A Unified Control Strategy for Three-Phase Inverter ... - Semantic Scholar

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 3, MARCH 2014

A Unified Control Strategy for Three-Phase Inverter in Distributed Generation Zeng Liu, Student Member, IEEE, Jinjun Liu, Senior Member, IEEE, and Yalin Zhao

Abstract—This paper presents a unified control strategy that enables both islanded and grid-tied operations of three-phase inverter in distributed generation, with no need for switching between two corresponding controllers or critical islanding detection. The proposed control strategy composes of an inner inductor current loop, and a novel voltage loop in the synchronous reference frame. The inverter is regulated as a current source just by the inner inductor current loop in grid-tied operation, and the voltage controller is automatically activated to regulate the load voltage upon the occurrence of islanding. Furthermore, the waveforms of the grid current in the grid-tied mode and the load voltage in the islanding mode are distorted under nonlinear local load with the conventional strategy. And this issue is addressed by proposing a unified load current feedforward in this paper. Additionally, this paper presents the detailed analysis and the parameter design of the control strategy. Finally, the effectiveness of the proposed control strategy is validated by the simulation and experimental results. Index Terms—Distributed generation (DG), islanding, load current, seamless transfer, three-phase inverter, unified control.

I. INTRODUCTION ISTRIBUTED generation (DG) is emerging as a viable alternative when renewable or nonconventional energy resources are available, such as wind turbines, photovoltaic arrays, fuel cells, microturbines [1], [3]. Most of these resources are connected to the utility through power electronic interfacing converters, i.e., three-phase inverter. Moreover, DG is a suitable form to offer high reliable electrical power supply, as it is able to operate either in the grid-tied mode or in the islanded mode [2]. In the grid-tied operation, DG deliveries power to the utility and the local critical load. Upon the occurrence of utility outage, the islanding is formed. Under this circumstance, the DG must be tripped and cease to energize the portion of utility as soon as possible according to IEEE Standard 929-2000 [4]. However, in order to improve the power reliability of some local critical

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Manuscript received December 15, 2012; revised March 4, 2013; accepted April 21, 2013. Date of current version September 18, 2013. This work was supported in part by the National Basic Research Program (973 Program) of China under Project 2009CB219705, and by the State Key Laboratory of Electrical Insulation and Power Equipment under Project EIPE09109. This paper was presented in part at the 26th IEEE Applied Power Electronics Conference and Exposition, Fort Worth, TX, USA, March 6–11, 2011. Recommended for publication by Associate Editor D. Xu. The authors are with the State Key Lab of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China (e-mail: [email protected]; [email protected]; [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.2013.2262078

load, the DG should disconnect to the utility and continue to feed the local critical load [5]. The load voltage is key issue of these two operation modes, because it is fixed by the utility in the grid-tied operation, and formed by the DG in the islanded mode, respectively. Therefore, upon the happening of islanding, DG must take over the load voltage as soon as possible, in order to reduce the transient in the load voltage. And this issue brings a challenge for the operation of DG. Droop-based control is used widely for the power sharing of parallel inverters [11], [12], which is called as voltage mode control in this paper, and it can also be applied to DG to realize the power sharing between DG and utility in the grid-tied mode [13]–[16], [53]. In this situation, the inverter is always regulated as a voltage source by the voltage loop, and the quality of the load voltage can be guaranteed during the transition of operation modes. However, the limitation of this approach is that the dynamic performance is poor, because the bandwidth of the external power loop, realizing droop control, is much lower than the voltage loop. Moreover, the grid current is not controlled directly, and the issue of the inrush grid current during the transition from the islanded mode to the grid-tied mode always exists, even though phase-locked loop (PLL) and the virtual inductance are adopted [15]. The hybrid voltage and current mode control is a popular alternative for DG, in which two distinct sets of controllers are employed [17]–[40]. The inverter is controlled as a current source by one sets of a controller in the grid-tied mode, while as a voltage source by the other sets of controller in the islanded mode. As the voltage loop or current loop is just utilized in this approach, a nice dynamic performance can be achieved. Besides, the output current is directly controlled in the grid-tied mode, and the inrush grid current is almost eliminated. In the hybrid voltage and current mode control, there is a need to switch the controller when the operation mode of DG is changed. During the interval from the occurrence of utility outage and switching the controller to voltage mode, the load voltage is neither fixed by the utility, nor regulated by the DG, and the length of the time interval is determined by the islanding detection process. Therefore, the main issue in this approach is that it makes the quality of the load voltage heavily reliant on the speed and accuracy of the islanding detection method [6]–[10]. Another issue associated with the aforementioned approaches is the waveform quality of the grid current and the load voltage under nonlinear local load. In the grid-tied mode, the output current of DG is generally desired to be pure sinusoidal [18]. When the nonlinear local load is fed, the harmonic component of the load current will fully flow into the utility. A single-phase DG, which injects harmonic current into the utility for mitigating

0885-8993 © 2013 IEEE

LIU et al.: UNIFIED CONTROL STRATEGY FOR THREE-PHASE INVERTER IN DISTRIBUTED GENERATION

Fig. 1.

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Schematic diagram of the DG based on the proposed control strategy.

the harmonic component of the grid current, is presented in [41]. The voltage mode control is enhanced by controlling the DG to emulate a resistance at the harmonic frequency, and then the harmonic current flowing into utility can be mitigated [42]. In the islanded mode, the nonlinear load may distort the load voltage [43], and many control schemes have been proposed to improve the quality of the load voltage, including a multiloop control method [43]–[46], resonant controllers [48], [49], sliding mode control [47]. However, existing control strategies, dealing with the nonlinear local load in DG, mainly focus on either the quality of the grid current in the grid-tied mode or the one of the load voltage in the islanded mode, and improving both of them by a unified control strategy is seldom. This paper proposes a unified control strategy that avoids the aforementioned shortcomings. First, the traditional inductor current loop is employed to control the three-phase inverter in DG to act as a current source with a given reference in the synchronous reference frame (SRF). Second, a novel voltage controller is presented to supply reference for the inner inductor current loop, where a proportional-plus-integral (PI) compensator and a proportional (P) compensator are employed in D-axis and Q-axis, respectively. In the grid-tied operation, the load voltage is dominated by the utility, and the voltage compensator in D-axis is saturated, while the output of the voltage compensator in Q-axis is forced to be zero by the PLL. Therefore, the reference of the inner current loop cannot regulated by the voltage loop, and the DG is controlled as a current source just by the inner current loop. Upon the occurrence of the grid outage, the load voltage is no more determined by the utility, and the voltage controller is automatically activated to regulate the load voltage. These happen naturally, and, thus the proposed control strategy does not need a forced switching between two distinct sets of controllers. Further, there is no need to detect the islanding quickly and accurately, and the islanding detection method is no more critical in this approach. Moreover, the proposed control strategy, benefiting from just utilizing the current and voltage feedback control, endows a better dynamic performance, compared to the voltage mode control. Third, the proposed control strategy is enhanced by introducing a unified load current feedforward, in order to deal with the issue caused by the nonlinear local load, and this scheme is implemented by adding the load current into the reference of the inner current loop. In the grid-tied mode, the DG injects

harmonic current into the grid for compensating the harmonic component of the grid current, and thus, the harmonic component of the grid current will be mitigated. Moreover, the benefit of the proposed load current feedforward can be extended into the islanded operation mode, due to the improved quality of the load voltage. The rest of this paper is arranged as follows. Section II describes the proposed unified control strategy for three-phase inverter in DG, including the power stage of DG, the basic idea, and the control diagram. The detailed operation principle of DG with the proposed control strategy is illustrated in Section III. The parameter design and small signal analysis of the proposed control system are given in Section IV. Section V investigates the proposed control strategy by simulation and experimental results. Finally, the concluding remarks are given in Section VI.

II. PROPOSED CONTROL STRATEGY A. Power Stage This paper presents a unified control strategy for a threephase inverter in DG to operate in both islanded and grid-tied modes. The schematic diagram of the DG based on the proposed control strategy is shown by Fig. 1. The DG is equipped with a three-phase interface inverter terminated with a LC filter. The primary energy is converted to the electrical energy, which is then converted to dc by the front-end power converter, and the output dc voltage is regulated by it. Therefore, they can be represented by the dc voltage source Vdc in Fig. 1. In the ac side of inverter, the local critical load is connected directly. It should be noted that there are two switches, denoted by Su and Si , respectively, in Fig. 1, and their functions are different. The inverter transfer switch Si is controlled by the DG, and the utility protection switch Su is governed by the utility. When the utility is normal, both switches Si and Su are ON, and the DG in the grid-tied mode injects power to the utility. When the utility is in fault, the switch Su is tripped by the utility instantly, and then the islanding is formed. After the islanding has been confirmed by the DG with the islanding detection scheme [6]–[10], the switch Si is disconnected, and the DG is transferred from the grid-tied mode to the islanded mode. When the utility is restored, the DG should be resynchronized with the utility first, and then the switch Si is turned ON to connect the DG with the grid.

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Fig. 2.

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 3, MARCH 2014

Overall block diagram of the proposed unified control strategy.

B. Basic Idea With the hybrid voltage and current mode control [17]–[40], the inverter is controlled as a current source to generate the reference power PDG + jQDG in the grid-tied mode. And its output power PDG + jQDG should be the sum of the power injected to the grid Pg + jQg and the load demand Pload + jQload , which can be expressed as follows by assuming that the load is represented as a parallel RLC circuit: 3 Vm2 · 2 R   1 3 − ωC . = · Vm2 · 2 ωL

Pload =

(1)

Qload

(2)

In (1) and (2), Vm and ω represent the amplitude and frequency of the load voltage, respectively. When the nonlinear local load is fed, it can still be equivalent to the parallel RLC circuit by just taking account of the fundamental component. During the time interval from the instant of islanding happening to the moment of switching the control system to voltage mode control, the load voltage is neither fixed by the utility nor regulated by the inverter, so the load voltage may drift from the normal range [6]. And this phenomenon can be explained as below by the power relationship. During this time interval, the inverter is still controlled as a current source, and its output power is kept almost unchanged. However, the power injected to utility decreases to zero rapidly, and then the power consumed by the load will be imposed to the output power of DG. If both active power Pg and reactive power Qg injected into the grid are positive in the grid-tied mode, then Pload and Qload will increase after the islanding happens, and the amplitude and frequency of the load voltage will rise and drop, respectively, according to (1) and (2).

With the previous analysis, if the output power of inverter PDG + jQDG could be regulated to match the load demand by changing the current reference before the islanding is confirmed, the load voltage excursion will be mitigated. And this basic idea is utilized in this paper. In the proposed control strategy, the output power of the inverter is always controlled by regulating the three-phase inductor current iL abc , while the magnitude and frequency of the load voltage vC abc are monitored. When the islanding happens, the magnitude and frequency of the load voltage may drift from the normal range, and then they are controlled to recover to the normal range automatically by regulating the output power of the inverter. C. Control Scheme Fig. 2 describes the overall block diagram for the proposed unified control strategy, where the inductor current iL abc , the utility voltage vg abc , the load voltage vC abc , and the load current iL L abc are sensed. And the three-phase inverter is controlled in the SRF, in which, three phase variable will be represented by dc quantity. The control diagram is mainly composed by the inductor current loop, the PLL, and the current reference generation module. In the inductor current loop, the PI compensator is employed in both D- and Q-axes, and a decoupling of the cross coupling denoted by ω0 Lf /kPW M is implemented in order to mitigate the couplings due to the inductor. The output of the inner current loop ddq  , together with the decoupling of the capacitor voltage denoted by 1/kPW M , sets the reference for the standard space vector modulation that controls the switches of the three-phase inverter. It should be noted that kPW M denotes the voltage gain of the inverter, which equals to half of the dc voltage in this paper.

LIU et al.: UNIFIED CONTROL STRATEGY FOR THREE-PHASE INVERTER IN DISTRIBUTED GENERATION

Fig. 3.

Block diagram of the current reference generation module.

The PLL in the proposed control strategy is based on the SRF PLL [50], [51], which is widely used in the three-phase power converter to estimate the utility frequency and phase. Furthermore, a limiter is inserted between the PI compensator GPLL and the integrator, in order to hold the frequency of the load voltage within the normal range in the islanded operation. In Fig. 2, it can be found that the inductor current is regulated to follow the current reference iL r ef dq , and the phase of the current is synchronized to the grid voltage vg abc . If the current reference is constant, the inverter is just controlled to be a current source, which is the same with the traditional grid-tied inverter. The new part in this paper is the current reference generation module shown in Fig. 2, which regulates the current reference to guarantee the power match between the DG and the local load and enables the DG to operate in the islanded mode. Moreover, the unified load current feedforward, to deal with the nonlinear local load, is also implemented in this module. The block diagram of the proposed current reference generation module is shown in Fig. 3, which provides the current reference for the inner current loop in both grid-tied and islanded modes. In this module, it can be found that an unsymmetrical structure is used in D- and Q-axes. The PI compensator is adopted in D-axes, while the P compensator is employed in Q-axis. Besides, an extra limiter is added in the D-axis. Moreover, the load current feedforward is implemented by adding the load current iL L dq to the final inductor current reference iL r ef dq . The benefit brought by the unique structure in Fig. 3 can be represented by two parts: 1) seamless transfer capability without critical islanding detection; and 2) power quality improvement in both grid-tied and islanded operations. The current reference iL r edq composes of four parts in D- and Q-axes respectively: 1) the output of voltage controller ir ef dq ; 2) the grid current reference Ig r ef dq ; 3) the load current iL L dq ; and 4) the current flowing through the filter capacitor Cf . In the grid-tied mode, the load voltage vC dq is clamped by the utility. The current reference is irrelevant to the load voltage, due to the saturation of the PI compensator in D-axis, and the output of the P compensator being zero in Q-axis, and thus, the inverter operates as a current source. Upon occurrence of islanding, the

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voltage controller takes over automatically to control the load voltage by regulating the current reference, and the inverter acts as a voltage source to supply stable voltage to the local load; this relieves the need for switching between different control architectures. Another distinguished function of the current reference generation module is the load current feedforward. The sensed load current is added as a part of the inductor current reference iL r ef dq to compensate the harmonic component in the grid current under nonlinear local load. In the islanded mode, the load current feedforward operates still, and the disturbance from the load current, caused by the nonlinear load, can be suppressed by the fast inner inductor current loop, and thus, the quality of the load voltage is improved. The inductor current control in Fig. 2 was proposed in previous publications for grid-tied operation of DG [18], and the motivation of this paper is to propose a unified control strategy for DG in both grid-tied and islanded modes, which is represented by the current reference generation module in Fig. 3. The contribution of this module can be summarized in two aspects. First, by introducing PI compensator and P compensator in D-axis and Q-axis respectively, the voltage controller is inactivated in the grid-tied mode and can be automatically activated upon occurrence of islanding. Therefore, there is no need for switching different controllers or critical islanding detection, and the quality of the load voltage during the transition from the grid-tied mode to the islanded mode can be improved. The second contribution of this module is to present the load current feedforward to deal with the issue caused by the nonlinear local load, with which, not only the waveform of the grid current in grid-tied is improved, but also the quality of the load voltage in the islanded mode is enhanced. Besides, it should be noted that a three-phase unbalanced local load cannot be fed by the DG with the proposed control strategy, because there is no flow path for the zero sequence current of the unbalanced load, and the regulation of the zero sequence current is beyond the scope of the proposed control strategy.

III. OPERATION PRINCIPLE OF DG The operation principle of DG with the proposed unified control strategy will be illustrated in detail in this section, and there are in total four states for the DG, including the grid-tied mode, transition from the grid-tied mode to the islanded mode, the islanded mode, and transition from the islanded mode to the grid-tied mode.

A. Grid-Tied Mode When the utility is normal, the DG is controlled as a current source to supply given active and reactive power by the inductor current loop, and the active and reactive power can be given by the current reference of D- and Q-axis independently. First, the phase angle of the utility voltage is obtained by the PLL, which consists of a Park transformation expressed by (3), a PI

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compensator, a limiter, and an integrator   ⎛ 2 cos θ cos θ − π   3 xd 2⎜ ⎜ = ⎜   3⎝ xq 2 − sin θ − sin θ − π 3 ⎛ ⎞ xa × ⎝ xb ⎠ . xc

 ⎞ 2 cos θ + π ⎟ 3 ⎟  ⎟ 2 ⎠ − sin θ + π 3 (3)

Second, the filter inductor current, which has been transformed into SRF by the Park transformation, is fed back and compared with the inductor current reference iL r ef dq , and the inductor current is regulated to track the reference iL r ef dq by the PI compensator GI . The reference of the inductor current loop iL r ef dq seems complex and it is explained as below. It is assumed that the utility is stiff, and the three-phase utility voltage can be expressed as ⎧ vg a = Vg cos θ∗ ⎪ ⎪ ⎪ ⎪   ⎪ ⎪ 2π ⎨ vg b = Vg cos θ∗ − (4) 3 ⎪ ⎪   ⎪ ⎪ ⎪ 2π ⎪ ⎩ vg c = Vg cos θ∗ + 3 where Vg is the magnitude of the grid voltage, and θ∗ is the actual phase angle. By the Park transformation, the utility voltage is transformed into the SRF, which is shown as  vg d = Vg cos(θ∗ − θ) (5) vg q = Vg sin(θ∗ − θ). vg q is regulated to zero by the PLL, so vg d equals the magnitude of the utility voltage Vg . As the filter capacitor voltage equals the utility voltage in the gird-tied mode, vC d equals the magnitude of the utility voltage Vg , and vC q equals zero, too. In the D-axis, the inductor current reference iL r ef d can be expressed by (6) according to Fig. 3 iL r ef d = Ig r ef d + iL L d − ω0 Cf · vC q .

(6)

The first part is the output of the limiter. It is assumed that the given voltage reference Vm ax is larger than the magnitude of the utility voltage vC d in steady state, so the PI compensator, denoted by GV D in the following part, will saturate, and the limiter outputs its upper value Ig r ef d . The second part is the load current of D-axis iL L d , which is determined by the characteristic of the local load. The third part is the proportional part −ω0 Cf · vC q , where ω0 is the rated angle frequency, and Cf is the capacitance of the filter capacitor. It is fixed as vC q depends on the utility voltage. Consequently, the current reference iL r ef d is imposed by the given reference Ig r ef d and the load current iL L d , and is independent of the load voltage. In the Q-axis, the inductor current reference iL r ef q consists of four parts as iL r ef q = vC q · kG v q + Ig r ef q + iL L q + ω0 Cf · vC d

(7)

where kG v q is the parameter of the P compensator, denoted by GV Q in the following part. The first part is the output of GV Q ,

Fig. 4. Simplified block diagram of the unified control strategy when DG operates in the grid-tied mode.

which is zero as the vC q has been regulated to zero by the PLL. The second part is the given current reference Ig r ef q , and the third part represents the load current in Q-axis. The final part is the proportional part −ω0 Cf · vC d , which is fixed since vC d depends on the utility voltage. Therefore, the current reference iL r ef q cannot be influenced by the external voltage loop and is determined by the given reference Ig r ef q and the load current iL L q . With the previous analysis, the control diagram of the inverter can be simplified as Fig. 4 in the grid-tied mode, and the inverter is controlled as a current source by the inductor current loop with the inductor current reference being determined by the current reference Ig r ef dq and the load current iL L dq . In other words, the inductor current tracks the current reference and the load current. If the steady state error is zero, Ig r ef dq represents the grid current actually, and this will be analyzed in the next section. B. Transition From the Grid-Tied Mode to the Islanded Mode When the utility switch Su opens, the islanding happens, and the amplitude and frequency of the load voltage will drift due to the active and reactive power mismatch between the DG and the load demand. The transition, shown in Fig. 5, can be divided into two time interval. The first time intervals is from the instant of turning off Su to the instant of turning off Si when islanding is confirmed. The second time interval begins from the instant of turning off inverter switch Si . During the first time interval, the utility voltage vg abc is still the same with the load voltage vC abc as the switch Si is in ON state. As the dynamic of the inductor current loop and the voltage loop is much faster than the PLL [52], while the load voltage and current are varying dramatically, the angle frequency of the

LIU et al.: UNIFIED CONTROL STRATEGY FOR THREE-PHASE INVERTER IN DISTRIBUTED GENERATION

Fig. 5. Operation sequence during the transition from the grid-tied mode to the islanded mode.

Fig. 6. Transient process of the voltage and current when the islanding happens.

load voltage can be considered to be not varied. The dynamic process in this time interval can be described by Fig. 6, and it is illustrated later. In the grid-tied mode, it is assumed that the DG injects active and reactive power into the utility, which can be expressed by (8) and (9), and that the local critical load, shown in (10), represented by a series connected RLC circuit with the lagging power factor 3 3 · (vC d ig d + vC q ig q ) = vC d ig d 2 2 3 3 Qg = · (vC q ig d − vC d ig q ) = − vC d ig q 2 2 1 Zsload = Rs + jωLs + jωCs   1 = Rs + j ωLs − ωCs Pg =

= Rs + jXs .

(8) (9)

(10)

When islanding happens, ig d will decrease from positive to zero, and ig q will increase from negative to zero. At the same time, the load current will vary in the opposite direction. The load voltage in D- and Q-axes is shown by (11) and (12), and each of them consists of two terms. It can be found that the load voltage in D-axis vC d will increase as both terms increase. However, the trend of the load voltage in Q-axis vC q is uncertain because the first term decreases and the second term increases, and it is not concerned for a while vC d = iL L d · Rs − iL L q · Xs

(11)

vC q = iL L q · Rs + iL L d · Xs .

(12)

With the increase of the load voltage in D-axis vC d , when it reaches and exceeds Vm ax , the input of the PI compensator GV D will become negative, so its output will decrease. Then, the output of limiter will not imposed to Ig r ef d any longer, and the current reference iL r ef d will drop. With the regulation of the inductor current loop, the load current in D-axis iL L d will

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decrease. As a result, the load voltage in D-axis vC d will drop and recover to Vm ax . After iL L d has almost fallen to the normal value, the load voltage in Q-axis vC q will drop according to (12). As vC q is decreased from zero to negative, then the input of the PI compensator GPLL will be negative, and its output will drop. In other words, the angle frequency ω will be reduced. If it falls to the lower value of the limiter ωm in , then the angle frequency will be fixed at ωm in . Consequently, at the end of the first time interval, the load voltage in D-axis vC d will be increased to and fixed at Vm ax , and the angle frequency of the load voltage ω will drop. If it is higher than the lower value of the limiter ωm in , the PLL can still operate normally, and the load voltage in Q-axis vC q will be zero. Otherwise, if it is fixed at ωm in , the load voltage in Q-axis vC q will be negative. As the absolute values of vC d and vC q , at least the one of vC d , are raised, the magnitude of the load voltage will increase finally. The variation of the amplitude and frequency in the load voltage can also be explained by the power relationship mentioned before. When the islanding happens, the local load must absorb the extra power injected to the grid, as the output power of inverter is not changed instantaneously. According to (1), the magnitude of the load voltage Vm will rise with the increase of Pload . At the same time, the angle frequency ω should drop, in order to consume more reactive power with (2). Therefore, the result through the power relationship coincides with the previous analysis. The second time interval of the transition begins from the instant when the switch Si is open after the islanding has been confirmed by the islanding detection method. If the switch Si opens, the load voltage vC abc is independent with the grid voltage vg abc . At the same time, vg abc will reduce to zero theoretically as the switch Su has opened. Then, the input of the compensator GPLL becomes zero and the angle frequency is invariable and fixed to the value at the end of the first interval. Under this circumstance, vC dq is regulated by the voltage loop, and the inverter is controlled to be a voltage source. With the previous analysis, it can be concluded that the drift of the amplitude and frequency in the load voltage is restricted in the given range when islanding happens. And the inverter is transferred from the current source operation mode to the voltage source operation mode autonomously. In the hybrid voltage and current mode control [17]–[40], the time delay of islanding detection is critical to the drift of the frequency and magnitude in the load voltage, because the drift is worse with the increase of the delay time. However, this phenomenon is avoided in the proposed control strategy. C. Islanded Mode In the islanded mode, switching Si and Su are both in OFF state. The PLL cannot track the utility voltage normally, and the angle frequency is fixed. In this situation, the DG is controlled as a voltage source, because voltage compensator GV D and GV Q can regulate the load voltage vC dq . The voltage references in Dand Q-axis are Vm ax and zero, respectively. And the magnitude of the load voltage equals to Vm ax approximately, which will

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IV. ANALYSIS AND DESIGN In this section, the three-phase inverter with the proposed control strategy is analyzed and designed in both steady state and transient state. In the steady state, the operation points of DG in both grid-tied and islanded modes are analyzed, and the limiters and references are selected. In the transient state, compensators in both inductor current loop and the external voltage loop are designed based on the small-signal model, and the impact of the load current feedforward is analyzed as well. A. Steady State

Fig. 7. Simplified block diagram of the unified control strategy when DG operates in the islanded mode.

be analyzed in Section IV. Consequently, the control diagram of the three-phase inverter in the islanded mode can be simplified as shown in Fig. 7. In Fig. 7, the load current iL L dq is partial reference of the inductor current loop. So, if there is disturbance in the load current, it will be suppressed quickly by the inductor current loop, and a stiff load voltage can be achieved.

D. Transition From the Islanded Mode to the Grid-Tied Mode If the utility is restored and the utility switch Su is ON, the DG should be connected with utility by turning on switch Si . However, several preparation steps should be performed before turning on switch Si . First, as soon as utility voltage is restored, the PLL will track the phase of the utility voltage. As a result, the phase angle of the load voltage vC abc will follow the grid voltage vg abc . If the load voltage vC abc is in phase with the utility voltage, vg d will equal the magnitude of the utility voltage according to (5). Second, as the magnitude of the load voltage Vm ax is larger than the utility voltage magnitude Vg , the voltage reference Vref will be changed to Vg by toggling the selector S from terminals 1 to 2. As a result, the load voltage will equal to the utility voltage in both phase and magnitude. Third, the switch Si is turned on, and the selector S is reset to terminal 1. In this situation, the load voltage will be held by the utility. As the voltage reference Vr ef equals Vm ax , which is larger than the magnitude of the utility voltage Vg , so the PI compensator GV D will saturate, and the limiter outputs its upper value Ig r ef d . At the same time, vC q is regulated to zero by the PLL according to (5), so the output of GV Q will be zero. Consequently, the voltage regulators GV D and GV Q are inactivated, and the DG is controlled as a current source just by the inductor current loop.

1) Analysis of Operation Points: As analyzed previously, in the grid-tied mode, the inverter is controlled as a current source, and the current reference for the inductor current loop iL r ef dq is expressed by (6) and (7). The steady-state error will be zero with the PI compensator in the inductor current loop, so the inductor current in steady state can be expressed as follows:  iL d = Ig r ef d − ω0 Cf · vC q + iL L d (13) iL q = vC q · kG v q + ω0 Cf · vC d + Ig r ef q + iL L q . In the SRF, the relationship between the voltage and the current of the filter capacitor in steady state can be expressed by  iC d = −vC q · ωCf (14) iC q = vC d · ωCf where ω represents the angle frequency of the DG and Cf denotes capacitance of the filter capacitor. As a result, the output current of the inverter iodq can be gained ⎧ ⎪ ⎨ iod = iL d − iC d = Ig r ef d − (ω0 − ω) · Cf · vC q + iL L d ioq = iL q − iC q = vC q · kG v q + Ig r ef q ⎪ ⎩ + (ω0 − ω) · Cf · vC q + iL L q . (15) As angle frequency ω is very close to the rated angle frequency ω0 , the output current iodq can be simplified as  iod = Ig r ef d + iL L d (16) ioq = vC q · kG v q + Ig r ef q + iL L q . It can be found that the output current follows Ig r ef dq and the load current iL L dq , as vC q equals zero in the grid-tied mode. The active and reactive power injected into utility can be obtained as follows. Consequently, the active power and reactive power flowing from the inverter to utility can be given by Ig r ef d and Ig r ef q , respectively ⎧ 3 ⎪ ⎪ Pg = · [vC d (iod − iL L d ) + vC q (ioq − iL L q )] ⎪ ⎪ 2 ⎪ ⎪ ⎪ ⎪ ⎪ 3 ⎪ ⎪ ⎨ = 2 · vC d Ig r ef d (17) ⎪ 3 ⎪ ⎪ Qg = · [vC q (iod − iL L d ) − vcC d (ioq − iL L q )] ⎪ ⎪ ⎪ 2 ⎪ ⎪ ⎪ ⎪ 3 ⎪ ⎩ = − · vC d Ig r ef q . 2 In the islanded mode, the inverter is controlled as a voltage source by the external voltage loop. In the D-axis, vC d is

LIU et al.: UNIFIED CONTROL STRATEGY FOR THREE-PHASE INVERTER IN DISTRIBUTED GENERATION

regulated by the PI compensator GV D , so the steady state error will be zero and vC d can be expressed as follows: vC d = Vref

(18)

where Vref is the voltage reference in D-axis. In the Q-axis, the regulator GV Q is P compensator, so the steady state error may not be zero. As the load current is added to the inductor reference, the condition shown as below can be achieved vC q · kG v q + Ig r ef q = 0.

(19)

And then, the load voltage in Q-axis can be expressed by (20). It should be noted that the absolute value of vC q rises with the increase of the current reference Ig r ef q which is related to the reactive power injected into the utility vC q = −

Ig r ef q . kG v q

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the maximum magnitude of the utility voltage in this paper. According to IEEE standard 1547-2003 [5], the range of the normal grid voltage is 0.88–1.1 p.u., so Vm ax can be selected as √ Vm ax = 1.1 · 2 · Vn (23) where Vn represents the RMS value of the rated phase voltage. In order to guarantee that the PLL operates normally in the grid-tied mode, the utility angle frequency ω should not touch the upper value ωm ax or lower value ωm in of the limier in the PLL. Besides, the angle frequency ω is restricted between ωm ax and ωm in in the islanded mode, and it should not drift from the normal value too far. So, ωm ax and ωm in are selected as the maximum and minimum angle frequencies allowed by the utility standard. B. Transient State

(20)

The magnitude of the load voltage Vm can be represented as follows. It equals to Vref approximately, because vC q should be much lower than Vref with proper current reference Ig r ef q   2 Ig r ef q 2 Vm = Vref + − ≈ Vref . (21) kG v q When the islanding happens, the angle frequency is restricted in the given range by the limiter. As analyzed previously, the angle frequency in the islanded mode is determined in the first time interval of the transition from the grid-tied made to the islanded mode. According to (20), if the current reference Ig r ef q is set to zero, vC q is zero. Then, it means that the angle frequency ω does not vary in the first time interval of the transition, and it should equal ωg 0 , which denotes the angle frequency of the utility before islanding happens. Consequently, the angle frequency of the load voltage ω in the islanded mode is determined by the current reference Ig r ef q , and it can be expressed by (22), where ωm in and ωm ax represent the upper and lower values of the limiter shown in Fig. 2, respectively ⎧ ⎪ ⎨ ωm in , Ig r ef q > 0 ω = ωg 0 , (22) Ig r ef q = 0 ⎪ ⎩ ωm ax , Ig r ef q < 0. 2) Selection of References and Limiters: In the grid-tied mode, the active power injected into the grid Pg is given by the current reference Ig r ef d , and it is the upper value of the limiter in D-axis. Therefore, the selection of Ig r ef d depends on the power rating of the inverter. For the current reference Ig r ef q , firstly it determines the reactive power injected into utility Qg in the grid-tied mode according to (17), and then it also affects the magnitude of the load voltage in the islanded mode according to (21). As a result, the reactive power Qg cannot be very large, in order to make the magnitude of the load voltage within the normal range in the islanded mode. In the grid-tied mode, Vm ax should be larger than the magnitude of the utility voltage Vg . At the same time, the load voltage is determined by Vm ax in the islanded mode by (21), so Vm ax should not be much larger than Vg . Therefore, it is selected as

1) Small-Signal Model of the Power Stage: Before the compensators in the voltage and current loops are designed and the transient performance is analyzed, the three-phase inverter in the DG needs to be modeled. According to the power stage shown in Fig. 1, the dc-link voltage Vdc is regulated by the front-end converter in DG. Then, it is assumed that the dc voltage Vdc is very stiff, and its dynamic is not concerned in this paper. Therefore, the average model of the power stage can be described by ⎞ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎛ da iL a iL a vC a d ⎜ Vdc ⎜ ⎟ ⎟ ⎟ ⎜ ⎟ ⎜ · ⎝ db ⎠ = Lf · ⎝ iL b ⎠ + Rl · ⎝ iL b ⎠ + ⎝ vC b ⎠ 2 dt dc iL c iL c vC c ⎛

⎞

⎛

⎞ ⎛

⎞ ⎛

⎞

(24)

iL a vC a iL L a ig a d ⎜ ⎜ ⎟ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ iL b ⎠ = Cf · ⎝ vC b ⎠ + ⎝ iL L b ⎠ + ⎝ ig b ⎠. (25) dt iL c vC c iL L c ig c In (24), da , db , and dc are the average duty cycle of each leg varying from −1 to 1, and Rl represents the equivalent series resistance of the filter inductor. Then, the average model in the SRF can obtained with the Park transformation shown in (3), which is represented by         dd iL d 0 −ωLf d iL d Vdc · · = Lf · + 2 dt iL q dq ωLf 0 iL q     iL d vC d + Rl · + (26) iL q vC q         vC d 0 −ωCf iL d d vC d · = Cf · + dt vC q iL q ωCf 0 vC q     iL L d ig d + + . (27) iL L q ig q With the stiff dc voltage Vdc , the small-signal model will be the same as the average model. Then, it can be found that there are couplings introduced by the inductor Lf and capacitors Cf between D and Q-axes in the SRF, and these couplings can be mitigated by the decoupling components ω0 Lf /kPW M and

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TABLE I PARAMETERS OF THE POWER STAGE

Fig. 9.

Fig. 10.

Fig. 8. Bode plot of the control-to-current transfer function in grid-tied and islanded modes.

ω0 Cf in Fig. 3 [12]. Therefore, the small-signal model can be simplified into two identical SISO systems, which is represented by (28) and the subscript d and q are ignored ⎧ Vdc d ⎪ ⎪ ⎨ 2 · dˆ = Lf · dt ˆiL + Rl · ˆiL + vˆC (28) ⎪ ⎪ ⎩ ˆiL = Cf · d vˆC + ˆiL L + ˆig . dt 2) Design and Analysis of the Current Loop: The inductor current loop should operate normally to regulate the inductor current loop in both islanded and grid-tied modes. In the islanded mode, the small-signal model of the control-to-current can be obtained according to (28), which is shown as Gid1 (s) =

ˆiL (s) sCf Vdc · 2 . = ˆ 2 s Lf Cf + sRl Cf + 1 d(s)

(29)

However, in the grid-tied mode, the dynamic of the capacitor Cf is ignored due to the stiff utility [34], and the small-signal model of the control-to-current is described by Gid2 (s) =

ˆiL (s) 1 Vdc · = . ˆ 2 sLf + Rl d(s)

(30)

The parameters of the power stage in this paper are shown in Table I, and the Bode plot of the control-to-current transfer function in both of operation modes is shown in Fig. 8. It can be found that huge difference appears in the low and medium

Bode plot of the loop gain of the inner current loop.

Block diagram of the simplified voltage loop.

frequency range, and it is difficult to design the compensator GI to achieve good performance in both of operation modes. The reason for this difference between the islanded mode and the grid-tied mode is that the inductor current is coupled with the capacitor voltage in the islanded mode. To mitigate this difference, the capacitor voltage is fed forward with the coefficient 1/kPW M in Fig. 2, and then the inductor current can be decoupled with the capacitor voltage. Consequently, the transfer function of control to current in the islanded mode is changed to be close to the one in the grid-tied mode, and the current compensator GI can be designed based on unified transfer function shown by (30). The PI compensator GI in (31) is designed, and the digital delay caused by the pulse width modulation (PWM) and sample is considered as well. The loop gain of the current loop is shown in Fig. 9, with the crossover frequency of 1100 Hz, and the phase margin of 65◦ Gi (s) = kG i ·

1+

s ωG i

s

.

(31)

3) Design and Analysis of the Voltage Loop: The voltage loop just operates in the islanded mode to regulate the load voltage, and the simplified block diagram is shown in Fig. 10, where Gic (s) and Gv i (s) denote the closed-loop transfer function of an inductor loop and the impedance of the filter capacitor Cf , respectively. In the D-axis, GV D is a PI compensator shown in (32), while a P compensator GV Q expressed by (33) is used in Q-axis. These two compensators are designed, and the loop gain of the current loop is shown in Fig. 11. It can be found that there is a little difference in the low frequency range. The phase margin is set to 55◦ , and the crossover frequency is around 600 Hz in

LIU et al.: UNIFIED CONTROL STRATEGY FOR THREE-PHASE INVERTER IN DISTRIBUTED GENERATION

Fig. 11.

Bode plot of the loop gain of the voltage loop in D- and Q-axes.

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Fig. 12. Bode plot of the output impedance with and without the load current feedforward, when DG operates in the islanded mode.

both D- and Q-axes Gv d (s) = kG v d ·

1+

Gv q (s) = kG v q .

s ωG v d

s

(32) (33)

4) Impact of Load Current Feedforward: In Fig. 10, the load current ˆiL L is a part of the inductor current reference, and the disturbance from the load current can be suppressed by the inductor current loop directly. To evaluate the effect of the load current feedforward in the islanded mode, the transfer function of the output impedance is derived. The output impedances with and without load current feedforward are expressed by Zo1 (s) =

vˆC (s) Gv i (s) · [1 − Gic (s)] (34) =− ˆiL L (s) 1 + Gv (s) · Gic (s) · Gv i (s)

vˆC (s) Gv i (s) Zo2 (s) = . (35) =− ˆiL L (s) 1 + Gv (s) · Gic (s) · Gv i (s) Comparing (34) and (35), it can be found that an extra factor [1 − Gic (s)] appears in the output impedance with load current feedforward, and the magnitude of the output impedance will be reduced in the low frequency range because the gain of the closed-loop transfer function Gic (s) closes to unity in the bandwidth of the current loop. The Bode plot of the output impedance of these two conditions is shown in Fig. 12, and it can be seen that the magnitude of the output impedance is reduced from dc to 600 Hz with the load current feedforward. Consequently, the quality of the load voltage vC abc will be improved with the load current feedforward. In the grid-tied mode, the inductor current is regulated by the inductor current loop directly, and the inductor current reference is mainly composed by the current reference Ig r ef dq , and the load current iL L dq . If the load current is not fed forward, the output current iodq of the inverter will be fixed by Ig r ef dq . As a result, the disturbance of the load current will be fully injected into the utility, and this can be represented by ˆig (s) = −1. ˆiL L (s)

(36)

Fig. 13. Bode plot of the transfer function from load current to grid current with and without the load current feedforward, when DG operates in the grid-tied mode.

With the load current feedforward, the disturbance of the load current can be compensated by the inverter, and the transfer function from the load current to the grid current can be described by (37). The Bode plots of transfer function [see (36) and (37)] are shown in Fig. 13, and the gain is mitigated up to 1050 Hz with the load current feedforward and therefore, the quality of the grid current can be improved ˆig (s) = Gic (s) − 1. ˆiL L (s)

(37)

V. SIMULATION AND EXPERIMENTAL RESULTS A. Simulation Results To investigate the feasible of the proposed control strategy, the simulation has been done in PSIM. The power rating of a three-phase inverter is 3 kW in the simulation. The parameters in the simulation are shown in Tables I and II. The RMS of the rated phase voltage is 115 V, and the voltage reference Vm ax is set as 10% higher than the rated value. The rated utility frequency

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TABLE II PARAMETERS IN THE CONTROL SYSTEM

Fig. 15. Simulation waveforms of load voltage v C a , grid current ig a , and inductor current iL a when DG is transferred from the grid-tied mode to the islanded mode with: (a) conventional hybrid voltage and current mode control, and (b) proposed unified control strategy.

Fig. 14. Simulation waveforms of load voltage v C a , grid current ig a , and inductor current iL a when DG is in the grid-tied mode under condition of the step down of the grid current reference from 9 A to 5 A with: (a) conventional voltage mode control, and (b) proposed unified control strategy.

is 50 Hz, and the upper and the lower values of the limiter in the PLL are given as 0.2 Hz higher and lower than the rated frequency, respectively. In the grid-tied mode, the dynamic performance of the conventional voltage mode control and the proposed unified control strategy is compared by stepping down the grid current reference from 9 A to 5 A. The simulation result of the voltage mode control is shown in Fig. 14(a), and the current reference is changed at the moment of 14 s. It is found that dynamic process lasts until around 15.2 s. In the proposed unified control strategy, the simulation result is represented in Fig. 14(b) and the time interval of the dynamic process is less than 5 ms. Comparing

the simulation results above, it can be seen that the dynamic performance of the proposed unified control strategy is better than the conventional voltage mode control. During the transition from the grid-tied mode to the islanded mode, the proposed unified control strategy is compared with the hybrid voltage and current mode control, and the simulation scenario is shown as follows: 1) Initially, the utility is normal, and the DG is connected with the utility; 2) at 0.5 s, islanding happens; and 3) at 0.52 s, the islanding is confirmed. Simulate results with the hybrid voltage and current mode control is shown in Fig. 15(a). It can be seen that the grid current drop to zero at 0.5 s, and that the load voltage is seriously distorted from 0.5 to 0.52 s. Then, the load voltage is recovered to the normal value after 0.52 s. Fig. 15(b) presents the simulate results with the proposed unified control strategy. Initially, the magnitude of grid current is 9 A and follows the current reference Ig r ef dq . The magnitude and frequency of the load voltage are held by the utility. After the islanding happens, the amplitude of the load voltage increases a little to follow the voltage reference Vm ax , and the output current of DG decreases autonomously to match the load power demand.

LIU et al.: UNIFIED CONTROL STRATEGY FOR THREE-PHASE INVERTER IN DISTRIBUTED GENERATION

Fig. 16.

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Diagram of the experimental prototype of DG.

Fig. 17. Experimental waveforms when DG is in the islanded mode: CH1, load current iL L a , 5 A/div; CH3, load voltage v C a , 100 V/div; CH4, inductor current iL a , 5 A/div.

Fig. 18. Experimental waveforms when DG is in the grid-tied mode: CH1, load current iL L a , 5 A/div; CH2, grid voltage v g a , 100 V/div; CH4, grid current ig a , 10 A/div.

Comparing the simulation results above, it can be found that the voltage quality is improved deeply by the proposed control strategy in the transition from the grid-tied mode to the islanded mode, and the speed of the islanding detection is no more critical.

Fig. 19. Experimental waveforms when DG is transferred from the grid-tied mode to the islanded mode with (a) conventional hybrid voltage and current mode control, and (b) proposed unified control strategy: CH2, load voltage v C a , 100 V/div; CH3, grid current ig a , 10 A/div; CH4, inductor current iL a , 10 A/div.

B. Experimental Results To verify the proposed control strategy, an experimental prototype of DG has been established, which is shown in Fig. 16. The utility for the DG is emulated by a three-phase transformer and a voltage regulator connected with the actual utility. The rated line voltage of the actual utility is 380 V. The emulated utility is called as utility in the below. Moreover, the inverter in the DG is fed by a three-phase diode rectifier, and the dc-bus voltage is set to 400 V approximately by the voltage

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Fig. 20. Experimental waveforms when DG is transferred from the islanded mode to the grid-tied mode: CH1, grid voltage vg a , 100 V/div; CH2, load voltage v C a , 100 V/div; CH3, grid current ig a , 10 A/div; CH4, inductor current iL a , 10 A/div.

regulator. Besides, the control system is implemented fully digitally by digital signal processor TMS320F28335 from Texas Instruments. The parameters in the experimental DG, shown in Tables I and II, are identical to the ones used in the simulation. Fig. 17 shows the experimental waveforms when DG is in the islanded mode, and it can be seen that the magnitude of the load voltage equals 180 V approximately, and the total harmonic distortion (THD) of the load voltage is 0.9%. Fig. 18 shows the experimental waveforms when DG is in the grid-tied mode. The magnitude of the grid current is closed to 9 A, and the THD of the grid current is 3.6% approximately. When the DG is transferred from the grid-tied mode to the islanded mode, the experimental results with the traditional hybrid voltage and current mode control and the proposed unified control strategy are given in Fig. 19. Before the islanding happens, the magnitude of the load voltage is around 163 V. The current injected into the utility ig a is in phase with the utility voltage, and the magnitude of ig a is approximately 9 A. When the switch Su opens, the islanding happens, and the grid current ig a drops to zero. In the traditional hybrid voltage and current mode control, it can be found that the load voltage is seriously distorted upon the occurrence of islanding. And this condition lasts until the islanding is confirmed by DG and the control structure is changed to regulate the load voltage. However, with the proposed unified control strategy, the distortion of the load voltage is obviously improved, and the magnitude of the load voltage increases slightly and is close to 180 V. Fig. 20 shows the process when DG is transferred from the islanded mode to the grid-tied mode. From 0 ms to around 300 ms, the phase of the load voltage is regulated to resynchronize with the utility voltage, and the phase difference is reduced gradually. Then, the magnitude of the load voltage is regulated to equal the utility voltage. At the moment of 350 ms, the switch Si is turned on, and the current injected into the grid ig a increases smoothly without huge inrush current, and the load voltage is stable during the transition. Fig. 21 shows the experimental waveforms when DG feeds nonlinear load in the islanded mode. It can be seen that the distortion of the load voltage is improved by the load current feedforward, and the THD of the load voltage is reduced from 4.7% to 3.2%.

Fig. 21. Experimental waveform when DG feeds nonlinear load in islanded mode (a) with load current feedforward and (b) without load current feedforward: CH1, load current iL L a , 5 A/div; CH3, load voltage v C a , 100 V/div; CH4, inductor current iL a , 5 A/div.

When the power of the nonlinear load is varied, the THD of the load voltage is also changed, and the experimental results are shown in Fig. 22. It can be seen that with the load current feedforward, the THD of the load voltage can always be mitigated under different power of the nonlinear load. Fig. 23 shows the experimental waveforms when DG feeds nonlinear load in the grid-tied mode. It can be seen that with the load current feedforward, there is harmonic component in the

LIU et al.: UNIFIED CONTROL STRATEGY FOR THREE-PHASE INVERTER IN DISTRIBUTED GENERATION

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Fig. 22. Variation of the THD of the load voltage with the power of the nonlinear load when DG is in the islanded mode.

Fig. 24. Variation of the THD of the grid current when DG is in the grid-tied mode with (a) the power of the nonlinear load, and (b) the amplitude of the grid current.

Fig. 23. Experimental waveforms when DG feeds nonlinear load in the gridtied mode (a) with load current feedforward and (b) without load current feedforward: CH1, inductor current iL a , 10 A/div; CH2, load current iL L a , 5 A/div; CH3, grid voltage v g a , 100 V/div; CH4, grid current ig a , 10 A/div.

inductor current iL a , and the harmonics component in the grid current is reduced. The THD of the grid current under different power of the nonlinear load and different amplitude of the grid fundamental

current is investigated, and the experimental results are shown in Fig. 24. In Fig. 24(a), the amplitude of the grid fundamental current is set at 7 A, and the power of nonlinear load is varied. It can be found that with the increase of the load power, the THD of the grid current rises, and the THD of the grid current is reduced with the load current feedforward. In Fig. 24(b), the power of the nonlinear load is set at around 600 W, and the amplitude of the grid fundamental current is changed. It can be seen that the THD of the grid current can be mitigated at different magnitude of the grid fundamental current. VI. CONCLUSION A unified control strategy was proposed for three-phase inverter in DG to operate in both islanded and grid-tied modes, with no need for switching between two different control architectures or critical islanding detection. A novel voltage controller was presented. It is inactivated in the grid-tied mode, and the DG operates as a current source with fast dynamic

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 3, MARCH 2014

performance. Upon the utility outage, the voltage controller can automatically be activated to regulate the load voltage. Moreover, a novel load current feedforward was proposed, and it can improve the waveform quality of both the grid current in the grid-tied mode and the load voltage in the islanded mode. The proposed unified control strategy was verified by the simulation and experimental results.

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LIU et al.: UNIFIED CONTROL STRATEGY FOR THREE-PHASE INVERTER IN DISTRIBUTED GENERATION

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Zeng Liu (S’09) received the B.S. degree in electrical engineering from Hunan University, Changsha, China, in 2006, and the M.S. degree in electrical engineering from Xi’an Jiaotong University, Xi’an, China, in 2009, where he is currently working toward the Ph.D. degree. His research interests include control of singlephase and multiphase power converters for uninterrupted power supply and utility application, modeling, and analysis and control of distributed power system based on three-phase ac bus.

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Jinjun Liu (M’97–SM’10) received the B.S. and Ph.D. degrees in electrical engineering from Xi’an Jiaotong University (XJTU), Xi’an, China, in 1992 and 1997, respectively. He then joined the XJTU Electrical Engineering School as a teaching faculty. In 1998, he led the founding of XJTU/Rockwell Automation Laboratory and served as the Lab Director. From 1999 until early 2002, he was with the Center for Power Electronics Systems, Virginia Polytechnic Institute and State University, USA, as a Visiting Scholar. He then came back to XJTU and in late 2002 was promoted to a Full Professor and the Head of the Power Electronics and Renewable Energy Center, XJTU. During 2005 to early 2010, he served as the Associate Dean with the School of Electrical Engineering, XJTU. He currently also serves as the Dean for Undergraduate Education, XJTU. He coauthored three books, published more than 100 technical papers, holds 13 patents. His research interests include power quality control, renewable energy generation and utility applications of power electronics, and modeling and control of power electronic systems. Dr. Liu is an AdCom member of the IEEE Power Electronics Society and serves as Region 10 Liaison. He received several national, provincial, or ministerial awards for scientific or career achievements, and the 2006 Delta Scholar Award. He also serves as an Associate Editor for the IEEE TRANSACTIONS ON POWER ELECTRONICS. He is an AdCom member and the Chair of Student Activities Committee for IEEE Xi’an Section. He is on the Executive Board and serving as a Deputy Secretary-General for the China Power Electronics Society, and also on the Executive Board and serving as a Deputy Secretary-General for the China Power Supply Society.

Yalin Zhao received the B.S. degree in electrical engineering from Xi’an Jiaotong University, Xi’an, China, in 2011, where he is currently working toward the M.S. degree. His research interests include dead-time compensation, stability analysis, and control of inverters.