Original articles
Fast power flow scheduling and sensitivity analysis for sizing a microgrid with storage

https://doi.org/10.1016/j.matcom.2015.11.010Get rights and content

Abstract

This article proposes a fast strategy for optimal dispatching of power flows in a microgrid with storage. The investigated approach is based on the use of standard mixed integer linear programming (MILP) algorithm in association with a coarse linear model of the microgrid. The resulting computational time is compatible with simulations over long periods of time allowing the integration of seasonal and stochastic features related to renewable energies. By using this fast scheduling strategy over a complete year of simulation, the microgrid cost effectiveness is considered. Finally, a sensitivity analysis is carried out in order to identify the most influent parameters that should be considered in a sizing loop. Different microgrid configurations are also investigated and compared in terms of cost-effectiveness.

Introduction

With the growing number of renewable energy sources the power grid topology has evolved and it could be now described as an aggregation of several microgrids both consumer and producer  [8]. For those “prosumers”, a classical strategy consists in selling all the highly subsidized production at important prices while all consumed energy is purchased  [7]. Smarter operations become possible with the development of energy storage technologies and evolving price policies  [28]. Those operations would aim at reducing the electrical bill taking account of consumption and production forecasts as well as the different fares and possible constraints imposed by the power supplier  [10], [14]. The microgrid considered in the paper is composed of a set of industrial buildings and factory with a subscribed power Ps of 156 kVA and a PV generator with a peak power of 175 kW (Fig. 1(a)). A 100 kW/100 kWh storage consisting in the association of ten high-speed flywheels is also introduced.

The strategy chosen to manage the overall system is based on a daily off-line optimal scheduling of power flows for the day ahead. Then, in real time, an on-line procedure adapts the same power flows in order to correct errors between forecasts and actual measurements  [22]. Thus prediction for both consumption  [3] and production  [13] is a very important issue in microgrid management problems but it is not considered here. Several algorithms have been investigated in previous works  [23] to perform the off-line optimization for a single day. In particular, trust-region-reflective algorithm  [9], clearing procedure  [18], particular swarm optimization  [15] and Dynamic Programming  [4], [20]have been compared in this context. But the high computational times observed did not comply with a sizing procedure that would require many runs of the procedure over long periods of time (e.g., weeks, months, years). The present study focuses on a faster approach consisting in two steps. Firstly, a basic Mixed Integer Linear Programming (MILP) algorithm solves the cost minimization problem with a coarse linear model of the system as in  [24], [17]. Then, a second procedure adapts the obtained solutions to comply with the requirements of a finer nonlinear model. The paper is organized as follows. Section  1 describes the nonlinear model of the system with the various losses taken into account. The text also refers to the optimization problem that aims at minimizing the electrical bill for the day ahead with the forecast for the production, consumption and prices. Then, Section  2 presents the fast optimization approach with the hypothesis considered for the coarse model. A particular attention is attached to the introduction of integer variable to consider the exceeding of subscribe power. Finally, the adaptation of the control references resulting from the MILP optimization is described. In Section  3, the results obtained for two test days are presented with or without considering grid constraints. The last section uses the developed algorithm to investigate different sizings of the microgrid with regard to the yearly cost. Finally, a sensitivity analysis is performed in order to estimate the most significant parameters that should be considered in a sizing procedure.

Section snippets

Power flow model

As illustrated in Fig. 1(b), the components are connected though a common DC bus. Voltages and currents are not considered so far. The microgrid sizing (cable length) is very limited. Thus losses within the lines can be aggregated with converter efficiencies. Furthermore, the paper focuses on the optimal scheduling of the system without considering a real-time management strategy (i.e. voltage/current control). The approach is “in power” with a study referring to the optimization of active

Definition of a coarse linear model

In a second step, a coarse model is developed in order to speed up the solving by using a linear formulation of the problem. Firstly, the converter efficiencies are neglected which leads to the reduction of the number of power flows used to describe the system (Eq. (9)). {p2(t)=p3(t)p4(t)=p5(t)p7(t)=p8(t)p10(t)=p11(t).

In this model, storage losses are also neglected as well as the self-discharge. Thus, the SOC is simply computed at each time step of duration Δt=1h (Eq. (10)) SOC(t+Δt)=SOC(t)Pst

Input data

Two test days are considered to compare the performances of the MILPc method with the results returned by the previous algorithm. The consumption profiles are extracted from data provided by the microgrid owner while the production estimation is based on solar irradiation forecasts, computed with a model of PV arrays  [11]. The load and production profiles for the two tested days are presented in Fig. 3 with different amount of consumed or generated energies. The “spring day” corresponds to

Simulation “day after day”

Estimating the cost effectiveness of the microgrid from an optimal power dispatching strategy implies to run simulations of longer periods than a single day. Algorithms with expensive CPU times cannot be considered in that context. For instance the DPa needs around 10 min to simulate the microgrid management over a single day. Considering one year would last nearly three days of computation. The MILPc then appears to be the most suitable here, leading to the best compromise with regard to cost

Conclusion

The study carried out in this article aims at proposing a fast procedure in terms of computation time that could be used to investigate cost-effectiveness of a microgrid with storage. In previous works, efficient algorithms have been developed to perform the daily scheduling of power flows. However, the main drawbacks of these methods reside in their computational times that become prohibitive if the microgrid has to be simulated over a long period of time. To overcome this problem, a fast

Acknowledgments

This study has been carried out in the framework of the SMART ZAE national project supported by ADEME (Agence de l’Environnement et de la Maîtrise de l’Energie). The authors thank the project leader INEO-SCLE-SFE and partners LEVISYS and CIRTEM.

References (28)

  • S. Reichelstein et al.

    The prospects for cost competitive solar PV power

    Energy Policy

    (2013)
  • R. Rigo-Mariani et al.

    Optimal power dispatching in smart microgrids with storage

    Renew. Sustainable Energy Rev.

    (2014)
  • M. Antonio, T. Clé, J. Maria, J. Policarpo, Design of experiments for sensitivity analysis of voltage sags variables,...
  • S. Bahramirad et al.

    Reliability-constrained optimal sizing of energy storage system in a microgrid

    Trans. Smart Grid

    (2012)
  • K. Basu, V. Debusshere, S. Bacha, Appliance usage prediction using a time series based classification approach, in:...
  • P. Bertsekas

    Dynamic Programming and Optimal Control

    (2000)
  • J. Bisshop

    Optimization Modeling

    (2012)
  • S. Bolognani, G. Cavraro, F. Cerruti, A. Costabeber, A linear dynamic model for microgrid voltages in presence of...
  • A. Campoccia, L. Dusonchet, E. Telaretti, G. Zizzo, Feed-in tariffs for gridconnected PV systems: the situation in the...
  • G. Celli, F. Pilo, G. Pisano, V. Allegranza, R. Cicoria, A. Iaria, Meshed vs. radial MV distribution network in...
  • T.F. Coleman et al.

    An interior trust region approach for nonlinear minimization subject to bounds

    SIAM J. Optim.

    (1996)
  • C.M. Colson, A review of challenges to real-time power management of microgrids, in: Power & Energy Society General...
  • C. Darras et al.

    Sizing of photovoltaic system coupled with hydrogen/oxygen storage based on the ORIENTE model

    Int. J. Hydrog. Energy

    (2010)
  • R. Gilbert et al.

    Sparse matrices in matlab: design and implementation

    J. Matrix Anal. Appl.

    (1992)
  • Cited by (14)

    • Developing optimal energy management of energy hub in the presence of stochastic renewable energy resources

      2021, Sustainable Energy, Grids and Networks
      Citation Excerpt :

      The optimization of renewable energy systems and ESSs have been done in a smart MG [5]. A fast power flow has been proposed in [6] to optimize an MG with storage. In [7], a methodology has been proposed to find a residential MG’s optimum capacity consisting of PV, wind units, diesel generators, and energy storage systems.

    • A day-ahead joint energy management and battery sizing framework based on θ-modified krill herd algorithm for a renewable energy-integrated microgrid

      2021, Journal of Cleaner Production
      Citation Excerpt :

      The MG’s primary frequency has been used in (Aghamohammadi and Abdolahinia, 2014) to efficiently determine the capacity of a BES system. The optimal power flow problem of MGs and sizing the storage systems has been solved in (Rigo-Mariani et al., 2017; Billionnet et al., 2016) within a mixed-integer linear programming framework. Meta-heuristic optimization methods have been utilized in (Sanajaoba and Fernandez, 2016; Zhang et al., 2017) to solve the optimal BES sizing problem, and the dynamic programming (DP) technique has been employed in (Nguyen et al., 2015; Rigo-Mariani et al., 2014) to solve the optimal dispatch problem of MGs, integrated with storage systems, both in the grid-tied and islanding modes.

    • Different aspects of microgrid management: A comprehensive review

      2020, Journal of Energy Storage
      Citation Excerpt :

      Energy management studies in the field of EV and HV include usage of vehicle batteries for management of renewable resources [25, 34, 64, 71, 82, 84], optimal parking lots [25, 68], controllable loads and demand response (DR) [38, 44, 64, 68, 71, 72, 82], optimize the size of components with EV scheduling [80], vehicle-to-home application to support the sustainable operation [131], plug-in EVs as a harmonic compensator and frequency control strategy [138, 140, 141, 173]. Furthermore, some of energy storages have been used for a special goal such as utilizing the FES for fast power flow scheduling, determining the size of microgrid and storage, voltage and frequency regulation [28, 55, 115]. As well, the supercapacitors (SCs) are considered for various proposes consisting of study the effects of poor service life of the batteries, optimal size and location and improve the charging/discharging process [49, 80, 113, 121, 124, 129, 146, 156].

    View all citing articles on Scopus
    View full text