Performance and Reliability Analysis of Wind Turbines Using Monte Carlo Methods Based on System Transport Theory

Abstract

Reliability and performance assessments of wind turbine systems are particularly challenging as they operate in highly stochastic, non-linear, coupled, multidisciplinary environments. The traditional approach has been to decouple performance from reliability and analyze them separately, which results in sub-optimal design and operational practices. In this paper, a method of jointly simulating both the performance and reliability of wind turbines is presented. The approach is based on system simulation using novel Monte Carlo algorithms derived from system transport theory (SPAR technology), a method originally developed for nuclear physics applications. In the representative wind turbine case study discussed in this paper, both machine availability and energy produced is simulated as a function of basic weather variables like wind speeds, turbulence intensity and design intent. In addition, statistical confidence bounds on energy and availability are also calculated for a full twenty year life. INTRODUCTION & OVERVIEW Wind Turbine systems are rapidly becoming an economically viable source of renewable energy. A key element in making wind energy both a technical and commercial success is the ability to develop accurate and computationally efficient modeling and simulation platforms which serve as the basis for machine design and performance optimization. Two key elements of wind turbine technology are turbine performance and availability. Turbine performance (energy produced) is a function of design variables and a highly stochastic operating environment. Machine availability is a function of system reliability, and is impacted by design, operating environment and maintenance considerations. Hence, the wind turbine simulation problem includes elements of probabilistic design, multi-state reliability theory, multidisciplinary optimization as well as traditional fields like engineering and operations research. Hence, any modeling framework will have to include elements of all these subjects. In recent years, researchers have recognized the benefits of incorporating both reliability and performance in a unified mathematical model, giving rise to the emerging field of “performability” analysis [Trivedi, 2001]. For wind turbines, “performability” analysis has applications in developing design specifications, in choosing wind farm sites, establishing maintenance and logistics protocols and in modeling power performance and equipment availability guarantees. This paper deals with a wind turbine case study analyzed using a new, unified approach to the wind turbine “performability” problem; and is based on a Monte Carlo approach derived from system transport theory of nuclear physics [Dubi, 2000]. The full paper will include a detailed description of system transport theory as applied to the reliability analysis of mechanical systems along with numerical implementation. In this extended abstract, a brief description of the theory is provided in subsequent sections. MULTI-STATE RELIABILITY ANALYSIS USING SYSTEM TRANSPORT THEORY Historically, reliability theory has been based on a binary approach, where a system can exist in two states – an “up” state where the system is completely operational and working at full performance; and a “down” state where the system has failed. The probability of a system existing in the “up” state is characterized by the reliability, R(t), which is the probability of the system being operational at time ‘t’, as well as system availability, A(t|k), which is the probability of the system being operational at time ‘t’ given that it has seen ‘k’ failures in the past. It is clear that R(t) refers to system survival before the first failure, and A(t|k) refers to system survival for repairable systems, i.e. R(t) is the special case of A(t|0). In reality, complex systems exist in multiple degraded states, which is studied under the emerging discipline of Multi-State reliability theory [Lisnianski, 2003]. There are two main approaches for modeling multistate problems for systems with non-exponential failure and repair distributions, (E.g. most mechanical systems) – Markovian Models, and a more general approach, which is System Transport Theory. Variations of Markov approaches include Semi-Markov or Generalized Markov theory [Bolch, et al, 1998]. Markov-based approaches work best when the failure and repair rates Copyright 2004 by S. Vittal (MemberAIAA) and M. Teboul. Published by the American Institute for Aeronautics & Astronautics with permission