Maike Hennen

Multi-objective synthesis of energy systems: Efficient identification of design trade-offs

Abstract The synthesis of energy systems usually has to consider several conflicting objectives leading to a large set of Pareto-optimal solutions with multiple trade-offs. From this large set of solutions, good compromise solutions have to be identified which is a complex and computationally demanding task. We therefore propose a method to reduce both the set of objectives and the solution space: First, the set of objectives is reduced by employing a method from the literature to determine the objectives best representing the design trade-offs. However, in practice, aggregated costs are the decisive criterion. Thus, in a second step, the solution space of the synthesis problem is restricted to an acceptable deviation from minimal aggregated costs. Thereby, only relevant solutions are obtained. The two steps significantly reduce the effort for multi-objective optimization focusing on the most relevant part of the solutions. The proposed method is applied to a real-world case study.

SPREAD - Exploring the decision space in energy systems synthesis

Abstract A method is presented to systematically analyze the decision space in the synthesis of energy supply systems. Commonly, synthesis problems are solved by mathematical optimization yielding a single optimal design. However, optimization is based on a model which never represents reality to perfection. Thus, the designer will be forced to revise parts of the optimal solution. We therefore support the design process by automatically identifying important features of good solutions. For this purpose, we analyze near-optimal solutions. To explore the decision space, we minimize and maximize both the number and the capacity of units while keeping the costs within a specified range. From this analysis, we derive insight into correlations between decisions. To support the decision maker, we represent the range of good design decisions and their correlations in the flowsheet of the energy system. The method is illustrated for the synthesis of an energy system in the pharmaceutical industry.

Rigorous synthesis of energy systems by decomposition via time-series aggregation

Abstract The synthesis of complex energy systems usually involves large time series such that a direct optimization is computationally prohibitive. In this paper, we propose a decomposition method for synthesis problems using time-series aggregation. To initialize the method, the time series is aggregated to one time step. A lower bound is obtained by relaxing the energy balances and underestimating the energy demands leading to a relaxed synthesis problem, which is efficiently solvable. An upper bound is obtained by restricting the original problem with the full time series to an operation problem with a fixed structure obtained from the lower bound solution. If the bounds do not satisfy the specified optimality gap, the resolution of the time-series aggregation is iteratively increased. The decomposition method is applied to two real-world synthesis problems. The results show the fast convergence of the decomposition method outperforming commercial state-of-the-art optimization software.

Rigorous synthesis of energy supply systems by time-series aggregation

Abstract A rigorous solution method is proposed for complex synthesis problems of energy supply systems with large time series. Time-series aggregation is used to iteratively tighten feasible solutions as upper bounds and best possible solutions as lower bounds. To initialize the method, the time series is aggregated to one time step. The lower bound is obtained by relaxing and underestimating the energy demands of all time steps which makes the corresponding equations redundant allowing for an efficient solution of the relaxed synthesis problem. The upper bound results from a restriction to an operation problem for the structure obtained from the lower bound solution. If the bounds do not satisfy the specified optimality gap, the resolution of the time series aggregation is increased and the solution process is restarted. The solution method is applied to an industrial real-world synthesis problem. The results show the fast convergence of the solution method outperforming a commercial state-of-the-art solver.

An Adaptive Normal Constraint Method for Bi-Objective Optimal Synthesis of Energy Systems

Abstract A novel approach is proposed for the efficient generation of the Pareto front for bi-objective optimal synthesis of energy systems. To avoid computationally expensive calculationsof solutions not relevant to the decision maker, the proposed method adapts the computation ofthe Pareto front to the part relevant for practical energy systems. The algorithm produces an evenly distributed set of Pareto optimal solutions employing a modified normal constraint method. In contrast to the classical normal constraint method, the algorithm is no more initialized at the – usually computationally most expensive – single-objective optima but uses an aggregated objective function as starting point for an adaptive exploration of the Pareto front. The presented approach is applied to a real-world synthesis problem of a distributed energy supply system. It is shown that the adaptive normal constraint algorithm automatically generates the most relevant part of the Pareto front for the bi-objective optimal synthesis of an energy system computationally more efficient than the weighted sum method or the e-constraint method.

Typical Periods for Two-Stage Synthesis by Time-Series Aggregation with Bounded Error in Objective Function

Two-stage synthesis problems simultaneously consider here-and-now decisions (e.g., optimal investment) and wait-and-see decisions (e.g., optimal operation). The optimal synthesis of energy systems reveals such a two-stage character. The synthesis of energy systems involves multiple large time series such as energy demands and energy prices. Since problem size increases with the size of the time series, synthesis of energy systems leads to complex optimization problems. To reduce the problem size without loosing solution quality, we propose a method for time-series aggregation to identify typical periods. Typical periods retain the chronology of time steps which enables modeling of energy systems, e.g., with storage units or start-up cost. The aim of the proposed method is to obtain few typical periods with few time steps per period, while accurately representing the objective function of the full time series, e.g. cost. Thus, we determine the error of time-series aggregation as the cost difference between operating the optimal design for the aggregated time series and for the full time series. Thereby, we rigorously bound the maximum performance loss of the optimal energy system design. In an initial step, the proposed method identifies the best length of typical periods by autocorrelation analysis. Subsequently, an adaptive procedure determines aggregated typical periods employing the clustering algorithm

Synthesis and Optimization of Distributed Energy Supply Systems using Automated Superstructure and Model Generation

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Rigorous synthesis of energy systems by relaxation and time-series aggregation to typical periods

-medoids which groups similar periods into clusters and selects one representative period per cluster. Moreover, the number of time steps per period is aggregated by a novel clustering algorithm maintaining chronology of the time steps in the periods. The method is iteratively repeated until the error falls below a treshold value. A case study based on a real-world synthesis problem of an energy system shows that time-series aggregation from 8760 time steps to 2 typical periods with each 2 time steps results in an error smaller than the optimality gap of of the synthesis problem (2%). This corresponds to a reduction of the number time steps and thus a reduction of the size of the synthesis problem by a factor of 1000 with excellent accuracy in cost estimation. Thus, the proposed method enables an efficient and accurate synthesis of energy systems.

Ensuring (n − 1)-reliability in the optimal design of distributed energy supply systems

Abstract A novel approach is presented for the automated generation of models representing superstructures for the synthesis and optimization of distributed energy supply systems (DESS). Based on a basic problem description (load cases, available technologies, and topographical constraints), the proposed algorithm automatically generates a model accounting for time-varying load profiles and part-load dependent operating efficiencies. Building upon the P-graph approach, the derived superstructure is extended to include multiple redundant conversion units as required for DESS optimization. In the present implementation, a GAMS model is generated that can be readily optimized. The approach is applied to the retrofit synthesis of the energy supply system of an industrial site. It is shown that the automated procedure provides a convenient and efficient optimization framework for DESS.

Integrated Synthesis of Batch Plants and Utility Systems

Abstract The synthesis of energy systems is a complex optimization task depending on multiple large time series. Time-coupling constraints, e.g., due to storage systems, complicate computation even further. To still efficiently solve time-coupled synthesis problems, we propose a rigorous synthesis method. In the proposed method, lower and upper bounds are calculated to obtain a feasible solution of the original synthesis problem with known quality. We compute the lower bound by binary relaxation. For the upper bound, we use time-series aggregation to obtain a feasible design for the system. Employing this feasible design, we solve an operational problem, which can be solved efficiently. To tighten the upper bound, we iteratively increase the time resolution of the aggregation. In a case study for an industrial energy system, we show that only few typical periods are required to obtain a solution of the original synthesis problem with excellent quality. The method has fast convergence outperforming a commercial state-of-the-art solver.