On the optimal capacity expansion of electric power systems

The analysis of investment in the electric power has been the subject of intensive research for many years. The efficient generation and distribution of electrical energy is a difficult task involving the operation of a complex network of facilities, often located over very large geographical regions. Electric power utilities have made use of an enormous range of mathematical models. Some models address time spans which last for a fraction of a second, such as those that deal with lightning strikes on transmission lines while at the other end of the scale there are models which address time horizons consisting of ten or twenty years; these usually involve long range planning issues. This thesis addresses the optimal long term capacity expansion of an interconnected power system. The aim of this study has been to derive a new, long term planning model which recognises the regional differences which exist for energy demand and which are present in the construction and operation of power plant and transmission line equipment. Perhaps the most innovative feature of the new model is the direct inclusion of regional energy demand curves in the nonlinear form. This results in a nonlinear capacity expansion model. After review of the relevant literature, the thesis first develops a model for the optimal operation of a power grid. This model directly incorporates regional demand curves. The model is a nonlinear programming problem containing both integer and continuous variables. A solution algorithm is developed which is based upon a resource decomposition scheme that separates the integer variables from the continuous ones. The decompostion of the operating problem leads to an interactive scheme which employs a mixed integer programming problem, known as the master, to generate trial operating configurations. The optimum operating conditions of each trial configuration is found using a smooth nonlinear programming model. The dual vector recovered from this model is subsequently used by the master to generate the next trial configuration. The solution algorithm progresses until lower and upper bounds converge. A range of numerical experiments are conducted and these experiments are included in the discussion. Using the operating model as a basis, a regional capacity expansion model is then developed. It determines the type, location and capacity of additional power plants and transmission lines, which are required to meet predicted electicity demands. A generalised resource decompostion scheme, similar to that used to solve the operating problem, is employed. The solution algorithm is used to solve a range of test problems and the results of these numerical experiments are reported. Finally, the expansion problem is applied to the Queensland electricity grid in Australia.

On the optimal capacity expansion of electric power systems

The analysis of investment in the electric power has been the subject of intensive research for many years. The efficient generation and distribution of electrical energy is a difficult task involving the operation of a complex network of facilities, often located over very large geographical regions. Electric power utilities have made use of an enormous range of mathematical models. Some models address time spans which last for a fraction of a second, such as those that deal with lightning strikes on transmission lines while at the other end of the scale there are models which address time horizons consisting of ten or twenty years; these usually involve long range planning issues. This thesis addresses the optimal long term capacity expansion of an interconnected power system. The aim of this study has been to derive a new, long term planning model which recognises the regional differences which exist for energy demand and which are present in the construction and operation of power plant and transmission line equipment. Perhaps the most innovative feature of the new model is the direct inclusion of regional energy demand curves in the nonlinear form. This results in a nonlinear capacity expansion model. After review of the relevant literature, the thesis first develops a model for the optimal operation of a power grid. This model directly incorporates regional demand curves. The model is a nonlinear programming problem containing both integer and continuous variables. A solution algorithm is developed which is based upon a resource decomposition scheme that separates the integer variables from the continuous ones. The decompostion of the operating problem leads to an interactive scheme which employs a mixed integer programming problem, known as the master, to generate trial operating configurations. The optimum operating conditions of each trial configuration is found using a smooth nonlinear programming model. The dual vector recovered from this model is subsequently used by the master to generate the next trial configuration. The solution algorithm progresses until lower and upper bounds converge. A range of numerical experiments are conducted and these experiments are included in the discussion. Using the operating model as a basis, a regional capacity expansion model is then developed. It determines the type, location and capacity of additional power plants and transmission lines, which are required to meet predicted electicity demands. A generalised resource decompostion scheme, similar to that used to solve the operating problem, is employed. The solution algorithm is used to solve a range of test problems and the results of these numerical experiments are reported. Finally, the expansion problem is applied to the Queensland electricity grid in Australia

A new approach to automatically producing schedules for cane railways

The scheduling of locomotive movements on cane railways has proven to be a very complex task. Various optimisation methods have been used over the years to try and produce an optimised schedule that eliminates or minimises bin supply delays to harvesters and the factory, while minimising the number of locomotives, locomotive shifts and cane bins, and also the cane age. This paper reports on a new attempt to develop an automatic scheduler using a mathematical model solved using mixed integer programming and constraint programming approaches and blocking parallel job shop scheduling fundamentals. The model solution has been explored using conventional constraint programming search techniques and found to produce a reasonable schedule for small-scale problems with up to nine harvesters. While more effort is required to complete the development of the full model with metaheuristic search techniques, the work completed to date gives confidence that the metaheuristic techniques will provide near optimal solutions in reasonable time.

Hybrid metaheuristic techniques for optimising sugarcane rail operations

Mixed integer programming and parallel-machine job shop scheduling are used to solve the sugarcane rail transport scheduling problem. Constructive heuristics and metaheuristics were developed to produce a more efficient scheduling system and so reduce operating costs. The solutions were tested on small and large size problems. High-quality solutions and improved CPU time are the result of developing new hybrid techniques which consist of different ways of integrating simulated annealing and Tabu search techniques.

Trade determination in multi-attribute exchanges

Electronic exchanges are double-sided marketplaces that allow multiple buyers to trade with multiple sellers, with aggregation of demand and supply across the bids to maximize the revenue in the market. Two important issues in the design of exchanges are (1) trade determination (determining the number of goods traded between any buyer-seller pair) and (2) pricing. In this paper we address the trade determination issue for one-shot, multi-attribute exchanges that trade multiple units of the same good. The bids are configurable with separable additive price functions over the attributes and each function is continuous and piecewise linear. We model trade determination as mixed integer programming problems for different possible bid structures and show that even in two-attribute exchanges, trade determination is NP-hard for certain bid structures. We also make some observations on the pricing issues that are closely related to the mixed integer formulations.

Control of dynamical systems with temporal logic specifications

This thesis is motivated by safety-critical applications involving autonomous air, ground, and space vehicles carrying out complex tasks in uncertain and adversarial environments. We use temporal logic as a language to formally specify complex tasks and system properties. Temporal logic specifications generalize the classical notions of stability and reachability that are studied in the control and hybrid systems communities. Given a system model and a formal task specification, the goal is to automatically synthesize a control policy for the system that ensures that the system satisfies the specification. This thesis presents novel control policy synthesis algorithms for optimal and robust control of dynamical systems with temporal logic specifications. Furthermore, it introduces algorithms that are efficient and extend to high-dimensional dynamical systems.

The first contribution of this thesis is the generalization of a classical linear temporal logic (LTL) control synthesis approach to optimal and robust control. We show how we can extend automata-based synthesis techniques for discrete abstractions of dynamical systems to create optimal and robust controllers that are guaranteed to satisfy an LTL specification. Such optimal and robust controllers can be computed at little extra computational cost compared to computing a feasible controller.

The second contribution of this thesis addresses the scalability of control synthesis with LTL specifications. A major limitation of the standard automaton-based approach for control with LTL specifications is that the automaton might be doubly-exponential in the size of the LTL specification. We introduce a fragment of LTL for which one can compute feasible control policies in time polynomial in the size of the system and specification. Additionally, we show how to compute optimal control policies for a variety of cost functions, and identify interesting cases when this can be done in polynomial time. These techniques are particularly relevant for online control, as one can guarantee that a feasible solution can be found quickly, and then iteratively improve on the quality as time permits.

The final contribution of this thesis is a set of algorithms for computing feasible trajectories for high-dimensional, nonlinear systems with LTL specifications. These algorithms avoid a potentially computationally-expensive process of computing a discrete abstraction, and instead compute directly on the system's continuous state space. The first method uses an automaton representing the specification to directly encode a series of constrained-reachability subproblems, which can be solved in a modular fashion by using standard techniques. The second method encodes an LTL formula as mixed-integer linear programming constraints on the dynamical system. We demonstrate these approaches with numerical experiments on temporal logic motion planning problems with high-dimensional (10+ states) continuous systems.

Distributed Control and Optimization for Communication and Power Systems

We are at the cusp of a historic transformation of both communication system and electricity system. This creates challenges as well as opportunities for the study of networked systems. Problems of these systems typically involve a huge number of end points that require intelligent coordination in a distributed manner. In this thesis, we develop models, theories, and scalable distributed optimization and control algorithms to overcome these challenges.

This thesis focuses on two specific areas: multi-path TCP (Transmission Control Protocol) and electricity distribution system operation and control. Multi-path TCP (MP-TCP) is a TCP extension that allows a single data stream to be split across multiple paths. MP-TCP has the potential to greatly improve reliability as well as efficiency of communication devices. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We clarify how algorithm parameters impact TCP-friendliness, responsiveness, and window oscillation and demonstrate an inevitable tradeoff among these properties. We discuss the implications of these properties on the behavior of existing algorithms and motivate a new algorithm Balia (balanced linked adaptation) which generalizes existing algorithms and strikes a good balance among TCP-friendliness, responsiveness, and window oscillation. We have implemented Balia in the Linux kernel. We use our prototype to compare the new proposed algorithm Balia with existing MP-TCP algorithms.

Our second focus is on designing computationally efficient algorithms for electricity distribution system operation and control. First, we develop efficient algorithms for feeder reconfiguration in distribution networks. The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed integer nonlinear program and hence hard to solve. We propose a heuristic algorithm that is based on the recently developed convex relaxation of the optimal power flow problem. The algorithm is efficient and can successfully computes an optimal configuration on all networks that we have tested. Moreover we prove that the algorithm solves the feeder reconfiguration problem optimally under certain conditions. We also propose a more efficient algorithm and it incurs a loss in optimality of less than 3% on the test networks.

Second, we develop efficient distributed algorithms that solve the optimal power flow (OPF) problem on distribution networks. The OPF problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. Traditionally OPF is solved in a centralized manner. With increasing penetration of volatile renewable energy resources in distribution systems, we need faster and distributed solutions for real-time feedback control. This is difficult because power flow equations are nonlinear and kirchhoff's law is global. We propose solutions for both balanced and unbalanced radial distribution networks. They exploit recent results that suggest solving for a globally optimal solution of OPF over a radial network through a second-order cone program (SOCP) or semi-definite program (SDP) relaxation. Our distributed algorithms are based on the alternating direction method of multiplier (ADMM), but unlike standard ADMM-based distributed OPF algorithms that require solving optimization subproblems using iterative methods, the proposed solutions exploit the problem structure that greatly reduce the computation time. Specifically, for balanced networks, our decomposition allows us to derive closed form solutions for these subproblems and it speeds up the convergence by 1000x times in simulations. For unbalanced networks, the subproblems reduce to either closed form solutions or eigenvalue problems whose size remains constant as the network scales up and computation time is reduced by 100x compared with iterative methods.

Hybrid model predictive control applied to switching control of burner load for a compact marine boi

This paper discusses the application of hybrid model predictive control to control switching between different burner modes in a novel compact marine boiler design. A further purpose of the present work is to point out problems with finite horizon model predictive control applied to systems for which the optimal solution is a limit cycle. Regarding the marine boiler control the aim is to find an optimal control strategy which minimizes a trade-off between deviations in boiler pressure and water level from their respective setpoints while limiting burner switches.The approach taken is based on the Mixed Logic Dynamical framework. The whole boiler systems is modelled in this framework and a model predictive controller is designed. However to facilitate on-line implementation only a small part of the search tree in the mixed integer optimization is evaluated to find out whether a switch should occur or not. The strategy is verified on a simulation model of the compact marine boiler for control of low/high burner load switches. It is shown that even though performance is adequate for some disturbance levels it becomes deteriorated when the optimal solution is a limit cycle. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.

任务分配问题的建模与求解

建立了极大极小任务分配问题的混合整数线性规划模型,提出一种矩阵作业解答,并与穷举解及混合整数线性规划解的计算复杂度进行了比较.理论分析和数值试验表明矩阵作业法对两类任务分配问题,极大极小和总体极小任务分配问题,有效地提供最优解.

Shop-scheduling problems with fixed and non-fixed machine orders of the jobs

The paper deals with the determination of an optimal schedule for the so-called mixed shop problem when the makespan has to be minimized. In such a problem, some jobs have fixed machine orders (as in the job-shop), while the operations of the other jobs may be processed in arbitrary order (as in the open-shop). We prove binary NP-hardness of the preemptive problem with three machines and three jobs (two jobs have fixed machine orders and one may have an arbitrary machine order). We answer all other remaining open questions on the complexity status of mixed-shop problems with the makespan criterion by presenting different polynomial and pseudopolynomial algorithms.

Two-stage mixed discrete-continuous identification of radial basis function (RBF) neural models for nonlinear systems

The identification of nonlinear dynamic systems using radial basis function (RBF) neural models is studied in this paper. Given a model selection criterion, the main objective is to effectively and efficiently build a parsimonious compact neural model that generalizes well over unseen data. This is achieved by simultaneous model structure selection and optimization of the parameters over the continuous parameter space. It is a mixed-integer hard problem, and a unified analytic framework is proposed to enable an effective and efficient two-stage mixed discrete-continuous; identification procedure. This novel framework combines the advantages of an iterative discrete two-stage subset selection technique for model structure determination and the calculus-based continuous optimization of the model parameters. Computational complexity analysis and simulation studies confirm the efficacy of the proposed algorithm.

Distributed energy resource short-term scheduling using signaled particle swarm optimization

Distributed Energy Resources (DER) scheduling in smart grids presents a new challenge to system operators. The increase of new resources, such as storage systems and demand response programs, results in additional computational efforts for optimization problems. On the other hand, since natural resources, such as wind and sun, can only be precisely forecasted with small anticipation, short-term scheduling is especially relevant requiring a very good performance on large dimension problems. Traditional techniques such as Mixed-Integer Non-Linear Programming (MINLP) do not cope well with large scale problems. This type of problems can be appropriately addressed by metaheuristics approaches. This paper proposes a new methodology called Signaled Particle Swarm Optimization (SiPSO) to address the energy resources management problem in the scope of smart grids, with intensive use of DER. The proposed methodology’s performance is illustrated by a case study with 99 distributed generators, 208 loads, and 27 storage units. The results are compared with those obtained in other methodologies, namely MINLP, Genetic Algorithm, original Particle Swarm Optimization (PSO), Evolutionary PSO, and New PSO. SiPSO performance is superior to the other tested PSO variants, demonstrating its adequacy to solve large dimension problems which require a decision in a short period of time.

An efficient method for optimal location and sizing of fixed and switched shunt capacitors in large distribution systems

This paper proposes a computationally efficient methodology for the optimal location and sizing of static and switched shunt capacitors in large distribution systems. The problem is formulated as the maximization of the savings produced by the reduction in energy losses and the avoided costs due to investment deferral in the expansion of the network. The proposed method selects the nodes to be compensated, as well as the optimal capacitor ratings and their operational characteristics, i.e. fixed or switched. After an appropriate linearization, the optimization problem was formulated as a large-scale mixed-integer linear problem, suitable for being solved by means of a widespread commercial package. Results of the proposed optimizing method are compared with another recent methodology reported in the literature using two test cases: a 15-bus and a 33-bus distribution network. For the both cases tested, the proposed methodology delivers better solutions indicated by higher loss savings, which are achieved with lower amounts of capacitive compensation. The proposed method has also been applied for compensating to an actual large distribution network served by AES-Venezuela in the metropolitan area of Caracas. A convergence time of about 4 seconds after 22298 iterations demonstrates the ability of the proposed methodology for efficiently handling large-scale compensation problems.

Optimal methodology for distribution systems reconfiguration based on OPF and solved by decomposition technique

This paper presents a new and efficient methodology for distribution network reconfiguration integrated with optimal power flow (OPF) based on a Benders decomposition approach. The objective minimizes power losses, balancing load among feeders and subject to constraints: capacity limit of branches, minimum and maximum power limits of substations or distributed generators, minimum deviation of bus voltages and radial optimal operation of networks. The Generalized Benders decomposition algorithm is applied to solve the problem. The formulation can be embedded under two stages; the first one is the Master problem and is formulated as a mixed integer non-linear programming problem. This stage determines the radial topology of the distribution network. The second stage is the Slave problem and is formulated as a non-linear programming problem. This stage is used to determine the feasibility of the Master problem solution by means of an OPF and provides information to formulate the linear Benders cuts that connect both problems. The model is programmed in GAMS. The effectiveness of the proposal is demonstrated through two examples extracted from the literature.

Application-specific modified particle swarm optimization for energy resource scheduling considering vehicle-to-grid

This paper presents a modified Particle Swarm Optimization (PSO) methodology to solve the problem of energy resources management with high penetration of distributed generation and Electric Vehicles (EVs) with gridable capability (V2G). The objective of the day-ahead scheduling problem in this work is to minimize operation costs, namely energy costs, regarding he management of these resources in the smart grid context. The modifications applied to the PSO aimed to improve its adequacy to solve the mentioned problem. The proposed Application Specific Modified Particle Swarm Optimization (ASMPSO) includes an intelligent mechanism to adjust velocity limits during the search process, as well as self-parameterization of PSO parameters making it more user-independent. It presents better robustness and convergence characteristics compared with the tested PSO variants as well as better constraint handling. This enables its use for addressing real world large-scale problems in much shorter times than the deterministic methods, providing system operators with adequate decision support and achieving efficient resource scheduling, even when a significant number of alternative scenarios should be considered. The paper includes two realistic case studies with different penetration of gridable vehicles (1000 and 2000). The proposed methodology is about 2600 times faster than Mixed-Integer Non-Linear Programming (MINLP) reference technique, reducing the time required from 25 h to 36 s for the scenario with 2000 vehicles, with about one percent of difference in the objective function cost value.