Multi-objective optimization of distributed energy systems with focus on robust solutions

Abstract

Primary energy consumption has increased exponentially in the last decades due to global economic growth. Energy is necessary for all aspects of modern life and is used in many sectors, such as electricity, heating and cooling generation, transportation and industry. However, energy consumption comes at a cost. Conventional energy systems rely on fossil fuels which have high carbon dioxide (CO2) emissions. As a result, the environment is affected due to the contribution of CO2 emissions to the greenhouse effect and by extension to climate change. Providing clean energy and tackling climate change are two of the most important challenges our planet faces. In the last years, the international community took measures to reduce CO2 emissions, such as the Kyoto protocol and more recently the Paris Agreement. European Union (EU) is implementing an ambitious set of policies in the fields of energy efficiency, promotion of renewable energy sources (RES) and reduction of CO2. Greece has also released an ambitious national energy plan recently based on European energy policies.

Moreover, in the last decades global population has increased dramatically, which leads to increased consumption of resources, including energy. Additionally, it has been calculated that about 52% of the global population live in cities, with the number expected to rise in the following decades. Urban areas account to a large share of energy demand, which leads to several challenges in order to satisfy it. In this context, urban energy systems are expected to play a significant role. The future urban energy systems need to be redesigned and offer sustainable solutions.

A solution towards this goal is the development of Distributed Energy Systems (DES). DES have many advantages, with the most significant one being the local energy generation which minimizes energy losses. DES can offer better integration between conventional energy systems and renewables and can satisfy the energy demand at a single building, a complex of buildings or even up to a whole city with a varied degree of decentralization. A DES can be designed to satisfy local energy needs in electricity, heating, and cooling. Also, they can lead to a reduction of total annual cost (TAC) and CO2 emissions. In the last years, several models have been proposed for the design of DES, based on mathematical programming. Those models applied either single- or multi- objective optimization problems with the most common objective functions being the minimization of TAC (which includes capital, operational and maintenance costs) and CO2 emissions.

Designing a DES is a complex problem in which many aspects need to be considered. This thesis aims to provide a methodology for the optimal design of DES using multi-objective mixed-integer linear programming (MILP), with TAC and CO2 emissions as the objective functions. The candidate technologies are: (a) cogeneration units, (b) heat pumps, (c) absorption chillers, (d) boilers, (e) solar thermal collectors, (f) solar photovoltaics, (g) wind turbines, (h) thermal energy storage, (i) electric energy storage, (j) district heating network (DHN) and (k) microgrid. The results offer as outputs the selected technologies and their respective sizes at each building, the layout of the DHN (if formed), the operational profile of the installed technologies, and the electricity exchange through the microgrid (if selected) and the national grid. Additionally, in literature all the developed methods can be broadly separated into two categories, namely: (a) “Method A” in which a simultaneous selection and sizing of candidate technologies and (b) “Method B” in which the sizes of the candidate technologies are predefined.

This thesis presents some innovative aspects in the field of optimal design of DES. Particularly, two approaches for the modelling of technologies are developed, expanding previous relevant work in literature. In addition, mathematical models for all available candidate technologies are presented. Those approaches are compared as they offer different solutions, and their advantages and disadvantages are assessed. Moreover, this thesis examines the robustness of solutions and it combines multi-objective mathematical programming with several techniques for optimization under uncertainty.

To examine the benefits of DES and to compare these two methods, a case study was carried out for a neighbourhood of six buildings in an area in Attica and three scenarios are depicted, with Scenario 1 being business-as-usual, Scenario 2 – Renewables and Scenario 3 – Green. The results show that between these three scenarios, Scenario 3 offers the most attractive solutions. In addition, the comparison between “Method A” and “Method B” shows that “Method A” offers better results at each solution, specifically between 3% and 11% for TAC, which was expected due to the higher degrees of freedom it has. Regarding carbon emissions both methods show similar results. Moreover, several differences exist between each solution at each method regarding system’s structure, operational profiles of technologies, formation of DHN and electricity exchange with microgrid and national grid. A recommended strategy for designing a DES it is suggested to apply “Method A” at first to get a first approximation of the capacities of technologies, and afterwards, when the capacity bounds become constrained (which means less combinations and therefore lower computational complexity) apply “Method B” which will offer more accurate results.

Furthermore, this thesis aims to examine the optimal design of DES under uncertainty. Changes in the values of several parameters can affect the optimal design of a DES, and the scope of this thesis is to provide a decision-maker (DM) with robust solutions. In this thesis uncertainty is assumed to exist in energy prices (electricity and natural gas), interest rate, energy loads (electricity, heating, and cooling), solar radiation, and wind speed. To examine uncertainty and identify robust solutions four techniques are used, which are in the fields of robust optimization (RO) and stochastic optimization (SO), namely: (a) objective-wise worst case, (b) minimax regret criterion (MMR), (c) minimax expected regret (MER) and (d) Monte Carlo simulations. Those techniques are applied to “Method A” either as multi-objective optimization problem (objective-wise method) or as single-objective optimization problems (MMR, MER and Monte Carlo simulations). For the transformation of the multi-objective deterministic problem to a single-objective one it is assumed that the TAC is the objective function and carbon emissions becoming a constraint with an upper bound of 100,000 kg/year.

For the application of MMR and MER it is assumed that uncertainty exists only in economic parameters (interest rate and energy prices) and five scenarios are depicted, namely Scenario R1 to Scenario R5, where parameters take a high and low value respectively. Regarding the application of MER, it is assumed that each Scenario R1 to R5 has a specific probability to occur, which leads to less conservative results. As for the application of objective-wise worst case and Monte Carlo simulations, two scenarios are depicted for each method, Scenarios OW1 and OW2 and Scenarios MC1 and MC2, respectively. Scenarios OW1 and MC1 assume that uncertainty exists in economic parameters, while Scenarios OW2 and MC2 assume uncertainty in all parameters. Each method generates different solutions, with the worst results occurring at objective-wise worst-case method as it considers the worst value of the uncertain parameters. MMR and MER show solutions with small values of regret, indicating that uncertainty in economic parameters does not affect results significantly. Finally, at the application of Monte Carlo simulations each parameter is assigned a specific probability distribution and the results show the range of TAC values at each scenario. It is noted that for each method the results of system’s configuration and operation profile of technologies are different.

Overall, these techniques provide solutions that are notably different of the results of the deterministic approach and can be characterized as robust, highlighting the importance of considering uncertainty for the design process. This thesis concludes that considering uncertainty in designing a DES is necessary as the optimal solutions change significantly, which is very important for the optimal design of the system, its financial viability and operational stability. Finally, it is noted that the developed methodologies are generic and can be easily adopted and applied according to the preferences of a DM.