which is costly. This method takes the advantage of high PV penetration and assume exploiting (sharing) the same PV system’s (existing at the CP) inverter to control the voltage at the node where both PV and WEC systems are connected. In this case, the PV system will be modeled as a complex power load (PQ) as it is interface with the grid through a fully controlled inverter; however, since the IG is directly connected to the grid, a detailed model of the WECS is needed especially in the case of unbalanced system. It is also proposed that the reactive power consumed by the IG should be also provided by the same inverter instead of the investing in capacitor banks which may take more space and represent more expenses. Moreover, the capacitors must be controlled to match loads to avoid large discharge through motors and to lower power factor from too much leading

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The 2nd IEEE Conference on Power Engineering and Renewable Energy (ICPERE) 2014

10A1-3

TABLE I C ONSTANTS OF SAMPLE FEEDER MODEL .

21

22

23

24

13

14

15

16

31

32

Line impedance at each section Power factor of each load Rated capacity PV node Rated capacity interfaced inverter Transformation ratio on 1 tap change

LRT 11

12

: SVR

IG based WECS

33

34

0.04 + 𝑗0.04pu 0.8 0.08pu (400kW) 0.08pu (400kW) 1.00%

TABLE II W IND E NERGY C ONVERSION S YSTEMS ’ S PARAMETERS USED FOR SIMULATIONS .

35

: node with PV system

Fig. 4.

Model of distribution system.

impedance. the reactive power needed to improve the IG power factor depends mainly on the nominal active power output 𝑃𝑤𝑁 . Thus, it can be expressed as follows: 𝑄𝑃 𝐹 = 𝛽𝑃𝑤𝑁

(15)

where 𝛽 is a constant between 0 and 1 which can be calculated according to the desired new machine power factor. Also, the necessary reactive power considered to mitigate the voltage fluctuations caused by the active power fluctuations of the WECS is set to be proportional to the active power generated. Hence, the maximum reactive power required to mitigate the voltage fluctuations 𝑄𝑤𝑚𝑡𝑔𝑚𝑎𝑥 can be formulated as: 𝑄𝑤𝑚𝑡𝑔𝑚𝑎𝑥 = 𝛼𝑃𝑤𝑁

(16)

where 𝛼 is a proportionality constant which can be fixed or controlled to be between 0 and 1. The maximum PV active power output 𝑃𝑃 𝑉𝑚𝑎𝑥 installed at the same CP can be also expressed as a ratio of the nominal WECS active power using a constant 𝛾 as follows: 𝑃𝑃 𝑉𝑚𝑎𝑥 = 𝛾𝑃𝑤𝑁

(17)

The PV inverter has to be over-sized (or even super-sized) since the concerned inverter will be used to ensure the voltage control, voltage fluactuations mitigation (generated by WECS), and power factor correction. Thus, according to (15), (16) and (17), the capacity of the PV inverter installed at the CP should be chosen as follows: √ 2 + (𝑄𝑤𝑚𝑡𝑔𝑚𝑎𝑥 + 𝑄𝑃 𝐹 )2 (18) 𝑆𝑃 𝑉𝐶𝑃 ⩾ 𝑃 𝑉𝑚𝑎𝑥 in another way 𝑆𝑃 𝑉𝐶𝑃 ⩾ 𝑃𝑤𝑁

√

𝛼2 + (𝛽 + 𝛾)2

(19)

V. S IMULATION R ESULTS This section verifies the effectiveness of the proposed voltage control method in an unbalanced three-phase distribution system. The model of the simulated distribution system is shown in Fig. 4. Since high penetration of PV in the power systems is a concern in this research, the modelled 14-bus radial distribution feeder is supposed to contain 10 PV systems and one WECS installed at bus 35. Also, there are two step voltage regulators (SVRs) placed between the distribution nodes, and one load ratio control transformer (LRT) at the

Wind turbine Rotor diameter 47 𝑚 Air density 1.225 𝐾𝑔/𝑚3 Cut-in wind speed 4 𝑚/𝑠 Rated wind speed 12 𝑚/𝑠 Cut-out wind speed 25 𝑚/𝑠 Induction generator Rated power 660 𝑘𝑊 Base power (chosen) 990 𝑘𝑊 Number of pole pairs 2 Statorique resistance 0.0064 𝑝𝑢 Statorique inductance 0.0049 𝑝𝑢 Rotorique resistance 0.006 𝑝𝑢 Rotorique inductance 0.0589 𝑝𝑢 Mutual inductance 2.88 𝑝𝑢 TABLE III U NBALANCED LOAD RATIO IN THE DISTRIBUTION SYSTEM . Node 13 16 21 24 31

Phase 𝑎 𝑐 𝑏 𝑐 𝑎

Load [pu] 0.0 0.3 0.3 0.0 0.3

substation. Line impedances, power factor of load demand, and the rated capacity of the PV interfaced inverter of sample feeder model are given in table I, where the nominal capacity of the distribution system and the nominal voltage are 5 MVA and 6.6 kV, respectively. The WECS parameters are given in table II. The simulations were conducted under an unbalance three-phase load, where the imbalance loading at the concerned buses are provided in table III. Fig. 5 illustrates the conditions used to conduct the simulations. The forecast and exact values of the PV generated power and load demand -urban residential load nature- are shown in Fig. 5(a). In this paper, the PV active power output varies in the same way for all the DG nodes. Fig. 5(b) depicts the wind speed variation in the operation day where it can be noticed that it may exceed the rated wind speed (12𝑚/𝑠). Fig. 5(c)-(f) respectively show the voltage control reference (positive sequence) and the tap position of each voltage control device was determined in [4] without taking into consideration the integration of the WECS, using 30 minutes average value of the predicted values on one day. The voltage reference schedule, shown in Fig. 8, is the positive sequence of the optimal three-phase voltage. The tap position of the LRT, SVR1 and SVR2 are shown in Figs. 9(a) to (c) respectively, where the LRT and SVRs considered in this paper are supposed to have 32 steps. The three ratios of the LRT are the same because the voltage at the substation has to be balanced.

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The 2nd IEEE Conference on Power Engineering and Renewable Energy (ICPERE) 2014

PV power and Load PPV PL [pu]

0.05 0.04 0.03 0.02 0

2

4

6

8

10 12 14 16 Time [hour]

18

20

22

24

(a) Actual PV output and load demand.

Wind speed Vw [pu]

10

5

0 0

2

4

6

8

10 12 14 Time [hour]

16

18

20

22

24

16

18

20

22

24

16

18

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22

24

16

18

20

22

24

16

18

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(b) Wind Speed. 1.04 1.03 1.02 1.01 1 0.99 0.98 0.97 0.96 0.95 0.94 0

2

4

6

8

10 12 14 Time [hour]

(c) Voltage reference schedule.

T

8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8

Phase a Phase b Phase c

0

2

4

6

8

10 12 14 Time [hour]

(d) LRT tap positions. 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8

Phase a Phase b Phase c

0

2

4

6

8

10 12 14 Time [hour]

(e) SVR1 tap positions.

S VR2

SVR Tap position 2 [pu] T

This paper proposed a voltage control method for DGs based on PV and WEC systems in unbalanced distribution systems. The control method aimed to keep the voltage within the acceptable range using a voltage droop controller for PV systems and mitigate the voltage fluctuations caused by the intermittent nature of the WECS. The WECS used was based on a directly connected IG, thus a detailed modeling was necessary. The PV inverter at CP where the WECS was integrated was oversized to match the reactive power necessary for voltage control, voltage fluctuations mitigation and power factor improvement of the WECS. Simulations have been conducted to valid the effectiveness of the proposed method in controlling and smoothing the unbalanced distribution voltage.

0

15

1

VI. C ONCLUSION

PV generation Load

0.07 0.06

0.01

Voltage reference V + [pu]

thus, the inverter size was decided to be 0.2𝑝𝑢. This result confirms that using one inverter of 0.2𝑝𝑢 capacity is better that using two different inverters with 0.17𝑝𝑢 and 0.08𝑝𝑢 which may cost more for the installation and the maintenance. The rest of the reactive power injected through the PV inverter into the grid is shown in Fig. 6(f), where it can be seen that since the inverters’ capacity was not oversized a shortage of reactive power is observed around noon which caused the voltage raise. Fig. 6(g) shows the pitch angle of the wind turbine where it is obvious that the control was activated when the wind speed was above 12𝑚/𝑠. By increasing the pitch angle the power was kept constant at the 𝑃𝑤𝑁 which helped to smooth the voltage otherwise the power spikes could manifestly fluctuate the voltage. The last figure shows the IG electrical speed since it is important in the modeling of directly connected machines.

0.08

LRT tap position TL R [pu]

Fig. 6 describes the simulation results of the distribution system based on the conditions shown in Fig. 5 and using the proposed control method except for Fig. 6(a) where the method of voltage variation mitigation of the WECS using reactive power was not used. Thus, the voltage is that subfigure is highly fluctuated compared to Fig. 6(b) where reactive power is injected in the CP to mitigate the voltage fluctuation caused by the WECS. The reactive power used for that reason is proportional to the active power, shown in Fig. 6(c), of the WECS with an 𝛼 equal to 0.6 (Subsection 4-b). Also, another amount of reactive power had to be injected in the same point to compensate the reactive power consumed by the IG shown in Fig. 6(d) which was about 0.7 time the nominal IG active power. Moreoever, the reactive power decide by PV droop controller was also injected in the CP. The total reactive power injected in node 35 is illustrated in Fig. 6(e). In order to secure that amount of reactive power, the inverter size at the CP (node 35) is chosen according to (19) as follows: √ 𝑆 ⩾ 𝑃𝑤𝑁 (0.6 + 0.7)2 + 0.62 ⇒ 𝑆 ⩾ 1.43𝑃𝑤𝑁

SVR1Tap position T S V R [pu]

10A1-3

8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8

Phase a Phase b Phase c

0

2

4

6

8

10 12 14 Time [hour]

(f) SVR2 tap positions. Fig. 5.

Simulation conditions

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The 2nd IEEE Conference on Power Engineering and Renewable Energy (ICPERE) 2014

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24

0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

24

0.1 0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 -0.1 0

24

10 9 8 7 6 5 4 3 2 1 0 0

1.04

Reactive power at CP QCP [pu]

Node voltage V [pu]

1.02

abc

1 0.98 0.96 0.94 0.92 0

2

4

6

8

10 12 14 Time [hour]

16

18

20

22

(a) Three-phase node voltage (without voltage smoothing).

1 0.98 0.96 0.94 2

4

6

8

10 12 14 Time [hour]

16

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2

(b) Three-phase node voltage (with voltage smoothing). WECS pitch angle b [degree]

WECS active power Pw [pu]

0.12 0.1 0.08 0.06 0.04 0.02 2

4

6

8

10 12 14 Time [hour]

16

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20

22

2

WECS electrical speed W r [RPM]

WECS reactive power Qw [pu]

-0.055

1506

-0.06

-0.065 -0.07

-0.075 -0.08 4

6

8

10 12 14 Time [hour]

16

18

20

22

24

(d) WECS reactive power output. Fig. 6.

10 12 14 Time [hour]

16

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8

10 12 14 Time [hour]

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10 12 14 Time [hour]

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(g) Wind turbine pitch angle. 1507

2

4

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(c) WECS active power output. -0.05

-0.085 0

8

(f) PV inverters reactive power output.

0.14

0

6

Reactive power QPV [pu]

Node voltage Vabc [pu]

1.02

0

4

(e) Reactive power output at WECS CP.

1.04

0.92 0

2

1505 1504 1503 1502 1501 1500 1499 0

2

4

6

8

10 12 14 Time [hour]

16

(h) WECS electrical speed.

Simulation results of the distribution system.

R EFERENCES [1] F. A. Viawan and D. Karlsson, ”Voltage and Reactive Power Control in Systems with Synchronous Machine-Based Distribution Generation,” IEEE Trans. Power Del., vol. 23, no. 2, pp. 1079-1087, Apr. 2008. [2] R. H. Liang and Y. S. Wang, ”Fuzzy-Based Reactive Power and Voltage Control in a Distribution System,” IET Renew. Power Del., vol. 18, no. 2, pp. 610-618, Apr. 2003. [3] A.E. Kiprakis, A.R. Wallace, and G.P. Harrison, ”Centralized and Distributed Voltage Control: Impact on Distributed Generation Penetration,” IEEE Trans. Power Syst., vol. 22, no. 1, pp. 476-483, Feb. 2007. [4] Z. Ziadi, M. Abdel-Akher, A. Yona, T. Senjyu, T. Funabashi, ”Optimal Scheduling of Voltage Control Resources in Unbalanced Three-Phase Distribution Systems,” IEEE Int. Conf. on Power and Energy (PECon), Kota Kinabalu, Malaysia, Dec. 2012. [5] Z. Ziadi, A. Yona, T. Senjyu, M. Abdel-Akher, and T. Funabashi, ”Real time voltage control of unbalanced distribution systems with photovoltaic generation,” IEEE Int. Conf. on Renewable Energy Research and Applications (ICRERA), pp. 1-6. Nagasaki, Japan, 11-14 Nov. 2012. [6] Z. Ziadi and M. Abdel-Akher, ”Optimal scheduling and Real Time Voltage Control Method for Unbalanced Distribution Systems,” IEEE Int. Conf. on Industrial Technology (ICIT), pp. 559-564, Busan, Korea, Feb. 26 - Mar. 1, 2014.

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