Advanced sensorless power control strategy of renewable microgrids for reliability enhancement

Applied Energy 255 (2019) 113850

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Advanced sensorless power control strategy of renewable microgrids for reliability enhancement

T

Ping Liua, Yanbo Wangb, , Jie Lic, Dong Liub ⁎

a

College of Electrical and Information Engineering, Hunan University, Changsha, China Department of Energy Technology, Aalborg University, Aalborg, Denmark c Hebei University of Technology, Tianjin, China b

HIGHLIGHTS

power control strategy for renewable microgrids. • Sensorless strategies are developed to replace AC voltage and current sensors. • Reconstruction and experimental tests are performed with paralleled inverters. • Simulation • Improvement in fault-tolerant capability and reduction in operating cost. ARTICLE INFO

ABSTRACT

Keywords: Sensorless power control Microgrid Current reconstruction Voltage reconstruction Virtual flux Small signal stability Reliability

Microgrids are able to reduce fossil fuel emissions by integrating renewable energy resources, and to improve reliability and resilience of electrical grid. This paper presents a sensorless droop control strategy to enhance reliability and reduce operation cost of microgrids, where virtual flux-based voltage reconstruction and current reconstruction strategies are proposed to estimate three-phase voltage and current signals according to DC-link current instead of direct measurement. Combined reconstruction strategy of three-phase voltages and currents is first developed, and the implementation procedure of sensorless droop control is given. Furthermore, small signal model of microgrid equipped with the proposed droop control strategy is established. And closed-loop stability and dynamic performance of sensorless droop control strategy are investigated. Simulation and experiments are implemented to validate the proposed sensorless droop control strategy. The verification results show that the proposed method is able to perform accurate three-phase voltages and currents reconstruction of inverters, and achieve desirable power sharing control performance. The proposed droop control strategy is able to improve fault-tolerant capability of microgrid in the presence of sensors faults due to sensorless operation. It thus provides a cost-effective and high reliability solution for practical application of microgrids.

1. Introduction Energy consumption throughout the world is expanding due to increasing population, improving quality of life, and global industrialization [1]. It is estimated that the energy utilization worldwide will have an amazing improvement up to 28% between 2015 and 2040 [2]. The current energy consumption is still dominated by fossil fuel. It is well-known that the utilizations of fossil fuels exert negative effects on carbon emissions, global warming and climate change, which are becoming complex issues throughout the world. Therefore, innovative energy technologies are critical to provide environment-friendly and cost-effective solutions in future energy market [3]. Renewable energy

⁎

source is clean and inexhaustible energy that is able to minimize environmental pollution, and improve the reliability and flexibility of modern energy system. The utilization of renewable energy sources is critical solution for human being and environment substantial development [4]. Renewable energy is becoming the fastest-growing energy source throughout the world due to government policies and incentives for non-fossil energy sources. Furthermore, rapid deployment of renewable energy promotes energy efficiency and economic benefits. The increasing exploitation of renewable energy sources such as wind power, photovoltaic and fuel cell is promoting deployment of distributed power generation. The distributed generators (DGs), together with local loads and energy storage devices, can form small-scale

Corresponding author. E-mail address: [email protected] (Y. Wang).

https://doi.org/10.1016/j.apenergy.2019.113850 Received 4 May 2019; Received in revised form 16 August 2019; Accepted 2 September 2019 Available online 11 September 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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power generation system like microgrid [5,6]. Microgrids as an effective solution have been paid increasing attention to integrate renewable energy resources into power grid [7,8], which can be used to improve reliability and resilience of electrical grid, to reduce fossil fuel emissions by applying distributed clean energy resources such as wind and solar photovoltaic generation, and to provide electricity in remote areas not served by main power network. In addition, microgrids have been taken into consideration as a cost-effective alternative because development of transmission networks in modern power grid such as High Voltage Direct Current is challenging the grid economic [9]. A microgrid is able to operate either in grid-connected mode or autonomous mode [10]. In grid-connected mode, the generated electricity can be sold to power system and participate in ancillary service markets [11]. In autonomous mode, the microgrid can be either intentional or unintentional disconnected, when the generated electricity is provided to local loads and energy storage devices in microgrid. In autonomous operation, one of significant issues is to perform proportional power sharing control among paralleled distributed generator. The power sharing control strategies consist of droop-based power control strategy [6–11] and droop-free power control strategy [12,13]. Droop-based power control strategies [6–11] have been frequently proposed to perform desirable power sharing without using critical communication facilities. Compared with droop-based control strategy, droop-free control strategy is commonly enabled by high bandwidth communication system [12,13], where sensors are required to collect local voltage and current information and power control is performed in framework of centralized control. Therefore, the droop-free control strategies tend to increase system cost due to application of highbandwidth communication devices and sensors. For existing droop control strategies, voltage and current sensors are required to collect electrical signals and implement closed-loop control [5–8,14–16]. However, droop-controlled microgrids may be disabled once faults of voltage and current sensors happen. A significant responsibility of microgird is to provide reliable electricity supply for critical loads in microgrid [15,16]. Therefore, fault-tolerant capability of microgrid is important to enhance reliability and resilience in the presence of faults. In addition, employment of sensors also causes complicated hardware layouts and expensive cost. Sensorless control techniques including voltage reconstruction [17–23] and current reconstruction [24–32] are promising solutions to improve reliability and reduce hardware cost. Voltage construction techniques are originally proposed in [17–23]. A virtual flux-based voltage-sensorless power control of voltage source converters is proposed to meet requirements of control system in [17]. A frequencyadaptive virtual flux estimation method for voltage-sensorless synchronization and control of voltage source converters is presented in [18], which is able to improve dynamic responses for unbalanced grid conditions and large variations in grid frequency. An improved sensorless control strategy for a variable speed-constant frequency generation system based on a doubly fed induction generator is proposed in [33]. A current sensorless power-angle-based power control strategy for single-stage grid-connected photovoltaic inverter is proposed in [34]. A sensorless current MPPT algorithm using model predictive control is presented in [35] without using sensing and communications equipment. To reduce the number of current sensors, a current reconstruction method through a stand-alone DC-link current sensor is earlier presented in [24], which can reduce operation cost and eliminate potential load unbalance caused by unequal gain of output terminal current sensors. According to relationship of DC-link current and phase currents on various states of inverter switches, phase currents can be extracted by sampling DC-link current at correct instants according to the given voltage vector during each modulation (PWM) period. A switching state phase shift (SSPS) method for three-phase current reconstruction adopting a single current sensor in DC-link is presented in [24]. The single-shunt sensing inverter has features of high performance and low cost. In [25], a current controller with single DC-link current

measurement based on an improved observer-structure is proposed. A three-phase current reconstruction and control strategy using DC-link current sensor and curve-fitting observer is developed in [26]. A current prediction method in vector-controlled PWM inverters using single DClink current sensor is proposed in [27]. However, sensorless control techniques in droop-controlled microgrids with multiple paralleled inverters are not concerned so far. Therefore, the aim of this work is to develop an advanced sensorless control strategy of microgrids to improve fault-tolerant capability once the fault of sensors happen, and to reduce operation cost of microgrids. Three-phase voltages are reconstructed by virtual flux method and three-phase current signals are reconstructed by measured DC-link current. Power sharing control is enabled through reconstructed voltage and current. The main contributions and suitability of this work are promising because of the following characteristics. (1) The proposed power control strategy is able to perform desirable power sharing without using three phase voltage and current sensors, which can reduce operation cost and improve reliability of renewable microgrid. (2) Small signal model of microgrid with the proposed sensorless power control strategy is established. Also, closed-loop stability and dynamic performance of sensorless power control strategy are analyzed. The proposed method provides a cost-effective and high-reliable solution for practical application of renewable microgrids and support systematic integration of various renewable energies. The rest of this paper is organized as follows. In Section 2, conventional droop control strategy is reviewed and discussed. In Section 3, the principle and implementation details of the proposed sensorless droop control strategy are given. In Section 4, small signal model of microgrid equipped with the proposed droop control strategy is established. Also, closed-loop stability and dynamic performance are analyzed. In Section 5, simulation and experiments are performed to validate the proposed control strategy. The conclusions are drawn in Section 6. 2. Review of conventional droop control strategies Droop control schemes have been frequently proposed to perform active and reactive power sharing control in autonomous microgrids without using critical communication links. Fig. 1 shows circuit configuration of a droop-controlled microgrid, which is composed of DG inverters and load. In practical operation of inverter, sensors are employed to collect AC voltage and currents as well as DC voltage as shown in Fig. 1. Active power-frequency (P- ) droop control and reactive powervoltage (Q-V) droop control has been widely proposed to perform power sharing in autonomous microgrid. As illustrated in Fig. 2, DG unit is initially controlled to generate active power Pi and reactive power Qi at angle frequency ω*i and voltage V*i. Once load disturbances happen, angle frequency and voltage associated with DG i-th will be decreased to track the increased power in accordance with droop curves. Then, new steady-state frequency and voltage can be obtained through Eqs. (1) and (2).

V

i

=

0

m i (Pi

P0)

(1)

i

= V0

n i (Q i

Q0 )

(2)

where mi is the active power droop coefficient (Hz/W), ω0 is angular frequency of inverter at no load (rad/s), ni is the reactive power droop coefficient (V/var), V0 is voltage amplitude of inverter at no load (V). To share load requirement in proportion to its power rating, the droop coefficient usually is designed in inverse proportion to DG units rating [6–8]. However, voltage and current measurements are required to perform power control for conventional droop control strategies. Fig. 3 shows control diagram of the proposed sensorless droop control strategy. A comparison between conventional droop control strategy 2

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Fig. 1. Circuit configuration of a droop-controlled microgrid.

and proposed droop control strategy is given in Table 1. The proposed droop control strategy can reduce number of sensors, auxiliary power sources and signal conditioning circuits. For an islanded microgrid with n inverters, 5n sensors and 5n power sources can be reduced, which thus decreases hardware cost and increases system reliability.

SVPWM signals. The concept of virtual flux is originally introduced based on voltage integration in [17], which can be applied to estimate output voltages of voltage-source converters. Voltage-sensorless operation based on virtual flux estimation is designed to replace voltage measurements, where three-phase output voltages are assumed to be stator voltage magnitude of virtual motor. Resistance and inductance of filter inductor are assumed as stator resistance and leakage inductance of virtual motor, and output voltages are induced by a virtual magnetic flux. Therefore, integration of the output voltage space vector yields a virtual flux space vector as given in Eq. (3)

3. Proposed sensorless droop control strategy Fig. 4 shows diagram of the proposed sensor-less droop control strategy, where three-phase output voltages are reconstructed by virtual flux estimation according to DC-link voltage and SVPWM signals, and three-phase currents are estimated by current reconstruction algorithm according to measured DC-link current. Then, sensorless droop-based power controller and inner voltage/current controller are enabled to implement proportional power sharing by reconstructed voltages and currents.

=

v dt +

(3)

0

where ψ is virtual flux (Wb), v is output voltage of filter capacitor (V), and ψ0 is initial virtual flux (Wb). The output voltages of inverters can be given according to DC-link voltage and switching function as Eq. (4)

3.1. Virtual flux-based voltage reconstruction method

Vin Vin

In this work, virtual flux algorithm is employed to reconstruct inverter output voltages. Three-phase output voltages of inverter are reconstructed by virtual flux estimation according to DC-link voltage and

=

2 1 3 0

1 2 3 2

1 2 3 2

sa s b Vdc sc

(4)

However, application of pure integration can cause DC offset in

Fig. 2. The conventional droop control scheme. (a) Active power-frequency droop control. (b) Reactive power-voltage droop control. 3

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Fig. 3. The circuit configuration of microgrid enabled by proposed sensorless droop control strategy.

shown in Fig. 6. During PWM operation, one of the three-phase currents appears in the DC-link current whenever an active (i.e., non-zero) voltage vector is applied to the load. The relationship of DC-link current (idc) and AC phase currents in different vectors is illustrated in Table 2. Thus, measuring the DC-link current makes it possible to estimate the phase currents sequentially as the inverter switching states change. For instance, suppose that the reference voltage is in sector 1 as shown in Fig. 7. When the vector (1 0 0) is applied, ia is equal to idc. And when vector (1 1 0) is applied, ic is equal to -idc. Thus, during this switching period, the third phase current ib can be calculated using Eq. (7).

Table 1 Hardware comparison of conventional droop control strategy and proposed droop control strategy.

Number of AC voltage sensor Number of AC current sensor Number of DC voltage sensor Number of DC current sensor Number of sampling interface Number of power sources in sampling circuit Total number of sensors

Conventional droop control strategy

Proposed droop control strategy

3 3 1 0 7

0 0 1 1 2

7

2

7

2

i a + ib + i c = 0

To measure the DC-link current and reconstruct accurately phase currents, the minimum active vector time should be satisfied as Eq. (8)

output voltages, which mitigates accuracy of voltage reconstruction [17]. To eliminate DC offset in steady-state, first-order low pass filter is used to establish virtual flux linkage. Then, output flux and voltage in ɑβ-frame can be reconstructed as Eqs. (5) and (6). f f

=

1 V s + f in

Lf io

=

1 V s + f in

Lf io

Vo = Vo =

0 0

Tmin = Tdead + TAD + Tset

(8)

where Tdead is the inverter dead time (s), TAD is the summation of sampling time and A/D conversion time (s), Tset is the finite settling time for a fine DC-link current (s). Fig. 8 shows the unmeasurable areas in the inverter output voltage space vector plane for which at least one of the PWM duty cycle intervals is not long enough to measure the phase currents available in the DC-link current. If the inverter is in a low modulation or the reference voltage passes near one of the six active vectors, one or more of the active state vectors are not applied long enough, thus the three-phase currents will not be reliably detected. The switching state phase shift method proposed in [24] is adopted here to solve this problem, which modifies the PWM patterns by shifting phase to the switching-state waveforms to ensure that the duration of the active vectors satisfies the requirement of Tmin [31]. The modification of the SVPWM pattern do not change the duty ratios of switching waveforms, so the average reference voltage remains the same in a switching cycle. Fig. 9 shows the block diagram of phase current reconstruction. The operating principles of SSPS method are shown in Figs. 10 and 11, where the voltage vectors are lying on the regions of sector boundary and low modulation, respectively. By the SSPS method, the waveform of Sap or Scp as shown in Fig. 10(a) and Fig. 11(a) will be shifted along the time axis (in a correct direction) to allow a minimum time window

(5)

f f

(7)

(6)

where the ψfαβ is virtual flux in αβ frame (Wb), ωf is cut-off frequency of first-order filter (rad/s), Vinαβ is inverter voltage in αβ frame (V), Lf is virtual inductor (mH). Fig. 5 shows diagram of virtual flux estimation-based voltage reconstruction strategy. 3.2. Current reconstruction strategy Three-phase output currents of inverter also can be reconstructed based on SVPWM. There are eight switch state combinations in threephase voltage source converter modulated by SVPWM, which are 4

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Fig. 4. The detailed control diagram of proposed sensorless droop control strategy for individual inverter. Table 2 Relationship between DC-link current and phase current in different voltage vectors. U¯ i

(1 0 0)

(1 1 0)

(0 1 0)

(0 1 1)

(0 0 1)

(1 0 1)

idc

+ia

−ic

+ib

−ia

+ic

−ib

Fig. 5. Virtual flux estimation-based voltage reconstruction strategy. Fig. 7. DC-link current waveform corresponding to SVPWM with sector.

Fig. 6. Voltage space vector diagram of SVPWM algorithm.

Fig. 8. Unmeasurable areas in the voltage space vector plane.

for current measurement. Figs. 10(b) and 11 (b) show the modified PWM patterns and sampling points. Two sampling events happen during every single switching cycle to perform two phase currents measurement.

3.3. Sensorless droop control strategy Once three-phase voltages and currents of inverter are reconstructed, power control then can be implemented. Fig. 12 shows the 5

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Fig. 9. Block diagram of phase current reconstruction.

Fig. 11. PWM Patterns when voltage vectors are lying on the regions of sector low-modulation. (a) Original PWM pattern. (b) Modified PWM patterns and sampling points.

V odi = V0

(12)

ni Qi , V oqi = 0

4. Dynamic performance and stability analysis 4.1. Dynamic performance analysis of sensorless droop control As explained in Section 1, the presence of pure integral can cause DC offset due to inaccuracy initial value. Therefore, the pure integral is replaced by 1st-order integration so that the DC bias caused by the inaccuracy initial value can be removed. The effect of cut-off frequency (ωf) in voltage reconstruction loop is first analyzed. Fig. 13(a)–(d) show phase diagram of virtual flux as increase of cut-off frequency (ωf). It can be seen that virtual flux becomes stable as increasing of ωf.

Fig. 10. PWM Patterns when voltage vectors are lying on the regions of sector boundary. (a) Original PWM pattern. (b) Modified PWM patterns and sampling points.

4.2. Small signal analysis of microgrid with the sensorless droop control strategy

control diagram of the proposed sensorless droop control strategy. The average active power and reactive power then can be estimated by reconstructed voltages and currents as Eqs. (9) and (10).

Pi =

Qi =

c

s+

c

c

s+

c

(Vodi i odi + Voqi ioqi )

(Vodi i oqi

Voqi i odi )

Small signal dynamic equation of active power and reactive power can be obtained by linearizing Eqs. (9) and (10) as Eq. (13)

Pi

(9)

i

0

mi Pi

Pi

+ Ainv2

Qi

Qi

Vodi Voqi

+ Ainv3

i indi i inqi

(13)

where Ainv1, Ainv2 and Ainv3 are parameter matrix, which is given in Appendix. Vodi0, Voqi0, iodi0, ioqi0 are output voltages and currents in dqframe at initial operating point for small signal stability analysis. Small signal model of droop controller can be given by Eqs. (11) and (12) as Eqs. (14) and (15).

(10)

where the i means the i-th DG inverter, Vodi , Voqi , i odi , i oqi are reconstructed output voltages (V) and currents (A) in dq-frame. Then, active power-frequency and reactive power-voltage droop controller can be derived by reconstructed active power and reactive power as Eqs. (11) and (12).

=

= Ainv1

i

=

Vodi =

(11)

(14)

mi Pi

ni Qi ,

V oqi = 0

(15)

The dynamic equation of output angle generated by droop 6

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Fig. 12. Control diagram of the proposed sensorless droop control strategy.

controller as shown in Fig. 4 can be given as Eq. (16) [7]. i

=

i

com

= Aw Pi

B w P1

matrix. Small signal dynamic equation of reconstructed output voltages in αβ-frame is obtained by combining and linearizing Eqs. (5) and (6) as Eq. (17).

(16)

where com is angle frequency on common dq-frame (rad/s), the dqframe of DG1 is selected as common dq-frame. Aw , B w are parameter

Fig. 13. Phase diagram of virtual flux. (a) ωf = 5. (b) ωf = 10. (c) ωf = 15. (d) ωf = 20. 7

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V ind = Vin*q

=

1

Voq + Kpv ( V od

c c

Vod ) + Kiv L

Vod + Kpv ( Voq

Voq ) +

di

ci

1 Kiv L ci

qi

(23)

Kpv and Kiv are parameters of voltage controller as shown in Fig. 12. The small signal equation can be rewritten by combining Eq. (15) and Eq. (22) as Eq. (24).

V ind

Vod

Pi + Binv2 Qi

= Binv1

Vin*q

Voq

+ Binv3

di qi

(24)

where Binv1, Binv2 and Binv3 are parameter matrix, which are given in Appendix. Small signal dynamic equation of reconstructed converter-side current in dq-frame is given as Eq. (25).

i indq = Ainv8 i indqi + Ainv9

0

Vo =

f

0

f

+

Vin +

0 Lf

Vin

0 Lf

io + io

0 Lf 0 Lf

io

(17)

i indq

The transformation relationship between αβ-frame and dq-frame is given as Eq. (18).

i indq

So So

=

0

cos sin

f

i i

f

sin i cos i

0

f

Sod Soq

= T0

Sod + Sodq0 Soq

Vodq = A d1 i

= V od

Vod

q

= V oq

Voq

i indi i inqi

(19)

+ Ad4

= Ainv16

Qi

(20)

+ Ainv17

i odi =

(26)

i + Ad5

indq

V

odq

(27)

dqi

R ci L ci

i odi

i

i oqi +

1 L ci

Vodi

1 L ci

Vbdi

R ci L ci

i oqi +

i

i odi +

1 Lci

Voqi

1 L ci

Vbqi (28)

(i = 1, 2) (21)

The small signal equation of (26) can be obtained by combining and linearized Eqs. (14) and (15) and (26) as Eq. (29).

where Ainv16 and Ainv17 are parameter matrix of Eq. (20). The voltage relationship of inverter can be obtained as shown in Fig. 12 as Eq. (22).

V indq = Vindq

di

(i = 1, 2)

Vodi Voqi

Voqi

where Ad1, Ad2, Ad3, Ad4, Ad5 are parameter matrix, which can be given in Appendix. As shown in Fig. 14, the output voltage Vi can be ideally tracked. Small signal dynamic equation of grid-side currents in dq-frame can be given as Eq. (28)

i oqi = dq

Vodi

qi

+ Ad2 P + A d3

The voltage equation can be rewritten as Eq. (21).

Pi

Pi + C2 Qi

+ C1

where C1, C2 and C3 are parameter matrix, which can be given in Appendix. Small signal dynamic equation of output voltage in dq-frame can be derived by combining Eqs. (17), (19), (21)–(24), (26) as Eq. (27).

(18)

Vod0 Vind0 Iind0 cos 0 sin 0 where T0 = , V0 = , Vin0 = ,I = . Voq0 Vinq0 in0 Iinq0 sin 0 cos 0 The small signal equation of voltage controller shown in Fig. 12 can be derived as Eq. (20). d

= Ainv8

+ C3

where Soαβ refers to V0, Vin0 or i0 in αβ-frame. Small signal model of output voltage and current can be derived as Eq. (19) by linearizing Eq. (18).

So So

(25)

where Ainv8, Ainv9, Ainv10 and Ainv11 are parameter matrix, which are given in Appendix. Small signal equation of reconstructed converter-side current can be rewritten by combining Eq. (21), Eq. (23) and Eq. (25) as Eq. (26).

io

f

+ Ainv10 Vindq

+ Ainv11 Vodq

Fig. 14. Eigenvalue trajectory of state matrix as a function of parameter of virtual flux-based voltage reconstruction strategy.

Vo =

i

i odi

= Ainv12

i oqi

(22)

+ Ainv14

Linearized model of reference voltage is derived by Eqs. (20) and (21) as Eq. (23).

8

Vodi Voqi

i odi ioqi

+ Ainv13

+ Ainv15

Vbd Vbq

Pi Qi

(29)

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where Ainv12, Ainv13, Ainv14 and Ainv15 are parameter matrix, which are given in Appendix. Small signal model of individual inverter is then established by combining Eqs. (13), (16), (20), (24), (28) and (29) as Eq. (30)

x = Ainvi x invi + Binvi Vbdqi

invi

Table 3 Parameters of system setup.

(30)

where Vbdqi is bus voltage connected into microgrid in dq-frame. Ainvi x invi = and Binvi are parameter matrix.

Parameters

Value

Parameters

Value

Power Rating Switching Frequency Lf1/Lf2 Cf1/Cf2

5 kW 10 kHz 1.5 mH/1.5 mH 25 µF/25 µF

Lc1/Lc2 mp1/mp2 nq1/nq2

1.8 mH/1.8 mH 1 × 10−4/1 × 10−4 1 × 10−3/1 × 10−3

[ Pi , Qi , i , Vodqi , i indqi , i odqi , dq ]T , Ainvi and Binvi are parameters matrices, which are given in Appendix. Similarly, small signal model of inverter2 can be established by aforementioned procedure in the state-space form. The complete small signal model of microgrid as shown in Fig. 4 can be established as Eq. (31).

x = AMG xMG

(31)

MG

where AMG is system parameter matrix. Fig. 14 shows the eigenvalue trajectory of state matrix (AMG) as a function of cut-off frequency. It can be seen that the eigenvalue trajectory can move toward right-half plane (unstable region) as increase of cut-off frequency. The analysis results show that small signal stability of the proposed sensorless droop controller can be affected by cut-off frequency. 5. Simulation and experimental verification To validate the proposed sensorless droop control strategy, simulation verification is performed in MATLAB/SIMULINK with PLECS blockset, and experimental verification is implemented in a scale-down microgrid with two inverters. The circuit configuration is shown in Fig. 1. The picture of experimental setup is shown in Fig. 15, where the microgrid consists of two three-phase inverters with LC filter. The circuit parameters applied in simulation and experiment are listed in

Fig. 16. Simulation results about current reconstruction. (a) The reconstructed current and measured current of inverter1. (b) The reconstructed current and measured current of inverter2.

Table 3. The whole platform is controlled by dSPACE 1006. Dynamic current and voltage reconstruction strategies are first validated. Fig. 16 shows that the simulated current reconstruction (Phase A) results of 2 inverters in the presence of load disturbance at 0.2 s. It can be seen that the reconstructed output currents accurately match the measured currents. Also, Fig. 17 shows experimental results about current reconstruction (Phase A) of two inverters. It can be seen that the reconstructed output currents accurately match measured currents. Fig. 18 shows simulation results about unstable output current and stable output current, which agrees with the analysis result as shown in Fig. 14. Fig. 19 shows that the simulated voltage reconstruction (Phase A) results of two inverters. It can be seen that the reconstructed voltages accurately match the measured voltages. Fig. 20 shows experimental results about voltage reconstruction (Phase A) of two inverters. It can be seen that the reconstructed output voltages accurately match measured voltages. Figs. 21 and 22 show the simulated results about reconstructed active power and reactive power. It can be seen that the reconstructed active power and reactive power match accurately measured active power and reactive power. The results from Figs. 16–22 show the desirable power sharing is implemented among paralleled inverters with the proposed sensorless droop control strategy.

Fig. 15. Photo of experimental setup. 9

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2A/div

(a)

(a) 2A/div

(b)

(b)

Fig. 19. Simulation voltage reconstruction results. (a) The reconstructed voltage and measured voltage of inverter1. (b) The reconstructed voltage and measured voltage of inverter2.

Fig. 17. Experimental results about current reconstruction. (a) The reconstructed current and measured current of inverter1. (b) The reconstructed current and measured current of inverter2.

iod1

20 V/div

i oq1 (a) (a)

iod1

ioq1

(b) Fig. 20. Experimental results about voltage reconstruction. (a) The reconstructed voltage and measured voltage of inverter1. (b) The reconstructed voltage and measured voltage of inverter2.

6. Conclusion

(b)

Innovative energy technologies are critical to provide environmentfriendly and cost-effective solutions in future energy market. Microgrids are able to reduce fossil fuel emissions by integrating renewable energy resources, and to improve reliability and resilience of electrical grid. A microgrid is able to operate either in grid-connected mode or

Fig. 18. Simulation results about output current. (a) The unstable output current of inverter1 in dq-frame. (b) The stable output current of inverter1 in dqframe.

10

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autonomous mode. In autonomous operation, one of significant issues is to perform proportional power sharing control among paralleled distributed generator. Droop-based power control strategies have been frequently proposed to perform power sharing without using critical communication facilities. For existing power control strategies, voltage and current sensors are required to collect electrical signals and implement closed-loop control. However, droop-controlled microgrids may be disabled once faults of voltage and current sensors happen. Therefore, this paper presents a sensorless droop control strategy for AC microgrids, where three-phase voltages and currents are reconstructed by measuring DC-link voltage and current to enable power sharing control instead of directly using AC current and voltage sensors. The principle and implementation procedures of the droop control are given. Furthermore, small signal model of microgrid equipped with the proposed sensorless droop controller is established and stability of the proposed droop control strategy is investigated. Simulation and experimental results shows that the proposed method is able to perform desirable current and voltage reconstruction of inverters, and provide desirable power sharing performance in microgrids with multiple paralleled inverters. In summary, our main contributions and results are explained as follows.

(a)

(1) Sensorless power control strategy is developed without using AC current and voltage sensors, which is able to reduce hardware cost, and decrease volume of distributed generator inverter. (2) Virtual flux-based voltage reconstruction method is developed, where the effect of cut-off frequency in voltage reconstruction loop is investigated. Also, small signal stability of microgrid with proposed sensorless power control strategy is investigated.

(b) Fig. 21. The active power and reactive power reconstruction results of inverter1.

A strong point of the proposed sensorless control strategy is to reduce hardware cost and improve reliability of microgrid. The faulttolerant capability of microgrid is improved to enhance reliability and resilience in the presence of sensors fault. Therefore, the proposed sensorless droop control strategy provides a cost-effective and high performance solution for practical application of microgrids. 7. Future work Future work in progress will extend the application of the proposed control strategy to grid-connected renewable microgrids, which will promote the penetration of renewable energies in a cost-effective way. With the increase of inverter number, the benefit of the proposed control strategy is more evident. Furthermore, the effects of reconstruction errors caused by DC voltage offset, measurement noises, and degradation of DC-link capacitor will be analyzed and mitigated, and design guideline of reconstruction error mitigation strategy will be given. In addition, further advanced control capability in the framework of the proposed sensor-less power control will be developed, including seamless transfer between islanded microgrid and grid-connected microgrid, and energy optimization management in a costeffective way. From the viewpoint of grid support, inertia emulation capability of distributed generator will be developed with sensor-less power control strategy to support the inertia of power grid. In addition, frequency support methods of grid-connected microgirds at different time scale will be developed to support frequency regulation of power system.

(a)

(b) Fig. 22. The active power and reactive power reconstruction results of inverter2.

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Appendix

m p 0 ];

Bw = [

0

c

Ainv1 =

0

c i odi0

, Ainv2 =

c

c i oqi 0

c i oqi0

Kpv

Binv2 =

c

Kpv

c

c Vodi0

, Ainv3 =

c i odi0

c Voqi0

c Voqi0

, Binv3 =

Kiv Lc

0

0

Kiv Lc

c Vodi0

0 0

, Binv1 =

nq Kpv , 0

;

Ainv4 = T1 V0 + T2 Vi0 + T4 I0, T1 =

0

f

0

f

, T2 =

0 0

0

0

0

, T3 =

0 Lf

0 Lf

0

0

, T4 =

0

f Lf

0 f Lf

0

,

Tt1 = T1 V0 + T3 T0 C2, Tt 2 = T2 V0 + T3 T0 Ainv10 , Tt 3 = T4 V0 + T3 T0 Ainv8 , Tt 4 = T1 V0 + T2 Vin0 + T4 I0, Tt5 = T3 T0 C1, Tt 6 = T3 T0 C3, Tt 7 = V0 T3 I0; Ainv8 =

Rfi L fi

0

0

Ainv10 =

1 Lf i

0

0

1 L fi

i ind0 , i inq0

, Ainv9 =

Rfi L fi

, Ainv11 =

1 L fi

0 1 L fi

0

;

C1 = Ainv9 B w + Ainv10 Binv1, C2 = Ainv11 + Ainv10 Binv2, C3 = Ainv10 Binv3; Ad1 = T0 1 (T1 V0 + T2 Vi0 + T4 I0 ), Ad2 = T0 1 (Tt 2 Binv1 + Tt 5 1

Tt 7), Ad3 = T0 1 (Tt1 + Tt 2 Binv2), 1

Ad4 = T0 (T4 T0 + T3 T0 Ainv8 ), Ad5 = T0 (Tt 2 Binv3 + Tt 6 ); Rci L ci

Ainv12 =

i0

Ainvi =

i0 R ci L ci

, Ainv14 =

1 L ci

0

0

1 L ci

, Ainv15 =

Ainv1 , O2 × 1, Ainv2 , Ainv3 , O2 × 4 Ainv3a , O1 × 9 C1, Ainv4 , C2, Ainv7 , O2× 2 , C3 C4, O2 × 1, C5, Ainv8 , O2× 2, C6 Ainv13 ,O2× 1, Ainv14 , O2× 2, Ainv12 , O2 × 2 Ainv16 , O, Ainv17 , O

1 L ci

0

0 1 L ci

;

T

.

systems using component connection method. IEEE Trans Smart Grid 2018;9(5):5301–10. [12] Wang Z, Wu W, Zhang B. A distributed quasi-newton method for droop-free primary frequency control in autonomous microgrids. IEEE Trans. Smart Grid 2018;9(3):2214–23. [13] Nasirian V, Shafiee Q, Guerrero JM, Lewis FL, Davoudi A. Droop-free distributed control for AC microgrids. IEEE Trans Power Electroni 2015;31(2):1600–17. [14] Nutkani IU, Loh PC, Wang P, Blaabjerg F. Cost-priorized droop schemes for autonomous AC microgrids. IEEE Trans Power Electron 2015;30(2):1109–19. [15] Razeghi G, Gu F, Neal R, Samuelsen S. A generic microgrid controller: Concept, testing, and insights. Appl Energy 2018;229:660–71. [16] Wang Y, Liu D, Liu P, Deng F, Zhou D, Chen Z. Lifetime-oriented droop control strategy for AC islanded microgrids. IEEE Trans Ind Appl 2019;55(3):3252–63. [17] Suul JA, Luna A, Rodríguez P, Undeland T. Virtual-flux-based voltage-sensor-less power control for unbalanced grid conditions. IEEE Trans Power Electron 2012;27(9):4071–87. [18] Suul JA, Luna A, Rodriguez P, Undeland T. Voltage-sensor-less synchronization to unbalanced grids by frequency-adaptive virtual flux estimation. IEEE Trans Ind Electron 2012;59(7):2910–23. [19] Ohnishi T, Hojo M. DC voltage sensorless single-phase PFC converter. IEEE Trans Power Electron 2014;19(2):404–10. [20] Yang H, Zhang Y, Liang J, Gao J, Walker PD, Zhang N. Sliding-mode observer based voltage-sensorless model predictive power control of PWM rectifier under unbalanced grid conditions. IEEE Trans Ind Electron 2018;65(7):5550–60. [21] Gholami-Khesht H, Monfared M. Novel grid voltage estimation by means of the NewtonRaphson optimisation for three-phase grid connected voltage source converters. IET Power Electron 2014;7(12):2945–53. [22] Gholami-Khesht H, Monfared M, Golestan S. Low computational burden grid voltage estimation for grid connected voltage source converter-based power applications. IET Power Electron 2015;8(5):656–64. [23] Bozorgi A, Chayjani MS, Nejad RM, Monfared M. Improved grid voltage sensorless control

References [1] Hannan M, Lipu M, Ker P, Begum R, Agelidis V, Blaabjerg F. Power electronics contribution to renewable energy conversion addressing emission reduction: Applications, issues, and recommendations. Appl Energy 2019;251. 113404. [2] Global energy institute. https://www.globalenergyinstitute.org/internationalenergyagency-releases-its-world-energy-outlook [accessed 22.08.18]. [3] Hirsch A, Parag Y, Guerrero J. Microgrids: A review of technologies, key drivers, and outstanding issues. Renew Sustain Energy Rev 2018;90:402–11. [4] Adefarati T, Bansal RC. Reliability, economic and environmental analysis of a microgrid system in the presence of renewable energy resources. Appl Energy 2019;236:1089–114. [5] Li Y, Zhang P, Yue M. Networked microgrid stability through distributed formal analysis. Appl Energy 2018;228:279–88. [6] Yu M, Huang W, Tai N, Zheng X, Wu P, Chen W. Transient stability mechanism of gridconnected inverter-interfaced distributed generators using droop control strategy. Appl Energy 2018;210:737–47. [7] Wang Y, Chen Z, Wang X, Tian Y, Tan YC, Yang C. An estimator-based distributed voltage predictive control strategy for AC islanded microgrids. IEEE Trans Power Electron 2015;30(7):3934–51. [8] Li J, Xiong R, Yang Q, Liang F, Zhang M, Yuan W. Design/test of a hybrid energy storage system for primary frequency control using a dynamic droop method in an isolated microgrid power system. Appl Energy 2017;201:257–69. [9] Hussain A, Bui VH, Kim HM. Microgrids as a resilience resource and strategies used by microgrids for enhancing resilience. Appl Energy 2019;240:56–72. [10] Wang Y, Wang X, Chen Z, Blaabjerg F. Distributed optimal control of reactive power and voltage in islanded microgrids. IEEE Trans Ind Appl 2017;53(1):340–9. [11] Wang Y, Wang X, Chen Z, Blaabjerg F. Small-signal stability analysis of inverter-fed power

12

Applied Energy 255 (2019) 113850

P. Liu, et al. strategy for railway power conditioners. IET Power Electron 2015;8(12):2454–61. [24] Kim H, Jahns TM. Phase current reconstruction for AC motor drives using a DC link single current sensor and measurement voltage vectors. IEEE Trans Power Electron 2006;21(5):1413–9. [25] Wolbank TM, Macheiner PE. Current-controller with single DC link current measurement for inverter-fed AC machines based on an improved observer-structure. IEEE Trans Power Electron 2004;19(6):1562–7. [26] Saritha B, Janakiraman PA. Sinusoidal three-phase current reconstruction and control using a DC-Link current sensor and a curve-fitting observer. IEEE Trans Ind Electron 2007;54(5):2657–64. [27] Gan C, Wu J, Yang S, Hu Y. Phase current reconstruction of switched reluctance motors from DC-Link rurrent under double high-frequency pulses injection. IEEE Trans Ind Electron 2015;62(5):3265–76. [28] Cho Y, LaBella T, Lai J. A three-phase current reconstruction strategy with online current offset compensation using a single current sensor. IEEE Trans Ind Electron 2012;59(7):2924–33. [29] Song S, Xia Z, Fang G, Ma R, Liu W. Phase current reconstruction and control of threephase switched reluctance machine with modular power converter using single DC-Link current sensor. IEEE Trans Power Electron 2018;33(10):8637–49.

[30] Lu H, Cheng X, Qu W, Sheng S, Li YZ, Wang Z. A three-phase current reconstruction technique using single DC current sensor based on TSPWM. IEEE Trans Power Electron 2014;29(3):1542–50. [31] Gu Y, Ni F, Yang D, Liu H. Switching state phase shift method for three-phase-current reconstruction with a single DC-Link current sensor. IEEE Trans Ind Electron 2011;58(11):5186–94. [32] Lai Y, Lin Y, Chen C. New hybrid pulsewidth modulation technique to reduce current distortion and extend current reconstruction range for a three-phase inverter using only DC-link sensor. IEEE Trans Power Electron 2013;28(3):1331–7. [33] Akel F, Ghennam T, Berkouk EM, Laour M. An improved sensorless decoupled power control scheme of grid connected variable speed wind turbine generator. Energy Convers Manag 2014;78:584–94. [34] Dousoky GM, Shoyama M. Current-sensorless power-angle-based MPPT for single-stage grid-connected photovoltaic voltage-source inverters. In Energy Conversion Congress and Exposition (ECCE); 2013. p. 2757–63. [35] Metry M, Shadmand MB, Balog RS, Abu-Rub H. MPPT of photovoltaic systems using sensorless current-based model predictive control. IEEE Trans Ind Appl 2017;53(2):1157–67.

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