Long-term optimal operation of a parallel multireservoir power system

Long-term optimal operation of a multireservoir system is complex because it is a dynamic problem (present decisions for one reservoir depend on future decisions for all reservoirs); the optimal operating policy for one reservoir depends not only on its own energy content, but also on the corresponding content of each one of the other reservoirs; it is a highly stochastic problem with respect to the reservoir inflows and it is a nonlinear problem. This paper presents a new method for determining the optimal monthly operating policy of a power system consisting of multireservoirs on a multiriver system taking into account the stochasticity of the river flows. Functional optimization techniques and minimum norm formulation have been used. Results for a numerical example composed of three rivers with four reservoirs, three reservoirs, and two reservoirs on each river, respectively, are presented.This work was supported by the National Research Council of Canada, Grant. No. A4146.     

Optimization of reservoirs in series on a river with a nonlinear storage curve for long-term regulation

We present in this paper a new approach to finding the monthly optimal operation of a multireservoir power system connected in series on a river. The hydroelectric power generation is a highly nonlinear function of the storage, and the conversion factor assigned to each power plant is also a nonlinear function of the storage. We use for both a quadratic function of the storage; the resulting problem has a highly nonlinear objective function and linear constraints. We propose a transformation such that the system equations are reduced to linear-quadratic form. Lagrange and Kuhn-Tucker multipliers are used to adjoin the equality and inequality constraints to the objective function. Numerical results are presented for a real system in operation consisting of two reservoirs in series on a river for widely different water conditions.This work was supported by the National Research Council of Canada, Grant No. A4146. The authors would like to acknowledge data obtained from B.C. Hydro.     

Optimal discrete long-term operation of nuclear-hydrothermal power systems

We discuss in this paper an algorithm for solving the optimal long-term operating problem of a hydrothermal-nuclear power system by application of the minimum norm optimization technique. The algorithm proposed here has the ability to deal with large-scale power systems and with equality and/or inequality constraints on the variables. A discrete model for the xenon and iodine concentrations is used, as well as a discrete model for hydro reservoirs. The optimization is done on a monthly time basis. For simplicity of the problem formulation, the transmission line losses are considered as a part of the load.This work supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. A4146.     

Long-term optimal operation of series parallel reservoirs for critical period with specified monthly generation and average monthly storage

We present in this paper an efficient approach for solving the problem of planning the long-term (multiyear) operation of a multireservoir hydroelectric power system for the critical period with a monthly variable load. This load is equal to a certain percentage of the total generation at the end of the year, subject to satisfying a number of constraints on the hydrosystem, using the minimum norm formulation.The proposed method is efficient in computing time and in calculating the total expected benefits from the system during the critical period. Numerical results are reported for a real system in operation consisting of two rivers. Each river has two series reservoirs.This work was supported by the Natural Science and Engineering Research Council of Canada, Grant No. A4146.     

Optimal control of an M/M/2 queueing system with finite capacity operating under the triadic (0,Q,N,M) policy

operating under the triadic (0,Q, N,M) policy, where L is the maximum number of customers in the system. The number of working servers can be adjusted one at a time at arrival epochs or at service completion epochs depending on the number of customers in the system. Analytic closed-form solutions of the controllable M/M/2 queueing system with finite capacity operating under the triadic (0,Q, N,M) policy are derived. This is a generalization of the ordinary M/M/2 and the controllable M/M/1 queueing systems in the literature. The total expected cost function per unit time is developed to obtain the optimal operating (0,Q, N,M) policy at minimum cost.     

Minimum norm approach to optimal long-term operation of multireservoir power systems with specified monthly generation

The aim of this paper is to present a new algorithm to maximize the value of the energy produced from a multireservoir power system, plus the estimated value of water remaining in storage at the end of the 12-month planning period. The systems described here are characterized by having a specified monthly generation, and this generation is equal to a certain percentage of the total generation at the end of the year.The problem is formulated as a minimum norm problem in the framework of analytic optimization. Numerical results are reported for a real system in operation consisting of three rivers; each river has two series reservoirs. The proposed algorithm is efficient in computing time and in calculating the total expected benefits from the system.This work was supported by the National Research Council of Canada, Grant No. A4146. The authors would like to acknowledge data obtained from B.C. Hydro, Vancouver, B.C., Canada.     

On optimal operating conditions for a data processing system: A stochastic approach

In this paper, we consider the problem of determining optimal operating conditions for a data processing system. The system is burned‐in for a fixed burn‐in time before it is put into field operation and, in field operation, it has a work size and follows an age‐replacement policy. Assuming that the underlying lifetime distribution of the system has a bathtub‐shaped failure rate function, the properties of optimal burn‐in time, optimal work size and optimal age‐replacement policy will be derived. It can be seen that this model is a generalization of those considered in the previous works, and it yields a better optimal operating conditions. This paper presents an analytical method for three‐dimensional optimization problem. An algorithm for determining optimal operating conditions is also given. Copyright © 2007 John Wiley & Sons, Ltd.     

Multi-objective analysis of dam release flows in rivers downstream from hydropower reservoirs

This paper assesses dam releases from hydropower reservoirs in order to optimize power production and fish habitat protection. A multi-objective programming model includes output from 2-D hydraulic simulation for habitat assessment to optimize power production and fish habitat suitability as a Pareto set. To identify the optimal Pareto set two different approaches are used and compared: ε-constraint methods and non-dominant-sorting genetic algorithm (NSGA II). To formulate the ecological objective the river habitat quality is quantified by the weighted usable area (WUA). The relation between the WUA and the river flow-rate is obtained by using a 2D hydraulic model in which the hydraulic characteristics of river current – depth and velocity – are calculated by a finite difference numerical integration of two-dimensional shallow water equations on a boundary fitted non orthogonal curvilinear mesh. This approach allows the integration of motion equations on geometrically complex domains as those representing the morphology of natural watercourses. The performance of the proposed methodology is analyzed in a case study of a stretch of the Piave river downstream of the dam of the Pieve di Cadore reservoir (Belluno, Italy).     

Optimum load scheduling of nuclear-hydro-thermal power systems

This paper considers the problem of short-term optimal operation of nuclear-hydro-thermal electric power systems. The solution is obtained by use of a functional analytic optimization technique that employs the minimum norm formulation.A power system with an arbitrary number of generating stations is considered. The limited flexibility exhibited by the thermal nuclear reactors, when operating in a load-following mode, is accounted for by means of a model of the xenon concentration in their cores. The nonlinear effects induced by trapezoidal water reservoirs and the time delay of the water flow between upstream and downstream hydroplants is taken into consideration as well.A two-level iterative scheme of the feasible type is proposed for implementing the optimal solution.This work was supported in part by the National Research Council of Canada, Grant No. A-4146.     

Optimal charging times of a battery for memory backup

This paper considers the following charging policy for a battery to back up memories of a computer system: If the voltage of a battery is lower than a prespecified threshold level when the power is on, a battery is charged for a fixed time T. Using the probability theory, an availability of the system is derived and an optimal time T^* to maximize it is discussed. A numerical example is finally given.     

On the use of phase‐type distributions for inventory management with supply disruptions

Maintaining the continuity of operations becomes increasingly important for systems that are subject to disruptions due to various reasons. In this paper, we study an inventory system operating under a (q, r) policy, where the supply can become inaccessible for random durations. The availability of the supply is modeled by assuming a single supplier that goes through ON and OFF periods of stochastic duration, both of which are modeled by phase‐type distributions (PTD). We provide two alternative representations of the state transition probabilities of the system, one with integral and the other employing Kolmogorov differential equations. We then use an efficient formulation for the analytical model that gives the optimal policy parameters and the long‐run average cost. An extensive numerical study is conducted, which shows that OFF time characteristics have a bigger impact on optimal policy parameters. The ON time characteristics are also important for critical goods if disasters can happen. Copyright © 2011 John Wiley & Sons, Ltd.     

Threshold start-up control policy for polling systems

A threshold start-up policy is appealing for manufacturing (service) facilities that incur a cost for keeping the machine (server) on, as well as for each restart of the server from its dormant state. Analysis of single product (customer) systems operating under such a policy, also known as the N-policy, has been available for some time. This article develops mathematical analysis for multiproduct systems operating under a cyclic exhaustive or globally gated service regime and a threshold start-up rule. It pays particular attention to modeling switchover (setup) times. The analysis extends/unifies existing literature on polling models by obtaining as special cases, the continuously roving server and patient server polling models on the one hand, and the standard M/G/1 queue with N-policy, on the other hand. We provide a computationally efficient algorithm for finding aggregate performance measures, such as the mean waiting time for each customer type and the mean unfinished work in system. We show that the search for the optimal threshold level can be restricted to a finite set of possibilities. This revised version was published online in June 2006 with corrections to the Cover Date.     

Optimal control of a removable and non-reliable server in an infinite and a finite M/H2/1 queueing system

This paper deals with a single removable and non-reliable server in both an infinite and a finite queueing system with Poisson arrivals and two-type hyper-exponential distribution for the service times. The server may be turned on at arrival epochs or off at service completion epochs. Breakdown and repair times of the server are assumed to follow a negative exponential distribution. Conditions for a stable queueing system, that is steady-state, are provided. Cost models for both system capacities are respectively developed to determine the optimal operating policy numerically at minimum cost. This paper provides the minimum expected cost and the optimal operating policy based on assumed numerical values given to the system parameters, as well as to the cost elements. Sensitivity analysis is also investigated.     

Stochastic vs deterministic programming in water management: the value of flexibility

In the paper we develop a two stage scenario-based stochastic programming model for water management in the Indus Basin Irrigation System (IBIS). We present a comparison between the deterministic and scenario-based stochastic programming model. Our model takes stochastic inputs on hydrologic data i.e. inflow and rainfall. We divide the basin into three rainfall zones which overlap on 44 canal commands. Data on crop characteristics are taken on canal command levels. We then use ten-daily and monthly time intervals to analyze the policies. This system has two major reservoirs and a complex network of rivers, canal head works, canals, sub canals and distributaries. All the decisions on hydrologic aspects are governed by irrigation and agricultural development policies. Storage levels are maintained within the minimum and maximum bounds for every time interval according to a power generation policy. The objective function is to maximize the expected revenue from crops production. We discuss the flexibility of two stochastic optimization models with varying time horizon.     

Optimal long-term operation of a multireservoir power system for critical water conditions

We present in this paper a new method for solving the optimization problem of a variable head multireservoir power system under a critical water condition for long-term regulation. The problem is formulated as a minimum norm problem. The proposed method is efficient in computing time and in calculating the expected benefits from the system during the critical period. Numerical results are presented for a real system in operation consisting of two rivers; each river has two reservoirs connected in a series.This work was supported by the National Research Council of Canada, Grant No. A4146. The authors wish to thank B. C. Hydro for providing the reservoir data.     

Age-based vs. stock level control policies for a perishable inventory system

In this study, we investigate the impact of modified lotsize-reorder control policy for perishables which bases replenishment decisions on both the inventory level and the remaining lifetimes of items in stock. We derive the expressions for the key operating characteristics of a lost sales perishable inventory model, operating under the proposed age-based policy, and examine the sensitivity of the optimal policy parameters with respect to various system parameters. We compare the performance of the suggested policy to that of the classical (Q,r) type policy through a numerical study over a wide range of system parameters. Our findings indicate that the age-based policy is superior to the stock level policy for slow moving perishable inventory systems with high service levels.     

Notes of M/G/1 system under the {\langle p, T \rangle} policy with second optional service

We optimize the operating cost of the ${\langle p, T \rangle}We optimize the operating cost of the áp, T ?{\langle p, T \rangle} policy for an M/G/1 queueing system with second optional service, where the customer may depart from the system either after the first essential service with probability 1 − r or at the end of the first service may immediately go for a second service with probability r. Moreover, the server takes a vacation of fixed length T if the system becomes empty. If customers are found in the queue after T time units have elapsed since the end of the busy period, the server reactivates with probability p or leaves for a vacation of the same length T with probability 1 − p. Alternatively, if no customers present in the queue upon returning from the vacation, the server leaves for another a vacation of the same length. We call this áp, T ?{\langle p, T \rangle} policy. The total expected cost function per unit time is developed to determine the optimal thresholds of p and T at a minimum cost. Based on the optimal cost the explicit form for joint optimum values of p and T are obtained.     

Optimal Control of an M/G/1/K Queueing System with Combined <Emphasis Type="Italic">F</Emphasis> Policy and Startup Time

We investigate the optimal management problem of an M/G/1/K queueing system with combined F policy and an exponential startup time. The F policy queueing problem investigates the most common issue of controlling the arrival to a queueing system. We present a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining service time, to obtain the steady state probability distribution of the number of customers in the system. The method is illustrated analytically for exponential service time distribution. A cost model is established to determine the optimal management F policy at minimum cost. We use an efficient Maple computer program to calculate the optimal value of F and some system performance measures. Sensitivity analysis is also investigated.