An Islanding Microgrid Power Sharing Approach Using ... - IEEE Xplore

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 11, NOVEMBER 2013

An Islanding Microgrid Power Sharing Approach Using Enhanced Virtual Impedance Control Scheme Jinwei He, Student Member, IEEE, Yun Wei Li, Senior Member, IEEE, Josep M. Guerrero, Senior Member, IEEE, Frede Blaabjerg, Fellow, IEEE, and Juan C. Vasquez

Abstract—In order to address the load sharing problem in islanding microgrids, this paper proposes an enhanced distributed generation (DG) unit virtual impedance control approach. The proposed method can realize accurate regulation of DG unit equivalent impedance at both fundamental and selected harmonic frequencies. In contrast to conventional virtual impedance control methods, where only a line current feed-forward term is added to the DG voltage reference, the proposed virtual impedance at fundamental and harmonic frequencies is regulated using DG line current and point of common coupling (PCC) voltage feed-forward terms, respectively. With this modification, the impacts of mismatched physical feeder impedances are compensated. Thus, better reactive and harmonic power sharing can be realized. Additionally, this paper also demonstrates that PCC harmonic voltages can be mitigated by reducing the magnitude of DG unit equivalent harmonic impedance. Finally, in order to alleviate the computing load at DG unit local controller, this paper further exploits the bandpass capability of conventionally resonant controllers. With the implementation of proposed resonant controller, accurate power sharing and PCC harmonic voltage compensation are achieved without using any fundamental and harmonic components extractions. Experimental results from a scaled single-phase microgrid prototype are provided to validate the feasibility of the proposed virtual impedance control approach. Index Terms—Distributed generation (DG), droop control, microgrid, point of common coupling (PCC) harmonic voltage compensation, power sharing, resonant controller, virtual impedance.

I. INTRODUCTION UE to the growing importance of renewable energybased distributed power generation and the advancement in power electronics technologies, a large number of inverterbased distributed generation (DG) units have been installed in conventional low-voltage power distribution systems [1], [2]. To achieve better operation of multiple DG units, the microgrid concept using coordinated control among parallel DG interfacing

D

Manuscript received July 19, 2012; revised October 24, 2012; accepted January 16, 2013. Date of current version May 3, 2013. This paper was presented in part at the 3rd International Symposium on Power Electronics for Distributed Generation Systems (PEDG2012) and the Applied Power Electronics Conference and Exposition (APEC2013). Recommended for publication by Associate Editor A. Kwasinski. J. He and Y. W. Li are with the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2R3, Canada (e-mail: [email protected]; [email protected]). J. M. Guerrero, F. Blaabjerg, and J. C. Vasquez are with the Institute of Energy Technology, Aalborg University, 9220 Aalborg Ø, Denmark (e-mail: [email protected]; [email protected]; and [email protected].) Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPEL.2013.2243757

converters has been well accepted [3]–[12]. As an important component of the future smart grid, microgrid can operate in both grid-connected and intentional islanding modes. As a result, it offers more reliable power to critical loads. When the microgrid is disconnected from the utility grid to form an autonomous islanding system, the droop control method can be applied to realize decentralized power sharing among DG units [3]–[17], [27]–[29]. In this situation, the response of interfacing inverter is similar to the synchronous generator [3]. Nevertheless, the accuracy of power sharing and the stability of droop-controlled DG units are often affected by DG unit feeder impedances [4]–[6]. To cope with stability issues, conventional droop control was modified using virtual frequencyvoltage frame or virtual real and reactive power concept [7], [8]. However, by using modified droop control methods, the accuracy of reactive power sharing can hardly be improved at the same time. On the other hand, virtual impedance-based methods have been reported in a few literature references, where the main focus is the behavior of virtual impedance at fundamental frequency [4], [5], [9]–[11]. In addition to the stability improvement, the combination of droop slope adjustment and virtual impedances control [4] also reduces steady-state reactive power sharing errors. As a result, virtual impedance aided DG operation is often considered to be a promising way to enhance microgrid performances [5], [17]. On the other hand, the islanding microgrid may have serious power quality problems due to the increasing presence of nonlinear loads. To mitigate harmonic distortions, more passive or active power filters are required. Further, considering that DG units normally have higher control bandwidth compared to synchronous generators, they can also provide ancillary power line conditioning service through their interfacing converter control [12]–[16], [28]. In [12] and [13], the shunt resistive active power filter (R-APF) concept was embedded in the current control schemes of grid-connected DG unit. Unfortunately, the current-controlled method can hardly be used to achieve power sharing among parallel islanded DG units. To solve this issue, an improved active power filtering method was proposed for multiple DG units in islanded systems [14]. In this method, only an inductor is adopted as the DG output filter. When LC or LCL filters are applied, it may not be able to address the inherent resonances of high-order filters. Alternatively, the voltage-controlled active power filtering method using the adjustment of DG unit equivalent harmonic impedances was recently proposed in [15]. However, only grid-tied operation of DG units was verified. Also, the phase angle of DG equivalent harmonic impedance equals to the phase angle of existing physical feeder impedance.

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HE et al.: ISLANDING MICROGRID POWER SHARING APPROACH USING ENHANCED VIRTUAL IMPEDANCE CONTROL SCHEME

Fig. 1.

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Diagram of a single-phase microgrid with parallel DG units.

When multiple DG units are connected to PCC by feeders with mismatched impedance phase angle, the harmonic impedance shaping method in [15] will cause harmonic circulating currents among DG units. In response to the aforementioned issues, this paper proposes an enhanced control method using virtual impedance at the fundamental and selected harmonic frequencies. At first, this paper discusses a reactive power sharing improvement method using virtual fundamental impedance regulation. Afterward, PCC harmonic voltage compensation and accurate harmonic load sharing through the adjustment of DG unit equivalent harmonic impedances are also presented. In addition, with the flexible arrangement of resonant voltage controllers, the proposed virtual fundamental and harmonic impedances are implemented without any obvious interference between them, and the fundamental and harmonic components extractions in the DG unit local controller are avoided. Finally, experimental results are obtained from a single-phase islanding microgrid prototype.

II. OPERATION PRINCIPLE OF ISLANDING MICROGRID Fig. 1 illustrates an example of microgrid, where N parallel single-phase inverters are interfaced to PCC with feeders (Ri,1 to Ri,N and Li,1 to Li,N ). Note that when grid-connected DG units with LCL filters are switched to islanding operation with filter capacitor voltage control, the PCC side filter inductors shall be lumped together with DG feeders. The microgrid also consists of linear and nonlinear loads at PCC. To provide enhanced voltage quality to PCC loads, DG units shall compensate PCC voltage distortions through their local voltage regulation. Finally, the microgrid also has a control center, which sends the measured PCC harmonic voltage signals to DG local controllers with a low-bandwidth communication system [16], [33]. With this communication link, remote PCC voltage measurement is not necessary for DG unit local controllers. The details of the communication technique will be explained later in this section.

A. Principle of Droop Control The droop control method was developed based on the analysis of steady-state power flow in an inductive feeder [10]. The conventional frequency and voltage magnitude droop controllers in a DG unit are shown in (1) and (2) as ωDG = ω ∗ − DP · Pave

(1)

EDG = E ∗ − Dq · Qave

(2)

where ω ∗ and ωDG respectively are the nominal and reference angular frequencies of the DG unit; E ∗ and EDG are the nominal and reference DG voltage magnitudes; Pave and Qave are the measured power after low-pass filtering [9], [10]; and Dp and Dq are the droop coefficients of the controllers. With the knowledge of reference voltage magnitude and angular frequency, the instantaneous DG unit reference voltage Vdro op α can be obtained accordingly. Note that strict frequency and voltage magnitude ranges [such as ωDG = (1 ± 1.0%)ω ∗ and EDG = (1 ± 5%)E ∗ ] shall be applied to avoid any dissynchronizations between islanding DG units [8]. Consequently, the reference voltage Vdro op α is always sinusoidal with little distortion. As will be discussed later, this feature can be further utilized to alleviate the computing complexity of DG local controllers. B. Reactive Power Sharing To share the fundamental load demand in proportion to DG rated power, the droop slope shall be designed in inverse proportion to their rated power [27]. For the islanded microgrid with N parallel inverters as shown in Fig. 1, the droop slopes yield the following formulas: DP ,1 · PRated,1 = DP ,2 · PRated,2 = · · · = DP ,N · PRated,N (3) DQ ,1 · QRated,1 = DQ ,2 · QRated,2 = · · · = QQ ,N · QRated,N (4)

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where DP ,1 to DP ,N are the real power droop slopes of DG units 1 to N, PRated,1 to PRated,N are the rated real power of DG units 1 to N . Similarly, DQ ,1 to DQ ,N and QRated,1 to QRated,N are the reactive power droop slopes and the rated reactive power of DG units 1 to N , respectively. With the aforesaid constraints, an accurate real power sharing can be achieved at steady state [4], [25]. Nevertheless, the accuracy of reactive power sharing is affected by mismatched DG unit feeder impedances [4], [25], [27]. To eliminate the reactive power sharing errors, the DG unit equivalent fundamental impedance shall also be designed to be in inverse proportion to DG rating. Accordingly, following constraints on DG equivalent fundamental impedances shall also be satisfied: RDGf ,1 · PRated,1 = RDGf ,2 · PRated,2 = · · · = RDGf ,N · PRated,N

(5)

XDGf ,1 · QRated,1 = XDGf ,2 · QRated,2 = · · · = XDG f ,N · QRated,N

ZDGf = RDGf + jXDGf = (Ri + jω ∗ Li ) + (Rv f + jω ∗ Lv f ) (7) where Ri and Li are the physical DG feeder resistance and inductance, respectively. Rv f and Lv f are the virtual fundamental impedance to be implemented by the DG unit. It is obvious that with the knowledge of physical feeder impedance and the desired DG equivalent fundamental impedance ZDGf , the virtual fundamental impedance can be determined accordingly. The DG physical feeder impedance can be estimated through either online or offline methods. For instance, an on-line estimation method through the injection of low frequency noncharacteristic current distortions during DG unit grid-tied operation has been proposed in [21]. Nevertheless, further discussion on detailed estimation schemes is out of the scope of this paper. Once the virtual fundamental impedance is determined, its associated voltage drop Vv f shall be deducted from Vdro op α as shown in (8): α

− Vv f

= Vdro op

α

− (Rv f · ILinef

Illustration of series virtual fundamental impedance control using (8).

Without considering the dynamics of closed-loop DG voltage tracking, the equivalent circuit of a DG unit at fundamental frequency is illustrated in Fig. 2. It can be seen that the virtual impedance is placed between the physical feeder impedance Ri and Li , and the voltage reference Vdro op α derived from droop control in (1) and (2). Note again that the small out impedance [5] associated with the closed-loop DG voltage tracking is not included in this diagram.

(6)

where RDGf ,1 to RDGf ,N are the resistance of DG equivalent fundamental impedances, and XDG f ,1 to XDG f ,N are the reactance of DG equivalent fundamental impedances. Without considering the small output impedance introduced by DG unit closed-loop voltage tracking [5], the DG equivalent fundamental impedances in (5) and (6) are composed of two series parts:

Vref = Vdro op

Fig. 2.

C. Harmonic Power Sharing For a microgrid with intensive nonlinear loads, an inaccurate sharing of load harmonic currents may lead to DG unit over current protection [30]. To solve this issue, DG equivalent harmonic impedance can also be adjusted to ensure better harmonic current sharing. In a microgrid with multiple DG units at the same power rating, DG units equipped with the same equivalent harmonic impedance will minimize the harmonic circulating current between them. Furthermore, when the magnitude of DG unit equivalent harmonic impedance is properly reduced, the PCC voltage quality can be improved [15]. To regulate DG equivalent harmonic impedances, a line harmonic current feedforward term was added to the DG voltage reference [9], [10]. However, it should be pointed out that previous research was mainly focused on the situation with small DG physical feeder impedance. In a weak microgrid with higher feeder impedance, the harmonic voltage drops on the feeder impedance must be addressed during DG equivalent harmonic impedance regulation. To compensate the harmonic voltage drops on the DG feeder, negative series virtual harmonic impedance can be produced in a similar way: Vref = Vdro op

α

= Vdro op

α

− Vv h − (Rv h · ILineh

α

− hω ∗ Lv h · ILineh β )

h=3,5,7···

α

− ω ∗ Lv f · ILinef

β)

(8)

where Vref is the modified voltage reference considering virtual fundamental impedance regulation, ILinef α is the fundamental component of DG unit line current, and ILinef β is obtained by delaying ILinef α for quarter-fundamental cycle. Note that in the case of a single-phase DG unit, it can be described in the artificial α − β reference frame, where the α-axis describes the instantaneous values of the system and β-axis describes the orthogonal components.

(9) where Vref is the modified voltage reference considering series virtual harmonic impedance control, Vv h is the voltage drop on the harmonic virtual impedance, Rv h and Lv h are the negative virtual resistance and inductance at hth harmonic order, ILineh α is the hth line harmonic current, and LLineh β is obtained by delaying ILineh α for quarter-hth harmonic cycle. The associated equivalent circuit at the selected harmonic frequencies is illustrated in Fig. 3. As shown, the DG unit is modeled as virtual harmonic impedance connecting to ground, as the


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plex number gain-based compensation strategy at each selected harmonic frequency as

Fig. 3.

Illustration of series virtual harmonic impedance control using (9).

RDGh + jhω ∗ LDG h = (Ri + jhω ∗ Li )/(1 + Gcom plex h ) (12) where RDGh and LDG h are the equivalent DG resistance and inductance at hth harmonic frequency, and Gcom plex h is the complex number feedback gains. According to (12), the real and imaginary part of the feedback gain number is obtained as Gcom plex

voltage reference Vdro op α derived from droop control contains only fundamental component. Nevertheless, to implement virtual series harmonic impedances, the extraction of line harmonic currents at all selected harmonic orders is necessary. Moreover, to ensure accurate equivalent harmonic impedance regulation, preknowledge of harmonic frequency responses of DG feeders is required. However, the feeder impedance detection method in [21] is mainly focused on the response around fundamental frequency, and the physical feeder inductance may attenuate at harmonic frequencies. Therefore, the assumption of fixed feeder inductance at harmonic frequency may cause capacitive DG equivalent harmonic impedance (due to over compensation), which can adversely affect the stability of the system. Alternatively, another DG unit equivalent harmonic impedance shaping method was proposed in [15], where the DG unit voltage reference from droop control is modified by deducting an additional term associated with PCC harmonic voltages as Gh · VPCCh α Vref = Vdro op α − Vv h = Vdro op α − h=3,5,7···

(10) where Vref is the modified voltage reference to adjust DG unit equivalent harmonic impedance, Vv h is the harmonic voltage reference. Gh and VPCCh α are the real number feedback gain and the PCC harmonic voltage component at the harmonic order h, respectively. Note that if the harmonic PCC voltages in (10) are provided by microgrid central controller, the measurement of PCC harmonic voltage is not necessary for DG unit local controllers. With a positive gain Gh , the magnitude of DG unit equivalent harmonic impedance ZDGh can be reduced as ∗

ZDGh = (Ri + jhω Li )/(1 + Gh ).

(11)

From (11), it can be further seen that the equivalent harmonic impedance is inductive as long as the physical feeder impedance is inductive and therefore it provides better stability performance. To eliminate harmonic circulating currents among parallel DG units in a microgrid, the equivalent harmonic impedance ZDGh of all DG units shall have the same phase angle in addition to magnitude requirements. However, the equivalent harmonic impedance tuning method using real number gain Gh in (11) cannot regulate the phase angle of the equivalent harmonic impedance. Accordingly, harmonic circulating current appears for multiple DG units with unequal feeder impedance angles. To overcome the impacts of unequal feeder impedance phase angle among multiple DG units, this paper proposes a com-

= GR h + jGI h = (Ri + jhω ∗ Li )/

h

(RDGh + jhω ∗ LDG h ) − 1.

(13)

For virtual harmonic impedance control using complex feedback gains, the complex number representation of reference harmonic voltage is illustrated as ⎤ ⎡ (GR h + jGI h )·VPCCh α ⎦ Vv h = Re ⎣ h=3,5,7···

⎛

= Re ⎝

⎞ GR

h

· VPCCh α ⎠

h=3,5,7···

⎛

⎞

+ Re ⎝

GI

h

· jVPCCh α ⎠ .

(14)

h=3,5,7···

As will be discussed in the next subsection, the low-bandwidth communication system is employed to send the PCC harmonic voltages VPCCh α and their respective conjugated signals VPCCh β from the microgrid central controller to the DG unit local controller. It is obvious that they satisfy VPCCh α = jVPCCh β , which can be further utilized to simplify associated terms in (14). As a result, (14) is revised as ⎛

⎞

Vv h = Re ⎝

GR

h

· VP C C h

α

⎠

h = 3 , 5 , 7 ···

⎛

⎞

+ Re ⎝

GI

h

· jVP C C h

α

⎠

h = 3 , 5 , 7 ···

⎛

⎞

= Re ⎝

GR

h

· VP C C h

α

⎠

h = 3 , 5 , 7 ···

⎛

⎞

+ Re ⎝

GI

h

· j(jVP C C h

β)

⎠

h = 3 , 5 , 7 ···

=

h = 3 , 5 , 7 ···

GR

h

· VP C C h

α

−

GI

h

· VP C C h

β.

(15)

h = 3 , 5 , 7 ···

With the harmonic voltage reference in (15), the DG unit equivalent circuit at the selected harmonic frequencies is tuned as presented in Fig. 4, where the combined effects of DG unit harmonic voltages and physical feeder impedance in the upper part are modeled as small equivalent harmonic impedance in the lower part.

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At the DG local controller, the received signals need to be transformed back to the original harmonic signals using InversePark Transformations. Considering that the DG unit fundamental voltage (see Fig. 6) is linked with PCC fundamental voltage with very little phase angle difference, a DG local PLL is employed to get the angle for Inverse-Park Transformations. III. PROPOSED VOLTAGE CONTROLLER

Fig. 4. Illustration of equivalent harmonic impedance regulation using PCC harmonic voltage feedbacks.

By combining the virtual fundamental impedance control in (8) and harmonic impedance control in (15) together, a new voltage control reference to regulate both equivalent fundamental and harmonic impedances is obtained in (16) as Vre f = Vd ro o p

α

− Vv f − Vv h

= Vre f d ro o p − (Rv f · IL in e f α − ω ∗ Lv f · IL in e f β ) ⎛ GR h · VP C C h α − GI h · VP C C h −⎝ h = 3 , 5 , 7 ···

In order to minimize the interference between virtual fundamental impedance and virtual harmonic impedance, the control method discussed so far involves fundamental/harmonic components extraction. This is challenging for low-cost DG units with limited computing capability. In addition to the adoption of low-bandwidth communication to avoid the measurement and extraction of PCC harmonic voltages, the DG unit local controller can be further simplified. In this section, a modified resonant controller is proposed to combine the fundamental/harmonic components extraction and the closed-loop voltage tracking together. A. Conventional Double-Loop Voltage Tracking Scheme

⎞ β

⎠.

h = 3 , 5 , 7 ···

(16) D. PCC Harmonic Voltage Measurement In the previous subsections, the PCC harmonic voltages (with α in the subscript) and their corresponding conjugated signals (with β in the subscript) are utilized for single-phase DG unit equivalent harmonic impedance shaping. These PCC harmonic voltage signals can be transmitted from the microgrid central controller to the DG unit local controller by using a synchronized phase-locked loop (PLL)-based communication algorithm in [16], [27], [28], and [34], where the three-phase system was selected for case study. For the single-phase system, various types of single-phase PLL methods have been developed [26]. In this paper, the sliding discrete Fourier transformation (SDFT) [32] method is adopted to construct the PLL systems. The detailed diagram of the low-bandwidth system is shown in Fig. 5. At the microgrid central controller, the fundamental and harmonic PCC voltages are first extracted by SDFT. The fundamental voltage components are adopted to determine the PCC voltage phase angle θPCC as −1 tan (VPCCf β /VPCCf α ) if VPCCf α ≥ 0 θPCC = . −1 tan (VPCCf β /VPCCf α ) + π if VPCCf α < 0 (17) Afterward, the harmonic components are transformed into the values at their corresponding synchronized rotating frames by Park Transformations. For the steady-state harmonic voltage signals, they behave as dc components at their respective rotating frames. These signals at rotating frames are sent to DG unit local controller by the low-bandwidth communication bus.

First, the DG unit using conventional double-loop voltage tracking scheme [20] is briefly reviewed in this subsection. The diagram of DG local controller is presented in Fig. 6. Because of the “whack a mole” effects [16], mitigation of PCC harmonics will inevitably introduce some DG unit voltage distortions. Additionally, due to the interactions between DG harmonic voltage and harmonic line current, the power calculation using measured DG voltages and line currents will introduce some steady-state dc power offsets, which cannot be filtered out by LPFs. As a result, the fundamental DG voltage VDGf α and line current ILinef α components and their conjugate signals VDGf β and ILinef β are preferred to be extracted to calculate the fundamental power Pave and Qave . For a single-phase DG unit, its fundamental power is calculated in the stationary artificial α − β frame as Pave = 1/2 · (VC f

α

· ILinef

α

+ VC f

β

· ILinef

β)

(18)

Qave = 1/2 · (VC f

β

· ILinef

α

− VC f

α

· ILinef

β ).

(19)

Moreover, these fundamental voltage and current components are also needed to carry out another two tasks. The first one is to form the DG unit local PLL, which is important to realize the low-bandwidth communication-based PCC harmonic voltage acquisition as shown in Fig. 5. Additionally, the fundamental components of DG line current are also utilized to calculate the voltage drops on the virtual fundamental impedance in (8). As shown in Fig. 6, the modified voltage referenceVref can be obtained by combining the voltage reference from droop control, virtual fundamental impedance regulation, and virtual harmonic impedance regulation together. Afterward, the double-loop voltage controller is adopted to track this modified voltage reference. In this diagram, the outer loop uses proportional controllers and multiple quasi-resonant controllers as shown in (20) 2Kih ωc s (20) GOuter (s) = KP + s2 + 2ωc s + ωh2 h=f ,3,5,7,9


Fig. 5.

PCC harmonic voltage measurement using low-bandwidth communication system.

Fig. 6.

Power sharing and harmonic compensation using conventional double-loop voltage controller.

where Kp is the outer loop proportional gain, Kih is the gain of resonant controller at different frequencies, ωh is the angular frequency, and ωc is the cutoff bandwidth of resonant controllers. The inner loop is a simple proportional control KInner with filter inductor current feedback as GInner (s) = KInner .

(21)

B. Proposed Controller Without Fundamental-Harmonic Components Separation This section discusses the opportunities of realizing virtual impedance regulation without using any fundamental and harmonic components extractions (SDFT) in the DG unit local controller. First, the input of DG unit local PLL is replaced by the voltage reference Vdro op α and its quarter-cycle delayed conjugate signal Vdro op β . This is very convenient as these voltage references are always sinusoidal with little harmonics. Moreover, when a small equivalent fundamental impedance RDGf and LDG f is considered for the reactive power sharing accuracy enhancement, the voltage reference Vdro op α is even closer to PCC fundamental voltage VPCCf α , compared to the case using measured filter capacitor fundamental voltage (see Fig. 2). Accordingly, the accuracy of PCC harmonic voltage measurement in Fig. 5 is also improved.

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Furthermore, in the proposed implementation method, the power calculation uses the voltage references Vdro op α and Vdro op β from droop control and nonfiltered DG line current ILine α and ILine β . As Vdro op α and Vdro op β are ripple free, the harmonic ripples in DG line harmonic current ILine α and ILine β will not introduce any steady-state dc power offset and the dominant ripples in the calculated power are at 120 Hz (due to the contribution of third harmonic line current). Therefore, the power ripples can be easily filtered out by first-order LPFs. The formula of power calculation is then expressed as Pave =

ωL P F · (Vd ro o p 2(s + ωL P F )

α

· IL in e

α

+ Vd ro o p

β

· IL in e

β)

(22) Qave

ωL P F · (Vd ro o p = 2(s + ωL P F )

β

· IL in e

α

− Vd ro o p

α

· IL in e

β)

(23) where ωLPF is the cutoff frequency of LPFs. Finally, the voltage reference for virtual fundamental impedance control is also obtained without using DG line current fundamental components. The fundamental/harmonic component extraction blocks (SDFT) in Fig. 6 can be completely removed in the proposed method. This can be done by using the modified voltage drop on fundamental virtual impedance as Vv∗f = Rv f · ILine

α

− ωf Lv f · ILine β .

(24)

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Fig. 7.


Power sharing improvement and PCC harmonic compensation using proposed modified voltage controller.

Note that ILine α and ILine β in (24) are the DG line current without any filtering. When (24) is used as the reference voltage drop on virtual fundamental impedance, it seems that the ripple voltages in Vv∗f will have some interferences with virtual harmonic impedance control. However, it can also be seen that harmonic filtering capability has already been embedded in the resonant controller in (20). By the flexible arrangement of parallel resonant controllers, the harmonic voltages in Vv∗f can also be easily filtered out without any additional efforts. The improved DG voltage controller is shown in Fig. 7, where the power calculation, PCC harmonic voltage measurement, and voltage drop on fundamental virtual impedance are obtained without any fundamental and harmonic components separation. To achieve similar performance compared to the case using the control scheme in Fig. 6, the conventional double-loop voltage controller is revised as a controller with multiple inputs. The detailed expression of the proposed outer loop voltage tracking controller is described as Ire f =

KP 1 ⎛

2Ki f ωc s + 2 s + 2ωc s + ωf2

+ ⎝KP 2 +

h = 3,5,7,9

· (Vd ro o p

α

− Vv∗f − VC

α)

⎞ 2Ki h ωc s ⎠ · (0 − Vv h − VC s2 + 2ωc s + ωh2

α)

(25) where the voltage drop Vv∗f for the fundamental virtual impedance control is mainly regulated by fundamental resonant controller. Therefore, the majority of the harmonic ripples in Vv∗f can be filtered out automatically. Meanwhile, resonant controllers at harmonic frequencies are responsible for the DG unit harmonic voltage tracking. It is true that the proportional gain KP 1 and KP 2 can still introduce minor interference between fundamental and harmonic voltage regulations. However, as indicated by [23] and [24], to maintain proper system stability margin, the proportional gains in the PR controller are normally very small compared to resonant controller gains. In [24], it even suggested that the proportional controller gains can be set to zero to achieve better performance. In this paper, as very small values (KP 1 = KP 2 = 0.11)

Fig. 8.

Simplified diagram of single-phase experimental setup.

are selected, proportional gains will not cause any noticeable disturbances.

IV. EXPERIMENTAL RESULT Experiments have been performed on a simple single-phase islanding microgrid, where two H-bridge-based DG units at the same power rating are connected to PCC with different feeder impedances. The simplified diagram of the single-phase experimental setup is shown in Fig. 8. To emulate the behavior of low-bandwidth communication system, the measured PCC harmonic voltage signals are sent to DG unit local controller using a zero-order hold with 0.5 ms delay [16]. The detailed circuit and control parameters of the system are provided in Table I. First, to verify the effectiveness of the proposed reactive power sharing enhancement method, a low power factor linear RL load is placed at PCC. The corresponding power sharing performance is presented in Fig. 9. As shown, when the conventional droop control without virtual impedance (corresponding to Vv f = 0 and Vv h = 0 in Fig. 6) is used in Region1, the real power sharing is accurate while reactive power sharing appears as nontrivial errors. On the other hand, the proposed virtual fundamental impedance control can significantly reduce the reactive power sharing error as shown in Region3. To avoid excess real power jittering in the beginning of the reactive power compensation, the virtual fundamental impedance is slowly changed from zero to the desired value in Region2.


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TABLE I PARAMETERS IN EXPERIMENTS

Fig. 10. Experimental results without the implementation of virtual impedance. (a) DG unit1 voltage (100 V/div); (b) DG unit2 voltage (100 V/div); (c) DG unit1 line current (2 A/div); and (d) DG unit2 line current (2 A/div). (Voltage controller in Fig. 6 is adopted.)

Fig. 11. Experimental results with the implementation of virtual fundamental impedance. (a) DG unit1 voltage (100 V/div); (b) DG unit2 voltage (100 V/div); (c) DG unit1 line current (2 A/div); and (d) DG unit2 line current (2 A/div). (Voltage controller in Fig. 7 is adopted.)

Fig. 9. Power sharing performance in the microgrid. (a) DG unit1 real power (20 W/div); (b) DG unit2 real power (20 W/div); (c) DG unit1 reactive power (20 Var/div); and (d) DG unit2 reactive power (20 Var/div).

The associated current and voltage waveforms are also obtained in Figs. 10 and 11. Fig. 10 describes the performance of the microgrid before the implementation of virtual fundamental impedance. It can be seen that there are noticeable magnitude and phase errors between DG unit1 and DG unit2 line currents. After the implementation of the virtual fundamental impedance, the enhanced performance is illustrated in Fig. 11. It can be noticed that line currents of DG unit1 and DG unit2 are almost identical. To investigate the effectiveness of the proposed virtual harmonic impedance control method, the linear load at PCC is

Fig. 12. Experimental voltage waveform without the implementation of virtual impedance. (a) DG unit1 voltage (100 V/div); (b) DG unit2 voltage (100 V/div); and (c) PCC voltage (100 V/div). (Voltage controller in Fig. 6 is adopted.)

replaced by a diode rectifier load. The performance without using any virtual impedance is presented in Figs. 12 and 13. In Fig. 12, it can be seen that the voltages of DG unit1 and DG unit2 are sinusoidal with 3.91% and 3.81% THD (total harmonic distortions), respectively. On the other hand, PCC voltage (with 10.55% THD) is distorted by the harmonic voltage drop on the DG unit feeders.

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Fig. 13. Experimental current waveform without the implementation of virtual impedance. (a) DG unit1 line current (2 A/div); and (b) DG unit2 line current (2 A/div). (Voltage controller in Fig. 6 is adopted.)

Fig. 15. Experimental voltage waveform with the implementation of virtual fundamental and harmonic impedances. (a) DG unit1 line current (2 A/div); and (b) DG unit2 line current (2 A/div). (Voltage controller in Fig. 7 is adopted.)

Fig. 16. Voltage harmonic spectrum without the implementation of the proposed virtual impedance (corresponding to Fig. 12). Fig. 14. Experimental voltage waveform with the implementation of virtual fundamental and harmonic impedances. (a) DG unit1 voltage (100 V/div); (b) DG unit2 voltage (100 V/div); and (c) PCC voltage (100 V/div).) (Voltage controller in Fig. 7 is adopted.)

Meanwhile, the harmonic current sharing performance without the control of virtual impedance is presented in Fig. 13. As virtual harmonic impedance control is not activated in this test, the DG equivalent harmonic impedance equals to its feeder harmonic impedance. It is obvious that the DG unit1 absorbs more harmonic currents as it has smaller equivalent harmonic impedance. The microgrid voltage waveforms with the control of the proposed virtual fundamental and harmonic impedances are illustrated in Fig. 14. In this experiment, the desired equivalent harmonic impedances for these two DG units are the same as listed in Table I, and the voltage controller as presented in Fig. 7 is responsible for voltage tracking. It can be seen from Fig. 14 that when smaller DG equivalent harmonic impedance is selected for both DG units, the PCC voltage distortions is mitigated with 6.24% THD. Meanwhile, due to “whack a mole” effects [14], [16], the DG voltages are polluted since the harmonic voltage drops on DG feeders are compensated by DG units. In this case, the THDs of DG unit1 and DG unit2 are 5.70% and 15.04%, respectively. The allocation of nonlinear currents with the control virtual harmonic impedance is obtained in Fig. 15. It shows that the harmonic load currents are almost equally shared by these two DG units.

Fig. 17. Voltage harmonic spectrum after the implementation of the proposed virtual impedance (corresponding to Fig. 14).

To get a better understanding of microgrid harmonic voltage compensation performance using the proposed method, the THDs of DG units and PCC are illustrated in Figs. 16 and 17. In Fig. 16, it obviously shows that the PCC harmonic voltage is higher than DG harmonic voltages without the DG virtual impedance control, and the dominate PCC voltage distortion is the third harmonic voltage. After the implementation of the proposed virtual impedance, it can be seen from Fig. 17 that the PCC harmonic voltage is mitigated. In this case, the harmonic voltage drops on DG feeders are compensated by DG local voltage control, and therefore DG unit voltage appears with more distortions. Finally, the performance comparison between the proposed virtual impedance control method and the conventional methods is provided in Table II. It demonstrates that the combination


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TABLE II PERFORMANCE SUMMARY OF DIFFERENT CONTROL METHODS

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Jinwei He (S’10) received the B.Eng. degree from Southeast University, Nanjing, China, in 2005, and the M.Sc. degree from the Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing, China, in 2008. He is currently working toward the Ph.D. degree at the University of Alberta, Edmonton, AB, Canada. In 2007, he was a visiting student at Shanghai Maglev Transportation Engineering R&D Centre, Shanghai, China, where he worked on a linear induction motor design project. From 2008 to 2009, he was with China Electronics Technology Group Corporation. In 2012, he was a Visiting Scholar in the Department of Energy Technology, Aalborg University, Aalborg, Denmark. He is the author of more than 40 technical papers in refereed journals and conferences. His research interests include microgrid, distributed generation, active power filter, electromagnetic design of linear electric machine, and high-power converter for railway traction drives.

Yun Wei Li (S’04–M’05–SM’11) received the B.Sc.Eng. degree in electrical engineering from Tianjin University, Tianjin, China, in 2002, and the Ph.D. degree from Nanyang Technological University, Singapore, in 2006. In 2005, he was a Visiting Scholar with the Aalborg University, Aalborg, Denmark, where he was involved in the medium voltage dynamic voltage restorer system. From 2006 to 2007, he was a Postdoctoral Research Fellow at Ryerson University, Toronto, ON, Canada, working on the high-power converter and electric drives. In 2007, he also worked with Rockwell Automation Canada, Cambridge, ON, and was responsible for the development of power factor compensation strategies for induction motor drives. Since 2007, he has been with the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada, initially as an Assistant Professor and then an Associate Professor from 2013. His research interests include distributed generation, microgrid, renewable energy, power quality, high-power converters, and electric motor drives. Dr. Li serves as an Associate Editor for the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS and a Guest Editor for the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Special Session on Distributed Generation and Microgrids.

Josep M. Guerrero (S’01–M’04–SM’08) received the B.S. degree in telecommunications engineering, the M.S. degree in electronics engineering, and the Ph.D. degree in power electronics all from the Technical University of Catalonia, Barcelona, Spain, in 1997, 2000, and 2003, respectively. He was an Associate Professor in the Department of Automatic Control Systems and Computer Engineering, Technical University of Catalonia, teaching courses on digital signal processing, fieldprogrammable gate arrays, microprocessors, and control of renewable energy. In 2004, he was at the Renewable Energy Laboratory, Escola Industrial de Barcelona. Since 2011, he has been a Full Professor in the Department of Energy Technology, Aalborg University, Aalborg, Denmark, where he is responsible for the microgrid research program. Since 2012, he has also been a Guest Professor at the Chinese Academy of Science, Beijing, China, and the Nanjing University of Aeronautics and Astronautics, Nanjing, China. His research interests include different microgrid aspects, including power electronics, distributed energy-storage systems, hierarchical and cooperative control, energy management systems, and optimization of microgrids and islanded minigrids. Dr. Guerrero is an Associate Editor for the IEEE TRANSACTIONS ON POWER ELECTRONICS, the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, and the IEEE Industrial Electronics Magazine. He has been a Guest Editor of the IEEE TRANSACTIONS ON POWER ELECTRONICS Special Issues: Power Electronics for Wind Energy Conversion and Power Electronics for Microgrids, and the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Special Sections: Uninterruptible Power Supplies systems, Renewable Energy Systems, Distributed Generation and Microgrids, and Industrial Applications and Implementation Issues of the Kalman Filter. He is the Chair of the Renewable Energy Systems Technical Committee of the IEEE Industrial Electronics Society. Frede Blaabjerg (F’13) received the Ph.D. degree from Aalborg University, Aalborg, Denmark, in 1992. He was with ABB-Scandia, Randers, Denmark, from 1987 to 1988. He Joined Aalborg University in 1988, where he became an Assistant Professor in 1992, an Associate Professor in 1996, and a Full Professor in power electronics and drives in 1998. He has been a part-time Research Leader with Research Center Risoe, Denmark, in wind turbines. In 2006– 2010, he was the Dean of the Faculty of Engineering, Science and Medicine and became a Visiting Professor at Zhejiang University, Zhejiang, China, in 2009. His research interests include power electronics and its applications like in wind turbines, PV systems, and adjustable speed drives. Dr. Blaabjerg has been the Editor-in-Chief of the IEEE Transactions on Power Electronics from 2006 to 2012. He was a Distinguished Lecturer for the IEEE Power Electronics Society in 2005–2007 and for the IEEE Industry Applications Society from 2010 to 2011. He has been the Chairman of the European Conference on Power Electronics in 2007 and the Power Electronics for Distributed Generation Systems in 2012, both held at Aalborg. He received the 1995 Angelos Award for his contribution in modulation technique and the Annual Teacher Prize at Aalborg University. In 1998, he received the Outstanding Young Power Electronics Engineer Award from the IEEE Power Electronics Society. He has received 13 IEEE Prize Paper Awards and another Prize Paper Award at Power Electronics and Intelligent Control for Energy Conservation, Poland, in 2005. He received the IEEE Power Electronics Society Distinguished Service Award in 2009 and the Power Electronics and Motion Control Conference (EPE-PEMC) 2010 Council Award. Finally, he has received a number of major research awards in Denmark. Juan C. Vasquez received the B.S. degree in electronics engineering from the Autonoma University of Manizales, Manizales, Colombia, in 2004. In 2009, he received the Ph.D. degree from the Department of Automatic Control Systems and Computer Engineering, Technical University of Catalonia, Barcelona, Spain. At the Autonoma University of Manizales, he taught courses on digital circuits, servo systems, and flexible manufacturing systems. He was as a Postdoctoral Assistant at the Technical University of Catalonia, where he taught courses based on renewable energy systems. He is currently an Assistant Professor at Aalborg University, Aalborg, Denmark. His research interests include modeling, simulation, and power management applied to the distributed generation in microgrids.