A Voltage-sensorless Current Control of Grid-connected Inverter Using Frequency-adaptive Observer

Available online at www.sciencedirect.com 2019 IFAC Workshop on Control of Smart Grid and Renewable Energy Systems Jeju, Korea, June 10-12, 2019 IFAC Workshop on 2019 Control of Smart Grid and Renewable Energy Systems IFAC PapersOnLine 52-4 (2019) 63–68 Jeju, Korea, June 10-12, 2019

ScienceDirect

A Voltage-sensorless Current Control of Grid-connected Inverter Using Observer A Voltage-sensorless Frequency-adaptive Current Control of Grid-connected Inverter Using Frequency-adaptive Observer Thuy Vi Tran*. Kyeong-Hwa Kim** 

Thuy Vi Tran*. Kyeong-Hwa Kim** * Department of Electrical and Information Engineering, Seoul National University of Science and Technology,  232 Gongneung-ro, Nowon-gu, Seoul, 01811, Korea (Tel: +82-2-970-9867; e-mail: [email protected]). * Department ** Departmentof ofElectrical Electricaland andInformation InformationEngineering, Engineering,Seoul SeoulNational NationalUniversity Universityof ofScience Scienceand andTechnology, Technology, 232 232 Gongneung-ro, Gongneung-ro, Nowon-gu, Nowon-gu, Seoul, Seoul, 01811, 01811, Korea Korea (Tel: (Tel: +82-2-970-9867; +82-2-970-6406; e-mail: e-mail: [email protected]). [email protected]). ** Department of Electrical and Information**Engineering, Seoul National University of Science and Technology, Corresponding author 232 Gongneung-ro, Nowon-gu, Seoul, 01811, Korea (Tel: +82-2-970-6406; e-mail: [email protected]). ** Corresponding author Abstract: This paper presents a grid voltage-sensorless current control design based on the linear quadratic regulator (LQR) approach for an LCL-filtered grid-connected inverter. The proposed scheme Abstract: presentsfrom a grid currenttocontrol design the linear relies only This on thepaper information the voltage-sensorless grid-side current sensors implement the based controlon algorithm as quadratic (LQR) for an LCL-filtered grid-connected inverter. The proposed well as toregulator synchronize the approach inverter system with the utility grid. Basically, the construction of scheme current relies only consists on the information from feedback the grid-side currentaugmented sensors to implement the control algorithm as controller of a full-state regulator with an integral control term for well as tocontrol synchronize the inverter system with the utility grid. Basically,thethe construction of current achieving objectives, and a frequency-adaptive observer to estimate system state variables and controller of aeven full-state augmented an integral control term for grid voltageconsists parameters under afeedback non-idealregulator grid environment withwith frequency variation. A systematic achieving control objectives, and aapproach frequency-adaptive observer to optimal estimategains the system variables and design method based on the LQR is introduced to obtain for thestate controller as well grid parameters a non-ideal gridproposed environment withisfrequency A simulation systematic as thevoltage adaptive observer.even Theunder effectiveness of the scheme validated variation. through the design results.method based on the LQR approach is introduced to obtain optimal gains for the controller as well as the adaptive observer. The effectiveness of the proposed scheme is validated through the simulation Keywords: adaptive observer; frequency variation; Control) grid-connected internal © 2019, IFAC (International Federation of Automatic Hostinginverter; by Elsevier Ltd. Allmodel; rights linear reserved. results. quadratic regulator. Keywords: adaptive observer; frequency variation; grid-connected inverter; internal model; linear  quadratic regulator. characteristic of the LCL filter causes a difficulty in the 1. INTRODUCTION  current control strategies to stabilize the system. Generally, characteristic of the LCL filter causes a difficulty in are the damping methods of the LCL resonant behaviour A recent power-electronics technology creates a trend toward the 1. INTRODUCTION current control strategies stabilize system.realized Generally, in two types:tothe passivethe damping by integration of the renewable energy from wind and solar categorized damping methods of the LCL resonant are A recent power-electronics technology creates toward additional physical components on LCL circuitsbehaviour (Peña-Alzola power generation systems into the utility gridatotrend reduce the the categorized in two the passive damping realized by integration of the renewable from wind andelectric solar et al., 2013), and types: the active damping implemented environmental impacts causedenergy by the traditional additional physical components LCLZhao, circuits (Peña-Alzola power generation utility grid to reduce the modifying the control algorithmon(Jia, and Fu, 2014). generation systems system.into In the these applications, a grid2013), the active damping implemented by environmental impacts the totraditional Dueal., to the main and drawback of the passive damping that causes connected voltage sourcecaused inverterby (VSI) supply theelectric power et modifying the control algorithm (Jia, Zhao, and Fu, 2014). power generation system. In these applications, a gridextra losses through heat dissipation, the active damping to the mains grids attracts numerous studies on the control Due to the main of the passive that causes connected voltage source inverter (VSI) to supply thecurrent power approaches are drawback usually preferred and damping used popularly to strategies to provide a high quality of grid-injected extra losses dissipation, the active damping to theunder mainsnon-ideal grids attracts numerous studies onInthe control maintain the through system heat efficiency. However, it is worth to even grid voltage environment. particular, approaches usually and usedrealized popularly to strategies provide a highofquality of grid-injected current thatare some active preferred damping schemes by the the power to quality standard distributed generation such as mention maintain the system efficiency. However, it the is worth to even underinnon-ideal environment. particular, resistance require extra sensors to obtain capacitor IEEE-519 USA or grid IEC voltage 61000-3-2 in EuropeInrequires the virtual mention that some active damping schemes realized by and the the power quality standard (THD) of distributed generation such5% as currents or voltages, which increases the system cost total harmonic distortion of current less than virtual resistance requireAs extra sensorsapproach, to obtain the IEEE-519and in USA or IEC1989). 61000-3-2 Europe requires the hardware complexity. another a capacitor full-state (Duffey Stratford, Gridin frequency variation currents orcontrol voltages,scheme which increases cost and total harmonic distortion of current less isthan provides the a system convenient caused by different faults (THD) in distribution network one5% of feedback hardware complexity. approach, and a full-state (Duffey and grid Stratford, 1989). which Grid frequency way to As fulfilanother the performance stability unexpected conditions, causes a variation serious straightforward feedback control scheme provides a convenient caused by different faults in distribution one the of requirements in LCL-filtered inverter system when all and the degradation of current control performance.network To copeiswith straightforward to fulfil and stability unexpected grid byconditions, which causes a seriousa system states areway available. In the orderperformance to reduce the number of challenge raised adverse grid voltage environment, requirements ina LCL-filtered inverter system when all the degradation of current performance. To cope with the measurements, full-state observer is normally employed in robust control scheme control and fast frequency detection method system stateswhereupon are available. order toofreduce the sensors number of challenge raised by adverse grid voltage environment, a this work, the Innumber needed is are required. measurements, a full-state observer employed in robust control scheme and fast frequency detection method compatible with the design of theis normally conventional L filter Aside from the concern of current control design, the filter this work, whereupon the number of needed sensors is are required. counterpart (Tran, Yoon, and Kim, 2018). connected between the mains grid and VSI plays an essential compatible with the design of the conventional L filter Asidetofrom the concern of current controlindesign, the filter For the purpose of reducing the cost and improving the role attenuate the current harmonics high switching counterpart (Tran, Yoon, and Kim, 2018). connected between andmodulated VSI plays inverter. an essential frequency due to the mains pulse grid width In reliability of the grid-connected inverter, it is desirable to For thereduce purpose reducing the costdevices and improving role to attenuate the current harmonics in high switching theofnumber of sensing in system.the A general, the LCL filters are regarded as being satisfactory for further reliability of the grid-connected inverter, it is desirable to frequency due to the pulse width modulated inverter. In feasible option which gains a lot of interest of researchers three-phase voltage source grid-connected inverter because further reduce the number of sensing devices sensors in system. A general, the LCL filters are regarded being with satisfactory for recently, is to replace the use of grid voltage by an they provide a better grid-side currentasquality lower cost feasible option which the gains a lot of interest three-phase sourcesize grid-connected inverterwith because However, great challenge of of thisresearchers approach and smallervoltage physical in comparison the estimator. recently, is tohigh replace the use of grid voltage sensorsscheme by an they provide a better grid-side Nevertheless, current quality with cost relies on the accuracy of grid voltage estimation conventional L filters. the lower resonant estimator. However, the great technique challenge inof order this approach and smaller physical size in comparison with the and the grid synchronization to inject conventional L filters. Nevertheless, the resonant relies on the high accuracy of grid voltage estimation scheme and the grid synchronization technique in order to inject 2405-8963 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2019.08.156 Copyright © 2019 IFAC

63

2019 64 IFAC CSGRES Jeju, Korea, June 10-12, 2019

Thuy Vi Tran et al. / IFAC PapersOnLine 52-4 (2019) 63–68

sinusoidal currents in phase with the fundamental component of grid voltage even under non-ideal grid condition such as frequency variation. In particular, several studies have presented grid voltage-sensorless and frequency-adaptive control schemes (Jorge, Solsona, and Busada, 2014; Lee et al., 2009; Bimarta, Tran, and Kim, 2018). In the research work (Jorge, Solsona, and Busada, 2014), a grid voltage-sensorless current control scheme which is unaffected by grid frequency variation is presented to produce high quality of injection current under distorted grid conditions. However, this approach is applied for an L-filtered grid-connected inverter. Another sensorless technique is introduced to deal with unbalanced and harmonic contents in grid (Lee et al., 2009). Nevertheless, the grid frequency variation is not taken into account in this design method. In the study (Bimarta, Tran, and Kim, 2018), a frequency-adaptive current controller design based on the linear quadratic regulator (LQR) state feedback approach is proposed to cope with the issue on the grid frequency deviation. However, this scheme still requires the measurement of the grid voltage.

block diagram of the proposed control scheme is also shown in this figure, which is constructed by an integral full-state feedback current control and an adaptive full-state observer with only the use of grid-side current sensors.

In order to address the above mentioned challenges in regard to the control design and system performance, this paper presents a voltage-sensorless current control scheme for a grid-connected inverter with an LCL filter by using frequency-adaptive observer. The current control design is accomplished in the synchronous reference frame (SRF) by a full-state feedback control for system stabilization, which does not require extra damping method. In addition, integral terms are augmented into the control structure to ensure asymptotic reference tracking. To reduce the total number of sensing devices required for the control of an LCL-filtered grid-connected inverter, only the grid-side current measurement is employed. With the aim, a frequencyadaptive observer is presented to estimate both the system states and the grid voltage. The proposed frequency-adaptive observer provides an excellent estimation capability even in the presence of grid frequency deviation.

The continuous-time model of inverter system can be expressed in the SRF as follows:

Instead of using grid voltage sensors as in the conventional methods, the proposed sensorless scheme estimates the grid voltages from the adaptive observer to extract the information of the grid phase angle for synchronization purpose. Furthermore, a zero-crossing detection technique is employed on the phase angle to determine the grid frequency, which presents a compatible performance to the conventional phase locked-loop (PLL) method. In order to select the feedback and observer gains in a systematic way, the optimal LQR approach is adopted in this paper. By minimizing the cost function to satisfy the stability and robustness of system, the overall control system can be designed in an effective and straightforward way. The simulations based on the PSIM software are presented to demonstrate the effectiveness and validity of the proposed control scheme. 2. SYSTEM DESCRIPTION Fig. 1 shows a configuration of three-phase grid-connected inverter with an LCL filter, in which ��� denotes the DC-link voltage, �� , �� , �� , and �� are the filter resistances and filter inductances, respectively, and � is the filter capacitance. The

64

i1

VDC

+

i2

L1

���

R1

L2

���

_



���



C 6

�∗

�∗ ��

��

���∗

Integral full-state feedback current control

�

�

�̂ � �̂�

� �̂ � ����

� �

� �̂� ����

abc qd

��

� � � ��∗

Space vector PWM

Grid

R2



���∗ ���∗ Adaptive fullstate observer

� �� ���

Fig. 1. Configuration of a grid-connected inverter and the block diagram of the proposed control scheme.

(1)

�̇ (�) = ��(�) + ��(�) + ��(�) �(�) = ��(�)

(2)

�

where � = ���� ��� ��� ��� ��� ��� � is the system state vector, �

� = ���� ��� � is the system input vector, � = [�� �� ]� is the grid voltage vector, the superscript “q” and “d” denote the q-axis and d-axis variables, respectively, �� is the inverterside current, �� is the grid-side current, �� is the capacitor voltage, and �� is the inverter output voltage. The system matrices �, �, �, and � are expressed as −� /� ⎡ � � ⎢ � �=⎢ 0 ⎢ 0 ⎢ −1/� ⎣ 0

−� −�� /�� 0 0 0 −1/�

0 0 0 0 −� −�� /�� −�� /�� � 0 1/� 1/� 0

1/�� 0 −1/�� 0 0 �

0 ⎤ 1/�� ⎥ 0 ⎥ −1/�� ⎥ −� ⎥ 0 ⎦

0 0 0 −1/�� ⎡ 0 ⎤ ⎡ 0 0 −1/�� ⎤ ⎢ ⎥ ⎢ ⎥ 1/�� 0 ⎥, � = ⎢ 0 0 ⎥ �=⎢ 0 ⎥ 1/�� ⎥ ⎢ 0 ⎢ 0 ⎢ 0 0 ⎥ ⎢ 0 0 ⎥ ⎣ 0 ⎣ 0 0 ⎦ 0 ⎦ 1 0 0 0 0 0 � C=� 0 1 0 0 0 0 where � is the angular frequency of the grid voltage.

(3)

For a digital implementation, the discretized model of inverter system is obtained by using the zero-order hold (ZOH) with the sampling time �� as (Franklin, Powell, and Workman, 2006) �(� + 1) = �� �(�) + �� �(�) + �� �(�) �(�) = �� �(�)

(4) (5)

2019 IFAC CSGRES Jeju, Korea, June 10-12, 2019

Thuy Vi Tran et al. / IFAC PapersOnLine 52-4 (2019) 63–68

where the matrices �� , �� , �� , and �� can be calculated as follows: �� = � ��� = � +

��� �� ��� + +⋯ 1! 2!

�� = ��� (�� − �)� �� = �

�� = ��� (�� − �)�.

(6)

(7) (8)

3. PROPOSED CONTROL SCHEME 3.1 Proposed Current Control In order to ensure that the tracking error converges to zero asymptotically, an integral state feedback control term is augmented in the full-state feedback controller based on the internal model principle. An integral term in the state-space is expressed as �

� � (�) � � (�) ��̇ (�) � = ��� � �� � + ��� � � � � (�) �� (�) ���̇ (�) �

The discrete-time counterparts of � �� and ��� , which are defined as ��� and ��� can be obtained by the ZOH method as in (6) and (7). Then, the entire control system can be constructed as follows: �� � �(� + 1) �(�) �=� � �� −��� �� � �� �� (�) �� (� + 1) � � � + � � � �(�) + � � � �(�) + � � �(�) ��� � �

�

�(�) = [�� �

� where �� = ��� ��� � .

�] �

�(�) � �� (�)

(10)

(11)

With the augmented system, the state feedback control is obtained as �(�) = −[� � � � ] �

�(�) � = � � (�) + �� (�) �� (�)

An adaptive observer is constructed in this section by utilizing the models of inverter and disturbance to eliminate the need of grid voltage sensing devices. Regarding to the inverter model, it is obvious in (3) that the inverter system expressed in the SRF contains the information of the grid angular frequency, which causes a discrepancy in the discretized system model when the grid frequency varies. This can be overcome by introducing a discrete-time fullstate observer designed in the stationary reference frame instead of using the SRF. Then, the system model becomes independent of the frequency information. As a result, the inverter system model can be discretized simply by using the offline ZOH method and the observer model is not affected by non-ideal grid conditions. For simplification in notation, the subscripts “α” and “β” in the system model description in the stationary reference frame are omitted. In addition, the control design can be accomplished by considering only one axis without the loss of generality because the equations in the α-axis and β-axis are independent of each other. The system model for the LCL-filtered grid-connected inverter is expressed in the stationary frame as follows:

(9)

where � = [� � � � ]� = � − �� � is the current error vector, � = � 0 0 �∗ �, and ��� ���∗ � is the reference current vector, ��� = � 0 0 1 0 �. ��� = � 0 1

(12)

where �� (�) = −� � �(�) and �� (�) = −� � �� (�).

If the gain matrix [� � �� ] in (12) is evaluated systematically by the LQR method (Tran, Yoon, and Kim, 2018), the state feedback control input �(�) becomes an optimal control input to ensure the control performance and system stability. This task is accomplished easily by utilizing the Matlab function “dlqr” in this paper. 3.2 Design of Frequency-adaptive Observer

65

65

�̇ � (�) = � � � � (�) + �� u� (�) + �� �� (�) �� (�) = �� �� (�)

(13) (14)

where � � = [�� �� �� ]� , �� = �� , �� = � , and the parametric matrices are described as follows: −�� /�� −1/�� 0 0 −1/� � �� = � 1/� 0 1/�� −�� /�� �� = [1/�� 0 0]� , �� = [0 0 1/�� ]� �� = [0

0 1].

Then, the discretized model of (13) and (14) can be obtained by the similar procedure to (6)-(8) to provide the discretetime counterparts of � �� , ��� , ��� , ��� . To estimate the grid phase angle without using the grid voltage measurement, a discrete-time disturbance model for the grid voltages are used in the stationary frame. This model is presented in the statespace as follows: �

� (�) � (�) �� (� + 1) � = �� � � � + �� � �� � �� (� + 1) �� (�) ��� (�)

where �� = �

(15)

2���(��� ) 1 ���(��� ) � , �� = � � −1 0 −1 �

and � = ��� �� � is a sinusoidal disturbance vector and �� = [��� ��� ]� is an arbitrary input vector. Combining the inverter and disturbance models to � = [� � �� �� ]� , a compact form including the inverter system and disturbance model can obtained as �(� + 1) = �� �(�) + �� �(�) �(�) = �� �(�)

(16) (17)

2019 66 IFAC CSGRES Jeju, Korea, June 10-12, 2019

Thuy Vi Tran et al. / IFAC PapersOnLine 52-4 (2019) 63–68

��� ��� 0 where �� = � 0 2 ���(��� ) 1� 0 −1 0 ��� �� = � 0 � , �� = [��� 0 0]. 0

3.3 Proposed Grid Synchronization Method

Then, a frequency-adaptive observer which estimates the system states and grid voltage from the inverter reference voltage �(�) and the grid-side current measurement �(�) under the grid frequency variation can be achieved as follows:

where � = [� �

���

��� ]�

�� ��� �� = ���� ���(��� )�, � � = � 0 −��� 0

���

2 ���(� � �� ) −1

with �� being an observer gain matrix.

(18)

0 1� 0

For the purpose of designing the observer gain �� , the observer error dynamics can be obtained by subtracting (18) from (16) as �� (� + 1) = �(� + 1) − �(� + 1) � � − �� �� ���(�) − �� �(�). = �� �(�) − ��

(19)

Although the grid may suffer from frequency deviations, the grid frequency can be considered as a slowly-varying parameter along with time. In addition, the dynamics of the proposed observer can be designed sufficiently fast by selecting observer poles as compared with the frequency variation. As a result, it is valid to state that �� is close to �� in steady-state period, and then, the observer error dynamics can be rewritten as below: �� (� + 1) = (�� − �� �� )�� (�).

�� = tan��

(20)

By selecting the poles of the matrix (�� − �� �� ) in the stable region, the estimated and disturbance states converge to the actual values asymptotically. In other words, the proposed adaptive observer is able to estimate both the system states and the grid voltage as a disturbance signal without using any sensing devices except for grid-side current sensors. For the purpose of choosing a robust and optimal observer gain matrix �� under grid frequency uncertainty, the LQR approach used to design � in the previous section can be applied in (20). Similar to the selection of the current control feedback gains, the observer gains are computed by the Matlab function “dlqr”. The simulation results are presented in next Section to demonstrate the robustness of the proposed adaptive observer scheme. In this paper, the grid frequency and phase angle are an unknown constants and need to be estimated. Therefore, an estimation method must be designed to ensure that the observer works and the inverter is synchronized to the actual grid voltage in the grid-connected mode.

66

���� . ����

(21)

The phase angle �� is directly used in the current controller to guarantee the injected currents from inverter to be in phase with the fundamental component of the grid voltage. The grid frequency � � is easily acquired by applying the zero-crossing detection technique on phase angle �� . The proposed grid frequency estimator is explained in Fig. 2. By measuring the time duration between zero crossing points, the information of grid frequency can be calculated fast and accurately. Phase angle (rad)

� � − �� �� )�̂(�) + �� �(�) + �� �(�) �(� + 1) = (�

From the estimated grid voltages in (18), the grid frequency and phase angle can be determined, which provides precise information used for the synchronization process. In addition, the online estimated grid frequency is utilized to update the system matrix in observer. From the estimated grid voltages in α-axis and β-axes in the stationary frame, the phase angle of grid voltage is simply obtained as

Zero crossing

0 � � Time (s)

Fig. 2. Zero-crossing detection technique for grid frequency estimation. 4. SIMULATION RESULTS In order to verify the feasibility and validity of the proposed current control scheme and adaptive observer, the simulations have been carried out for an LCL-filtered three-phase gridconnected inverter based on the PSIM software. The configuration of the inverter system and the proposed control scheme are depicted in Fig 1. The system parameters are listed in Table 1. Fig. 3 represents three-phase grid voltages used for the simulations. The grid voltages experience a frequency variation from 60 Hz to 50 Hz at 0.3 sec. Table 1. System parameters of a grid-connected inverter Parameters DC-link voltage Filter resistance Filter capacitance Inverter-side filter inductance Grid-side filter inductance Grid voltage (line-to line rms) Grid frequency

Value 420 0.5 4.5 1.7 0.9 220 60

Units V Ω µF mH mH V Hz

2019 IFAC CSGRES Jeju, Korea, June 10-12, 2019

0 -100 -200

60 Hz 0.2

0.24

50 Hz 0.28

Time (s)

0.32

0.36

0.4

Fig. 3. Three-phase grid voltages with frequency change at 0.3 sec. First, the current control performance of the integral state feedback current control is presented under a step change in current reference from 4 A to 7 A at 0.15 sec. It is clearly shown in Fig. 4(a) and (b) that the grid-side currents track the reference values with satisfactory transient and steady-state performance at both the grid frequencies of 60 Hz and 50 Hz. The THD values of grid-side a-phase current are 3.55% at 60 Hz and 3.28% at 50 Hz, respectively, which satisfies the IEEE-519 requirement for injected current of inverter. ���

Current (A)

10 5

���

���

�̂ ��

10 5

���

�

�̂ �

�

��

0 -5

60 Hz

-10 0.2

50 Hz

0.24

0.28

Time (s)

0.32

0.36

0.4

(a) �̂��

10 5

�

��

0 -5

60 Hz

-10 0.2

0

���

�

�̂�

50 Hz

0.24

0.28

Time (s)

0.32

0.36

0.4

(b)

-5

60 Hz 0.1

0.12

0.14

Time (s)

0.16

0.18

0.2

(a) ���

10 5

100

���

�

���

�

��

0

-100

���

���

����

200

Voltage (V)

-10

Current (A)

67

voltages also show an asymptotical convergence to the real values in less than half of grid voltage fundamental period during frequency jump at 0.3 sec. Clearly, a good performance of the adaptive observer not only ensures the stability for whole system but also minimizes the total sensing devices required for LCL-filtered inverter.

��

Current (A)

Voltage (V)

100

��

Current (A)

��

200

Thuy Vi Tran et al. / IFAC PapersOnLine 52-4 (2019) 63–68

-200

60 Hz 0.2

0.24

50 Hz 0.28

0

Time (s)

0.32

0.36

0.4

(c)

-5

0.12

0.14

Time (s)

0.16

0.18

0.2

(b)

Voltage (V)

0.1

�̂ �

200

50 Hz

-10

100

��

�̂ �

��

0

-100

Fig. 4. Simulation results for three-phase measured grid-side currents of the proposed scheme under a step change in reference current at 0.15 sec. (a) At 60 Hz; (b) At 50 Hz In order to demonstrate the proposed adaptive observer at the stationary frame, Fig. 5 shows the simulation results for the measured and estimated system states of the inverter and grid voltages under the grid frequency variation from 60 Hz to 50 Hz at 0.3 sec. Fig. 5(a) through (c) represent the measured and estimated values for the grid-side currents, inverter-side currents, and capacitor voltages, respectively. Fig. 5(d) shows the estimation performance of grid voltages. A fast and stable estimating capability of the proposed observer is obviously validated even under the frequency variation. In particular, the waveforms of estimated grid-side currents, inverter-side currents, and capacitor voltages rapidly match to the actual states in transient period. Similarly, the estimated grid

67

-200

60 Hz 0.2

0.24

50 Hz 0.28

Time (s)

0.32

0.36

0.4

(d)

Fig. 5. Simulation results for measured and estimated values of the proposed scheme under the frequency change from 60 Hz to 50 Hz at t = 0.3 sec in the stationary frame. (a) Gridside currents; (b) Inverter-side currents; (c) Capacitor voltages; (d) Grid voltages. To evaluate the performance of estimators for the grid frequency and phase angle proposed in the last section, Fig. 6(a) shows the comparative results of frequency estimation between the conventional PLL and the proposed frequency estimator when the grid frequency is subject to variation.

2019 68 IFAC CSGRES Jeju, Korea, June 10-12, 2019

Thuy Vi Tran et al. / IFAC PapersOnLine 52-4 (2019) 63–68

Phase angle (rad)

To evaluate the performance of estimators for grid phase angle in the last section, Fig. 6(a) shows the comparative results of phase angle estimation between the conventional PLL with grid voltage measurement and the proposed scheme based on estimated grid voltages from the adaptive observer. It is clearly shown in Fig. 6(a) that the estimated phase angle is well matched with the real value in steady-state without any noticeable difference in a short time when the grid frequency is subject to variation. The acceptable performance of estimated grid phase angle ensures not only the stability of synchronization process but also the accuracy of the estimated frequency. Fig 6(b) presents the compatible results of frequency estimation between the conventional PLL and the proposed frequency estimator with zero-crossing detection technique. :;

:

6 4 2 0

60 Hz

0.2

0.24

50 Hz

0.28

Time (s)

0.32

0.36

0.4

Grid voltage frequency (Hz)

(a) 70

Conventional PLL

65

Proposed frequency estimator

60 55 50 45 40

0.2

0.24

0.28

Time (s)

0.32

0.36

0.4

(b) Fig. 6. Simulation results for the estimation of grid frequency and phase angle under the frequency change from 60 Hz to 50 Hz at t = 0.3 sec. (a) Performance comparison of phase angle estimation between the conventional PLL and the proposed estimator. (b) Performance comparison of frequency estimation between the conventional PLL and the proposed estimator. 4. CONCLUSIONS This paper has presented a grid voltage-sensorless current control scheme for an LCL-filtered grid-connected inverter using a frequency-adaptive observer. The current control of the inverter has been implemented by means of full-state feedback approach after augmenting integral control terms, which is known as a straightforward method to deal with the resonant behaviour of LCL filter and to ensure the system stability. Though this approach requires the availability of the full system states, the proposed scheme uses only the gridside current sensing devices for the purpose of reducing cost and improving the system reliability. A full-state frequencyadaptive observer has been introduced, which not only estimates the system states but also provides the grid voltage

68

information. Based on the estimates of grid voltages, the grid frequency and phase angle are easily determined. Theoretical analyses and comparative simulation results have been provided to confirm the usefulness of the proposed control scheme. ACKNOWLEDGMENTS This work was supported by the Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), grant funded by the Korea government Ministry of Trade, Industry & Energy (NO. 20174030201840). REFERENCES Bimarta, R., Tran, T., and Kim, K.H. (2018). Frequencyadaptive current controller design based on LQR state feedback control for a grid-connected inverter under distorted grid. Energies, 11(10), 2674. Duffey, C. and Stratford, R. (1989). Update of harmonic standard IEEE-519: IEEE recommended practices and requirements for harmonic control in electric power systems. IEEE Trans. on Indus. Applicat., 25(6), 10251034. Franklin, G.F, Powell, J.D., and Workman, M. (1997). Digital control of dynamic systems. AddisonWesley. Menlo Park, CA. Jorge, S., Solsona, J., and Busada, C. (2014). Control scheme for a single-phase grid-tied voltage source converter with reduced number of sensors. IEEE Trans. on Power Electr., 29(7), 3758-3765. Lee, K., Jahns, T., Lipo, T., Blasko, V., and Lorenz, R. (2009). Observer-based control methods for combined source-voltage harmonics and unbalance disturbances in PWM voltage-source converters. IEEE Trans. on Indus. Applicat., 45(6), 2010-2021. Peña-Alzola, R., Liserre, M., Blaabjerg, F., Sebastián, R., Dannehl, J., and Fuchs, F. (2013). Analysis of the passive damping losses in LCL-filter-based grid converters. IEEE Trans. on Power Electr., 28(6), 26422646. Tran, T., Yoon, S., and Kim, K.H. (2018). An LQR-based controller design for an LCL-filtered grid-connected inverter in discrete-time state-space under distorted grid environment. Energies, 11(8), 2062. Jia, Y., Zhao, J., and Fu, X. (2014). Direct grid current control of LCL-filtered grid-connected inverter mitigating grid voltage disturbance. IEEE Trans. on Power Electr., 29(3), 1532-1541.