Optimization of the production of hydroelectric power systems with a variable head

We present in this paper a new approach for optimization of the production of hydroelectric power systems with a variable head. The problem is formulated as a minimum norm problem.The method takes into account the water head variation. To avoid underestimation of production for rising water levels and overestimation for falling water level, an average head (of begin and end of time step) is used. The method also takes into account the stochasticity of the river flows. Numerical results for a real system in operation including up to six reservoirs are reported for different water conditions. The proposed method is computationally efficient compared to other approaches.This work was supported by the National Research Council of Canada, Grant No. A-4146. The authors would like to acknowledge the data obtained from British Columbia Hydro.     

Planning the production of a fleet of domestic combined heat and power generators

This paper describes a planning problem, arising in the energy supply chain, that deals with the planning of the production runs of micro combined heat and power (microCHP) appliances installed in houses, cooperating in a fleet. Two types of this problem are described. The first one is the Single House Planning Problem (SHPP), where the focus is on supplying heat in the household. The second one combines many microCHPs into a Fleet Planning Problem (FPP) and focuses on the mutual electricity output, while still considering the local heat demand in the individual households. The problem is modeled as an ILP. For practical use a local search method is developed for the FPP, based on a dynamic programming formulation of the SHPP.     

Restricted power domination and fault-tolerant power domination on grids

The power domination problem is to find a minimum placement of phase measurement units (PMUs) for observing the whole electric power system, which is closely related to the classical domination problem in graphs. For a graph G=(V,E), the power domination number of G is the minimum cardinality of a set S⊆V such that PMUs placed on every vertex of S results in all of V being observed. A vertex with a PMU observes itself and all its neighbors, and if an observed vertex with degree d>1 has only one unobserved neighbor, then the unobserved neighbor becomes observed. Although the power domination problem has been proved to be NP-complete even when restricted to some special classes of graphs, Dorfling and Henning in [M. Dorfling, M.A. Henning, A note on power domination in grid graphs, Discrete Applied Mathematics 154 (2006) 1023-1027] showed that it is easy to determine the power domination number of an n×m grid. Their proof provides an algorithm for giving a minimum placement of PMUs. In this paper, we consider the situation in which PMUs may only be placed within a restricted subset of V. Then, we present algorithms to solve this restricted type of power domination on grids under the conditions that consecutive rows or columns form a forbidden zone. Moreover, we also deal with the fault-tolerant measurement placement in the designed scheme and provide approximation algorithms when the number of faulty PMUs does not exceed 3.     

A hybrid method for large-scale short-term scheduling of make-and-pack production processes

Due to the ongoing trend towards increased product variety, fast-moving consumer goods such as food and beverages, pharmaceuticals, and chemicals are typically manufactured through so-called make-and-pack processes. These processes consist of a make stage, a pack stage, and intermediate storage facilities that decouple these two stages. In operations scheduling, complex technological constraints must be considered, e.g., non-identical parallel processing units, sequence-dependent changeovers, batch splitting, no-wait restrictions, material transfer times, minimum storage times, and finite storage capacity. The short-term scheduling problem is to compute a production schedule such that a given demand for products is fulfilled, all technological constraints are met, and the production makespan is minimised. A production schedule typically comprises 500–1500 operations. Due to the problem size and complexity of the technological constraints, the performance of known mixed-integer linear programming (MILP) formulations and heuristic approaches is often insufficient.     

Batch machine production with perishability time windows and limited batch size

This article provides a theoretical analysis of the problem of scheduling jobs in batches by family on a batch-processing machine, in the presence of perishability time windows of equal length. The problem arises in the context of production planning in a microbiological laboratory, and has application in wafer-fab production and for wireless broadcasting. The combined features of multiple families and time windows are new to the literature. The study is restricted to unit job processing times. We prove that the problem is NP-hard, thus solving an open problem by Uzsoy [24]. A Dynamic Programme is developed, with running time polynomial in the input variables of maximum batch size, the number of families and the length of the demand time horizon. In addition, we show that an heuristic approach to minimising the perishability time window can provide a 2-approximation to the optimum.     

A control method for speeding up response of hydroelectric station power canals

A control method which, through the suitable servo-operation of the check gates, attains a consistent improvement in the speed of response of hydroelectric power canals is presented. Its application allows the size of the canal headpond to be reduced at the design stage of the power station as well. The proposed method is based on the constant volume control concept and uses a mathematical model of the power canal derived from linearization of the Saint-Venant equations. The results of the computer simulation of a controlled real system's dynamic behavior obtained through the use of the method of characteristics are presented.     

Efficient algorithms for combined heat and power production planning under the deregulated electricity market

Combined heat and power (CHP) production is an important energy production technology that can yield much higher total energy efficiency than separate heat and power generation. In CHP production, the heat and power production follows a joint characteristic, which means that the production planning must be done in coordination. Cost-efficient operation of a CHP system can be planned by using an optimization model. A long-term planning model decomposes into thousands of hourly models. Earlier, in the regulated electric power market, the planning problem was symmetrically driven by heat and power demand. The liberalization of the power market has created an asymmetrical planning problem, where heat production responds to the demand and power production to the volatile market price. In this paper, we utilize this asymmetry to develop novel envelope-based dual algorithms for solving the hourly CHP models efficiently. The basic idea is to transform the three-dimensional characteristic operating region for heat and power production of each CHP plant into a two-dimensional envelope by taking the power price as a parameter. Then the envelopes of each plant are used for looking up the optimal solution rapidly. We propose two versions of the algorithm: the on-line envelope construction algorithm (ECON) where the envelopes are constructed for each hour based on the power price and the off-line envelope construction algorithm (ECOFF) where envelopes are pre-computed for all different power price ranges. We derive the theoretical time complexity of the two algorithms and compare their performance empirically with realistic test models against the ILOG CPLEX solver and the Power Simplex (PS) algorithm. PS is an extremely efficient specialized primal algorithm developed for the symmetrical CHP planning problem under the regulated market. On average, when reusing previous basic solutions, ECON is 603 times faster than CPLEX and 1.3 times faster than PS. ECOFF is 1860 times faster than CPLEX and four times faster than PS.     

Identical part production in cyclic robotic cells: Concepts, overview and open questions

Robotic cells consist of a flow-shop with a robot for material handling. A single part is to be produced cyclically and the objective is to minimize production rate. This document introduces basic concepts and tools for dealing with cyclic production. In particular, it concentrates on k-cycles which are production cycles where exactly k parts enter and leave the cell. One defines the cycle function which is the smallest value of k so that the set of all k-cycles up to size contains an optimal cycle for all instances. Known results and conjectures on these functions are given for the classical case where parts can remain on the machine waiting for the robot and for the no-wait case where parts have to be removed from the machine as soon as their processing is finished.     

Stability improvement of multimachine power system via new coordinated design of PSSs and SVC

In this article, the assessment of new coordinated design of power system stabilizers (PSSs) and static var compensator (SVC) in a multimachine power system via statistical method is proposed. The coordinated design problem of PSSs and SVC over a wide range of loading conditions is handled as an optimization problem. The bacterial swarming optimization (BSO), which synergistically couples the bacterial foraging with the particle swarm optimization (PSO), is used to seek for optimal controllers parameters. By minimizing the proposed objective function, in which the speed deviations between generators are involved; stability performance of the system is enhanced. To compare the capability of PSS and SVC, both are designed independently, and then in a coordinated manner. Simultaneous tuning of the BSO‐based coordinated controller gives robust damping performance over wide range of operating conditions and large disturbance in compare to optimized PSS controller based on BSO (BSOPSS) and optimized SVC controller based on BSO (BSOSVC). Moreover, a statistical T test is executed to validate the robustness of coordinated controller versus uncoordinated one. © 2014 Wiley Periodicals, Inc. Complexity 21: 256–266, 2015     

On the power graph and the reduced power graph of a finite group

In this paper, for a finite group, we investigate to what extent its directed (resp. undirected) reduced power graph determines its directed power graph (resp. reduced power graph). Moreover, we investigate the determination of the orders of the elements of a finite group from its directed (resp. undirected) reduced power graph. Consequently, we show that some classes of finite groups are recognizable from their undirected reduced power graphs. Also, we study the relationship between the isomorphism classes of groups corresponding to the equivalence relations induced by the isomorphism of each of these graphs on the set of all finite groups.     

Risk management in power markets: The Hedging value of production flexibility

Since the 1990s power markets are being restructured worldwide and nowadays electrical power is traded as a commodity. The liberalization and with it the uncertainty in gas, fuel and electrical power prices requires an effective management of production facilities and financial contracts. Thereby derivatives build essential instruments to exchange volume as well as price risks. The challenge for participants in the newly competitive market environment is how to design, price and hedge derivative contracts in particular combination with the flexibility embedded in dispatch strategies of production assets. Accordingly, an adequate basis for management and investment decisions is needed which responds to the highly complex market situation.     

Application of Benders’ decomposition to power plant preventive maintenance scheduling

Power plant preventive maintenance scheduling consists of knowing which generating units to take off line for regular safety inspection. This problem is extremely important because a failure in a power station may cause a general breakdown in an electric network. The principal danger is that customer electricity demand will not be satisfied in such cases. The problem is approached from the operations research perspective as a question of optimisation. Benders’ decomposition technique is used to solve the resulting model. An example of this application is included. The algorithm is put to use in a real power plant setting. The obtained result is a schedule that allows the efficient organisation of preventive maintenance over the time horizon considered.     

Optimization of power production and costs in microgrids

This paper proposes a mathematical formulation for energy management in a connected microgrid. The aim is determining the optimal operating strategy for energy storage, to fulfil a time-varying energy demand and operational constraints while achieving a tradeoff between microgrid running costs and energy storage system life. The microgrid is composed by various renewable power production plants, storage devices and controllable loads, and has the ability to increase energy efficiency and reduce costs for energy purchasing from the main grid. The problem is formulated as a mixed-integer linear optimization problem. The optimization is aimed at minimizing the overall cost function of the system while satisfying the customer demand and safety of the electrical network. A case study of an existing microgrid is investigated: the microgrid consists of a photovoltaic and a hydroelectric power plant, a battery storage, an office building and an industrial facility. The optimization problem is solved in an efficient way by using commercial software. Simulation results show the feasibility and the effectiveness of the proposed approach to satisfy the load and reduce total costs.     

Scheduling production of multiple part-types in a system with pre-known demands and deterministic inactive time intervals

We introduce and formalise a scheduling problem that consists in determining an optimum policy (i.e. one that minimises total inventory holding costs) to produce n part-types using a system that is able to share its capacity at all times among these part-types and that switches between an active and an inactive state for pre-known periods of time. Consequently, when active the system must produce enough reserves to meet the demand during the inactive interval. We show that there is always a simple optimum policy in which the production of the part-types is prioritised and, provided the units are properly defined, the optimum priority ordering corresponds to a non-decreasing sequence of the unit holding costs of the part-types.     

正规幂环和一致幂环

文[1]首次提出了HX环（幂环）的概念,文[2]探索了幂环的性质和结构,本文类似于幂群的研究,提出了正规幂环和一致幂环的概念,研究了它们的结构和它们之间的关系,对它们进行了分类,并讨论了它们的交与和,从而构造了它们的子环链和理想链。     

Some open problems in the design and use of modern production systems

During the past two decades, manufacturing systems have moved towards automation, integration and modularity. These trends will certainly continue in the future due to the constraints of the market and to evolution of resources and worker requirements. As a consequence, the design and use of manufacturing systems are increasingly expensive. Numerous methods and tools have been developed to face up to this situation, but some complementary aids could be provided for designers and manufacturing engineers. The goal of this paper is to present important open problems whose solutions could certainly significantly improve the design and use of modern production systems.     

An efficient envelope-based Branch and Bound algorithm for non-convex combined heat and power production planning

Combined heat and power (CHP) production is universally accepted as one of the most energy-efficient technologies to produce energy with lower fuel consumption and fewer emissions. In CHP technology, heat and power generation follow a joint characteristic. Traditional CHP production is usually applied in backpressure plants, where the joint characteristic can often be represented by a convex model. Advanced CHP production technologies such as backpressure plants with condensing and auxiliary cooling options, gas turbines, and combined gas and steam cycles may require non-convex models. Cost-efficient operation of a CHP system can be planned using an optimization model based on forecasts for heat load and power price. A long-term planning model decomposes into thousands of single-period models, which can be formulated in the convex case as linear programming (LP) problems, and in the non-convex case as mixed integer programming (MIP) problems.     

Factorization of matrix functions and their inverses via power product expansions

The conversion of a power series with matrix coefficients into an infinite product of certain elementary matrix factors is studied. The expansion of a power series with matrix coefficients as the inverse of an infinite product of elementary factors is also analyzed. Each elementary factor is the sum of the identity matrix and a certain matrix coefficient multiplied by a certain power of the variable. The two expansions provide us with representations of a matrix function and its inverse by infinite products of elementary factors. Estimates on the domain of convergence of the infinite products are given.     

Weighted Banzhaf power and interaction indexes through weighted approximations of games

The Banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game. The Banzhaf interaction index was then proposed to measure the interaction degree inside coalitions of players. It was shown that the power and interaction indexes can be obtained as solutions of a standard least squares approximation problem for pseudo-Boolean functions. Considering certain weighted versions of this approximation problem, we define a class of weighted interaction indexes that generalize the Banzhaf interaction index. We show that these indexes define a subclass of the family of probabilistic interaction indexes and study their most important properties. Finally, we give an interpretation of the Banzhaf and Shapley interaction indexes as centers of mass of this subclass of interaction indexes.     

The impact of process deterioration on production and maintenance policies

This paper examines a single-stage production system that deteriorates with production actions, and improves with maintenance. The condition of the process can be in any of several discrete states, and transitions from state to state follow a semi-Markov process. The firm can produce multiple products, which differ by profit earned, expected processing time, and impact on equipment deterioration. The firm can also perform different maintenance actions, which differ by cost incurred, expected down time, and impact on the process condition. The firm needs to determine the optimal production and maintenance choices in each state in a way that maximizes the long-run expected average reward per unit time.