Hydro Turbine and Governor Modelling
نویسندگان
چکیده
.............................................................................................................................................................. II TABLE OF CONTENTS .............................................................................................................................................. III LIST OF FIGURES ..................................................................................................................................................... VI LIST OF TABLES ....................................................................................................................................................... IX PREFACE .................................................................................................................................................................. X LIST OF SYMBOLS ................................................................................................................................................... XII 1 INTRODUCTION ............................................................................................................................................... 1 1.1 BACKGROUND INFORMATION ........................................................................................................................................... 1 1.2 OBJECTIVE .................................................................................................................................................................... 1 1.3 SCOPE ......................................................................................................................................................................... 1 1.4 OUTLINE OF THE PROJECT ................................................................................................................................................ 2 2 PRESSURE WATER CONDUIT SYSTEM ............................................................................................................... 3 2.1 HYDRAULIC TRANSIENTS FUNDAMENTALS .......................................................................................................................... 3 2.1.1 Pressure wave velocity in conduits .................................................................................................................... 4 2.1.2 Wave propagation and reflections in the conduit ............................................................................................. 4 2.1.3 Head losses due to Friction ............................................................................................................................... 5 2.2 CLOSED‐CONDUIT SYSTEMS ............................................................................................................................................. 6 2.2.1 Basic Assumptions ............................................................................................................................................. 6 2.2.2 Basic Differential Equations for Transient Flow ................................................................................................ 6 2.2.2.1 Equation of Continuity ................................................................................................................................................. 7 2.2.2.2 Equation of Motion ...................................................................................................................................................... 9 2.2.2.3 General Remarks ........................................................................................................................................................ 10 2.2.3 Mathematical Model ...................................................................................................................................... 11 2.3 PRESSURE CONTROL SYSTEMS ........................................................................................................................................ 15 2.3.1 Governing Equations ....................................................................................................................................... 15 2.3.2 Surge Tank Mathematical Model .................................................................................................................... 17 3 HYDRAULIC TURBINES ................................................................................................................................... 18 3.1 HYDRAULIC TURBINES OVERVIEW ................................................................................................................................... 18 3.1.1 Impulse turbines .............................................................................................................................................. 18 3.1.2 Reaction Turbines ............................................................................................................................................ 19 3.2 GENERAL TECHNICAL ASPECTS ....................................................................................................................................... 20 3.2.1 Neat Head, Power and Efficiency .................................................................................................................... 20 3.2.2 Turbine Hill Charts ........................................................................................................................................... 21 3.3 HYDRAULIC TURBINE MODELLING ................................................................................................................................... 22 3.3.1 Simplified Nonlinear Turbine model ................................................................................................................ 23 3.3.2 The linearized hydro turbine model ................................................................................................................ 23 4 SYNCHRONOUS MACHINE ............................................................................................................................. 26 4.1 SYNCHRONOUS GENERATOR .......................................................................................................................................... 26 4.2 SYNCHRONOUS GENERATOR EQUATIONS ......................................................................................................................... 27 4.3 SYNCHRONOUS GENERATOR MODELS .............................................................................................................................. 28 4.3.1 Synchronous Machine Represented by the Classical Model ........................................................................... 29 5 TURBINE GOVERNING SYSTEMS ..................................................................................................................... 30 5.1 GOVERNING SYSTEM .................................................................................................................................................... 30 5.2 MECHANICAL‐HYDRAULIC GOVERNOR ............................................................................................................................. 31 5.2.1 Mathematical Modelling ................................................................................................................................ 31 5.3 ELECTRO‐HYDRAULIC GOVERNING SYSTEM ....................................................................................................................... 34 5.3.1 Mathematical Model ...................................................................................................................................... 34 Hydro Turbine and Governor Modelling
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