An iterative adaptive virtual impedance loop for reactive power sharing in islanded meshed microgrids
Introduction
The transition from a centralized to a hybrid centralized/distributed power system concept is due to the high penetration of renewable-based distributed generation (DG) [1]. In this context, microgrids (MGs) were introduced as a very effective configuration for the integration into power systems of the non-dispatchable renewable energy sources (RESs) [2]. In the case of grid-connected MGs, the exchange of active and reactive powers can be imposed by the grid [3], [4]. On the contrary, in the case of islanded MGs, the load demand should be properly shared between the different generators operating in the MG [5]. Droop control is often used to regulate active and reactive powers [6] without the use of any external communication link [7].
Whereas the sharing of active power is usually easy to achieve as all the DGs work at the same frequency, the regulation of the reactive power sharing is more complicated because of the different voltage of the DGs due to the difference in the impedances of the feeders [7]. Different droop control-based regulators have been developed and presented in the literature [8]. In [9] a “Q-V dot droop” method is proposed to improve the sharing of the reactive power. In [10] the injection of small real power disturbances is used to estimate the reactive power control error. Different methods based on the estimation of the impedance lines are presented in [11] and [12]. Secondary droop control has been used in [13], [14], [15] in order to eliminate the reactive power sharing error by compensating the voltage level. A virtual Impedance (VI) method has been widely used with good results in many applications including reactive power sharing in MGs [16], [17] and improvement of the power control stability [18].
The VI approach used in [19] differs from traditional methods because of its capability to prevent high harmonics content. In [20] a virtual harmonic impedance has been developed to control the harmonic power sharing in an islanded MG. Virtual impedance-based controllers have been presented in [21], [22]. In [23] an Adaptive Virtual Impedance (AVI) based on the integration of the voltage drop between different distributed generators is proposed. In [24] the authors introduced a proper inductance in order to improve the reactive power sharing by estimating the feeder impedances. In [25] and [26] the voltage is compensated by a secondary controller that optimizes the reactive power sharing. In this case, the knowledge of the voltage at the Point of Common Coupling (PCC) is required. A comprehensive review showing the advantages and the limits of the most common control methods used for the reactive power sharing in islanding MGs can be found in [27].
It is worth mentioning that the most of the aforementioned methods have been developed based on a classical MG structure where the reactive power sharing is related only to the feeders impedance mismatch.
In this paper, a new control strategy named Iterative Adaptive Virtual Impedance (IAVI) is presented. The IAVI is adjusted considering two contributes: the first is proportional to the reactive power at the previous iterations, while the second is proportional to the sum of the reactive power variations at the previous iterations. The investigated islanded meshed MG consists of three parallel-connected distributed generators. The share of the reactive power in the MG has been evaluated considering two different control techniques: the first one is based on a simple droop control, while the second uses a droop control virtual impedance. The controllers have been developed without the use of any communication link between the different DG units. The performance of the proposed control strategy has been compared with the well known droopless technique [18].
The rest of the paper is organized as follows: Section 2 describes the use of the conventional droop control. To eliminate the reactive power inaccuracy, an analysis based on reactive power sharing without and with virtual impedances is presented in Section 3. The proposed IAVI control strategy, stability analyses, controller parameters setting, and controller synchronizations are provided in Section 4. The results are presented and discussed in Section 5.
Section snippets
Droop control
Active power–frequency ( P–f) and reactive power–voltage ( Q–V) droop-based control techniques have been effectively applied in MGs to control the share of active and reactive powers [7], [12]. These methods have been widely used because they are simple and they do not require any communication link between the generators operating in the MG.
Fig. 1 shows a microgrid with two generators feeding a common load. The currents produced by the two generators are:
Conventional droop control
Fig. 3 shows a meshed MG with two generators with the same nominal power operating in an islanded mode. Each generator feeds both a local and two common loads. The relationships between the DGs voltages and their reactive power is given by:
If the resistive parts of the feeder impedances are negligible, then the voltage drops have to be smaller than the 5% of the nominal voltage (i.e., E 0 E1) in order to avoid system instabilities [16]. The voltage drops are given by [16]
The IAVI controller
In this section, the proposed controller based on the iterative adaptive virtual impedance control strategy is presented. As shown in Fig. 6, the controller is made of three stages. The first stage (named droop control) is used to generate the reference voltage based on the indirect measurement of active and reactive powers. The second stage consists of two control loops, one for the voltage and one for the current. The IAVI controller with its output represents the third stage. The
Results and discussion
In order to verify the performance of the IAVI controller depicted in Fig. 11, the meshed microgrid with three distributed generators shown in Fig. 12 has been considered.
The performance of the developed controller has been simulated in a Matlab/Simulink environment for the following three case studies:
(1) Case study 1: The power demand is kept constant, while the structure of the microgrid together with the parameters of the IAVI controller are kept fixed;
(2) Case study 2: The power demand is
Conclusion and future work
In this paper, an iterative adaptive virtual impedance (named IAVI) control strategy for the elimination of the mismatch between the impedances of the feeders in a meshed microgrid powered by a certain number of distributed generators has been presented.
The iterative virtual impedance consists of two elements: one proportional to the reactive power delivered by each generator, and a second that depends on the reactive power variation between two iterations. The proposed strategy is of
CRediT authorship contribution statement
H. Sellamna: Developed the theory and performed the computations, Verified and analysed the method, Written the paper. A. Massi Pavan: Conceived of the presented idea, Written the paper, Disused the results, Checked and revised the paper. A. Mellit: Conceived of the presented idea, Verified and analysed the method, Supervised the finding of this work, Written the paper, Disused the results. Josep M. Guerrero: Checked and revised the paper.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
A. Mellit would like to thank the International Centre for Theoretical Physics (ICTP), Trieste (Italy) for providing the materials and the computer facilities used to develop some parts of the work presented in the paper. A. Massi Pavan acknowledges the financial support provided by “DEEP-SEA – Development of energy efficiency planning and services for the mobility of Adriatic Marinas”, a project co-financed by the European Regional Development Fund (ERDF) via the cross-border cooperation
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