Economic Topology Optimization of District Heating Networks using a Pipe Penalization Approach

In the presented study, a pipe penalization approach for the economic topology optimization of District Heating Networks is proposed, drawing inspiration from density-based topology optimization. For District Heating Networks, the upfront investment is a crucial factor for the rollout of this technology. Today, the pipe routing is usually designed relying on a linearization of the underlying heat transport problem. This study proposes to solve the optimal pipe routing problem as a non-linear topology optimization problem, drawing inspiration from density-based topology optimization. The optimization problem is formulated around a non-linear heat transport model and minimizes a detailed net present value representation of the heating network cost. By relaxing the combinatorial problem of pipe placement, this approach remains scalable for large-scale applications. A discrete network topology and near-discrete pipe design is achieved by using an intermediate pipe penalization strategy. For a realistic test case, the proposed algorithm achieves a discrete network topology and near-discrete pipe design that outperforms simple post-processing steps.Comment: Changed article template and minor reformulations in abstract, introduction and conclusio

Design and operations of gas transmission networks

Problems dealing with the design and the operations of gas transmission networks are challenging. The difficulty mainly arises from the simultaneous modeling of gas transmission laws and of the investment costs. The combination of the two yields a non- linear non-convex optimization problem. To obviate this shortcoming, we propose a new formulation as a multi-objective problem, with two objectives. The first one is the investment cost function or a suitable approximation of it; the second is the cost of energy that is required to transmit the gas. This energy cost is approximated by the total energy dissipated into the network. This bi-criterion problem turns out to be convex and easily solvable by convex optimization solvers. Our continuous optimization formulation can be used as an efficient continuous relaxation for problems with non-divisible restrictions such as a limited number of available commercial pipe dimensions.gas transmission networks, reinforcement, convex optimization

DESIGN AIDS FOR AIR VESSELS FOR TRANSIENT PROTECTION OF LARGE PIPE NETWORKS - A FRAMEWORK BASED ON PARAMETERIZATION OF KNOWLEDGE-BASE DERIVED FROM OPTIMIZED NETWORK MODELS

The need for optimal air vessel sizing tools, in protecting large pipe networks from undue transient pressures is well known. Graphical and other heuristic methods reported in literature are limited to sizing the air vessels for simple rising mains. Although attempts have been made to utilize optimization techniques, they have been largely unsuccessful due to their impractical computational requirements. This research work proposes a robust framework for developing surge protection design tools and demonstrates the usefulness of the framework through an example air vessel sizing tool. Efficiency and robustness of the proposed framework are demonstrated by developing a design aid for air vessel sizing for protecting large pipe network systems against excessive high pressures generated by rapid valve closures. The essence of the proposed framework is in identification of key transient response parameters influencing air vessel parameters from seemingly unmanageable transient response data. This parameterization helps in exploiting the similarity between transient responses of small pipe networks and sub-sections of large pipe networks. The framework employs an extensive knowledgebase of transient pressure and flow scenarios defined from several small network models and corresponding optimal air vessel sizes obtained from a genetic algorithm optimizer. A regression model based on an artificial neural network was used on this knowledgebase to identify key parameters influencing air vessel sizes. These key parameters were used as input variables and the corresponding air vessel parameters as output variables to train the neural network model. The trained neural network model was successfully applied for large complex pipe networks to obtain optimal air vessel sizes for transient protection. The neural network model predictions were compared with optimal air vessel parameters to assess the efficacy of the proposed framework. The validity and limitation of the design aid developed and areas in the framework that need further research are also presented. The proposed frame work requires generation of hundreds of optimization data for small and simple network systems which is a daunting task since genetic algorithm-based optimization is computationally expensive. Selection of a numerically efficient and sufficiently accurate transient analysis method for use inside a genetic algorithm based optimization scheme is crucial as any reduction in transient analysis time for a network system would tremendously reduce the computational costs of bi-level genetic algorithm optimization scheme. This research work also demonstrate that the Wave Plan Method is computationally more efficient than the Method of Characteristics for similar accuracies and the resulting savings in computational costs in the transient analysis of pipe networks and subsequently in the genetic algorithm based optimization schemes are significant

Pipeline Network Optimization using Hybrid Algorithm between Simulated Annealing and Genetic Algorithms

The pipeline network is one of the most complex optimization problems consisting of several elements: reservoirs, pipes, valves, etc. The pipeline network is designed to deliver water to consumers by considering the demand and adequate pressure on the water pipe network. The main problem in designing reliable pipelines is the cost. The amount of cost that most influences the design of pipelines is the diameter of the pipe used. Therefore, this study aims to combine (hybrid) simulated annealing algorithm with genetic algorithm to optimize water pipe networks. The simulated annealing algorithm is the main algorithm in finding the optimal cost.Meanwhile, the genetic algorithm will assist in the pipeline update process using the roulette wheel selection. Simulation data is used to test the hybrid algorithm performance compared to the standard simulated annealing algorithm. The results show that the simulated annealing hybrid algorithm is able to get a more optimal cost in designing a water pipe network compared to the standard simulated annealing algorithm. Keywords: Optimization, Epanet 2.0, Simulated Annealing, and Genetic Algorith

Optimization of Water Distribution System Using WaterGEMS: The Case of Wukro Town, Ethiopia

This study was aimed to optimize the designed water distribution system in the Wukro town using WaterGEMS model. The Darwin Designer in WaterGEMS was applied for finding optimal pipe diameter to supply adequate quantity of water at satisfactory pressures to the end users. In the WaterGEMS model, the Darwin Scheduler of daily pumping operations tools also used for optimal control and operation of pump systems. The WaterGEMS model was implemented in water distribution networks which include 117 pipes (40.67km), 99 demand nodes (equivalent to 50480 end users) that are spread across a hilly area over a 1989m to 2046m elevation gradient. The model was calibrated at the selected nodes within very good performance. The results have shown that the maximum pressure before optimization is 31.1m and after optimization increased to 38.1m, the minimum pressure on the former is 7.9m and 16m later during peak hour demand. Comparison of results showed that the optimized networks reduce the cost by 9.6% than those of before optimization networks by traditional hydraulic. In addition to this, the optimal tanks filling/emptying arrangement decreased the daily cost of energy consumptions by 12.5% compare as a currently scheduled pump. The finding of this study indicated that the WaterGEMS model is a promising approach for optimal sizing of pipes in design water distribution networks and pumping operational schedules. Keywords: Water Distribution Network, Genetic Algorithm, Pipe Diameter, Energy consumption, Darwin Designer, Darwin scheduler DOI: 10.7176/CER/12-6-01 Publication date:June 30th 202

Optimal design of water distribution systems based on entropy and topology

A new multi-objective evolutionary optimization approach for joint topology and pipe size design of water distribution systems is presented. The algorithm proposed considers simultaneously the adequacy of flow and pressure at the demand nodes; the initial construction cost; the network topology; and a measure of hydraulic capacity reliability. The optimization procedure is based on a general measure of hydraulic performance that combines statistical entropy, network connectivity and hydraulic feasibility. The topological properties of the solutions are accounted for and arbitrary assumptions regarding the quality of infeasible solutions are not applied. In other words, both feasible and infeasible solutions participate in the evolutionary processes; solutions survive and reproduce or perish strictly according to their Pareto-optimality. Removing artificial barriers in this way frees the algorithm to evolve optimal solutions quickly. Furthermore, any redundant binary codes that result from crossover or mutation are eliminated gradually in a seamless and generic way that avoids the arbitrary loss of potentially useful genetic material and preserves the quality of the information that is transmitted from one generation to the next. The approach proposed is entirely generic: we have not introduced any additional parameters that require calibration on a case-by-case basis. Detailed and extensive results for two test problems are included that suggest the approach is highly effective. In general, the frontier-optimal solutions achieved include topologies that are fully branched, partially- and fully-looped and, for networks with multiple sources, completely separate sub-networks

Efficient Dynamic Compressor Optimization in Natural Gas Transmission Systems

The growing reliance of electric power systems on gas-fired generation to balance intermittent sources of renewable energy has increased the variation and volume of flows through natural gas transmission pipelines. Adapting pipeline operations to maintain efficiency and security under these new conditions requires optimization methods that account for transients and that can quickly compute solutions in reaction to generator re-dispatch. This paper presents an efficient scheme to minimize compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flow. The optimization scheme relies on a compact representation of gas flow physics, a trapezoidal discretization in time and space, and a two-stage approach to minimize energy costs and maximize smoothness. The resulting large-scale nonlinear programs are solved using a modern interior-point method. The proposed optimization scheme is validated against an integration of dynamic equations with adaptive time-stepping, as well as a recently proposed state-of-the-art optimal control method. The comparison shows that the solutions are feasible for the continuous problem and also practical from an operational standpoint. The results also indicate that our scheme provides at least an order of magnitude reduction in computation time relative to the state-of-the-art and scales to large gas transmission networks with more than 6000 kilometers of total pipeline