Chapter 4. Phase-Shifting Transformers

Chapter 4. Phase-Shifting Transformers - 4 Phase-Shifting...

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4 Phase-Shifting Transformers Gust av Preininge r Consultant 4.1 Introduction . ........................................................................ 4 -1 4.2 Basic Principle of Application . ........................................... 4 -2 4.3 Load Diagram of a PST . ..................................................... 4 -4 4.4 Total Power Transfer . .......................................................... 4 -5 4.5 Ty pes of Phase-Shifting Transformers . .............................. 4 -7 General Aspects . Single-Core Design . Two-Core Design . Quadrature Booster Transformers 4.6 Details of Transformer Design . ........................................ 4 -13 4.7 Details of On-Load Tap-Changer Application . .............. 4 -14 4.8 Other Aspects. .................................................................... 4 -16 Connection . Tests 4.1 Introduction The necessit y to control the power flow rose early in the histor y of the development of electrical power systems. When hig h-voltage grids were superimposed on local systems, parallel-connected systems or transmission lines of different voltage levels became standard. Nowadays large hig h-voltage power grids are connected to increase the reliabilit y of the electrical power supply and to allow exchange of electrical power over large distances. Complications, attributed to several factors such as variation in power- generation output and = or power demand, can arise and have to be dealt w ith to avoid potentially catastrophic system distur bances. Additional tools in the form of phase-shifting transformers (PSTs) are available to control the power flow to stabilize the grids. These may be justified to maintain the required qualit y of the electrical power supply. To transfer electrical power between two points of a system, a difference between source voltage ( V S ) and load voltage ( V L ) in quantit y and = or in phase ang le is necessar y. See Figure 4.1 . Using the notation of Figure 4.1, it follows that: Z ¼ R þ jX ¼ Z * e j g z (4 : 1) Z ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R 2 þ X 2 p (4 : 2) g Z ¼ arc tan X R ±² (4 : 3) V S ¼ V S * (cos g S þ j sin g S ), V L ¼ V L * g L þ j sin g L )( 4 : 4) D V ¼ V S ± V L (4 : 5) ß 2006 by Taylor & Francis Group, LLC.
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D V ¼ ( V S * cos g S ± V L * cos g L ) þ j( V S * sin g S ± V L * sin g L ) ¼ D V * e ± j g D (4 : 6) D V ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V 2 S ± 2 * V S * V L * cos ( g S ± g L ) þ V 2 L q (4 : 7) g D ¼ arc tan V S * sin g S ± V L * sin g L V S * cos g S ± V L * cos g L ±² (4 : 8) I ¼ D V Z * e j ( g D ± g Z ) (4 : 9) For sy mmetrical conditions V S ¼ V L ¼ V, and g S ¼ g = 2, and g L ¼ ± g = 2, R ² X, then D V ¼ V * 2 * sin ( g = 2) (4 : 10) g D ¼ p = 2( 4 : 11) I ¼ V * 2 * sin ( g = 2) X (4 : 12) 4.2 Basic Principle of Application Because of the predominantly inductive character of the power system, an active power flow between source and load must be accomplished w ith a phase lag between the terminals. Phase-shifting trans- formers are a preferred tool to achieve this goal. Two principal configurations are of special interest: (1) the power flow between transmission systems operating in parallel where one system includes a PST and (2) where a sing le transmission line which includes a PST is connecting two other w ise independent power systems. The latter is in fact a special case of the first, but it has become more import ant nowadays
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Chapter 4. Phase-Shifting Transformers - 4 Phase-Shifting...

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