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A control scheme for voltage unbalance compensation in an islanded microgrid
Electric Power Systems Research 177 (2019) 106016
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A control scheme for voltage unbalance compensation in an islanded microgrid
T
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Sajad Hoseinniaa, Mahdi Akhbaria, , Mohsen Hamzehb, J.M. Guerreroc a
Department of Electrical Engineering, Shahed University, Tehran, Iran Department of Electrical Engineering, Shahid Beheshti University, Tehran, Iran c Department of Energy Technology, Aalborg University, Aalborg, Denmark b
A R T I C LE I N FO
A B S T R A C T
Keywords: Power quality Photovoltaic Inverters Active filters Microgrid
One of the major power quality issues in low-voltage (LV) microgrids is the voltage unbalance which has adverse effects on electrical devices. This paper presents a novel control scheme to mitigate the voltage unbalance by a photovoltaic (PV) system. In this study, load current sensors are eliminated and the PV system mitigates the voltage unbalance by analyzing its terminal voltage. This could effectively reduce the cost and complexity of compensation system because of the difficulties of load current sensors. The proposed control strategy is developed for a three-phase PV. As the inverter detects the voltage unbalance at its terminal, the proposed control algorithm calculates the compensation reference currents based on the double synchronous reference frame (DSRF) analysis of the PV terminal voltage. Therefore, the PV inverter injects the compensating currents to the microgrid. The effectiveness of the control scheme is verified by simulation studies in the PSCAD/EMTDC environment.
1. Introduction Nowadays, the increasing installation of distributed generation (DG) in low-voltage (LV) networks make the control of microgrids a remarkable issue. The existence of linear and non-linear loads as well as single-phase and three-phase ones in the microgrids presents different power quality challenges for the consumers. One of major power quality challenges in LV microgrids is the voltage unbalance which has adverse effects on electrical instruments including induction motors and those contain power electronic converters [1]. This challenge could be mainly caused by high penetration of single-phase residential loads as well as single-phase sources such as single-phase PVs [2]. The literature demonstrates much research dedicated to the voltage unbalance compensation using series/shunt active power filters (APFs), hybrid APFs, static synchronous compensators (STATCOMs), static VAR compensators (SVCs) [3–9]. Series APF generates negative sequence voltage over the line [3,4] while shunt APFs injects negative sequence current to reduce the voltage unbalanced which is made by these currents [5]. Combining series and shunt APF leads to hybrid series-parallel compensators. A popular type of hybrid compensators is the unified power quality conditioner (UPQC) that injects negative sequence voltage with
its series filter and negative sequence current via its shunt filter [8,9]. Another option is the static synchronous compensators (STATCOMs) that compensates the voltage unbalance by injecting negative sequence reactive power to the network [10–13]. However, the cost of these filters could be a challenge that result in the increase of the system investment costs. Additionally, controlling these facilities would increase the overall system complexity. Recently, photovoltaic (PV) systems spread in distribution grids and arise threats and opportunity for the grid managers. For example, high penetration of single phase PV systems could be the cause of voltage unbalanced and should be assessed and regulated. In Refs. [14,15] authors introduce an assessment of PV systems in distribution grids and evaluate the grids’ emission limits for these generations. The existence of three phase PV systems can provide an opportunity for the utility companies to use these sources as APFs [16,17] without installing extra instruments such as aforementioned STATCOM, SVC, and UPQC. PVs contain valuable inverters that hardly operate at their maximum rated power because of the variation of solar radiation over the day. Therefore, it is more efficient to use the excess capacity of the inverters for compensating the voltage unbalance [18–22]. A PV system with active power filtering functionality is presented in Ref. [20] to compensate the
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Corresponding author at: Shahed University, Department of Electrical Engineering, Persian Gulf Freeway, 33191 18651, Tehran, Iran. Tel.: +98 21 5121 2066; fax: +98 21 5121 2021. E-mail addresses: [email protected] (S. Hoseinnia), [email protected] (M. Akhbari), [email protected] (M. Hamzeh), [email protected] (J.M. Guerrero). https://doi.org/10.1016/j.epsr.2019.106016 Received 20 April 2019; Received in revised form 30 July 2019; Accepted 22 August 2019 Available online 04 October 2019 0378-7796/ © 2019 Elsevier B.V. All rights reserved.
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voltage unbalance. The system measures the unbalanced load current and extracts the compensating current based on generalized instantaneous reactive power theory. Authors in Ref. [21] develop a control strategy for single-phase PVs propagated throughout the distribution network to mitigate the voltage unbalance. The control strategy is based on the fact that in the case of voltage unbalance, active and reactive powers could vary across each phases of the network according to the connected single phase loads on each phase. Therefore, the voltage unbalance in different buses could be compensated by curtailing the active and reactive power injected by single-phase PVs which are installed in different phases over the network. However, it lacks a scheme for three phase inverters. Moreover, changing the phase of single-phase PVs needs extra instruments which would increase the costs. In Ref. [22], the authors consider electric vehicles and PV systems for unbalance compensation. It is supposed that the inverters of these systems could transfer different amount of power per each phase and it is not necessary for the power to be equally divided across the three phases. Accordingly, the study presents a centralized algorithm for the network to manage the power in each phase of PV inverters and electric vehicles systems to improve the voltage imbalance. However, the control strategy for each inverter system is not discussed and the paper considers the idea from the system level point of view. Reviewing the literature, the APFs and PV-based APFs generally suppose that the current and voltage of network or unbalanced loads are accessible. In this condition, the APFs analyze the unbalanced currents and calculate and inject the compensating current to reduce the voltage unbalance. However, in many real applications, the PV senses only its terminal voltage and its injected current and the unbalanced currents of the local loads are inaccessible for the PV system. Moreover, installing extra measurement hardware for measuring these unbalanced currents could increase the system cost and complexity. Therefore, the main purpose of this paper is to present a control strategy for a PV system to mitigate the voltage unbalance without the need to supplementary devices that measure the local unbalanced load current. When the loads of the microgrid become unbalanced, the corresponding unbalanced currents are initially supplied by the voltagecontrolled sources which stabilize and regulate the voltage of the microgrid. The unbalanced currents from these sources pass through the feeders’ impedances and therefore, result in the voltage unbalance at the consumer terminals. When the proposed control scheme is activated, the PV analyzes its terminal voltages based on the double synchronous reference frame (DSRF) and extracts the negative part of the voltage caused by unbalanced loads. Then, the compensating currents are calculated in order to reduce the voltage unbalance at the PV terminal and these currents are injected to the microgrid. Injecting the compensating currents by the PV system removes negative sequense currents of the voltage-controlled voltage sources and makes these currents balanced. This could leads to the mitigation of the voltage unbalance at the consumer side. The proposed control strategy is developed for a three-phase four-wire PV system in an islanded LV microgrid. The effectiveness of the control scheme is verified by simulation studies in the PSCAD/EMTDC environment.
G= kp +
ki s2 + ωc . s+ ω20
(1)
where kp and ki are the proportional and integral gains and ω0 and ωc are the reference frequency of the microgrid and the bandwidth around this frequency respectively. 3. Proposed control scheme Analysing the voltage unbalance in the networks, the International Electrotechnical Commission (IEC) in the 61000-2-2: 2000 Standard introduces the voltage unbalanced factor (VUF) [24]:
VUF%=
V− . 100 V+
(2)
where V− and V+ are negative and positive sequence voltages respectively. This definition considers both magnitude and phase angle unbalance. Therefore, the main purpose of the control strategy is to reduce the VUF at the terminal of the PV system according to the IEC definition. As voltage unbalance could have adverse effects, the acceptable compatibility level of VUF is limited in the networks. This limitation varies country by country ranging between 1–5% [14]. In this paper, it is supposed that the VUF should be lower than 2% according to the aforementioned IEC standard. As the solar radiation varies during the day, PV systems hardly operate at their maximum power and in this condition, according to the inverter’s switch ratings, the PV inverter has a surplus capacity per phase that is not in use. Therefore, it is possible to inject the dc-link power unequally through different phases to respond different per phase load demands. On the other hand, by injecting more current through the phase with higher load demand, it is possible to reduce the voltage unbalance at the PV terminal. To make this concept operational, the control scheme of Fig. 2 is used. This figure demonstrates the block diagram of the proposed control scheme which produces reference current for the inner inverter control loop. This reference current could be calculated from the sum of positive components (green blocks) and negative components (red blocks): − i+ ⎡ ia ⎤ ⎡ a ⎤ ⎡ i−a ⎤ ⎢ ib ⎥ = ⎢ i+b ⎥ + ⎢ ib ⎥ ⎢ i ⎥ ⎢ + ⎥ ⎢ i− ⎥ ⎥ ⎣ c⎦ ⎣ c⎦ ⎢ ⎣ ic ⎦
(3)
Following this concept, by means of Park’s transformation which is introduced in Ref. [23,25], positive and negative voltages in the DSRF could be identified by Eqs. (4) and (5) as follows:
⎡ cos(θ) cos( θ− + ⎡ vd ⎤ ⎢ 2 + ⎢ vq ⎥ = ⎢ ⎢ ⎥ 3 ⎢ sin(θ) sin( θ− + ⎢ ⎢ ⎣ v0 ⎥ ⎦ 0.5 ⎣ 0.5
2π ) cos( θ+ 3 2π ) sin( θ− 3 0.5
⎡ cos(−θ) cos(− θ− − ⎢ ⎡ v −d ⎤ 2 ⎢vq ⎥ = ⎢ 3 ⎢ sin(−θ) sin(− θ− ⎢ v −⎥ ⎣ 0⎦ ⎢ 0.5 ⎣ 0.5
2. Control strategy for PV inverters
2π ⎤ ) 3 ⎥ ⎡ va ⎤ 2π ⎥ ⎢ vb ⎥ )⎥ 3 ⎥ ⎣ vc ⎦ ⎦
2π ) cos(− θ+ 3 2π ) sin(− θ− 3 0.5
2π ⎤ ) 3 ⎥ ⎡ va ⎤ 2π ⎥ ⎢ vb ⎥ )⎥ 3 ⎥ ⎣ vc ⎦ ⎦
(4)
(5)
where v+d , v+q and v+0 are positive d, q and zero voltages and v −d , v −q and v −0 are negative d, q and zero voltages respectively. As it is formulated in Eqs. (4) and (5), v+0 and v −0 are indeed equal. In a balanced load condition, only positive d and q components of voltage exist and the inverter injects equal power across three phases. In this conditions, positive reference currents are needed and are calculated in the upper control loop (green blocks) of Fig. 2. This control loop produces the positive d and q reference currents based on the d and q components of the inverter output voltage. The d component regulates the dc-link voltage and is responsible for the active power of
The PV source generally consists of PV array, DC/DC converter and DC/AC inverter as depicted in Fig. 1. The DC/DC converter increases the dc output voltage of the PV and also controls the PV array in maximum power point tracking (MPPT) operation mode. The inverter sets the dc-link voltage to its reference value and regulates this voltage. The inverter of PV system operates in current control mode (CCM) to inject the PV power to the microgrid. To develop the control scheme, the natural frame (abc) model of a three-phase inverter in is used [23]. Therefore, a proportional resonant (PR) controller is tuned to track the sinusoidal reference generated from outer control loops: 2
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Fig. 1. PV power electronic interface.
of the PV inverter is calculated as follows:
the inverter. The q component adjusts the output AC voltage of the inverter to its reference value and is dedicated to the reactive power injection of the inverter. By means of reverse Park’s transformation which is introduced in Ref. [23], synchronous reference current components are transformed into the natural frame current components as follows:
sin(θ) 1⎤ ⎡ cos(θ) + + 2π 2π ⎥ ⎡ id ⎤ ⎡ ia ⎤ ⎢ ⎢ i+b ⎥ = ⎢ cos( θ− 3 ) sin( θ− 3 ) 1⎥. ⎢ i+q ⎥ ⎥ ⎢ ⎥ ⎢ +⎥ ⎢ + 2π 2π ⎢ ⎣ ic ⎥ ⎦ ⎢ cos( θ+ ) sin( θ+ ) 1⎥ ⎢ ⎣ i0 ⎥ ⎦ ⎥ ⎢ 3 3 ⎦ ⎣
→ →+ →− total Iabc = Iabc + Iabc
(8) → → → + total where Iabc , Iabc and Ia−bc are the total, positive and negative currents in vector space, respectively. The final reference currents should not exceed the rating of inverter’s switches (Isw ):
→ total 2 Isw 2 ≥ | Iabc |
Therefore, the amount of total injected current could be calculated from the law of cosines:
(6)
+ 2 − 2 total 2 |Iabc | ≤ |Iabc | + |Iabc |
As an unbalanced load connects to the microgrid, negative d and q components emerge in the terminal voltages. In this condition, the negative sequence currents are initially provided by the voltage-controlled voltage sources and the PV source does not participate in the voltage unbalance compensation. When the voltage unbalance compensator (VUC) of the PV inverter (red blocks) in Fig. 2 is activated, negative d, q and zero components of the inverter terminal voltages are calculated by (5). Then, these values are compared with a zero and by means of PI controllers, the negative d, q and zero components of reference current are generated. Then, by means of reverse negative Park’s transformation Eq. (7), negative reference currents in the natural frame are obtained:
sin (−θ) 1⎤ ⎡ cos (−θ) − − ⎡ia ⎤ ⎢ cos (−θ − 2π ) sin (−θ − 2π ) 1⎥ ⎡ id− ⎤ ⎥ ⎢ i ⎢ib− ⎥ = ⎢ . q ⎥ 3 3 ⎥ ⎢ −⎥ ⎢i − ⎥ ⎢ 2 π 2 π i 1 c ⎥ ⎢ ⎣ ⎦ cos (−θ + ) sin (−θ + ) 1 ⎣0⎦ ⎥ ⎢ 3 3 ⎦ ⎣
(9)
(10)
Accordingly, the right side of the (9) is replaced by the right side of the (10) and should satisfy this inequality. If (11) is satisfied, we would be assured that (9) was satisfied too: + 2 − 2 (Isw )2 − |Iabc | ≥ |Iabc |
(11) − 2 | the |Iabc
+ 2 | on |Iabc
based and Therefore, (11) determines the limit for (Isw )2 . The negative component of PV current follows these equations:
→− Iabc = (Id− + j. Iq−). e−j . θ
(12)
− 2 |Iabc | = (Id−)2 + (Iq−)2
(13)
By substituting (13) in (11), (14) could be concluded: + 2 (Isw )2 − |Iabc | ≥ (Id−)2 + (Iq−)2
(14)
According to (14), as the PVs are controlled to maximize the active power, the positive component of current has priority and the rest of the difference between the switch rating of the inverter and the positive current component is dedicated to the negative d and q components of current respectively. This constraint is shown in Fig. 2 as some saturation blocks before the reverse negative sequence transformation. Fig. 3 shows the effect of the PV participation in the unbalanced current compensation. After the connection of the unbalanced load to the microgrid, negative d, q and zero components of the load current
(7)
The resulted negative current components then is used in the Eq. (3) and is added to the positive ones to generate reference currents for the inverter’s inner control loop. This means that in the unbalanced load condition, the inverter could produce negative component currents to mitigate the VUF at the terminal of the PV system. On the other hand, the total injected current
Fig. 2. The proposed control system. 3
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Fig. 3. Supply of negative current components (a) before and (b) after compensation.
are supplied by the voltage-controlled voltage sources. Because of the line impedances between these sources and the unbalanced load, negative current components of the unbalanced load produce negative voltage components in the PV terminal. After the activation of the VUC, either a share of or all the negative current components are injected to the load terminal by the PV instead of voltage-controlled voltage sources. Therefore, the negative voltages at the terminal of the load decrease and then, the VUF reduces consequently. 4. Simulation validation To verify the performance of the proposed control scheme, two cases are considered in this section. The objective of case I is to verify the ability of the system in detecting and mitigating of voltage unbalance at the terminal of a PV system. In this case, two unbalanced load would be connected to the microgrid and the proposed control scheme would be verified. Then, in case II, adaptation of the control system will be verified when two unbalanced loads disconnect from the network. Therefore, a benchmark AC microgrid is nominated and simulated using PSCAD/EMTDC software. The AC microgrid utilized in this paper is illustrated in Fig. 4. This microgrid is taken from International Council on Large Electric Systems (CIGRE) Benchmark microgrid network [26] which has been specially designed for LV microgrid studies and contains real utility parameters. It is supposed that the microgrid is disconnected from the main grid and consists of seven feeders. Furthermore, the loads are grouped into three- and singlephase loads and are residential consumers. The power factor for all loads is assumed to be 0.85 lagging. The microgrid parameters could be seen in the Table 1. DG1, DG2 and DG3 are voltage-controlled voltage sources and regulate the voltage of the microgrid. Because of the resistive feeder impedances, they work under a resistive droop control. Moreover, DG4 and DG5 are PV sources that initially inject the maximum produced power to the microgrid. The proposed control strategy is applied to the DG4 PV inverter and is validated in the case study. The sources initially supply balanced loads according to Table 1 and all of single-phase consumers of load 4 and 5 are disconnected from the microgrid. The PV source of DG4 and DG5 initially injects active power equal to 6.8 kW and 5 kW respectively. Characteristics of the PV source of DG4 could be seen in the Table 2.
Fig. 4. Under study system adjusted from CIGRE LV microgrid network.
4.1. Case I
the other phases remain almost constant (the green and red lines in Fig. 6(a)) (Table 3 and 4). The positive d component of DG4’s terminal voltage is illustrated in Fig. 7(a) and the positive q and zero components of the output voltage of DG4 are almost zero. By the first unbalanced load connection, the negative d and q components of the output voltage appear in Fig. 7(b). Moreover, positive d and q component of the reference currents are demonstrated in Fig. 6(b). At t = 2 s, another 5 kVA single-phase load connects to the phase ‘C’ of the feeder F07. At this moment, the VUF falls a bit to 0.52% and a decrease in the terminal voltage in phase ‘C’ of DG4 could be seen in the Fig. 6(a).
In this case study, the sources initially supply balanced loads according to Table 1 and all of single-phase consumers of load 4 and 5 are disconnected from the microgrid. The PV source of DG4 and DG5 initially inject active power equal to 6.8 kW and 5 kW respectively. As the PV of DG4 operates with an active power lower than its rated power (i.e. 10 kW), there is a surplus switching capacity to be utilized for injecting compensating current. At t = 1 s, a single-phase 5 kVA load connects to the phase ‘A’ of the feeder F06 which increases the VUF at the terminal of DG4 from 0 to 0.59% (Fig. 5). Moreover, the terminal voltage in phase ‘A’ of DG4 decreases (the blue line in Fig. 6 (a)) while 4
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Table 1 Microgrid characteristics. Parameters
Values
Voltage Frequency
400Vrms- line to line 50 Hz
Feeders(Length, Size) F01 F02 F03 F04 F05 F06 F07
280 m, Twisted cable 4 × 120 mm2 Al 30 m, Service Connection 4 × 6 mm2 Cu 30 m, Service Connection 4 × 16 mm2 Cu 30 m, Twisted cable 3 × 70 mm2 Al 30 m, Service Connection 4 × 25 mm2 Cu 30 m, Service Connection 4 × 6 mm2 Cu 30 m, Service Connection 4 × 16 mm2 Cu
Sources DG1 DG2 DG3 DG4 DG5
30 kW, 30 kW, 10 kW, 10 kW, 10 kW,
Droop m1, n1 m2, n2 m3, n3
2.69e-5, 5.43e-4 8.07e-5, 0.0016 2.69e-5, 5.43e-4
Loads Load 1 Load 2 Load 3 Load 4
3 × Φ, 3 × Φ, 3 × Φ, 3 × Φ, 3 × Φ,
1 × 3Φ, 1 × 3Φ, 1 × 3Φ, 3 × 1Φ, 1 × 3Φ, 3 × 1Φ,
Load 5
Fuel Cell Microturbine Fuel Cell Photovoltaic Photovoltaic
15 kVA, Cos Φ = 0.85 Lag 30 kVA, Cos Φ = 0.85 Lag 5 kVA, Cos Φ = 0.85 Lag 5 kVA, Cos Φ = 0.85 Lag, 5 kVA, Cos Φ = 0.85 Lag 5 kVA, Cos Φ = 0.85 Lag
Fig. 6. Effective (a) Voltages and (b) Currents of DG4 in Case I. Table 2 PV system characteristics.
Table 3 First scenario timeline.
Parameters
Values
Power stage DC link voltage Switching frequency Inverter-side inductor Grid-side inductor Inverter capacitor Inductor resistance
700 V 15 kHz 2 mH 0.2 mH 0.7 μF 0.05 Ω
Primary control Proportional gain Resonant gain Secondary Control id+ Proportional & iq+ Proportional & id− Proportional & iq− Proportional &
gains gains gains gains
Event
VUF (%)
0–1 1–2 2–3 3–5
Microgrid Statrup A 5 kVA, 1 ph. load connects to phase A at F06 in t = 1 s A 5 kVA, 1 ph. load connects to phase C at F07 in t = 2 s DG4 compensation is activated in t = 3 s
0 0.59 0.52 0.01
Table 4 Second scenario timeline.
0.3 300 Integral Integral Integral Integral
Time (s)
0.1, 10 0.1, 0.1 1, 10 1, 10
Time (s)
Event
0–3 3–6 6–9
Stable compensation of unbalanced loads by the DG4 A 5 kVA, 1 ph. load disconnects from phase A at F06 in t = 3 s A 5 kVA, 1 ph. load disconnects from phase C at F07 in t = 6 s
currents of DG4 in order to decrease the voltage unbalance. The currents in phases ‘A’ and ‘C’ of DG4 which have higher load demands increase while the corresponding value in the phase ‘B’ with lower load demand decreases. The change in DG4 currents results in the increase of the voltages of phase ‘A’ and ‘C’ at the terminal of the DG4. As it could be seen in Fig. 5, the voltage unbalance is almost improved and VUF falls from 0.52% to almost 0. Fig. 9 depicts the active and reactive powers of the PV source of DG4 injected to the microgrid. A double frequency ripple appears in these powers because of unbalanced current injection. This case approves that the scheme could effectively reduce the voltage unbalance in the microgrid. 4.2. Case II
Fig. 5. Voltage unbalance factor in percent in the Case I.
In this case the adaptation of the VUC is tested in the condition of removing unbalanced loads. The DG4 initially compensates the unbalanced voltages of its terminal at the presence of the unbalanced loads of the Case I. At t = 3 s, the single-phase 5 kVA load on the phase
Finally, at t = 3 s, the VUC is activated and negative currents (i.e. id−, iq−) are injected by the DG4 in order to reduce the VUF (Fig. 8(b)). As it is demonstrated in Fig. 6(b), the VUC changes the equality in phase 5
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Fig. 9. (a) Active power, and (b) reactive power of DG4 in Case I. Fig. 7. (a) Vd+ and (b) Vd− and Vq− at the DG4 terminal in Case I.
Fig. 10. Voltage unbalance factor at the DG4 terminal in percent in Case II.
period, the VUF approaches to zero. The effective value of DG4 terminal voltage is depicted in the Fig. 11(a). After disconnecting of the first unbalanced load, the currents remain unbalanced to compensate the other unbalanced load. Finally, after disconnecting of the second load at t = 6 s, the VUF sets to almost zero and the currents become equal in three phases as could be seen in the Fig. 11(b). The d component of the terminal voltage increases after the disconnection of the unbalanced loads (Fig. 12(a)). The positive and negative component of the PV current is demonstrated in Fig. 13. After t = 6 s, the compensation process analyzes the negative component of the terminal voltage and as it is zero because of the balanced power demand in the microgrid, injecting negative component currents is automatically terminated (Fig. 13(b)). The instantaneous currents of the PV before and after the disconnection of the last unbalanced load is depicted in the Fig. 14. As it could be seen there, the PV current is unbalanced before t = 6 s, while it tends to balanced values after this time. This case study approves that the compensation technique remains effective when unbalanced loads are disconnected from the microgrid and the voltage unbalance is solved.
Fig. 8. (a) id+ and iq+ , and (b) id− , iq− and i 0− at the DG4 terminal in Case I.
‘A’ of the feeder F06 is disconnected and at t = 6 s, the other 5 kVA single-phase load is disconnected from the phase ‘C’ of the feeder F07. As it could be seen in the Fig. 10, the VUF is near zero in the presence of the unbalanced loads from 2 s to 3 s which is the result of compensation. At t = 3 s and t = 6 s when unbalanced load disconnects from the grid, sudden change with an overshoot occur and after a transient
5. Conclusion In this paper, a new control strategy for a three-phase four-wire PV 6
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Fig. 11. Effective (a) Voltages and (b) Currents of DG4 in Case II.
Fig. 13. (a) id+ and iq+ , and (b) id−, iq− at the DG4 terminal in Case II.
Fig. 14. Instantaneous currents of DG4 in Case II.
control system identifies the voltage unbalance by detecting negative sequence voltages. Based on these voltages, the control system calculates the required negative sequence compensating current which could reduce the voltage unbalance at the PV terminal. This control technique does not need to measure unbalanced load current and therefore, the compensation system could be applicable without local load current sensors. Although using the PV inverter as an active power filter could reduce the cost of compensating system, the proposed control system would be able to reduce the cost of the compensation once more. The effectiveness of the control scheme was validated using PSCAD/EMTDC environment. The simulation scenarios approved that the PV system could beneficially mitigate the voltage unbalance while the unbalanced loads connect to or disconnect from the LV microgrid. While the proposed control strategy was presented for an islanded microgrids, it could be recommended for any distribution networks with voltage unbalance difficulties.
Fig. 12. (a) Vd+ and (b) Vd− and V −q at the DG4 terminal in Case II.
inverter was developed to mitigate the voltage unbalance. Unlike APFs, the load current sensor was eliminated and the compensation scheme calculated the reference currents by analyzing the PV terminal voltage and therefore, the cost and complexity could be reduced. The proposed control strategy benefited from the double synchronous reference frame (DSRF) which identifies the positive and negative sequence of the PV terminal voltages. As an unbalanced load connects to the network, the
Conflict of interest None.
7
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[1] B. Singh, A. Chandra, K. Al-Haddad, Power Quality: Problems Mitigation Techniques, Wiley, Hoboken, NJ, USA, 2015. [2] D. Gallo, R. Langella, A. Testa, et al., Case studies on large PV plants: harmonic distortion unbalance and their effects, Proceedings of the IEEE Power Energy Society General Meeting, July, 2013, pp. 1–5. [3] S.D. Swain, P.K. Ray, K.B. Mohanty, Improvement of power quality using a robust hybrid series active power filter, IEEE Trans. Power Electron. 32 (May 5) (2017) 3490–3498. [4] D. Li, M. Song, J. Hu, et al., Improved series active power filter with fundamental and harmonic magnetic flux hybrid compensation, IET Power Electron. 11 (6) (2018) 1038–1045. [5] N.D. Dinh, N.D. Tuyen, G. Fujita, et al., Adaptive notch filter solution under unbalanced and/or distorted point of common coupling voltage for three-phase fourwire shunt active power filter with sinusoidal utility current strategy, IET Gener. Transm. Distrib. 9 (13) (2015) 1580–1596. [6] C.B. Mellado, C.H. Carimán, et al., Experimental evaluation of a CPT-Based 4-leg active power compensator for distributed generation, IEEE J. Emerging Sel. Topics Power Electron. 5 (2) (2017) 747–759. [7] A. Javadi, L. Woodward, et al., Real-time implementation of a three-phase THSeAF based on VSC and P+R controller to improve power quality of weak distribution systems, IEEE Trans. Power Electron. 33 (3) (2018) 2073–2082. [8] K. Senthilnathan, I. Annapoorani, Implementation of unified power quality conditioner (UPQC) based on current source converters for distribution grid and performance monitoring through LabVIEW simulation interface toolkit server: a cyberphysical model, IET. Gener. Transm. Distrib. 10 (11) (2016) 2622–2630. [9] R.K. Patjoshi, K. Mahapatra, High performance unified power quality conditioner using command generator tracker based direct adaptive control strategy, IET Power Electron 9 (6) (2016). [10] Q. Zhu, Q. Li, J. Zhang, Virtual resistor circuit-based control strategy of STATCOM during network unbalance, J. Eng. 13 (2017) 1804–1808. [11] A.F. Cupertino, J.V.M. Farias, H.A. Pereira, Comparison of DSCC and SDBC modular multilevel converters for STATCOM application during negative sequence compensation, IEEE Trans. Ind. Electron. 66 (3) (2019) 2302–2312. [12] L. Wang, W.S. Liu, C.C. Yeh, et al., Reduction of three-phase voltage unbalance subject to special winding connections of two single-phase distribution transformers of a microgrid system using a designed D-STATCOM controller, IEEE Trans. Ind. Appl. 54 (3) (2018) 2002–2011.
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
A control scheme for voltage unbalance compensation in an islanded microgrid
T
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Sajad Hoseinniaa, Mahdi Akhbaria, , Mohsen Hamzehb, J.M. Guerreroc a
Department of Electrical Engineering, Shahed University, Tehran, Iran Department of Electrical Engineering, Shahid Beheshti University, Tehran, Iran c Department of Energy Technology, Aalborg University, Aalborg, Denmark b
A R T I C LE I N FO
A B S T R A C T
Keywords: Power quality Photovoltaic Inverters Active filters Microgrid
One of the major power quality issues in low-voltage (LV) microgrids is the voltage unbalance which has adverse effects on electrical devices. This paper presents a novel control scheme to mitigate the voltage unbalance by a photovoltaic (PV) system. In this study, load current sensors are eliminated and the PV system mitigates the voltage unbalance by analyzing its terminal voltage. This could effectively reduce the cost and complexity of compensation system because of the difficulties of load current sensors. The proposed control strategy is developed for a three-phase PV. As the inverter detects the voltage unbalance at its terminal, the proposed control algorithm calculates the compensation reference currents based on the double synchronous reference frame (DSRF) analysis of the PV terminal voltage. Therefore, the PV inverter injects the compensating currents to the microgrid. The effectiveness of the control scheme is verified by simulation studies in the PSCAD/EMTDC environment.
1. Introduction Nowadays, the increasing installation of distributed generation (DG) in low-voltage (LV) networks make the control of microgrids a remarkable issue. The existence of linear and non-linear loads as well as single-phase and three-phase ones in the microgrids presents different power quality challenges for the consumers. One of major power quality challenges in LV microgrids is the voltage unbalance which has adverse effects on electrical instruments including induction motors and those contain power electronic converters [1]. This challenge could be mainly caused by high penetration of single-phase residential loads as well as single-phase sources such as single-phase PVs [2]. The literature demonstrates much research dedicated to the voltage unbalance compensation using series/shunt active power filters (APFs), hybrid APFs, static synchronous compensators (STATCOMs), static VAR compensators (SVCs) [3–9]. Series APF generates negative sequence voltage over the line [3,4] while shunt APFs injects negative sequence current to reduce the voltage unbalanced which is made by these currents [5]. Combining series and shunt APF leads to hybrid series-parallel compensators. A popular type of hybrid compensators is the unified power quality conditioner (UPQC) that injects negative sequence voltage with
its series filter and negative sequence current via its shunt filter [8,9]. Another option is the static synchronous compensators (STATCOMs) that compensates the voltage unbalance by injecting negative sequence reactive power to the network [10–13]. However, the cost of these filters could be a challenge that result in the increase of the system investment costs. Additionally, controlling these facilities would increase the overall system complexity. Recently, photovoltaic (PV) systems spread in distribution grids and arise threats and opportunity for the grid managers. For example, high penetration of single phase PV systems could be the cause of voltage unbalanced and should be assessed and regulated. In Refs. [14,15] authors introduce an assessment of PV systems in distribution grids and evaluate the grids’ emission limits for these generations. The existence of three phase PV systems can provide an opportunity for the utility companies to use these sources as APFs [16,17] without installing extra instruments such as aforementioned STATCOM, SVC, and UPQC. PVs contain valuable inverters that hardly operate at their maximum rated power because of the variation of solar radiation over the day. Therefore, it is more efficient to use the excess capacity of the inverters for compensating the voltage unbalance [18–22]. A PV system with active power filtering functionality is presented in Ref. [20] to compensate the
⁎
Corresponding author at: Shahed University, Department of Electrical Engineering, Persian Gulf Freeway, 33191 18651, Tehran, Iran. Tel.: +98 21 5121 2066; fax: +98 21 5121 2021. E-mail addresses: [email protected] (S. Hoseinnia), [email protected] (M. Akhbari), [email protected] (M. Hamzeh), [email protected] (J.M. Guerrero). https://doi.org/10.1016/j.epsr.2019.106016 Received 20 April 2019; Received in revised form 30 July 2019; Accepted 22 August 2019 Available online 04 October 2019 0378-7796/ © 2019 Elsevier B.V. All rights reserved.
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voltage unbalance. The system measures the unbalanced load current and extracts the compensating current based on generalized instantaneous reactive power theory. Authors in Ref. [21] develop a control strategy for single-phase PVs propagated throughout the distribution network to mitigate the voltage unbalance. The control strategy is based on the fact that in the case of voltage unbalance, active and reactive powers could vary across each phases of the network according to the connected single phase loads on each phase. Therefore, the voltage unbalance in different buses could be compensated by curtailing the active and reactive power injected by single-phase PVs which are installed in different phases over the network. However, it lacks a scheme for three phase inverters. Moreover, changing the phase of single-phase PVs needs extra instruments which would increase the costs. In Ref. [22], the authors consider electric vehicles and PV systems for unbalance compensation. It is supposed that the inverters of these systems could transfer different amount of power per each phase and it is not necessary for the power to be equally divided across the three phases. Accordingly, the study presents a centralized algorithm for the network to manage the power in each phase of PV inverters and electric vehicles systems to improve the voltage imbalance. However, the control strategy for each inverter system is not discussed and the paper considers the idea from the system level point of view. Reviewing the literature, the APFs and PV-based APFs generally suppose that the current and voltage of network or unbalanced loads are accessible. In this condition, the APFs analyze the unbalanced currents and calculate and inject the compensating current to reduce the voltage unbalance. However, in many real applications, the PV senses only its terminal voltage and its injected current and the unbalanced currents of the local loads are inaccessible for the PV system. Moreover, installing extra measurement hardware for measuring these unbalanced currents could increase the system cost and complexity. Therefore, the main purpose of this paper is to present a control strategy for a PV system to mitigate the voltage unbalance without the need to supplementary devices that measure the local unbalanced load current. When the loads of the microgrid become unbalanced, the corresponding unbalanced currents are initially supplied by the voltagecontrolled sources which stabilize and regulate the voltage of the microgrid. The unbalanced currents from these sources pass through the feeders’ impedances and therefore, result in the voltage unbalance at the consumer terminals. When the proposed control scheme is activated, the PV analyzes its terminal voltages based on the double synchronous reference frame (DSRF) and extracts the negative part of the voltage caused by unbalanced loads. Then, the compensating currents are calculated in order to reduce the voltage unbalance at the PV terminal and these currents are injected to the microgrid. Injecting the compensating currents by the PV system removes negative sequense currents of the voltage-controlled voltage sources and makes these currents balanced. This could leads to the mitigation of the voltage unbalance at the consumer side. The proposed control strategy is developed for a three-phase four-wire PV system in an islanded LV microgrid. The effectiveness of the control scheme is verified by simulation studies in the PSCAD/EMTDC environment.
G= kp +
ki s2 + ωc . s+ ω20
(1)
where kp and ki are the proportional and integral gains and ω0 and ωc are the reference frequency of the microgrid and the bandwidth around this frequency respectively. 3. Proposed control scheme Analysing the voltage unbalance in the networks, the International Electrotechnical Commission (IEC) in the 61000-2-2: 2000 Standard introduces the voltage unbalanced factor (VUF) [24]:
VUF%=
V− . 100 V+
(2)
where V− and V+ are negative and positive sequence voltages respectively. This definition considers both magnitude and phase angle unbalance. Therefore, the main purpose of the control strategy is to reduce the VUF at the terminal of the PV system according to the IEC definition. As voltage unbalance could have adverse effects, the acceptable compatibility level of VUF is limited in the networks. This limitation varies country by country ranging between 1–5% [14]. In this paper, it is supposed that the VUF should be lower than 2% according to the aforementioned IEC standard. As the solar radiation varies during the day, PV systems hardly operate at their maximum power and in this condition, according to the inverter’s switch ratings, the PV inverter has a surplus capacity per phase that is not in use. Therefore, it is possible to inject the dc-link power unequally through different phases to respond different per phase load demands. On the other hand, by injecting more current through the phase with higher load demand, it is possible to reduce the voltage unbalance at the PV terminal. To make this concept operational, the control scheme of Fig. 2 is used. This figure demonstrates the block diagram of the proposed control scheme which produces reference current for the inner inverter control loop. This reference current could be calculated from the sum of positive components (green blocks) and negative components (red blocks): − i+ ⎡ ia ⎤ ⎡ a ⎤ ⎡ i−a ⎤ ⎢ ib ⎥ = ⎢ i+b ⎥ + ⎢ ib ⎥ ⎢ i ⎥ ⎢ + ⎥ ⎢ i− ⎥ ⎥ ⎣ c⎦ ⎣ c⎦ ⎢ ⎣ ic ⎦
(3)
Following this concept, by means of Park’s transformation which is introduced in Ref. [23,25], positive and negative voltages in the DSRF could be identified by Eqs. (4) and (5) as follows:
⎡ cos(θ) cos( θ− + ⎡ vd ⎤ ⎢ 2 + ⎢ vq ⎥ = ⎢ ⎢ ⎥ 3 ⎢ sin(θ) sin( θ− + ⎢ ⎢ ⎣ v0 ⎥ ⎦ 0.5 ⎣ 0.5
2π ) cos( θ+ 3 2π ) sin( θ− 3 0.5
⎡ cos(−θ) cos(− θ− − ⎢ ⎡ v −d ⎤ 2 ⎢vq ⎥ = ⎢ 3 ⎢ sin(−θ) sin(− θ− ⎢ v −⎥ ⎣ 0⎦ ⎢ 0.5 ⎣ 0.5
2. Control strategy for PV inverters
2π ⎤ ) 3 ⎥ ⎡ va ⎤ 2π ⎥ ⎢ vb ⎥ )⎥ 3 ⎥ ⎣ vc ⎦ ⎦
2π ) cos(− θ+ 3 2π ) sin(− θ− 3 0.5
2π ⎤ ) 3 ⎥ ⎡ va ⎤ 2π ⎥ ⎢ vb ⎥ )⎥ 3 ⎥ ⎣ vc ⎦ ⎦
(4)
(5)
where v+d , v+q and v+0 are positive d, q and zero voltages and v −d , v −q and v −0 are negative d, q and zero voltages respectively. As it is formulated in Eqs. (4) and (5), v+0 and v −0 are indeed equal. In a balanced load condition, only positive d and q components of voltage exist and the inverter injects equal power across three phases. In this conditions, positive reference currents are needed and are calculated in the upper control loop (green blocks) of Fig. 2. This control loop produces the positive d and q reference currents based on the d and q components of the inverter output voltage. The d component regulates the dc-link voltage and is responsible for the active power of
The PV source generally consists of PV array, DC/DC converter and DC/AC inverter as depicted in Fig. 1. The DC/DC converter increases the dc output voltage of the PV and also controls the PV array in maximum power point tracking (MPPT) operation mode. The inverter sets the dc-link voltage to its reference value and regulates this voltage. The inverter of PV system operates in current control mode (CCM) to inject the PV power to the microgrid. To develop the control scheme, the natural frame (abc) model of a three-phase inverter in is used [23]. Therefore, a proportional resonant (PR) controller is tuned to track the sinusoidal reference generated from outer control loops: 2
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Fig. 1. PV power electronic interface.
of the PV inverter is calculated as follows:
the inverter. The q component adjusts the output AC voltage of the inverter to its reference value and is dedicated to the reactive power injection of the inverter. By means of reverse Park’s transformation which is introduced in Ref. [23], synchronous reference current components are transformed into the natural frame current components as follows:
sin(θ) 1⎤ ⎡ cos(θ) + + 2π 2π ⎥ ⎡ id ⎤ ⎡ ia ⎤ ⎢ ⎢ i+b ⎥ = ⎢ cos( θ− 3 ) sin( θ− 3 ) 1⎥. ⎢ i+q ⎥ ⎥ ⎢ ⎥ ⎢ +⎥ ⎢ + 2π 2π ⎢ ⎣ ic ⎥ ⎦ ⎢ cos( θ+ ) sin( θ+ ) 1⎥ ⎢ ⎣ i0 ⎥ ⎦ ⎥ ⎢ 3 3 ⎦ ⎣
→ →+ →− total Iabc = Iabc + Iabc
(8) → → → + total where Iabc , Iabc and Ia−bc are the total, positive and negative currents in vector space, respectively. The final reference currents should not exceed the rating of inverter’s switches (Isw ):
→ total 2 Isw 2 ≥ | Iabc |
Therefore, the amount of total injected current could be calculated from the law of cosines:
(6)
+ 2 − 2 total 2 |Iabc | ≤ |Iabc | + |Iabc |
As an unbalanced load connects to the microgrid, negative d and q components emerge in the terminal voltages. In this condition, the negative sequence currents are initially provided by the voltage-controlled voltage sources and the PV source does not participate in the voltage unbalance compensation. When the voltage unbalance compensator (VUC) of the PV inverter (red blocks) in Fig. 2 is activated, negative d, q and zero components of the inverter terminal voltages are calculated by (5). Then, these values are compared with a zero and by means of PI controllers, the negative d, q and zero components of reference current are generated. Then, by means of reverse negative Park’s transformation Eq. (7), negative reference currents in the natural frame are obtained:
sin (−θ) 1⎤ ⎡ cos (−θ) − − ⎡ia ⎤ ⎢ cos (−θ − 2π ) sin (−θ − 2π ) 1⎥ ⎡ id− ⎤ ⎥ ⎢ i ⎢ib− ⎥ = ⎢ . q ⎥ 3 3 ⎥ ⎢ −⎥ ⎢i − ⎥ ⎢ 2 π 2 π i 1 c ⎥ ⎢ ⎣ ⎦ cos (−θ + ) sin (−θ + ) 1 ⎣0⎦ ⎥ ⎢ 3 3 ⎦ ⎣
(9)
(10)
Accordingly, the right side of the (9) is replaced by the right side of the (10) and should satisfy this inequality. If (11) is satisfied, we would be assured that (9) was satisfied too: + 2 − 2 (Isw )2 − |Iabc | ≥ |Iabc |
(11) − 2 | the |Iabc
+ 2 | on |Iabc
based and Therefore, (11) determines the limit for (Isw )2 . The negative component of PV current follows these equations:
→− Iabc = (Id− + j. Iq−). e−j . θ
(12)
− 2 |Iabc | = (Id−)2 + (Iq−)2
(13)
By substituting (13) in (11), (14) could be concluded: + 2 (Isw )2 − |Iabc | ≥ (Id−)2 + (Iq−)2
(14)
According to (14), as the PVs are controlled to maximize the active power, the positive component of current has priority and the rest of the difference between the switch rating of the inverter and the positive current component is dedicated to the negative d and q components of current respectively. This constraint is shown in Fig. 2 as some saturation blocks before the reverse negative sequence transformation. Fig. 3 shows the effect of the PV participation in the unbalanced current compensation. After the connection of the unbalanced load to the microgrid, negative d, q and zero components of the load current
(7)
The resulted negative current components then is used in the Eq. (3) and is added to the positive ones to generate reference currents for the inverter’s inner control loop. This means that in the unbalanced load condition, the inverter could produce negative component currents to mitigate the VUF at the terminal of the PV system. On the other hand, the total injected current
Fig. 2. The proposed control system. 3
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Fig. 3. Supply of negative current components (a) before and (b) after compensation.
are supplied by the voltage-controlled voltage sources. Because of the line impedances between these sources and the unbalanced load, negative current components of the unbalanced load produce negative voltage components in the PV terminal. After the activation of the VUC, either a share of or all the negative current components are injected to the load terminal by the PV instead of voltage-controlled voltage sources. Therefore, the negative voltages at the terminal of the load decrease and then, the VUF reduces consequently. 4. Simulation validation To verify the performance of the proposed control scheme, two cases are considered in this section. The objective of case I is to verify the ability of the system in detecting and mitigating of voltage unbalance at the terminal of a PV system. In this case, two unbalanced load would be connected to the microgrid and the proposed control scheme would be verified. Then, in case II, adaptation of the control system will be verified when two unbalanced loads disconnect from the network. Therefore, a benchmark AC microgrid is nominated and simulated using PSCAD/EMTDC software. The AC microgrid utilized in this paper is illustrated in Fig. 4. This microgrid is taken from International Council on Large Electric Systems (CIGRE) Benchmark microgrid network [26] which has been specially designed for LV microgrid studies and contains real utility parameters. It is supposed that the microgrid is disconnected from the main grid and consists of seven feeders. Furthermore, the loads are grouped into three- and singlephase loads and are residential consumers. The power factor for all loads is assumed to be 0.85 lagging. The microgrid parameters could be seen in the Table 1. DG1, DG2 and DG3 are voltage-controlled voltage sources and regulate the voltage of the microgrid. Because of the resistive feeder impedances, they work under a resistive droop control. Moreover, DG4 and DG5 are PV sources that initially inject the maximum produced power to the microgrid. The proposed control strategy is applied to the DG4 PV inverter and is validated in the case study. The sources initially supply balanced loads according to Table 1 and all of single-phase consumers of load 4 and 5 are disconnected from the microgrid. The PV source of DG4 and DG5 initially injects active power equal to 6.8 kW and 5 kW respectively. Characteristics of the PV source of DG4 could be seen in the Table 2.
Fig. 4. Under study system adjusted from CIGRE LV microgrid network.
4.1. Case I
the other phases remain almost constant (the green and red lines in Fig. 6(a)) (Table 3 and 4). The positive d component of DG4’s terminal voltage is illustrated in Fig. 7(a) and the positive q and zero components of the output voltage of DG4 are almost zero. By the first unbalanced load connection, the negative d and q components of the output voltage appear in Fig. 7(b). Moreover, positive d and q component of the reference currents are demonstrated in Fig. 6(b). At t = 2 s, another 5 kVA single-phase load connects to the phase ‘C’ of the feeder F07. At this moment, the VUF falls a bit to 0.52% and a decrease in the terminal voltage in phase ‘C’ of DG4 could be seen in the Fig. 6(a).
In this case study, the sources initially supply balanced loads according to Table 1 and all of single-phase consumers of load 4 and 5 are disconnected from the microgrid. The PV source of DG4 and DG5 initially inject active power equal to 6.8 kW and 5 kW respectively. As the PV of DG4 operates with an active power lower than its rated power (i.e. 10 kW), there is a surplus switching capacity to be utilized for injecting compensating current. At t = 1 s, a single-phase 5 kVA load connects to the phase ‘A’ of the feeder F06 which increases the VUF at the terminal of DG4 from 0 to 0.59% (Fig. 5). Moreover, the terminal voltage in phase ‘A’ of DG4 decreases (the blue line in Fig. 6 (a)) while 4
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Table 1 Microgrid characteristics. Parameters
Values
Voltage Frequency
400Vrms- line to line 50 Hz
Feeders(Length, Size) F01 F02 F03 F04 F05 F06 F07
280 m, Twisted cable 4 × 120 mm2 Al 30 m, Service Connection 4 × 6 mm2 Cu 30 m, Service Connection 4 × 16 mm2 Cu 30 m, Twisted cable 3 × 70 mm2 Al 30 m, Service Connection 4 × 25 mm2 Cu 30 m, Service Connection 4 × 6 mm2 Cu 30 m, Service Connection 4 × 16 mm2 Cu
Sources DG1 DG2 DG3 DG4 DG5
30 kW, 30 kW, 10 kW, 10 kW, 10 kW,
Droop m1, n1 m2, n2 m3, n3
2.69e-5, 5.43e-4 8.07e-5, 0.0016 2.69e-5, 5.43e-4
Loads Load 1 Load 2 Load 3 Load 4
3 × Φ, 3 × Φ, 3 × Φ, 3 × Φ, 3 × Φ,
1 × 3Φ, 1 × 3Φ, 1 × 3Φ, 3 × 1Φ, 1 × 3Φ, 3 × 1Φ,
Load 5
Fuel Cell Microturbine Fuel Cell Photovoltaic Photovoltaic
15 kVA, Cos Φ = 0.85 Lag 30 kVA, Cos Φ = 0.85 Lag 5 kVA, Cos Φ = 0.85 Lag 5 kVA, Cos Φ = 0.85 Lag, 5 kVA, Cos Φ = 0.85 Lag 5 kVA, Cos Φ = 0.85 Lag
Fig. 6. Effective (a) Voltages and (b) Currents of DG4 in Case I. Table 2 PV system characteristics.
Table 3 First scenario timeline.
Parameters
Values
Power stage DC link voltage Switching frequency Inverter-side inductor Grid-side inductor Inverter capacitor Inductor resistance
700 V 15 kHz 2 mH 0.2 mH 0.7 μF 0.05 Ω
Primary control Proportional gain Resonant gain Secondary Control id+ Proportional & iq+ Proportional & id− Proportional & iq− Proportional &
gains gains gains gains
Event
VUF (%)
0–1 1–2 2–3 3–5
Microgrid Statrup A 5 kVA, 1 ph. load connects to phase A at F06 in t = 1 s A 5 kVA, 1 ph. load connects to phase C at F07 in t = 2 s DG4 compensation is activated in t = 3 s
0 0.59 0.52 0.01
Table 4 Second scenario timeline.
0.3 300 Integral Integral Integral Integral
Time (s)
0.1, 10 0.1, 0.1 1, 10 1, 10
Time (s)
Event
0–3 3–6 6–9
Stable compensation of unbalanced loads by the DG4 A 5 kVA, 1 ph. load disconnects from phase A at F06 in t = 3 s A 5 kVA, 1 ph. load disconnects from phase C at F07 in t = 6 s
currents of DG4 in order to decrease the voltage unbalance. The currents in phases ‘A’ and ‘C’ of DG4 which have higher load demands increase while the corresponding value in the phase ‘B’ with lower load demand decreases. The change in DG4 currents results in the increase of the voltages of phase ‘A’ and ‘C’ at the terminal of the DG4. As it could be seen in Fig. 5, the voltage unbalance is almost improved and VUF falls from 0.52% to almost 0. Fig. 9 depicts the active and reactive powers of the PV source of DG4 injected to the microgrid. A double frequency ripple appears in these powers because of unbalanced current injection. This case approves that the scheme could effectively reduce the voltage unbalance in the microgrid. 4.2. Case II
Fig. 5. Voltage unbalance factor in percent in the Case I.
In this case the adaptation of the VUC is tested in the condition of removing unbalanced loads. The DG4 initially compensates the unbalanced voltages of its terminal at the presence of the unbalanced loads of the Case I. At t = 3 s, the single-phase 5 kVA load on the phase
Finally, at t = 3 s, the VUC is activated and negative currents (i.e. id−, iq−) are injected by the DG4 in order to reduce the VUF (Fig. 8(b)). As it is demonstrated in Fig. 6(b), the VUC changes the equality in phase 5
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Fig. 9. (a) Active power, and (b) reactive power of DG4 in Case I. Fig. 7. (a) Vd+ and (b) Vd− and Vq− at the DG4 terminal in Case I.
Fig. 10. Voltage unbalance factor at the DG4 terminal in percent in Case II.
period, the VUF approaches to zero. The effective value of DG4 terminal voltage is depicted in the Fig. 11(a). After disconnecting of the first unbalanced load, the currents remain unbalanced to compensate the other unbalanced load. Finally, after disconnecting of the second load at t = 6 s, the VUF sets to almost zero and the currents become equal in three phases as could be seen in the Fig. 11(b). The d component of the terminal voltage increases after the disconnection of the unbalanced loads (Fig. 12(a)). The positive and negative component of the PV current is demonstrated in Fig. 13. After t = 6 s, the compensation process analyzes the negative component of the terminal voltage and as it is zero because of the balanced power demand in the microgrid, injecting negative component currents is automatically terminated (Fig. 13(b)). The instantaneous currents of the PV before and after the disconnection of the last unbalanced load is depicted in the Fig. 14. As it could be seen there, the PV current is unbalanced before t = 6 s, while it tends to balanced values after this time. This case study approves that the compensation technique remains effective when unbalanced loads are disconnected from the microgrid and the voltage unbalance is solved.
Fig. 8. (a) id+ and iq+ , and (b) id− , iq− and i 0− at the DG4 terminal in Case I.
‘A’ of the feeder F06 is disconnected and at t = 6 s, the other 5 kVA single-phase load is disconnected from the phase ‘C’ of the feeder F07. As it could be seen in the Fig. 10, the VUF is near zero in the presence of the unbalanced loads from 2 s to 3 s which is the result of compensation. At t = 3 s and t = 6 s when unbalanced load disconnects from the grid, sudden change with an overshoot occur and after a transient
5. Conclusion In this paper, a new control strategy for a three-phase four-wire PV 6
Electric Power Systems Research 177 (2019) 106016
S. Hoseinnia, et al.
Fig. 11. Effective (a) Voltages and (b) Currents of DG4 in Case II.
Fig. 13. (a) id+ and iq+ , and (b) id−, iq− at the DG4 terminal in Case II.
Fig. 14. Instantaneous currents of DG4 in Case II.
control system identifies the voltage unbalance by detecting negative sequence voltages. Based on these voltages, the control system calculates the required negative sequence compensating current which could reduce the voltage unbalance at the PV terminal. This control technique does not need to measure unbalanced load current and therefore, the compensation system could be applicable without local load current sensors. Although using the PV inverter as an active power filter could reduce the cost of compensating system, the proposed control system would be able to reduce the cost of the compensation once more. The effectiveness of the control scheme was validated using PSCAD/EMTDC environment. The simulation scenarios approved that the PV system could beneficially mitigate the voltage unbalance while the unbalanced loads connect to or disconnect from the LV microgrid. While the proposed control strategy was presented for an islanded microgrids, it could be recommended for any distribution networks with voltage unbalance difficulties.
Fig. 12. (a) Vd+ and (b) Vd− and V −q at the DG4 terminal in Case II.
inverter was developed to mitigate the voltage unbalance. Unlike APFs, the load current sensor was eliminated and the compensation scheme calculated the reference currents by analyzing the PV terminal voltage and therefore, the cost and complexity could be reduced. The proposed control strategy benefited from the double synchronous reference frame (DSRF) which identifies the positive and negative sequence of the PV terminal voltages. As an unbalanced load connects to the network, the
Conflict of interest None.
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Electric Power Systems Research 177 (2019) 106016
S. Hoseinnia, et al.
References
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