https://doi.org/10.6113/JPE.2018.18.1.251

ISSN(Print): 1598-2092 / ISSN(Online): 2093-4718

Strategy for the Seamless Mode Transfer of an Inverter in a Master–Slave Control Independent Microgrid

Yi Wang^†, Hanhong Jiang^*, and Pengxiang Xing^**

^†,*National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan, China

^**School of Electrical Engineering, Wuhan University, Wuhan, China

Abstract

To enable a master–slave control independent microgrid system (MSCIMGS) to supply electricity continuously, the microgrid inverter should perform mode transfer between grid-connected and islanding operations. Transient oscillations should be reduced during transfer to effectively conduct a seamless mode transfer. This study uses a typical MSCIMGS as an example and improves the mode transfer strategy in three aspects: (1) adopts a status-tracking algorithm to improve the switching strategy of the outer loop, (2) uses the voltage magnitude and phase pre-synchronization algorithm to reduce transient shock at the time of grid connection, and (3) applies the hybrid-sensitivity H_∞ robust controller instead of the current inner loop to improve the robustness of the controller. Simulations and experiments show that the proposed strategy is more practical than the traditional proportional–derivative control mode transfer and effective in reducing voltage and current oscillations during the transfer period.

Key words: H_∞ robust controller, Master–slave control microgrid, Pre-synchronization, Seamless mode transfer

Manuscript received Jun. 22, 2017; accepted Sep. 27, 2017

Recommended for publication by Associate Editor Tomislav Dragicevic.

^†Corresponding Author: wangyi500500@163.com  Tel: +86-18086058642, Naval University of Engineering

^*Nat’l Key Lab. of Sci. & Tech. on Vessel Integrated Power Syst., China

^**School of Electrical Engineering, Wuhan University, China

NOMENCLATURE

Abbreviations

MSCIMGS	master–slave control independent
	microgrid system
DG	distributed generation
SG	synchronous generator
UPS	uninterrupted power supply
PV	photovoltaic
BSS	battery storage system
PCC	point of common coupling
PQ	active power and reactive power
PI	proportional–integral
SCS	switch control signal
PLL	phase-locked loop
RES	renewable energy system

Parameters

P*ref	active power reference value
Q*ref	reactive power reference value
IInv	inverter output current
ISG	SG output current
ud, uq	terminal voltage dq-axes components
id, iq	terminal current dq-axes components
idref, iqref	current dq-axes reference values
usd, usq	inner loop output dq-axes components
ω	angular frequency signal
uref	voltage reference value
f0	reference frequency, 50 Hz
u0	inverter output voltage
iL	inductor current
iC	capacitor current
i1	microgrid AC bus current
upwm	inverter output control signal
iref	reference current input
kpi	current inner loop proportion parameters
kii	current inner loop integral parameters
kpu	voltage outer loop proportion parameters
kiu	voltage outer loop integral parameters
|UInv|	inverter voltage magnitude
|USG|	SG voltage magnitude
|UN|	inverter rated voltage magnitude
θInv	inverter phase
θSG	SG phase
KPCC	grid-connected/grid-disconnected breaker
kInv_SG	ratio factor between inverter and SG voltage
Kpwm	equivalent SPWM control gain coefficient

Ⅰ. INTRODUCTION

With the worsening environmental pollution, novel energy power generation has become a popular subject worldwide. The rapid development of distributed generation (DG) power technology and communication technology promotes the extended application of microgrid systems.

The master–slave control independent microgrid system (MSCIMGS) is an effective approach for supplying electricity to remote areas that large power grids cannot easily cover. The principle of MSCIMGS is to collect renewable energy (e.g., solar or wind energy) and connect it to a synchronous generator (SG) through an inverter [1]-[5]. To suppress fluctuation in renewable energy, MSCIMGS is generally equipped with a battery energy storage system that has a certain capacity. MSCIMGS performs worse than the parallel microgrid in terms of stability because it is independent of large power grids [6]-[8]. Therefore, this topic is currently under discussion.

One of the challenges in the study of independent microgrid technology is enabling an inverter to transfer in a seamless mode under grid-connected or islanding conditions to ensure the uninterrupted power supply (UPS) of critical loads in MSCIMGS. That is, a grid-connected inverter is required for a smooth transition between current control for grid-connected operation and voltage control for islanding operation [9], [10].

A. Related Works

Reference [1] illustrated that a dual-mode inverter should be capable of operating in grid-connected and stand-alone modes for DG. The optimal parameters of inverter output filters vary under different working modes. Reference [3] presented a strategy that uses the synchronized output regulation method to control inverters operating in stand-alone and grid-connected modes. In [4], a novel smooth transition technique between stand-alone and grid-connected modes for voltage-source inverters was developed. The test results show that this strategy provides reliable transition operation. However, References [1], [3], and [4] addressed only single-phase inverter control. Reference [5] proposed an indirect current control algorithm for the seamless transfer of a three-phase utility interactive inverter. With this method, the inverter can provide critical loads with a stable voltage during the entire transition period. However, this method should regulate the instantaneous values of injected current during transfer, which may be difficult to realize in engineering applications. Moreover, the implementation of this algorithm requires numerous calculations.

In [7], a load shedding algorithm was used to bring the inverter voltage back to the normal range for intentional islanding operation. However, grid current and inverter voltage exhibit oscillations during the transition from grid-connected to intentional islanding operations because seamless techniques are not applied. Meanwhile, one of the important issues in inverter connection to a grid is synchronization with grid voltage, for which a proposed phase-locked loop (PLL) is used for UPS applications [8], [9].

In [10]-[12], capacitor voltage in a single-phase or three-phase grid-connected inverter under both operation modes was controlled, and thus, critical loads with a stable and seamless voltage were provided during the entire transition period. However, the traditional proportional– derivative (PI) controller in the current inner loop exhibits poor robustness in mode transfer. In [13], a cascaded current–voltage control scheme was proposed to improve the power quality of the local load voltage and the current supplied to the grid by using the designed H_∞ robust controller. In [14], a new sliding mode controller with a rotating reference voltage algorithm was found to be robust against disturbance and load variations in islanding microgrids. In [15], the structure of each fuzzy PI controller was modified to avoid severe transition oscillations when the control system switches from a fast dynamic controller to a slow dynamic controller and vice versa. Fuzzy PI was used to effectively regulate microgrid frequency in [16]. However, the use of fuzzy PI to attenuate external disturbance may be difficult. In [17], an H∞ compensator was corrupted to attenuate the external disturbance and fuzzy approximation error in a static synchronous compensator.

A robust distributed controller was designed for a feedback linearized microgrid in [18]. In [19] and [20], an H_∞ robust controller was used instead of the PI current inner loop controller. The H_∞ controller, which exhibited explicit robustness in terms of grid-impedance variations, was proposed to incorporate the desired tracking performance and stability margin.

B. Approach and Contributions

In general, the double closed-loop PI control of three-phase inverters is used in MSCIMGS [21], [22]. The mode transfer is switched to the outer loop controller, whereas the current inner loop controller remains unchanged. To increase stability in mode transfer, the improvements made in the mode transfer include proposing a status-tracking algorithm to improve the switching mode of the outer loop, determining the grid-connected conditions that must be satisfied by voltage magnitude and phase angle through the pre-synchronization algorithm, and using a H_∞ robust controller instead of the traditional PI current inner loop controller to guarantee robustness during transfer.

The simulations and experiments prove that the proposed strategy is more effective in seamless mode transfer than the traditional PI control strategy. It reduces the transient oscillations of voltage and current, and it is easy to implement in engineering applications.

C. Structure of this Paper

The remainder of this paper is organized as follows. Section II provides the topology of a typical master–slave control DC/AC hybrid independent microgrid system and the conversion of its operation states. Section III discusses the traditional mode transfer and its problem. Section IV analyzes the improvement of the outer loop controller and the pre-synchronization algorithm. Section V illustrates the hybrid-sensitivity H∞ controller and discusses the design of the H_∞ robust controller for the current inner loop. The simulation and experiment results are presented in Sections VI and VII, respectively. Finally, conclusions are drawn in Section VIII.

Ⅱ. STRUCTURE OF MSCIMGS

An MSCIMGS is illustrated in Fig. 1. An ordinary independent microgrid involves a photovoltaic (PV) power generation system, a battery energy storage system (BSS), and a synchronous generator (SG) system. SG is the master power supply, and the inverter is the slave power supply.

The renewable energy power generation system has a DC bus. The inverter converts DC into AC, which is connected in parallel to the SG system to form an AC bus. At the time of grid-connected power generation, the SG system serves as a master voltage source, providing stable voltage and frequency support, whereas the renewable energy inverter works as the current source and adopts the PQ control mode. When the master power supply system is under fault condition, such as voltage sags/swells and interruptions, K_PCC is tripped by the fault detection signal, the inverter is switched from the grid-feeding inverter to the grid-forming inverter to supply electricity only to the critical loads, and the inverter control mode is switched from PQ to V/f. Thus, UPS can be guaranteed for critical loads [22].

The inverter can operate under grid-connected operation and stand-alone operation, and thus, SG also has two operation states. MSCIMGS has four operation state conversions, as shown in Fig. 2. This study emphasizes processes 1 and 2.

Fig. 1. Topology of a typical master–slave control DC/AC hybrid independent microgrid system.

Fig. 2. Block diagram of operation state conversion.

Ⅲ. ANALYSIS OF TRADITIONAL MODE TRANSFER

A. Grid-Connected and Islanding Operation Modes

The grid-connected operation mode of the inverter is generally based on the typical PQ double-loop control structure [22], as shown in Fig. 3.

Fig. 3. Grid-connected mode of the three-phase inverter.

In Fig. 3, P and Q are the power feedback signals of the inverter, which can be calculated using Eq. (1). P^*_ref and Q^*_ref are the power reference values. u_d, u_q, i_d, and i_q are the inverter terminal voltage and current dq-axes components. i_dref and i_qref are the reference values of the current inner loop. The signs of u_sd and u_sq denote the dq-axes components of the output voltage control signal of the controller.

 (1)

The inverter islanding operation mode is based on the V/f double-loop controller, as shown in Fig. 4.

In Fig. 4, ω denotes the angular frequency signal, u_ref denotes the voltage reference value, and f₀ denotes the reference frequency (50 Hz).

Fig. 4. Islanding mode of the three-phase inverter.

The double-loop controller cannot only improve the quality of the three-phase output power, but also buffer the output of both outer loop controllers during the time of mode transfer to reduce transient oscillations [23].

The V/f double-loop control is used as an example. The influences of the PI control parameters of the current inner loop and voltage outer loop on controller performance are analyzed.

The control equation for the dq coordinate system of the inverter inductance current is

 (2)

The equation shows that the current inner loop control is a coupled control, and the current d-axis and q-axis components are coupled to each other, and thus, should be decoupled. The decoupling control method is shown in Fig. 5.

Fig. 5. Block diagram of the decoupling control of the current inner loop.

Fig. 5 shows that the equation is obtained as follows:

      (3)

The substitution of Eq. (3) into Eq. (2) leads to

  (4)

Therefore, the control block diagram of the current inner loop control in Fig. 5 can be simplified into the diagram shown in Fig. 6.

Fig. 6. Simplified block diagram of the dq-axes control of the current inner loop.

In this case, the PI transfer function of the current inner loop is G_i(s) = k_pi + k_ii/s. The current inner loop is simplified for the analysis of the V/f double-loop controller [21]. The simplified control structure of the inverter is shown in Fig. 7.

In Fig. 7, u_ref denotes the voltage outer loop input reference voltage. The voltage outer loop PI controller transfer function is G_u(s) = k_pu + k_iu/s, and i_ref is the current inner loop input reference current. The equivalent gain coefficient of the SPWM control inverter is K_pwm. The signs of u₀, i_L, i_C, i₁, and u_pwm denote the inverter output voltage, inductor current, capacitor current, microgrid AC bus current, and output control signal, respectively.

Fig. 7. V/f double-loop control structure of the inverter.

When i_ref represents an input and i_C represents an output, the current inner loop transfer function is expressed as

,        (5)

where the current proportional gain is

 (6)

This study focuses on the influences of the current inner loop PI parameters on the performance of the controller and on inverter mode transfer.

A suitable k_pi should be designed to ensure that the system has good dynamic characteristics. k_pi considerably influences the stability margin of the system, whereas k_ii only slightly affects this variable. An increase in k_pi can improve the stability margin, but an excessive increase can easily cause the current inner loop PI controller to lose stability and create high-frequency oscillations [21], thereby affecting output voltage waveform. In addition, the system dynamic response characteristic will become poor when k_pi increases, which results in a decline in the capability to resist disturbance during inverter mode transfer [22],[23].

Thus, the inappropriate current inner loop PI parameters, k_pi and k_ii, are liable to cause transient oscillations during mode transfer.

B. Problem Description of Traditional Mode Transfer

The PQ and V/f controllers of the inverter differ from each other; hence, the implementation of its grid-connected and islanding smooth transfer must depend on logic switches for switching different controllers [22].

The switchable controller structure with logic switches K₁ and K₂ is shown in Fig. 8, where the grid-connected operation adopts the PQ control mode (K₁ is closed, K₂ is opened), and the islanding operation adopts V/f (K₁ is opened, K₂ is closed).

1) Cause for Outer Loop Controller

PQ transfer to V/f mode is used as an example to analyze the traditional mode transfer problem. The case of V/f transfer to PQ can be performed in the same manner.

While the PQ outer loop controller is operating, the V/f outer loop controller is also operating. However, the V/f output of the latter does not take effect. The unequal output states of both operations during transfer lead to a transient jump in the output of the outer loop controller.

To reduce transient shock from mode transfer, the output of the V/f outer loop controller can be set to zero before the transfer. The phenomenon of unmatched outputs of the two outer loop controllers cannot be substantially eliminated because a difference remains between the state of zero in which the V/f controller works and the state in which the PQ controller works. Consequently, transient oscillations still exist.

Fig. 8. Structure of traditional mode transfer.

Fig. 9 shows the simulation waveform when the outputs of PQ and the V/f outer loop controller are unequal and not initialized during the switching period at t = 3.8 s. The overshoot of the inverter phase voltage magnitude is higher than 310 V during mode transfer.

As shown in Fig. 10, when the output of the V/f outer loop controller is initialized to zero during transfer at t = 3.8 s, the oscillation phenomenon where the inverter voltage is less than 310 V can possibly occur during mode transfer.

Therefore, regardless of the outer loop output state, transient oscillations still occur during inverter mode transfer.

Fig. 9. Simulation waveform of traditional mode transfer when the outputs of PQ and the V/f outer loop controller are unequal and not initialized.

Fig. 10. Simulation waveform of traditional mode transfer when the outer loop controller output is initialized to zero.

2) Cause for the Inner Loop Controller

Mode transfer is mainly used for the outer loop controller. The current inner loop controller is a shared part, i.e., it is not switched. If its parameters are inappropriate for both gridconnected and islanding controllers, then considerable oscillations may occur in the transfer process and may even result in system instability.

As shown in Fig. 11, the inverter is switched at t = 3.8 s, k_pi = 110, and k_ii = 0.24 before and after transfer. The simulation results show that the system is stable in grid-connected operation, but its voltage and current become unstable after the inverter is switched to islanding operation.

The simulation results in Fig. 13 show that the parameters of the controllers have different optimal matched values under various control modes. In the inverter mode transfer, however, only the outer loop controller is switched, whereas the inner loop control parameters are not switched, which easily results in an unstable operation of the inverter after mode transfer.

On the basis of the preceding analysis, three aspects of inverter mode transfer are improved, as shown in Fig. 12.

Fig. 11. Simulation waveform of traditional mode transfer when the current inner loop parameters are inappropriate.

Fig. 12. Three improved aspects of inverter mode transfer.

First, a status-tracking algorithm is used to enable the PQ outer loop and V/f outer loop outputs to follow each other and to ensure that the outer loop value is the same before and after mode transfer.

Second, the pre-synchronization algorithm is adopted, and voltage magnitude and phase pre-synchronization are used to reduce transient oscillations during islanding transfer to grid-connected operation.

Third, a hybrid-sensitivity H∞ robust controller is used to replace the traditional PI current inner loop controller to reduce transient oscillations and improve anti-disturbance capability.

Ⅳ. IMPROVEMENT OF MODE TRANSFER

For a seamless smooth mode transfer and to reduce transient oscillations during transfer, the status-tracking algorithm is adopted to improve the mode transfer process of the outer loop controller.

A. Improvement of the Outer Loop Controller

The output of the V/f controller or the PQ controller can be designed as a negative feedback by using a status-tracking smooth transition method. Such feedback is used as an input by both controllers to ensure that they always have the same output status. The status-tracking process of the outer loop controller mode transfer is shown in Fig. 13.

As shown in Fig. 13(a), K₁, K₄, and K₆ are closed in the PQ control mode, whereas K₃, K₅, and K₂ are open. The output status of the V/f controller is always consistent with that of the PQ controller. Similarly, as shown in Fig. 13(b), K₃, K₅, and K₂ are closed in the V/f control mode, whereas K₁, K₄, and K₆ are open. The output status of the PQ controller is always consistent with that of the V/f controller.

Fig. 13. Status-tracking process of outer loop controller mode transfer. (a) PQ control mode. (b) V/f control mode.

(a)

(b)

B. Design of Pre-Synchronization Controller

For the connection of the inverter and the SG to the grid, pre-synchronization is required before grid connection to reduce instantaneous impact current. For this purpose, the pre-synchronization of voltage magnitude and phase is designed. In general, the grid-connected operation is performed when voltage magnitude and phase satisfy Eq. (7).

,         (7)

where |U_Inv| and |U_SG| are the inverter output voltage and SG voltage magnitude, respectively; |U_N| is the inverter rated voltage magnitude; and θ_Inv and θ_SG are the phases of the inverter and the SG, respectively.

1) Voltage Magnitude Pre-Synchronization

The design of a voltage magnitude pre-synchronization controller is shown in Fig. 14.

In this figure, U_{Inv_d} and U_{Inv_q} denote the output voltage dq-axes values of the inverter under an independent power supply; U_{SG_d} and U_{SG_q} are the output voltage dq-axes values of the SG; u_dref and u_qref are the reference voltage dq-axes values, which are the output of the dual-loop controller; and k_{Inv_SG} is the ratio factor, which is introduced when voltage levels on both sides differ. Voltage deviation is an output signal that is superimposed onto the V/f controller via the PI controller. The calculated result is then used as the input signal of the double-loop controller. When the inverter and the SG are connected to the grid, the pre-synchronization controller will stop working.

In general, pre-synchronization should also ensure that the inverter abc phase sequence corresponds to the SG to satisfy Eq. (7) [8]. First, voltage magnitude is synchronized, and then phase angle synchronization is performed.

Fig. 14. Structure of voltage magnitude pre-synchronization controller.

2) Phase Pre-Synchronization

The general phase pre-synchronization structure is shown in Fig. 15 [8], [9]. When the inverter is switched from islanding to grid-connected operation, PLL is used to acquire the phase (θ_SG) of the SG and obtain the difference (Δθ) between θ_SG and the inverter phase θ_Inv. Then, Δθ is used as an input to the PI controller to obtain the angular velocity (ω). At this time, the angular velocity of the inverter is adjusted to 2πf₀ + ω. Phase pre-synchronization is not finished until Δθ ≤ 0.1.

Fig. 16 shows the phase pre-synchronization process. At t∈(0, 0.07 s), the inverter is in the V/f mode. At t = 0.07 s, the inverter transfers from islanding mode to grid-connected mode.

At t = 0.02 s, a signal to start switching ctr = 1 is generated, and phase pre-synchronization starts. At t∈(0.02 s, 0.07 s), phase pre-synchronization is performed and phase angle difference Δθ begins to decrease gradually. Phase pre- synchronization does not finished until t = 0.07 s (Δθ ≤ 0.1).

Fig. 15. Structure of phase pre-synchronization control.

Fig. 16. Phase pre-synchronization process.

Ⅴ. H∞ ROBUST CONTROL METHOD THAT CONCERNS HYBRID-SENSITIVITY

A. Hybrid-Sensitivity

Hybrid-sensitivity is one of the most typical problems in H_∞ control. It refers to the suppression of interference in a system and to the uncertainty of a model, i.e., the performance requirements and stability indices of robustness that should be reasonably considered [20], [24].

The standard model related to hybrid-sensitivity is illustrated in Fig. 17. Three weighting functions W₁, W₂, and W₃ are shown in the figure. W₁ is a constraint on system performance requirements that can effectively suppress the interference effect and obtain a desirable output signal by adjusting its value. W₂ represents a limit to the additive uncertainty that can be regarded as a constraint on the amplitude of the control signal. W₃ is a limit to multiplicative uncertainty that is determined by the characteristics of the controlled object.

w = [r, d]^T, z = [z₁, z₂, z₃]^T, z₁, z₂, and z₃ denote the evaluation signals of a system; r is the external input; e is the tracking error; u is the control signal; d is the interference signal; y is the output signal; K(s) is the H∞ controller; and G(s) is the controlled object.

Hybrid-sensitivity functions include S(s), R(s), and T(s). S(s) is a sensitivity function, which is a transfer function of the interference input d to the system output y and of the reference input r to the tracking error e. R(s) is the input sensitivity function, which is the transfer function of the reference input r to the control input u. T(s) is a complementary sensitivity function, which is a transfer function of the reference input r to the system output y. The following formula is obtained from the hybrid-sensitivity model in Fig. 17:

       (8)

The transfer function from w to z is

        (9)

The H∞ control is designed to find a rational function controller K(s) to stabilize the closed-loop system and minimize the H_∞ norm of the transfer function T_zw(s), i.e., [25]

 (10)

Fig. 17. Hybrid-sensitivity problem-based model.

B. Mathematical Model of H∞ Robust Control Based ON Hybrid-Sensitivity

The standard framework for the weighted hybrid- sensitivity is

    (11)

where I is a unit matrix, K(s) is a H_∞ controller, and P is a generalized state matrix of the controlled object.

     (12)

The three weighting functions (W₁, W₂, and W₃) represent state spaces as follows:

         (13)

C. Design of the H∞ Robust Controller for Current Inner Loop

From the current inner loop control in Fig. 5, the mathematical model of the inverter in the dq rotating coordinate is

      (14)

In engineering applications, two types of uncertainties exist in the control parameters of the inverter. First, the parameters in the mathematical model of the inverter are uncertain, e.g., a deviation in the value of R or L exists. Second, the interference from the grid voltage is uncertain, e.g., the disturbance of u_d and u_q.

On the one hand, when the parametric uncertainty of the mathematical model is considered, the deviations of parameters R and L are assumed as ΔR and ΔL, respectively, i.e., L and R can be expressed as

,     (15)

where L₀ and R₀ are the given exact values of the inductance and resistance, respectively.

On the other hand, when the uncertainty of interference from the grid voltage is considered, the amounts of disturbance of u_d and u_q are assumed as w_ed and w_eq, respectively.

On the basis of the two types of uncertainty, Eq. (14) can be rewritten as

      (16)

From the preceding equation, parametric uncertainty and voltage disturbance can be made equivalent to external interference terms w_d and w_q, as follows:

 (17)

The current inner loop model of the inverter is obtained under the conditions of parametric uncertainty and grid voltage disturbance. The formula is

        (18)

The design of the current inner loop H_∞ robust controller aims to suppress the influences of model parametric variation and external disturbances to make the grid-connected current follow the expected values (i_dref and i_qref) effectively.

On the basis of the current inner loop controller in Fig. 5, the parameters can be defined as follows:

  (19)

where x, y, u, and w denote the system state, measured output, control input, and disturbance variables, respectively. Combined with Eq. (19), Eq. (18) can be expressed as a state equation:

        (20)

where

From the mathematical model of hybrid-sensitivity H_∞ robust control in Eq. (11), Eq. (20) can be designed as a block diagram of current inner loop hybrid-sensitivity H_∞ robust control, as shown in Fig. 18.

Fig. 18. Block diagram of current inner loop hybrid-sensitivity H_∞ robust control.

Combined with Eqs. (19) and (20) and Fig. 18, the calculation theory of hybrid-sensitivity is used to obtain A_P, B_P, C_P, and D_P in the generalized state matrix P of the controlled object in Eq. (12), which are

,

.

First, the weighting functions W₁, W₂, and W₃ are selected to calculate P using A_p, B_p, C_p, and D_p. Then, the current inner loop H∞ controller K(s) is determined by Eq. (11).

D. Selection of Weighting Functions and Calculation of K(s)

W₁ is a weighting function for sensitivity function S. To effectively suppress interference and accurately track an input signal in the low-frequency band, W₁ should be greater than the proportional coefficients of the command error and the interference suppression and its gain value should be as large as possible. However, in the high-frequency band beyond the system requirement, no such strict demand exists. The high-gain low-pass filter of W₁ selected in this study is as follows:

        (21)

W₂ is a weighting function for the sensitivity function R, and it represents the norm boundary of additive perturbation. R is a transfer function of system input r to the control quantity u, and W₂ is correspondingly introduced to limit control quantity u within the allowable range of the system and prevent oversaturation in system operation, Therefore, the static gain of W₂ should be appropriately large.

When the amplitude of W₂ increases, the calculated shear frequency of the control system will decrease. To ensure that the system has a sufficient bandwidth, the static gain of W₂ should be appropriately small. The selection of W₂ requires the compromise of several factors: the requirement of the system bandwidth, the saturation of the system, and the noise suppression of the system. The W₂ filter selected in this study is

 (22)

W₃ is a weighting function for sensitivity function T, which represents the norm of multiplicative perturbation and reflects the requirement of robust stability, i.e., the requirement of high frequency. The nominal object of the system is appropriate for describing the low-frequency characteristics of the object, but not its high-frequency characteristics. The unmodeled dynamic characteristic of the system can cause uncertainties in the gain and phase of the object. Therefore, the selected W₃ filter, which has large static and high-frequency gains but has no attenuation, is

        (23)

The use of the H∞ controller is based on the Riccati equation, which is solved using the Robust-Toolbox in MATLAB. The substitution of Eqs. (21)–(23) into Eqs. (11)–(13) leads to a generalized state matrix, P, of the controlled object. Then, by using MATLAB, the calculated results can be obtained for controller K(s) as follows:

 (24)

,

, 

,

Controller K(s) has been obtained in this study, and thus, the designed H∞ robust controller for the current inner loop is shown in Fig. 19.

Fig. 19. Block diagram of the current inner loop H∞ robust control system.

Ⅵ. SIMULATION STUDIES

To verify that the aforementioned three aspects can improve the transient stability of mode transfer, this study builds an MSCIMGS with an inverter and an SG in MATLAB/Simulink. The SG is the master power supply, whereas the inverter is the slave. The parameters of the microgrid system simulation model are shown in Table I and Appendix A.

TABLE I  Parameters of the Microgrid

Parameters	Parameter Values
Inverter rated power PInv0	15 kVA
DC side voltage	710 V
Filter capacitance C	47 µF
Filter inductance L	2.5 mH
Equivalent series resistance R	0.2 Ω
Current inner loop PI kpi, kii	2.4, 110
V/f outer loop PI kpu, kiu	4, 8
PQ outer loop PI kpPQ, kiPQ	0.81, 6
SG rated power PSG0	30 kVA
Rated frequency	50 Hz
AC voltage (line-to-line)	380 V
Critical load	5k W
Normal load	10 kW

Design of simulation scenario: At t = 0 s, the inverter and the synchronous power generation are the independent power supply. The inverter bears the critical load of 5 kW, whereas the SG bears the normal load of 10 kW. At t = 1.5 s, the inverter is connected to the microgrid and its control mode transfers from V/f to PQ. At t = 3.5 s, the inverter output power increases by 4 kW, whereas the SG output power decreases by 4 kW. At t = 4.5 s, the inverter is off the microgrid and the control mode transfers from PQ to V/f.

In the simulation scenario, the current inner loop of the inverter is taken by the H_∞ robust controller, the outer loop control adopts the status-tracking algorithm, and the improved pre-synchronization control is adopted in the process of islanding transfer to grid-connected operation.

Fig. 20 shows the simulation scenario waveforms, where SCS is the switching control signal from K_PCC, V_Inv is the inverter voltage magnitude, P_Inv is the inverter output power, and P_SG is the SG output power.

Fig. 21 shows the voltage and current waveforms of the inverter and the SG in the simulation scenario. Δt₁ denotes the V/f transfer to the PQ process, as shown in Fig. 22. Δt₂ represents the PQ transfer to the V/f process, as shown in Fig. 23.

Fig. 20. Simulation results of the mode transfer process with the proposed algorithm.

Fig. 21. Simulation voltage and current waveforms of mode transfer with the proposed algorithm.

Fig. 22. Simulation waveform of the H_∞ robust controller during the transition from V/f to PQ.

Fig. 23. Simulation waveform of the H_∞ robust controller during the transition from PQ to V/f.

Fig. 22 shows the voltage and current waveforms for V/f transfer to PQ during the Δt₁ period, which improves mode transfer in three aspects, and that the output power of the inverter is constant during the transfer.

In the figure, voltage and current are smooth during the V/f transfer to PQ and transient oscillation does not occur. A seamless mode transfer can be achieved during the grid- connected period.

Fig. 23 shows the PQ transfer to V/f during the Δt₂ period. The outer loop is used by the status-tracking control, whereas the inner loop is used by the H_∞ robust control. As shown in the figure, when the output power of the inverter is reduced after transfer, voltage and current are also smooth during the PQ transfer to V/f and no transient oscillation occurs.

To analyze the effect of the improved algorithm, the waveforms of the voltage and current at Δt₂ period are compared when the current inner loop adopts traditional PI control, as shown in Fig. 24.

Fig. 24. Simulation waveform of the traditional PI controller during the transition from PQ to V/f.

As shown in Fig. 24, the current inner loop uses the traditional PI controller when the inverter control mode transfers from PQ to V/f mode at Δt₂ period.

Voltage exhibits significant transient oscillations associated with the transition from the gird-connected mode to islanding mode because the current inner loop is used with the conventional PI control.

Ⅶ. EXPERIMENT RESULTS

To further confirm the feasibility and superiority of using the H_∞ robust controller instead of the traditional PI current inner loop controller and the effectiveness of the status- tracking and pre-synchronization algorithms, an experimental platform is set up to verify the seamless mode transfer of the microgrid inverter.

A. Setup of the Experimental Platform

The experimental system established in this study is shown in Fig. 25. The battery and PV are combined into the DC bus side with a DC output voltage of 710 V. The rated power of the RES inverter is 7.5 kVA, the critical load is P_Load2 = 1.5 kW, and the grid-connected/grid-disconnected breaker is K_PCC.

Fig. 25. Structure diagram of the microgrid experimental system.

Inductance L_Line = 3 mH is used to simulate line length, which is 3 km. The “back-to-back” converter is used to simulate the SG with a rated power of 20 kVA and an input of 380 V (city electricity). The normal load is P_load0 = 10 kW. The other parameters of the microgrid experimental system are provided in Appendix B. The main control chip of the converter is DSP F2812. The experimental system is shown in Fig. 26.

Fig. 26. Site of the microgrid experimental system.

B. Experimental Result

1) Experimental Scenario 1: The inverter and the virtual SG (VSG) are connected in parallel. The current inner loop is adopted by the H_∞ robust controller, and the inverter works in PQ mode for grid-connected operation. The inverter output power increases or decreases by 3 kW in this scenario.

In Fig. 27, when the current inner loop is adopted by the H_∞ robust controller as inverter output power increases or decreases by a step, the voltage waveform exhibits no oscillation and current is smooth. When the current inner loop is adopted by the traditional PI controller, the voltage and current waveforms are consistent with the waveforms of the H_∞ robust controller during the period when inverter output power increases/decreases.

Fig. 27. Experimental waveforms for the H_∞ controller when inverter output power changes. (a) Inverter output power increases. (b) Inverter output power decreases.

(a)

(b)

2) Experimental Scenario 2: The current inner loop is adopted by the H_∞ robust controller, the improved pre- synchronization control is applied, and the outer loop uses the status-tracking algorithm. The inverter transfers from V/f to PQ mode (Fig. 28(a)) or from PQ to V/f mode (Fig. 28(b)). The inverter output power remains constant during mode transfer.

As shown in Fig. 28, when a switching control command is received, the inverter transfers to V/f or PQ operation mode. Voltage and current are smooth during mode transfer, and the transition oscillation phenomenon does not occur. A seamless mode transfer can be achieved when inverter output power is not changed before and after mode transfer.

Fig. 28. Mode transfer experimental waveforms for the H∞ robust controller when inverter output power is not changed. (a) Waveforms from V/f to PQ operation mode. (b) Waveforms from PQ to V/f operation mode.

(a)

(b)

3) Experimental Scenario 3: The current inner loop is adopted by the traditional PI controller, and the other experimental conditions are the same as those in Experimental scenario 2. The inverter transfers from V/f to PQ mode (Fig. 29(a)) or from PQ to V/f mode (Fig. 29(b)). Inverter output power remains constant during mode transfer.

As shown in Fig. 29, voltage and current exhibit slight transient oscillations during mode switching. The effect of mode switching is worse than that in Experimental scenario 2 because the current inner loop is adopted by the traditional PI controller.

Fig. 29. Mode transfer experimental waveforms for the traditional PI controller when inverter output power is not changed. (a) Waveforms from V/f to PQ operation mode. (b) Waveforms from PQ to V/f operation mode.

(a)

(b)

4) Experimental Scenario 4: The inverter current inner loop uses the traditional PI controller for transfer from PQ to V/f mode, and inverter output power is reduced after transfer.

Fig. 30 shows the voltage and current curves when the current inner loop adopts the PI controller. Before mode transfer, the inverter and the VSG are connected to the grid and share a load of 10 kW. When a switch control command is received, the inverter goes off-grid and bears the critical load of 1.5 kW alone. The control mode of the inverter transfers from PQ to V/f.

From Fig. 30, a slight fluctuation in voltage amplitude and a significant oscillation in current waveforms occur when PQ mode is switched to V/f mode. An evident transient shock occurs when the current inner loop uses the PI controller.

Fig. 30. Experimental waveforms for the transition from PQ to V/f operation mode with the traditional PI controller.

5) Experimental Scenario 5: The inverter current inner loop uses the H∞ robust controller for transition from PQ to V/f mode, and inverter output power is reduced after transfer.

As shown in Fig. 31, the inverter can transfer smoothly to the islanding operation without voltage spikes and rush currents because the current inner loop adopts the H_∞ robust controller. Compared with that in Fig. 30, transient oscillation is small in Fig. 31. The proposed H_∞ robust controller is adopted and seamless mode transfer can be achieved.

Fig. 31. Experimental waveforms for the transition from the grid- connected to the islanding operation mode with the H_∞ robust controller.

Ⅷ. CONCLUSIONS

A study of the seamless mode transfer of an independent microgrid inverter and an analysis of the causes of transient oscillations in the traditional mode transfer are conducted. To effectively realize the seamless mode transfer of the inverter, improvements are achieved in three aspects. The simulations and experiments prove the effectiveness of the proposed method. This study presents the following contributions.

1) The dual-loop control structure of a microgrid inverter is presented, the traditional grid-connected/islanding mode transfer is analyzed, and the problem of traditional mode transfer is described.

2) The status-tracking algorithm is adopted to improve the transfer for the seamless connection of the outputs of the two outer loop controllers during transfer. The voltage magnitude and phase pre-synchronization control algorithm is used to reduce transient oscillations during the transition from islanding to grid-connected operation mode.

3) The H∞ robust controller is used instead of the traditional PI current inner loop controller to increase the adaptability and robustness of the controller and further improve power quality during switching.

APPENDIX A

Parameters of the Simulation Model

DC side voltage U_dc                                                                   710 V

filter inductance L                                                                   2.5 mH

filter capacitance C                                                                    47 µF

filter inductance parasitic resistance R                                                  0.2 Ω

current inner loop proportional coefficient k_pi                                              2.4

current inner loop integral coefficient k_ii                                                  110

voltage outer loop proportional coefficient k_pu                                               4

voltage outer loop integral coefficient k_iu                                                    8

inverter equivalent gain K_pwm                                                            409

ratio voltage factor k_{Inv_SG}                                                                  1

phase pre-synchronization PI k_{p_phase}, k_{i_phase}                                              9,10

voltage pre-synchronization PI k_{p_vol}, k_{i_vol}                                                 3,6

APPENDIX B

Parameters of the Experimental System

DC bus side with DC output voltage                                                    710 V

RES inverter rated power                                                            7.5 kVA

critical load P_Load2                                                                    1.5 kW

normal load P_load0                                                                    10 kW

simulative line length inductance L_Line                                                   3 mH

simulative SG rated power                                                           20 kVA

input of city electricity                                                                 380 V

ratio voltage factor k_{Inv_SG}                                                                  1

inverter equivalent gain K_pwm                                                            409

phase pre-synchronization PI k_{p_phase}, k_{i_phase}                                               4,7

voltage pre-synchronization PI k_{p_vol}, k_{i_vol}                                                 7,3

ACKNOWLEDGMENT

This work is supported by the National Natural Science Foundation of China (Grant No. 51377167) and the National Basic Research Program (973 Program) (2012GB215103).

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Yi Wang was born in Xiantao, China in 1985. He obtained his B.S. and M.S. from Wuhan University of Technology, Wuhan, China in 2008 and 2013, respectively. He is presently working for a Ph.D. in the Naval University of Engineering, Wuhan, China. His current research interests include microgrid control and protection and distribution network transformation and optimization.

Hanhong Jiang was born in Wuhan, China in 1960. He obtained his B.S., M.S., and Ph.D. in Electrical Engineering from Huazhong University of Science and Technology, Wuhan, China. He worked for the National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan, China. He was a chief technology officer for the Naval University of Engineering, China. His current research interests include vessel integrated power systems and microgrid energy management systems.

Pengxiang Xing was born in Anyang, China in 1990. He obtained his B.S. in Electrical Engineering from Wuhan University, China in 2012. He is currently working for a Ph.D. in the School of Electrical Engineering, Wuhan University. His research interests include renewable energy generation and microgrids.