Distributed Control for a Cost-based Droop-free Microgrid Manuel Martinez Gomez Dept. of Elect. Engineering University of Chile Santiago, Chile manuel.martinez.gmz@ieee.org Claudio Burgos Mellado Dept. of Elect. Engineering University of Nottingham Nottingham, UK claudio.burgosmellado1@nottingham.ac.uk Roberto Cardenas Dobson Dept. of Elect. Engineering University of Chile Santiago, Chile rcd@ieee.org Abstract—This paper proposes a distributed control scheme for the economic dispatch of islanded AC microgrids. The control goal is the economical power-sharing of distributed generators considering the marginal cost of active and reactive power. The controller is developed in a finite-time protocol over a droop-free strategy, without restoration needs for frequency. Simulations through the software PLECS are provided for validation pur- poses; they show adequate behaviour of the controllers under impact loads and plug & play operation. Index Terms—Distributed Control, Droop-Free AC Microgrid, Economic Dispatch, Finite-Time Control, I. I NTRODUCTION The reactive power supply is an important ancillary service in electricity markets, and its appropriate management is an essential element for the optimal economical operation of microgrids (MGs). The optimal economic dispatch in MGs is realized by the minimization of the distributed generators’ (DGs’) cost functions [1], and it can include reactive power to improve the system operation. The economic function for converter-interfaced DGs comes from their power source, which can be a battery energy storage system or a conven- tional fuel-based generator. Some works, using centralized ap- proaches, consider reactive power cost functions to realize the economic optimization problem [2]–[4]. However, this process involves high bandwidth communications and computation times. The formulation of a cost function for reactive power was originated in the optimal power flow of electric power systems; the reactive power sharing is determined by the solution of an optimization problem [2], [5]. In particular, in the economic dispatch approach of the optimal power flow, the cost functions of active power, reactive power and power losses are included [6], [7]. Since there is no actual cost for the generation of reactive power, concepts like opportunity cost, power losses and cost of synchronous condensers are considered by the literature to distribute the reactive power more efficiently [3], [8], [9]. The reactive power cost function, in a deregulated electricity market, can be represented by the This work was funded by the National Agency for Research and Develop- ment (ANID) / Scholarship Program / DOCTORADO BECAS CHILE/2019 - 21191757. Additionally, in part by the Advanced Center for Electrical and Electronic Engineering (AC3E) under Basal Project FB0008. weighted coefficients of the cost function of active power [10]. The weights come from the relation of the triangle of powers, i.e. the weights depend on the power factor cos(φ). In recent literature, authors have proposed a distributed co- operative control algorithms to perform the secondary control and power-sharing of AC MGs. In [11], it is proposed a consensus protocol for secondary control with a consensus protocol inside the voltage and frequency loops. The protocols are constructed based on a linear model obtained by means of the input-output feedback-linearisation technique. In [12], the authors studied further details about the inclusion of power-sharing features in the previous formulation. A slightly different approach was made by [13], where a distributed- proportional-integral (DAPI) controller was elaborated. This distributed protocol uses the error in average frequency of the MG as an auxiliary variable to perform the frequency restora- tion. This controller also incorporates the reactive power- sharing in the voltage loop, proposing a trade-off parameter for the voltage restoration weight. Another work proposed a cooperative controller replacing the frequency droop [14]. The authors drawn from the converter’s phase dynamics to avoid additional integrators in the frequency restoration loop, allowing a faster secondary control response without frequency measurements. This approach also benefits from the voltage observer proposed in [15]. Following a similar path, in [16] a multi-functional controller was made by the combination of [14] and [13]. For the economic dispatch consideration, several works such as [17], [18] have adapted consensus protocols of incremental cost replacing the conventional active power. In terms of reactive power regulation, works as [13], [16] give an equal contribution for every DG. However, this egal- itarian distribution of reactive power causes a large control effort due voltage restoration and line impedances in the MG. Also, it would not provide an actual economical benefit for MGs; Especially, for MGs that can implement a cost-based reactive remuneration [10]. Motivated by the above discussion, this work proposes a distributed strategy that combines the Incremental Cost (IC) and Reactive Marginal Cost (RMC) consensus in an isolated AC MG. To the best of the authors’ knowledge, secondary dis- tributed strategies implementing such reactive cost functions for reactive power-sharing have not been proposed.