Constrained distributionally robust optimization for day-ahead dispatch of rural integrated energy systems with source and load uncertainties
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As a deep connection between agriculture and energy, the rural integrated energy system (RIES) is a micro-scale supply–distribution–storage–demand network, which provides an important means to realize the utilization of rural clean energy. This paper proposes a day-ahead scheduling model of the RIES to improve its economical effectiveness, where three energy carriers, namely, biogas, electric power, and heat, are integrated. To address the source and load uncertainties composed of photovoltaic power, power load, and heat load, this paper develops a constrained distributionally robust optimization (CDRO), which optimizes the cost expectation related to the extreme distribution to enhance the robustness, while limiting the loss of cost expectation in the historical distribution to ensure economical effectiveness. In addition, an ambiguous set of the source and load uncertainties incorporating 1-norm and infinity-norm constraints is established, which realizes a flexible adjustment for the conservativeness of CDRO. The distributionally robust dispatch is formulated as a deterministic programming in a two-stage solving framework, where the subproblem uploads its extreme probability distribution to the master problem, and these two problems are iteratively optimized until the convergence. Finally, the numerical simulations in a modern farm park prove the performance of the constructed dispatch model and the flexibility of CDRO in balancing the economical effectiveness and robustness of the dispatch.Keywords:
Robust Optimization
Robustness
Demand Response
Load shifting
To efficiently facilitate the energy transition it is essential to evaluate the potential of demand response in practice. Based on the results of a Dutch smart grid pilot, this paper assesses the potential of both manual and semi-automated demand response in residential areas. To stimulate demand response, a dynamic tariff and smart appliances were used. The participating households were informed about the tariff day-ahead through a home energy management system, connected to a display installed on the wall in their living room. The tariff was intuitively displayed: self-consumption of photovoltaic generation was stimulated by means of a low tariff, but also the generation itself played a central role on the display. Household flexibility is analyzed, focusing on: (i) the load shift of (smart) appliances, and (ii) the response of the (overall) peak load towards the dynamic tariff. To assess the latter, i.e. price responsiveness, the participants were split up in two comparable groups which were subject to a different moment of evening peak-pricing. Based on the results, it is concluded that mainly the flexibility of the white goods (i.e. the washing machine, tumble dryer and dishwasher) is used for demand response. The main part of the flexible load of these (smart) appliances is shifted from the evening to the midday, to match local generation. This load shift remained stable over a long period of time (>1 year) and is not responsive to the exact moment of peak-pricing. Therefore, it is concluded that a simple and transparent design for dynamic tariffs is sufficient and most effective to stimulate (manual) residential demand response. Such a tariff should emphasize the ‘right’ moments to use electricity, intuitively linked to renewable generation.
Demand Response
Load shifting
Dynamic Pricing
Peak demand
Consumption
Rebound Effect
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Robust Optimization
Bilevel optimization
Robustness
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The objective of robust optimization is to find solutions that are immune to the uncertainty of the parameters in a mathematical optimization problem. It requires that the constraints of a given problem should be satisfied for all realizations of the uncertain parameters in a so-called uncertainty set. The robust version of a mathematical optimization problem is generally referred to as the robust counterpart problem. Robust optimization is popular because of the computational tractability of the robust counterpart for many classes of uncertainty sets, and its applicability in wide range of topics in practice. In this thesis, we propose robust optimization methodologies for different classes of optimization problems. In Chapter 2, we give a practical guide on robust optimization. In Chapter 3, we propose a new way to construct uncertainty sets for robust optimization using the available historical data information. Chapter 4 proposes a robust optimization approach for simulation-based optimization problems. Finally, Chapter 5 proposes approximations of a specific class of robust and stochastic bilevel optimization problems by using modern robust optimization techniques.
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Bilevel optimization
Robustness
L-reduction
Engineering optimization
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Demand Response
Load shifting
Load management
Electricity demand
Mains electricity
Peak demand
Market demand schedule
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Robust optimization is a common framework in optimization under uncertainty when the problem parameters are not known, but it is rather known that the parameters belong to some given uncertainty set. In the robust optimization framework the problem solved is a min-max problem where a solution is judged according to its performance on the worst possible realization of the parameters. In many cases, a straightforward solution of the robust optimization problem of a certain type requires solving an optimization problem of a more complicated type, and in some cases even NP-hard. For example, solving a robust conic quadratic program, such as those arising in robust SVM, ellipsoidal uncertainty leads in general to a semidefinite program. In this paper we develop a method for approximately solving a robust optimization problem using tools from online convex optimization, where in every stage a standard (non-robust) optimization program is solved. Our algorithms find an approximate robust solution using a number of calls to an oracle that solves the original (non-robust) problem that is inversely proportional to the square of the target accuracy.
Robust Optimization
Conic optimization
Realization (probability)
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The objective of robust optimization is to find solutions that are immune to the uncertainty of the parameters in a mathematical optimization problem. It requires that the constraints of a given problem should be satisfied for all realizations of the uncertain parameters in a so-called uncertainty set. The robust version of a mathematical optimization problem is generally referred to as the robust counterpart problem. Robust optimization is popular because of the computational tractability of the robust counterpart for many classes of uncertainty sets, and its applicability in wide range of topics in practice. In this thesis, we propose robust optimization methodologies for different classes of optimization problems. In Chapter 2, we give a practical guide on robust optimization. In Chapter 3, we propose a new way to construct uncertainty sets for robust optimization using the available historical data information. Chapter 4 proposes a robust optimization approach for simulation-based optimization problems. Finally, Chapter 5 proposes approximations of a specific class of robust and stochastic bilevel optimization problems by using modern robust optimization techniques.
Robust Optimization
Bilevel optimization
Robustness
L-reduction
Engineering optimization
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Abstract Robust optimization(RO) is an important tool for handling optimization problem with uncertainty. The main objective of RO is to solve optimization problems due to uncertainty associated with constraints satisfying all real-izations of uncertain values within a given uncertainty set. The challenge of RO is to reformulate the constraints so that the uncertain optimization problem is transformed into a tractable deterministic form. In this paper, we have given more emphasis to study the robust counterpart(RC) of the RO problems and have developed a mathematical model on the solution strategy for robust linear optimization problems, where the constraints only are associated with uncertainties. The box and ellipsoidal uncertainty sets are considered and some illustrative numerical examples have been solved in each corresponding case for validating our proposed method.
Robust Optimization
Ellipsoid
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The paper describes a demand-side response scheme
consisting of computer-controlled switches operated at end-users premises to shift loads targeting a homogenized national demand profile. The paper presents further simulation of the economic model corresponding to the above described scheme representing an incentive-based demand response. In the simulation the impact of these programs on load shape and peak load magnitudes, financial benefit to users as well as reduction of energy consumption are shown. The results demonstrated more
homogenized load curves at lesser peak load magnitudes and
reduced energy cost.
Demand Response
Peak demand
Load shifting
Peak load
Load management
Demand side
Load profile
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Load shifting
Consumption
Peak load
Demand side
Peak demand
Load management
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