Commitment and Dispatch of Heat and Power Units via Affinely Adjustable Robust Optimization

The joint management of heat and power systems is believed to be key to the integration of renewables into energy systems with a large penetration of district heating. Determining the day-ahead unit commitment and production schedules for these systems is an optimization problem subject to uncertainty stemming from the unpredictability of demand and prices for heat and electricity. Furthermore, owing to the dynamic features of production and heat storage units as well as to the length and granularity of the optimization horizon (e.g., one whole day with hourly resolution), this problem is in essence a multi-stage one. We propose a formulation based on robust optimization where recourse decisions are approximated as linear or piecewise-linear functions of the uncertain parameters. This approach allows for a rigorous modeling of the uncertainty in multi-stage decision-making without compromising computational tractability. We perform an extensive numerical study based on data from the Copenhagen area in Denmark, which highlights important features of the proposed model. Firstly, we illustrate commitment and dispatch choices that increase conservativeness in the robust optimization approach. Secondly, we appraise the gain obtained by switching from linear to piecewise-linear decision rules within robust optimization. Furthermore, we give directions for selecting the parameters defining the uncertainty set (size, budget) and assess the resulting trade-off between average profit and conservativeness of the solution. Finally, we perform a thorough comparison with competing models based on deterministic optimization and stochastic programming.Comment: 31 page

Unit commitment with valve-point loading effect

Valve-point loading affects the input-output characteristics of generating units, bringing the fuel costs nonlinear and nonsmooth. This has been considered in the solution of load dispatch problems, but not in the planning phase of unit commitment. This paper presents a mathematical optimization model for the thermal unit commitment problem considering valve-point loading. The formulation is based on a careful linearization of the fuel cost function, which is modeled with great detail on power regions being used in the current solution, and roughly on other regions. A set of benchmark instances for this problem is used for analyzing the method, with recourse to a general-purpose mixed-integer optimization solver

On Idle Energy Consumption Minimization in Production: Industrial Example and Mathematical Model

This paper, inspired by a real production process of steel hardening, investigates a scheduling problem to minimize the idle energy consumption of machines. The energy minimization is achieved by switching a machine to some power-saving mode when it is idle. For the steel hardening process, the mode of the machine (i.e., furnace) can be associated with its inner temperature. Contrary to the recent methods, which consider only a small number of machine modes, the temperature in the furnace can be changed continuously, and so an infinite number of the power-saving modes must be considered to achieve the highest possible savings. To model the machine modes efficiently, we use the concept of the energy function, which was originally introduced in the domain of embedded systems but has yet to take roots in the domain of production research. The energy function is illustrated with several application examples from the literature. Afterward, it is integrated into a mathematical model of a scheduling problem with parallel identical machines and jobs characterized by release times, deadlines, and processing times. Numerical experiments show that the proposed model outperforms a reference model adapted from the literature.Comment: Accepted to 9th International Conference on Operations Research and Enterprise Systems (ICORES 2020

Energy-Efficient Transmission Scheduling with Strict Underflow Constraints

We consider a single source transmitting data to one or more receivers/users over a shared wireless channel. Due to random fading, the wireless channel conditions vary with time and from user to user. Each user has a buffer to store received packets before they are drained. At each time step, the source determines how much power to use for transmission to each user. The source's objective is to allocate power in a manner that minimizes an expected cost measure, while satisfying strict buffer underflow constraints and a total power constraint in each slot. The expected cost measure is composed of costs associated with power consumption from transmission and packet holding costs. The primary application motivating this problem is wireless media streaming. For this application, the buffer underflow constraints prevent the user buffers from emptying, so as to maintain playout quality. In the case of a single user with linear power-rate curves, we show that a modified base-stock policy is optimal under the finite horizon, infinite horizon discounted, and infinite horizon average expected cost criteria. For a single user with piecewise-linear convex power-rate curves, we show that a finite generalized base-stock policy is optimal under all three expected cost criteria. We also present the sequences of critical numbers that complete the characterization of the optimal control laws in each of these cases when some additional technical conditions are satisfied. We then analyze the structure of the optimal policy for the case of two users. We conclude with a discussion of methods to identify implementable near-optimal policies for the most general case of M users.Comment: 109 pages, 11 pdf figures, template.tex is main file. We have significantly revised the paper from version 1. Additions include the case of a single receiver with piecewise-linear convex power-rate curves, the case of two receivers, and the infinite horizon average expected cost proble

Combined hydro-wind generation bids in a pool-based electricity market

Present regulatory trends are promoting the irect participation of wind energy in electricity markets. The final result of these markets sets the production scheduling for the operation time, including a power commitment from the wind generators. However, wind resources are uncertain, and the final power delivered usually differs from the initial power committed. This imbalance produces an overcost in the system, which must be paid by those who produce it, e.g., wind generators among others. As a result, wind farm revenue decreases, but it could increase by allowing wind farms to submit their bids to the markets together with a hydro generating unit, which may easily modify its production according to the expected imbalance. This paper presents a stochastic optimization technique that maximizes the joint profit of hydro and wind generators in a pool-based electricity market, taking into account the uncertainty of wind power prediction.En prens

A bi-objective genetic algorithm approach to risk mitigation in project scheduling

A problem of risk mitigation in project scheduling is formulated as a bi-objective optimization problem, where the expected makespan and the expected total cost are both to be minimized. The expected total cost is the sum of four cost components: overhead cost, activity execution cost, cost of reducing risks and penalty cost for tardiness. Risks for activities are predefined. For each risk at an activity, various levels are defined, which correspond to the results of different preventive measures. Only those risks with a probable impact on the duration of the related activity are considered here. Impacts of risks are not only accounted for through the expected makespan but are also translated into cost and thus have an impact on the expected total cost. An MIP model and a heuristic solution approach based on genetic algorithms (GAs) is proposed. The experiments conducted indicate that GAs provide a fast and effective solution approach to the problem. For smaller problems, the results obtained by the GA are very good. For larger problems, there is room for improvement