Optimal Power Dispatch in Energy Systems Considering Grid Constraints
1.2. Optimization of Energy Systems
2.1. Overview: Iterative Process
- Energy system structure: Here, the energy sectors to be considered are defined as well as the relevant technologies and their models. Natural renewable resources and demands time series must also be included. Time steps have to be big enough to make valid the steady-state assumption of the different energy sectors . In this work, only the electric and heat sector are considered and a time step of an hour during a year is evaluated. Although several technologies, markets, and demands could be present in a distributed energy system , only the ones presented in Table 1 were considered in this study. Furthermore, the energy system is seen as a system aggregator from the grid perspective. This means that the system can buy and sell electricity in the market.
- Linear unit commit: Using a holistic approach, an abstraction of the energy system structure is created in oemof-Solph. This abstraction contains all possible energy flows between sources and sinks, and between energy sectors through the coupling technologies as depicted in Figure 2.Costs and additional constraints can be associated with each of the energy flows . Here, the system will only consider the economical constraints of the energy flows. Therefore, the objective function is the cost minimization. From Equation (1), the following objective equation is derived for the considered energy system:In Equations (7) and (8), the parameters and refer to the PV generation and the CHP electric power generation within the system, whereas the parameters , , , and refer to the electric demand, the battery power consumption, electrical vehicle charging, and the heat pump demand, respectively. Every storage unit (including EVs) has been considered as a load. That means that a negative power represents a power injection to the system. The same convention has been used for the external grid power flow. As constraints for the optimization problem, the thermal and electric demands must be supplied at any time. Equations (9) and (10) depict such constraints where , , and are fixed time series.As a result, the optimized power dispatch for each non-fixed source to supply the demand at each time step is obtained. However, up to this point, just the total installed capacities and demands have been considered as per the inequality (4). The actual topology of the electrical and thermal grid has been also disregarded as a common practice in the optimization of energy systems .
- Grid topology consideration: Before integrating these flows into the electrical grid in PowerFactory, the flow distribution must be considered. This applies only to the electric sources, sinks, and sector coupling technologies. The distribution of heat technologies is disregarded since only the electrical grid topology is being considered in this study.To represent a typical low voltage grid, one of the so-called “Merit Order Netz-Ausbau 2030” (MONA) reference grids is used. The ONT_8003 grid model is used as reference  and depicted in Figure 3. This topology represents a typical low voltage grid in Germany.The energy flows for each node per technology are derived from the optimization results and the capacity installed per building.
- Power flow calculation: Once the flow distributions at each node have been obtained, these energy flows must be added as time characteristics to the corresponding elements in PowerFactory.To determine if the optimized dispatch complies with the grid standards, a quasi-dynamic power flow (QDPF) study is performed for a year with 1 h time steps. From the results of the QDPF, lines exceeding 100% loading and voltage variation outside of the range of of the nominal voltage are considered as grid violations .The time steps containing such violations will be re-optimized by PowerFactory to avoid line congestion and bus voltage violations. For the system to converge, a dispatchable source is considered as slack, so it has enough power to cover the demand in case that the renewable sources are curtailed due to system violations.
- Constraints generation: Similar to the constraint generation for the linear optimization , the oemof-Solph model will be limited by constraints generated from the OPF as denoted in Equation (4). Power time-series are the link between the two tools. Therefore, PowerFactory and oemof-Solph will exchange information about the active power flows, being the reactive power flow after the last OPF calculation considered as optimal.To build the OPF problem, the following objective function and constraints are considered:In Equation (11), the term for the thermal boiler is not considered. This is due to the fact that only electric units are taken into consideration in the OPF. The set is a sub set of T comprising only the periods of time that led to grid violations from step 4. The variables and denote the optimized power flows to avoid such violations. The constraints (12) and (13) ensure that the nominal capacity of any line of the system is not violated by the actual power flow . The set of all lines in the energy system is denoted by L. The actual power flow in the line is given by the square root of the sum of squares of the real power and the reactive power . To ensure voltage compliance, the constraint (14) is included. This keeps the voltage magnitude of all buses in the system, denoted by the set B, within of the nominal voltage . The constraint (15) limits the power that can be drawn by the batteries. The difference between the battery system capacity and the battery system energy content at the previous time-step provides the available energy to be drawn for charging the batteries. The energy content is provided from the linear optimization performed in step 2. The difference is divided by in order to get the charging power limit. A lower energy bound is given to allow the discharge of the batteries. This lower bound is equal to the negative of the energy content. In the OPF additional flexibility is provided with the PV system. The optimizer can reduce the power output as per constraint (16). Furthermore, to keep the thermal limits of all technologies within acceptable ranges, constraint (17) is included. Where the apparent power of each technology of the set N must not exceed the nominal apparent power . Similarly to the linear optimization, constraint (10) must be complied by the OPF, therefore:In Equation (18), the superscript denotes the power flow obtained from the OPF from the respective source or sink. Considering that and , Equations (18) and (9) can be combined to yield:Equation (19) shows how the changes in the OPF have to be compensated by the heat elements in the energy system. However, as previously indicated, the OPF only takes into consideration the electric components and the sector coupling technologies. Therefore, the changes in the OPF have to be reflected in the linear optimization. Equation (20) is employed to determine the deviation between the OPF and the initial power flow.The power flow per technology resulting from the OPF is represented by , whereas the initial power from the linear optimization is represented by . Whenever , the value of the OPF is passed as an upper bound in (4) for the linear optimization in the next iteration.
2.2. Evaluation Scenarios
- High generation scenario: The size of the PV installation is fixed to 1500 kWp and no storage or flexible loads are considered. The influence of line loading and voltage levels in the optimization is evaluated.
- Heat pump and heat storage scenario: The influence of heat pump and heat storage is analyzed. Here, the size of the PV installation is reduced to 700 kW. Heat pumps and heat storage are added with 600 kWth and 150 m of capacity, respectively. The potential for flexibilization services from the heat sector is evaluated in this scenario through the implementation of the proposed method.
- Electromobility scenario: A fleet of 62 EVs and 500 kWh of battery storage are added to the Heat pump and heat storage scenario. These are connected at eight different points within the network. It is assumed that the EVs are only connected from 6 p.m. to 7 a.m. of the next day . Additionally, it is assumed that the daily required demand of the EVs is around 10 kWh, which is approximately the double required per EV per day . Therefore, the state of charge is not the constraint for charging at the end of the charging period in the optimization, but to ensure enough daily coverage in a daily basis.
3.1. High Generation Scenario
3.1.1. Line Loading Constraint
3.1.2. Voltage Constraint
3.2. Heat Pump and Heat Storage
3.3. Electromobility Scenario
5. Summary and Outlook
- For scenarios with PV capacity above 5 kWp per household, the voltage and line loading constraints are violated, therefore affecting the optimization results. In the case study, curtailment of ∼60 MWh/year is needed to keep the grid within its limits. This due to the lack of storage or flexibilization options.
- If flexible technologies are present, parameters as curtailment and self consumption are affected by the grid constraints. In the case study, the self-consumption can increase and the curtailment be reduced by as compared with the typical optimization without grid constraints. The method successfully integrated the additional load from the heat pumps and EV without grid violations.
- In comparison to other approaches, the decoupled constraint generation in the optimization problem determines the techno-economical power dispatch for all the different energy sectors and storage technologies.
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
- United Nations Framework Convention on Climate Change (UNFCCC). The Paris Agreement. 2015. Available online: https://unfccc.int/process-and-meetings/the-paris-agreement/the-paris-agreement (accessed on 19 May 2021).
- Agora Energiewende. Energiewende: What do the new laws mean. In Ten Questions and Answers about EEG; Agora Energiewende: Berlin, Germany, 2017; Available online: https://www.agora-energiewende.de/en/publications/energiewende-what-do-the-new-laws-mean/ (accessed on 25 December 2021).
- Bundesministerium für Umwelt, Naturschutz und nukleare Sicherheit. Climate Action in Figures-Facts, Trends and Incentives for German Climate Policy; Federal Ministry for the Environment, Nature Conservation and Nuclear Safety (BMU): Berlin, Germany, 2018. [Google Scholar]
- David, A.; Mathiesen, B.V.; Averfalk, H.; Werner, S.; Lund, H. Heat roadmap Europe: Large-scale electric heat pumps in district heating systems. Energies 2017, 10, 578. [Google Scholar] [CrossRef][Green Version]
- Sensfuß, F.; Deac, G.; Bernath, C. Vorabanalyse Langfristige Rolle und Modernisierung der Kraft-Wärme-Kopplung; Kurzpapier. Hg. v. Bundesministerium für Wirtschaft und Energie BMWI: Berlin, Germany, 2017. [Google Scholar]
- Jochem, P.; Babrowski, S.; Fichtner, W. Assessing CO2 emissions of electric vehicles in Germany in 2030. Transp. Res. Part A Policy Pract. 2015, 78, 68–83. [Google Scholar] [CrossRef][Green Version]
- Jain, P.; Jain, T. Assessment of electric vehicle charging load and its impact on electricity market price. In Proceedings of the 2014 International Conference on Connected Vehicles and Expo (ICCVE), Vienna, Austria, 3–7 November 2014; pp. 74–79. [Google Scholar] [CrossRef]
- Arnold, M.; Friede, W.; Myrzik, J. Investigations in low voltage distribution grids with a high penetration of distributed generation and heat pumps. In Proceedings of the 2013 48th International Universities’ Power Engineering Conference (UPEC), Dublin, Ireland, 2–5 September 2013; pp. 1–6. [Google Scholar] [CrossRef]
- Bayer, B.; Matschoss, P.; Thomas, H.; Marian, A. The German experience with integrating photovoltaic systems into the low-voltage grids. Renew. Energy 2018, 119, 129–141. [Google Scholar] [CrossRef]
- Energetisches Nachbarschaftsquartier Fliegerhorst Oldenburg. Available online: https://www.enaq-fliegerhorst.de/ (accessed on 28 April 2021).
- Fortenbacher, P.; Ulbig, A.; Koch, S.; Andersson, G. Grid-constrained optimal predictive power dispatch in large multi-level power systems with renewable energy sources, and storage devices. In Proceedings of the IEEE PES Innovative Smart Grid Technologies, Europe, Istanbul, Turkey, 12–15 October 2014; pp. 1–6. [Google Scholar] [CrossRef]
- Zargar, B.; Monti, A.; Ponci, F.; Martí, J.R. Linear Iterative Power Flow Approach Based on the Current Injection Model of Load and Generator. IEEE Access 2020, 9, 11543–11562. [Google Scholar] [CrossRef]
- Handschin, E.; Kuhn, S.; Rehtanz, C.; Schultz, R.; Waniek, D. Optimaler Kraftwerkseinsatz in Netzengpasssituationen. Innovative Modellierung und Optimierung von Energiesystemen; LIT: Berlin, Germany, 2009; pp. 39–68. ISBN 978-3-8258-1359-8. [Google Scholar]
- Liu, Y.; Zhang, N.; Wang, Y.; Yang, J.; Kang, C. Data-driven power flow linearization: A regression approach. IEEE Trans. Smart Grid 2018, 10, 2569–2580. [Google Scholar] [CrossRef][Green Version]
- De Novoa, M.; Martinez, L. Optimal Solar PV, Battery Storage, and Smart-Inverter Allocation in Zero-Net-Energy Microgrids Considering the Existing Power System Infrastructure. Ph.D. Thesis, UC Irvine, Irvine, CA, USA, 2020. [Google Scholar]
- Jiang, M.; Guo, Q.; Sun, H.; Ge, H. Decoupled piecewise linear power flow and its application to under voltage load shedding. CSEE J. Power Energy Syst. 2020, 7, 976–985. [Google Scholar]
- Nolden, C.; Schönfelder, M.; Eßer-Frey, A.; Bertsch, V.; Fichtner, W. Network constraints in techno-economic energy system models: Towards more accurate modeling of power flows in long-term energy system models. Energy Syst. 2013, 4, 267–287. [Google Scholar] [CrossRef][Green Version]
- Lohmeier, D.; Cronbach, D.; Drauz, S.R.; Braun, M.; Kneiske, T.M. Pandapipes: An Open-Source Piping Grid Calculation Package for Multi-Energy Grid Simulations. Sustainability 2020, 12, 9899. [Google Scholar] [CrossRef]
- Geidl, M.; Andersson, G. Optimal power flow of multiple energy carriers. IEEE Trans. Power Syst. 2007, 22, 145–155. [Google Scholar] [CrossRef]
- Levron, Y.; Guerrero, J.M.; Beck, Y. Optimal power flow in microgrids with energy storage. IEEE Trans. Power Syst. 2013, 28, 3226–3234. [Google Scholar] [CrossRef][Green Version]
- Acha, S.; Green, T.C.; Shah, N. Techno-economical tradeoffs from embedded technologies with storage capabilities on electric and gas distribution networks. In Proceedings of the IEEE PES General Meeting, Minneapolis, MN, USA, 25–29 July 2010; pp. 1–8. [Google Scholar] [CrossRef]
- Qadrdan, M.; Ameli, H.; Strbac, G.; Jenkins, N. Efficacy of options to address balancing challenges: Integrated gas and electricity perspectives. Appl. Energy 2017, 190, 181–190. [Google Scholar] [CrossRef][Green Version]
- Hilpert, S.; Kaldemeyer, C.; Krien, U.; Günther, S.; Wingenbach, C.; Plessmann, G. The Open Energy Modelling Framework (oemof)-A new approach to facilitate open science in energy system modelling. Energy Strategy Rev. 2018, 22, 16–25. [Google Scholar] [CrossRef][Green Version]
- Gonzalez-Longatt, F.; Torres, J.L.R. Advanced Smart Grid Functionalities Based on Powerfactory; Springer: Berlin/Heidelberg, Germany, 2018. [Google Scholar] [CrossRef]
- Schmeling, L.; Schönfeldt, P.; Klement, P.; Wehkamp, S.; Hanke, B.; Agert, C. Development of a decision-making framework for distributed energy systems in a German district. Energies 2020, 13, 552. [Google Scholar] [CrossRef][Green Version]
- Forschungsstelle für Energiewirtschaft e.V. (FfE) CC BY 4.0. Basisnetztopologien MONA 2030. Available online: https://www.ffe.de/themen-und-methoden/speicher-und-netze/752-ffe-stellt-rechenfaehige-basisnetztopologien-aus-projekt-mona-2030-zur-verfuegung (accessed on 28 April 2021).
- Ben-Ameur, W.; Neto, J. A constraint generation algorithm for large scale linear programs using multiple-points separation. Math. Program. 2006, 107, 517–537. [Google Scholar] [CrossRef]
- Clement-Nyns, K.; Haesen, E.; Driesen, J. The impact of charging plug-in hybrid electric vehicles on a residential distribution grid. IEEE Trans. Power Syst. 2009, 25, 371–380. [Google Scholar] [CrossRef][Green Version]
- Passey, R.; Spooner, T.; MacGill, I.; Watt, M.; Syngellakis, K. The potential impacts of grid-connected distributed generation and how to address them: A review of technical and non-technical factors. Energy Policy 2011, 39, 6280–6290. [Google Scholar] [CrossRef]
- Mies, J.J.; Helmus, J.R.; Van den Hoed, R. Estimating the charging profile of individual charge sessions of Electric Vehicles in the Netherlands. World Electr. Veh. J. 2018, 9, 17. [Google Scholar] [CrossRef][Green Version]
- Hilpert, S. Effects of Decentral Heat Pump Operation on Electricity Storage Requirements in Germany. Energies 2020, 13, 2878. [Google Scholar] [CrossRef]
- Rubio, A.; Behrends, H.; Geißendörfer, S.; Maydell, K.v.; Agert, C. Determination of the required power response of inverters to provide fast frequency support in power systems with low synchronous inertia. Energies 2020, 13, 816. [Google Scholar] [CrossRef][Green Version]
- Ceseña, E.A.M.; Loukarakis, E.; Good, N.; Mancarella, P. Integrated Electricity–Heat–Gas Systems: Techno–Economic Modeling, Optimization, and Application to Multienergy Districts. Proc. IEEE 2020, 108, 1392–1410. [Google Scholar] [CrossRef]
- Huang, Z.; Fang, B.; Deng, J. Multi-objective optimization strategy for distribution network considering V2G-enabled electric vehicles in building integrated energy system. Prot. Control Mod. Power Syst. 2020, 5, 1–8. [Google Scholar] [CrossRef][Green Version]
- Clegg, S.; Mancarella, P. Integrated electrical and gas network flexibility assessment in low-carbon multi-energy systems. IEEE Trans. Sustain. Energy 2015, 7, 718–731. [Google Scholar] [CrossRef]
- Auer, S.; Liße, J.; Mandha, S.R.; Horn, C. Power-Flow-Constrained Asset Optimization for Off-Grid Power Systems Using Selected Open-Source Frameworks. In Proceedings of the 4th International Hybrid Power Systems Workshop, Crete, Greece, 22–23 May 2019. [Google Scholar]
- Pineda, S.; Morales, J.M.; Jiménez-Cordero, A. Data-driven screening of network constraints for unit commitment. IEEE Trans. Power Syst. 2020, 35, 3695–3705. [Google Scholar] [CrossRef][Green Version]
|Photovoltaic (PV)||Natural Gas||Battery||Heat Pump||Electricity|
|Cogeneration (CHP)||Electricity||Hot Water Storage||CHP||Heat|
|Without Grid Constraints||With Grid Constraints||Without Grid Constraints||With Grid Constraints|
|High PV Generation||288.60||288.60||270.04||270.04||0|
|Source||Considered Energy Carriers||Storage Technology||Grid Constraints||Approach|
|Cesena et al. ||Gas, heat, and power||Building heat inertia||Gas and power||MILP with heuristic penalization of grid constraints|
|Huang et al. ||Electromobility and power||EV battery||Power||Optimal EV charging scheduling through a genetic algorithm|
|Clegg et al. ||Gas, heat and power||—||Gas||Determination of flexibility according to gas availability and DC-OPF|
|Nolden et al. ||Power||—||Power||Unit commitment and power flow solver to achieve a techno-economic dispatch|
|This research||Electromobility, heat, gas, and power||Battery storage, EV battey, and heat storage||Power||MILP with iterative grid constraint generation|
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.
© 2021 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 (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Rubio, A.; Schuldt, F.; Klement, P.; von Maydell, K. Optimal Power Dispatch in Energy Systems Considering Grid Constraints. Energies 2022, 15, 192. https://doi.org/10.3390/en15010192
Rubio A, Schuldt F, Klement P, von Maydell K. Optimal Power Dispatch in Energy Systems Considering Grid Constraints. Energies. 2022; 15(1):192. https://doi.org/10.3390/en15010192Chicago/Turabian Style
Rubio, Alejandro, Frank Schuldt, Peter Klement, and Karsten von Maydell. 2022. "Optimal Power Dispatch in Energy Systems Considering Grid Constraints" Energies 15, no. 1: 192. https://doi.org/10.3390/en15010192