# A Horizon Optimization Control Framework for the Coordinated Operation of Multiple Distributed Energy Resources in Low Voltage Distribution Networks

^{1}

^{2}

^{3}

^{4}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

- A decision tool which provides support to the DSO for the minimization of the operational costs based on the coordinated operation of multiple DER. The tool is capable of mitigating the regulating of nodal voltages, minimizing curtailments of active power by the microgeneration, ensuring nominal rated power for the secondary for all time instances. Multiple active measures are posed based on different DER technologies.
- A three-phase multi-period OPF framework based on the exact formulation of the AC power flow equations. The overall problem is resolved through a nonlinear optimization problem addressed interior-point method where efficient explicit calculation for the gradients of the constraints and the Hessian of the Lagrangian are proposed leaning on sparsities.
- Analytical inter-temporal constraints (i.e., providing the limitations of each type of DER) and the counterpart inter-temporal cost dependencies are discussed with their subsequent burdens. In particular, a technique is proposed to address singularity of Jacobian matrix (i.e., of the nonlinear problem) induced by the inter-temporal constraints.

## 2. Proposed Models for Distributed Energy Resources and Distribution Network Models

#### 2.1. Distribution Network Models (Lines and Transformer)

#### 2.2. Battery Energy Storage System (BESS)

#### 2.3. Electric Vehicles (EVs)

#### 2.4. Microgeneration ($\mu $G)

#### 2.5. Three-Phase Power Flow

## 3. Multi-Period AC-OPF (MACOPF) Formulation-Coordinated Control Scheme

#### 3.1. Interior-Point Primal-Dual Method for the Proposed Control Scheme

**iff**${g}_{E},{h}_{I}$ are first order differentiable) for a local optimum point ${p}^{\ast}=({\mathbf{x}}^{\ast},{\mathbf{\lambda}}^{\ast},{\mathbf{\sigma}}^{\ast},{\mathbf{s}}^{\ast})$ are the following:

#### 3.2. Gradients of Nonlinear Constraints and Hessian of Lagrangian

#### 3.3. Solution of Karush–Kuhn–Tucker Equations

#### 3.4. Intertemporal Couplings and Singular Jacobian

#### 3.5. Inter-Temporal Costs

## 4. Case Study Synopsis

- Initial SoC for all EV models is $So{C}_{0}$ = 0.5, which is meant to be the same at the end of the horizon $So{C}_{H\tau}=So{C}_{0}$.
- The charging efficiency and discharging—when V2G—efficiency are considered 85% for all EV models.

- “Dumb” charging or uncontrolled charging where the EVs are not incorporated within the proposed operational scheme. Such uncontrolled charing profiles are extracted using the data in probability density function presented in Figure 6b.
- “Smart” charging, where the EV owner communicates relevant data (i.e., flexibility as defined above) regarding their commute and accordingly its availability to be charged according to the proposed tool. The V2G mode services enable the option to utilize the EV essentially for grid services. These constraints are automatically incorporated in the multiperiod-OPF scheme as the generalized set of Equations (13d)–(13e), whenever the availability of the EV allows it. The availability of the EV to charge is considered along the day during their idle periods (i.e., parked at the owner’s house).

## 5. Results

#### 5.1. Cases C01–C03

#### 5.2. Cases C04–C06

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

DER | Distributed Energy Resources |

LV | Low Voltage |

OPF | Optimal Power Flow |

PV | Photovoltaic |

BESS | Battery Storage System |

EV | Electric Vehicles |

DSO | Distribution System Operator |

A-DMS | Advanced Distribution Management Systems |

CL | Controllable Loads |

OLTC | On Load Tap Changer |

MACOPF | Multiperiod AC-OPF |

IP | Interior-Point |

SoC | State-of-Charge |

V2G | Vehicle-to-Grid |

APC | Active Power Curtailment |

QR | Reactive Power Control |

BFS | Backward-Forward Sweep |

KKT | Karush–Kuhn–Tucker |

LICQ | Linear Constraint Qualification |

CQ | Constraint Qualification |

CCV | Cost Constrained Variable |

## Appendix A. Complementary Data for Case Study

Points of PVconnections | 522.2/388.1/178.2/ 676.2/639.2/337.3/ 701.3/614.3/562.1/ 682.2/70.1/556.3/ 629.1/47.2/349.1/ 563.1/264.3/458.3/ 249.2/289.1 | 611.1/74.1/320.3/ 73.1/276.2/225.1/ 327.3/387.1/619.3/ 702.2 | 702.2/502.1/342.3/ 208.3/539.3/ 688.2/406.2 | 248.2/83.2/314.2/ 896.1/785.2/900.1/ 899.2/755.2/780.3/ 898.1/813.2 |

Scenarios[% of PV] | 30% | |||

55% | ||||

65% | ||||

85% |

Points of EV connections | 327.3/835.3/785.2/563.1/ 755.2/249.2/225.1/47.2/ 886.2/898.1/314.2/208.3/ 906.1/861.1/320.3/682.2/ 780.3/406.2/817.1/248.2 | 619.3/860.1/702.2/ 458.3/899.2/264.3/ 178.2/83.2/337.3/ 556.3 | 73.1/349.1/701.3/ 522.2/342.3/289.1 |

Scenarios [% of EV] | 30% | ||

55% | |||

65% |

## Appendix B. First and Second Order Derivatives for Multi-Variable Function

## References

- Eid, C.; Codani, P.; Perez, Y.; Reneses, J.; Hakvoort, R. Managing electric flexibility from Distributed Energy Resources: A review of incentives for market design. Renew. Sustain. Energy Rev.
**2016**, 64, 237–247. [Google Scholar] [CrossRef] [Green Version] - Lotfi, M.; Monteiro, C.; Shafie-khah, M.; Catalão, J.P.S. Evolution of Demand Response: A Historical Analysis of Legislation and Research Trends. In Proceedings of the 2018 Twentieth International Middle East Power Systems Conference (MEPCON), Cairo, Egypt, 18–20 December 2018; pp. 968–973. [Google Scholar] [CrossRef]
- Ochoa, L.F.; Mancarella, P. Low-carbon LV networks: Challenges for planning and operation. In Proceedings of the 2012 IEEE Power and Energy Society General Meeting, San Diego, CA, USA, 22–26 July 2012; pp. 1–2. [Google Scholar]
- Bruno, S.; La Scala, M. Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV and LV Distribution Grids. In From Smart Grids to Smart Cities: New Challenges in Optimizing Energy Grids; Wiley: Hoboken, NJ, USA, 2016; pp. 1–42. [Google Scholar] [CrossRef]
- Control and Management Architectures. Smart Grid Handbook; Wiley: Hoboken, NJ, USA, 2016. [Google Scholar] [CrossRef]
- Karagiannopoulos, S.; Roald, L.; Aristidou, P.; Hug, G. Operational Planning of Active Distribution Grids under Uncertainty. Available online: http://eprints.whiterose.ac.uk/120043/ (accessed on 7 January 2018).
- Bruno, S.; Lamonaca, S.; Rotondo, G.; Stecchi, U.; La Scala, M. Unbalanced three-phase optimal power flow for smart grids. IEEE Trans. Ind. Electron.
**2011**, 58, 4504–4513. [Google Scholar] [CrossRef] - Faria, P.; Spínola, J.; Vale, Z. Distributed Energy Resources Scheduling and Aggregation in the Context of Demand Response Programs. Energies
**2018**, 11, 1987. [Google Scholar] [CrossRef] - Soares, T.; Silva, M.; Sousa, T.; Morais, H.; Vale, Z. Energy and Reserve under Distributed Energy Resources Management—Day-Ahead, Hour-Ahead and Real-Time. Energies
**2017**, 10, 1778. [Google Scholar] [CrossRef] - Tonkoski, R.; Lopes, L.A.C.; El-Fouly, T.H.M. Coordinated Active Power Curtailment of Grid Connected PV Inverters for Overvoltage Prevention. IEEE Trans. Sustain. Energy
**2011**, 2, 139–147. [Google Scholar] [CrossRef] - Weckx, S.; Gonzalez, C.; Driesen, J. Combined Central and Local Active and Reactive Power Control of PV Inverters. IEEE Trans. Sustain. Energy
**2014**, 5, 776–784. [Google Scholar] [CrossRef] - Demirok, E.; González, P.C.; Frederiksen, K.H.B.; Sera, D.; Rodriguez, P.; Teodorescu, R. Local Reactive Power Control Methods for Overvoltage Prevention of Distributed Solar Inverters in Low-Voltage Grids. IEEE J. Photovolt.
**2011**, 1, 174–182. [Google Scholar] [CrossRef] - Heleno, M.; Rua, D.; Gouveia, C.; Madureira, A.; Matos, M.A.; Lopes, J.P.; Silva, N.; Salustio, S. Optimizing PV self-consumption through electric water heater modeling and scheduling. In Proceedings of the 2015 IEEE Eindhoven PowerTech, Eindhoven, The Netherlands, 29 June–2 July 2015; pp. 1–6. [Google Scholar] [CrossRef]
- Olivier, F.; Aristidou, P.; Ernst, D.; Van Cutsem, T. Active Management of Low-Voltage Networks for Mitigating Overvoltages Due to Photovoltaic Units. IEEE Trans. Smart Grid
**2016**, 7, 926–936. [Google Scholar] [CrossRef] - Degroote, L.; Renders, B.; Meersman, B.; Vandevelde, L. Neutral-point shifting and voltage unbalance due to single-phase DG units in low voltage distribution networks. In Proceedings of the 2009 IEEE Bucharest PowerTech, Bucharest, Romania, 28 June–2 July 2009; pp. 1–8. [Google Scholar] [CrossRef]
- Miranda, I.; Leite, H.; Silva, N. Coordination of multifunctional distributed energy storage systems in distribution networks. IET Gener. Transm. Distrib.
**2016**, 10, 726–735. [Google Scholar] [CrossRef] - Fortenbacher, P.; Zellner, M.; Andersson, G. Optimal sizing and placement of distributed storage in low voltage networks. In Proceedings of the 2016 Power Systems Computation Conference (PSCC), Genoa, Italy, 20–24 June 2016; pp. 1–7. [Google Scholar] [CrossRef]
- Hoppmann, J.; Volland, J.; Schmidt, T.S.; Hoffmann, V.H. The economic viability of battery storage for residential solar photovoltaic systems—A review and a simulation model. Renew. Sustain. Energy Rev.
**2014**, 39, 1101–1118. [Google Scholar] [CrossRef] - European Union. Directive 2009/72/EC of the European Parliament and of the Council of 13 July 2009 Concerning Common Rules for the Internal Market in Electricity and Repealing Directive 2003/54/EC. Off. J. Eur. Union
**2009**, 211, 55–93. [Google Scholar] - Efkarpidis, N.; De Rybel, T.; Driesen, J. Optimization control scheme utilizing small-scale distributed generators and OLTC distribution transformers. Sustain. Energy Grids Netw.
**2016**, 8, 74–84. [Google Scholar] [CrossRef] - Costa, H.M.; Sumaili, J.; Madureira, A.G.; Gouveia, C. A multi-temporal optimal power flow for managing storage and demand flexibility in LV networks. In Proceedings of the 2017 IEEE Manchester PowerTech, Manchester, UK, 18–22 June 2017; pp. 1–6. [Google Scholar] [CrossRef]
- Olival, P.C.; Madureira, A.G.; Matos, M. Advanced voltage control for smart microgrids using distributed energy resources. Electr. Power Syst. Res.
**2017**, 146, 132–140. [Google Scholar] [CrossRef] - Madureira, A.; Gouveia, C.; Moreira, C.; Seca, L.; Lopes, J.P. Coordinated management of distributed energy resources in electrical distribution systems. In Proceedings of the 2013 IEEE PES Conference on Innovative Smart Grid Technologies (ISGT Latin America), Sao Paulo, Brazil, 5–17 April 2013; pp. 1–8. [Google Scholar] [CrossRef]
- Kotsalos, K.; Silva, N.; Miranda, I.; Leite, H. Scheduling of operation in Low Voltage distribution networks with multiple Distributed Energy Resources. In Proceedings of the CIRED Workshop, Ljubljana, Slovenia, 7–8 June 2018. [Google Scholar]
- Connell, A.O.; Flynn, D.; Keane, A. Rolling Multi-Period Optimization to Control Electric Vehicle Charging in Distribution Networks. IEEE Trans. Power Syst.
**2014**, 29, 340–348. [Google Scholar] [CrossRef] - Campos, F.; Marques, L.; Kotsalos, K. Electric Vehicle CPMS and Secondary Substation Management. In Proceedings of the 8th Solar & 17th Wind Integration Workshop, Stockholm, Sweden, 16–17 October 2018. [Google Scholar]
- Efkarpidis, N.; De Rybel, T.; Driesen, J. Technical assessment of centralized and localized voltage control strategies in low voltage networks. Sustain. Energy Grids Netw.
**2016**, 8, 85–97. [Google Scholar] [CrossRef] - Sperstad, I.B.; Marthinsen, H. Optimal Power Flow Methods and Their Application to Distribution Systems with Energy Storage: A Survey of Available Tools and Methods; SINTEF Energi. Rapport; SINTEF: Trondheim, Norway, 2016. [Google Scholar]
- Sereeter, B.; Vuik, K.; Witteveen, C. Newton Power Flow Methods for Unbalanced Three-Phase Distribution Networks. Energies
**2017**, 10, 1658. [Google Scholar] [CrossRef] - Karagiannopoulos, S.; Aristidou, P.; Hug, G. Co-optimisation of Planning and Operation forActive Distribution Grids. In Proceedings of the 2017 IEEE Manchester PowerTech, Manchester, UK, 18–22 June 2017. [Google Scholar]
- Christakou, K.; Tomozei, D.C.; Le Boudec, J.Y.; Paolone, M. AC OPF in radial distribution networks–Part I: On the limits of the branch flow convexification and the alternating direction method of multipliers. Electr. Power Syst. Res.
**2017**, 143, 438–450. [Google Scholar] [CrossRef] - Ciric, R.M.; Feltrin, A.P.; Ochoa, L.F. Power flow in four-wire distribution networks-general approach. IEEE Trans. Power Syst.
**2003**, 18, 1283–1290. [Google Scholar] [CrossRef] [Green Version] - Cheng, C.S.; Shirmohammadi, D. A three-phase power flow method for real-time distribution system analysis. IEEE Trans. Power Syst.
**1995**, 10, 671–679. [Google Scholar] [CrossRef] - Bazrafshan, M.; Gatsis, N. Comprehensive Modeling of Three-Phase Distribution Systems via the Bus Admittance Matrix. IEEE Trans. Power Syst.
**2018**, 33, 2015–2029. [Google Scholar] [CrossRef] [Green Version] - Gorman, M.; Grainger, J. Transformer modelling for distribution system studies. II. Addition of models to Y/sub BUS/and Z/sub BUS. IEEE Trans. Power Deliv.
**1992**, 7, 575–580. [Google Scholar] [CrossRef] - Shirmohammadi, D.; Hong, H.W.; Semlyen, A.; Luo, G.X. A compensation-based power flow method for weakly meshed distribution and transmission networks. IEEE Trans. Power Syst.
**1988**, 3, 753–762. [Google Scholar] [CrossRef] - Kourounis, D.; Fuchs, A.; Schenk, O. Towards the Next Generation of Multiperiod Optimal Power Flow Solvers. IEEE Trans. Power Syst.
**2018**. [Google Scholar] [CrossRef] - Nocedal, J.; Wright, S.J. Numerical Optimization, 2nd ed.; Springer: New York, NY, USA, 2006; pp. 497–528. [Google Scholar]
- Zhu, J. Optimization of Power System Operation; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2015; pp. 1–12. [Google Scholar] [CrossRef]
- Wachter, A. An Interior Point Algorithm for Large-Scale Nonlinear Optimization with Applications in Process Engineering. Ph.D. Thesis, Carnegie Mellon University, Pittsburgh, PA, USA, 2003. [Google Scholar]
- Hauswirth, A.; Bolognani, S.; Hug, G.; Dörfler, F. Generic Existence of Unique Lagrange Multipliers in AC Optimal Power Flow. arXiv, 2018; arXiv:1806.06615. [Google Scholar] [CrossRef]
- Torres, G.L.; Quintana, V.H. An interior-point method for nonlinear optimal power flow using voltage rectangular coordinates. IEEE Trans. Power Syst.
**1998**, 13, 1211–1218. [Google Scholar] [CrossRef] - Wächter, A.; Biegler, L.T. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program.
**2006**, 106, 25–57. [Google Scholar] [CrossRef] - Coleman, T.; Branch, M.A.; Grace, A. Optimization toolbox. In For Use with MATLAB. User’s Guide for MATLAB 5, Version 2, Relaese II; MATLAB, MathWorks: Natick, MA, USA, 1999. [Google Scholar]
- Zimmerman, R.D. AC Power Flows, Generalized OPF Costs and Their Derivatives Using Complex Matrix Notation; Report; PSERC: Tempe, AZ, USA, 2010. [Google Scholar]
- Frank, S.; Rebennack, S. An introduction to optimal power flow: Theory, formulation, and examples. IIE Trans.
**2016**, 48, 1172–1197. [Google Scholar] [CrossRef] - Wood, A.J.; Wollenberg, B.F.; Sheblé, G.B. Power Generation, Operation, and Control, 3rd ed.; John Wiley & Sons: Hoboken, NJ, USA, 2013; book section 8. [Google Scholar]
- Gilbert, J.C.; Josz, C. Plea for a Semidefinite Optimization Solver in Complex Numbers. Available online: https://hal.inria.fr/hal-01497173/document (accessed on 28 January 2018).
- Baker, K.; Hug, G.; Xin, L. Inclusion of inter-temporal constraints into a distributed Newton-Raphson method. In Proceedings of the 2012 North American Power Symposium (NAPS), Boston, MA, USA, 4–6 August 2011; pp. 1–6. [Google Scholar] [CrossRef]
- Baker, K.; Zhu, D.; Hug, G.; Li, X. Jacobian singularities in optimal power flow problems caused by intertemporal constraints. In Proceedings of the 2013 North American Power Symposium (NAPS), Manhattan, KS, USA, 22–24 September 2013; pp. 1–6. [Google Scholar] [CrossRef]
- Espinosa, A.N. Dissemination Document “Low Voltage Networks Models and Low Carbon Technology Profiles”; The University of Manchester: Manchester, UK, 2015. [Google Scholar]
- Palizban, O.; Kauhaniemi, K. Energy storage systems in modern grids—Matrix of technologies and applications. J. Energy Storage
**2016**, 6, 248–259. [Google Scholar] [CrossRef] - Osório, G.; Shafie-khah, M.; Coimbra, P.; Lotfi, M.; Catalão, J. Distribution system operation with electric vehicle charging schedules and renewable energy resources. Energies
**2018**, 11, 3117. [Google Scholar] [CrossRef] - Efacec. EV Homecharger. Available online: http://electricmobility.efacec.com/wp-content/uploads/2016/10/CS195I1404C1_HC.pdf (accessed on 16 November 2018).
- Survey, N.T. National Travel Survey: England 2016; Report; National Travel Survey: Great Britain, UK, 2016.
- Pedersen, R.; Sloth, C.; Andresen, G.B.; Wisniewski, R. DiSC: A simulation framework for distribution system voltage control. In Proceedings of the 2015 European Control Conference (ECC), Linz, Austria, 15–17 July 2015; pp. 1056–1063. [Google Scholar]
- Richardson, P.; Moran, M.; Taylor, J.; Maitra, A.; Keane, A. Impact of electric vehicle charging on residential distribution networks: An Irish demonstration initiative. In Proceedings of the 22nd International Conference and Exhibition on Electricity Distribution (CIRED 2013), Stockholm, Sweden, 10–13 June 2013; Volume 2013, pp. 1–4. [Google Scholar] [CrossRef]
- Masetti, C. Revision of European Standard EN 50160 on power quality: Reasons and solutions. In Proceedings of the 2010 14th International Conference on Harmonics and Quality of Power (ICHQP), Bergamo, Italy, 26–29 September 2010; pp. 1–7. [Google Scholar]

**Figure 2.**Structure of optimization variables; discriminated by state vector, control variables and the auxiliary variables per each time step.

**Figure 3.**Cost function functions. (

**a**) cost function for utilizing a BESS-owned by the DSO; (

**b**) cost of active power curtailment; (

**c**) cost function of reactive power control for microgeneration; (

**d**) cost function of an EV with V2G operation.

**Figure 4.**The IEEE European LV benchmark network. Fifty-five consumers are connected to this case network.

**Figure 5.**Data profiles: (

**a**) load profiles; and (

**b**) micro-generation profiles using seasonal (e.g., summer profiles) and regional data.

**Figure 6.**Data profiles: (

**a**) trips in progress along a week. and (

**b**) probability density function for EV charging demand, used for the dumb charging scenarios (source: [57]).

**Figure 7.**State of the trip for Electric Vehicles used along the simulation period. Profiles were extracted for a summer week day.

**Figure 8.**Incremental integration of EV scenarios: (

**a**) minimum voltage range over all phases and buses and (

**b**) secondary transformer loading for each case of EV integration (the increase in loading is observed up to 120%).

**Figure 9.**Incremental integration of EV scenarios: (

**a**) minimum voltage range over all phases and buses and (

**b**) secondary transformer loading for each case of EV integration (the increase in loading is observable up to 120%).

**Figure 10.**Incremental integration of PV, Cases 01–03: (

**a**) Case 01; (

**b**) Case 01, solely APC was selected within the controller; (

**c**) Case 02; (

**d**) Case 03.

**Figure 11.**Control set-points and SoC derived by the MACOPF for centralized three-phase ${\mathrm{BESS}}_{101}$ for: (

**a**) Case 01; (

**b**) Case 02; (

**c**) Case 03.

**Figure 12.**Secondary transformer loading conditions for Cases 01–03, overloaded conditions are noticed due to reversed power injected by microgeneration units; admissible conditions are obtained applying the proposed coordinated operation.

**Figure 13.**Case 04: (

**a**) resulting voltage ranges and actions yielded for BESS${}_{101}$; (

**b**) control set-points and SoC for BESS${}_{101}$.

**Figure 14.**Case 05: (

**a**) resulting voltage ranges, coordinated charging in comparison with dumb charging; BESS${}_{101}$ scheduling of operation and V2G actions; (

**b**) SoC for all EVs; circled by red line correspond to V2G mode of operation.

**Figure 15.**Case 06: (

**a**) resulting voltage ranges, coordinated charging in comparison with dumb charging; BESS${}_{101}$ scheduling of operation and V2G actions; (

**b**) SoC for all EVs, circled with a red line, correspond to V2G mode of operation.

EV Model | Battery Capacity [kWh] | Charging Power [kW] | Driving Efficiency (km/kWh) | End-User Owner |
---|---|---|---|---|

Nissan Leaf | 24 | 4 | 6.7 | 249.2/861.1/264.3/522.2 |

Chevrolet Volt | 16 | 3.75 | 3.75 | 327.3/755.2/886.2/906.3/780.3/ 619.3/899.2/337.3/701.3 |

BMW i3 | 22 | 11 | 7.2 | 785.2/225.1/314.2/320.3/ 817.3/702.2/178.2/73.1/342.3 |

Tesla S | 60 | 11 | 6.7 | 563.1/47.2/208.3/682.2/406.2/ 248.2/458.3/83.2/349.1/289.1 |

Scenario | Case 01 (C1) | Case 02 (C2) | Case 03 (C3) | Case 04 (C4) | Case 05 (C5) | Case 06 (C6) |
---|---|---|---|---|---|---|

EV [%] | 0 | 0 | 0 | 35 | 55 | 65 |

PV [%] | 55 | 73 | 85 | 0 | 0 | 55 |

BESS 101 | ✔ | ✔ | ✔ | ✔ | ✔ | ✔ |

**Table 3.**Resulting curtailed active power and dispatched reactive power for the microgeneration units.

Scenario | Curtailed Energy [kWh] | Reactive Energy [kVArh] |
---|---|---|

Case 01 | 0 | 3.94 |

Case 02 | 0 | 7.43 |

Case 03 | 34.5 | 59.3 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kotsalos, K.; Miranda, I.; Silva, N.; Leite, H.
A Horizon Optimization Control Framework for the Coordinated Operation of Multiple Distributed Energy Resources in Low Voltage Distribution Networks. *Energies* **2019**, *12*, 1182.
https://doi.org/10.3390/en12061182

**AMA Style**

Kotsalos K, Miranda I, Silva N, Leite H.
A Horizon Optimization Control Framework for the Coordinated Operation of Multiple Distributed Energy Resources in Low Voltage Distribution Networks. *Energies*. 2019; 12(6):1182.
https://doi.org/10.3390/en12061182

**Chicago/Turabian Style**

Kotsalos, Konstantinos, Ismael Miranda, Nuno Silva, and Helder Leite.
2019. "A Horizon Optimization Control Framework for the Coordinated Operation of Multiple Distributed Energy Resources in Low Voltage Distribution Networks" *Energies* 12, no. 6: 1182.
https://doi.org/10.3390/en12061182