MILP-Based Short-Term Thermal Unit Commitment and Hydrothermal Scheduling Including Cascaded Reservoirs and Fuel Constraints

Reservoirs are often built in cascade on the same river system, introducing inexorable constraints. It is therefore strategically important to scheme out an efficient commitment of thermal generation units along with the scheduling of hydro generation units for better operational efficiency, considering practical system conditions. This paper develops a comprehensive, unit-wise hydraulic model with reservoir and river system constraints, as well as gas constraints, with head effects, to commit thermal generation units and schedule hydro ones in the short-term. A mixed integer linear programming (MILP) methodology, using the branch and bound & cut (BB&C) algorithm, is employed to solve the resultant problem. Due to the detailed modelling of individual hydro units and cascaded dependent reservoirs, the problem size is substantially swollen. Multithread computing is invoked to accelerate the solution process. Simulation results, conducted on various test systems, reiterate that the developed MILP-based hydrothermal scheduling approach outperforms other techniques in terms of cost efficiency

A Conic Model for Electrolyzer Scheduling

The hydrogen production curve of the electrolyzer describes the non-linear and non-convex relationship between its power consumption and hydrogen production. An accurate representation of this curve is essential for the optimal scheduling of the electrolyzer. The current state-of-the-art approach is based on piece-wise linear approximation, which requires binary variables and does not scale well for large-scale problems. To overcome this barrier, we propose two models, both built upon convex relaxations of the hydrogen production curve. The first one is a linear relaxation of the piece-wise linear approximation, while the second one is a conic relaxation of a quadratic approximation. Both relaxations are exact under prevalent operating conditions. We prove this mathematically for the conic relaxation. Using a realistic case study, we show that the conic model, in comparison to the other models, provides a satisfactory trade-off between computational complexity and solution accuracy for large-scale problems

Different Decomposition Strategies to Solve Stochastic Hydrothermal Unit Commitment Problems

Solving very-large-scale optimization problems frequently require to decompose them in smaller subproblems, that are iteratively solved to produce useful information. One such approach is the Lagrangian Relaxation (LR), a broad range technique that leads to many different decomposition schemes. The LR supplies a lower bound of the objective function and useful information for heuristics aimed at constructing feasible primal solutions. In this paper, we compare the main LR strategies used so far for Stochastic Hydrothermal Unit Commitment problems, where uncertainty mainly concerns water availability in reservoirs and demand (weather conditions). This problem is customarily modeled as a two-stage mixed-integer optimization problem. We compare different decomposition strategies (unit and scenario schemes) in terms of quality of produced lower bound and running time. The schemes are assessed with various hydrothermal systems, considering different configuration of power plants, in terms of capacity and number of units

Layout optimization and Sustainable development of waste water networks with the use of heuristic algorithms: The Luxemburgish case

Fresh water tends to increasingly comprise a scarcity today both in arid or demographically boosted regions of the world such as large and smaller cities. On this basis, research is directed towards minimization of fresh water supply into a Waste Water Network Topology (WWNT) and maximizing water re-use. This might be composed of a cluster of agents which have certain demands for fresh water as well as waste water dependent on their daily uses and living profiles. This work is divided into two parts. In the first part, different waste water flows within a reference building unit i.e. a typical household of four (4) occupants is simulated. This type of building represents a major part of the total building stock in Luxembourg. In its first part the present study attempts to examine the optimized fresh and waste water flow pathways between water using units of the building. Between water flows two domestic treatment units are adopted. The simulation of above mentioned system is attempted by adopting different algorithm methods such as the Sequential Quadratic Programming (SQP), the interior point and meta-heuristic optimization algorithms such as the Genetic Algorithms (GA’s).Suitable computational platform tools such as MATLAB and GAMS are incorporated. A comparison study on the most efficient approach is then realized on the single household unit by developing four (4) different mathematical model formulation versions. The second part of this study comprises simulation and development of the Waste Water Network Grid (WWNG) in the upscale level, such as the neighborhood level within or outside the urban context. This model encompasses all possible land uses and different kinds of buildings of different use envelopes thus demands. This range of units includes mainly building stock, agricultural and infrastructure of the tertiary sector. Integration of above mentioned model to the existing WWNG will enhance attempts to more closely reach the optimum points. The use of appropriate mathematical programming methods for the upscale level, will take place. Increased uncertainties within the built model will be attempted to be tackled by developing linear programming techniques and suitable assumptions without distorting initial condition largely. Assumptions are then drawn on the efficiency of the adopted method an additional essential task is the minimization of the overall infrastructure and network cost, which may in turn give rise to corresponding reduced waste effluents discharge off the proposed network. The case study comprises selected rural and semi-rural areas zone districts of similar living profiles outside the City of Luxembourg. Therefore a clustering of end users of similar demand will be attempted. Possible redesign of an optimized WWNG comprises a vital need within the context of large scale demographic growth of urban environments today.Open Acces

A Framework of Electricity Market based on Two-Layer Stochastic Power Management for Microgrids

This article develops a novel multi-microgrids (MMGs) participation framework in the day-ahead energy and ancillary services, i.e. services of reactive power and reserve regulation, markets incorporating the smart distribution network (SDN) objectives based on two-layer power management system (PMS). A bi-level optimization structure is introduced wherein the upper level models optimal scheduling of SDN in the presence of MMGs while considering the bilateral coordination between microgrids (MGs) and SDN’s operators, i.e. second layer’s PMS. This layer is responsible for minimizing energy loss, expected energy not-supplied, and voltage security as the sum of weighted functions. In addition, the proposed problem is subject to linearized AC optimal power flow (LAC-OPF), reliability and security constraints to make it more practical. Lower level addresses participation of MGs in the competitive market based on bilateral coordination among sources, active loads and MGs’ operator (first layer’s PMS). The problem formulation then tries to minimize the difference between MGs’ cost and revenue in markets while satisfying constraints of LAC-OPF equations, reliability, security, and flexibility of the MGs. Karush–Kuhn–Tucker method is exploited to achieve a single-level model. Moreover, a stochastic programming model is introduced to handle the uncertainties of load, renewable power, energy price, the energy demand of mobile storage, and availability of network equipment. The simulation results confirm the capabilities of the suggested stochastic two-layer scheme in simultaneous evaluation of the optimal status of different technical and economic indices of the SDN and© 2022 Authors. Published by IEEE. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/fi=vertaisarvioitu|en=peerReviewed

Uncertainty management in multiobjective hydro-thermal self-scheduling under emission considerations

In this paper, a stochastic multiobjective framework is proposed for a day-ahead short-term Hydro Thermal Self-Scheduling (HTSS) problem for joint energy and reserve markets. An efficient linear formulations are introduced in this paper to deal with the nonlinearity of original problem due to the dynamic ramp rate limits, prohibited operating zones, operating services of thermal plants, multi-head power discharge characteristics of hydro generating units and spillage of reservoirs. Besides, system uncertainties including the generating units\u27 contingencies and price uncertainty are explicitly considered in the stochastic market clearing scheme. For the stochastic modeling of probable multiobjective optimization scenarios, a lattice Monte Carlo simulation has been adopted to have a better coverage of the system uncertainty spectrum. Consequently, the resulting multiobjective optimization scenarios should concurrently optimize competing objective functions including GENeration COmpany\u27s (GENCO\u27s) profit maximization and thermal units\u27 emission minimization. Accordingly, the ε-constraint method is used to solve the multiobjective optimization problem and generate the Pareto set. Then, a fuzzy satisfying method is employed to choose the most preferred solution among all Pareto optimal solutions. The performance of the presented method is verified in different case studies. The results obtained from ε-constraint method is compared with those reported by weighted sum method, evolutionary programming-based interactive Fuzzy satisfying method, differential evolution, quantum-behaved particle swarm optimization and hybrid multi-objective cultural algorithm, verifying the superiority of the proposed approach

Comparing Spatial and Scenario Decomposition for Stochastic Hydrothermal Unit Commitment Problems

Solving very-large-scale optimization problems frequently require to decompose them in smaller subproblems, that are iteratively solved to produce useful information. One such approach is the Lagrangian Relaxation (LR), a general technique that leads to many different decomposition schemes. The LR produces a lower bound of the objective function and useful information for heuristics aimed at constructing feasible primal solutions. In this paper, we compare the main LR strategies used so far for Stochastic Hydrothermal Unit Commitment problems, where uncertainty mainly concerns water availability in reservoirs and demand (weather conditions). The problem is customarily modeled as a two-stage mixed-integer optimization problem. We compare different decomposition strategies (unit and scenario schemes) in terms of quality of produced lower bound and running time. The schemes are assessed with various hydrothermal systems, considering different configuration of power plants, in terms of capacity and number of units