ABSTRACT
To transfer electrical power between two points of a system, a di›erence between source voltage (VS) and load voltage (VL) in quantity and/or in phase angle is necessary. See Figure 4.1. Using the notation of Figure 4.1, it follows that:
Z = + =R jX Z e j z* γ (4.1)
Z R X= + 2 2 (4.2)
X R
= ⎛
⎝
⎜
⎞
⎠
⎟
arctan (4.3)
4.1 Introduction ...................................................................................... 4-1 4.2 Basic Principle of Application ......................................................... 4-3 4.3 Load Diagram of a PST ....................................................................4-4 4.4 Total Power Transfer ........................................................................4-6 4.5 Types of Phase-Shi¡ing Transformers ..........................................4-8
4.6 Details of Transformer Design ..................................................... 4-13 4.7 Details of On-Load Tap-Changer Application .......................... 4-15 4.8 Other Aspects .................................................................................. 4-18
Connection • Tests Bibliography ................................................................................................ 4-19
V * V *S S S S L L L L= + = +V j V j(cos sin ), (cos sin )γ γ γ γ (4.4)
Δ = −V V VS L (4.5)
Δ = − + − = Δ −
ΔV ( cos cos ) ( sin sin )V V V V V eS L S S L L j* * j * * *S Lγ γ γ γ γ (4.6)
Δ = − − +V V V V VS S L S L L2 22* * *cos( )γ γ (4.7)
γ γ γ
γ γΔ =
−
−
⎛
⎝
⎜
⎞
⎠
⎟
arc tan * * * *S
V V V V
sin sin cos cos
(4.8)
I V
Z e j Z= Δ Δ −* ( )γ γ (4.9)
For symmetrical conditions VS = VL = V, and γS = γ/2, and γL = −γ/2, R << X, then
Δ =
⎛
⎝
⎜
⎞
⎠
⎟
V V * sin2 2* γ (4.10)
γ pi
=
2 (4.11)
I
V X
=
/* *2 2sin( )γ (4.12)
Because of the predominantly inductive character of the power system, an active power «ow between source and load must be accomplished with a phase lag between the terminals. Phase-shi¡ing transformers are a preferred tool to achieve this goal. Two principal con–gurations are of special interest: (1) the power «ow between transmission systems operating in parallel where one system includes a PST and (2) where a single transmission line which includes a PST is connecting two otherwise independent power systems. e latter is in fact a special case of the –rst, but it has become more important nowadays for the interconnection of large systems. For the following considerations, it is assumed that the ohmic resistance R is small compared with the reactance X and thus has been neglected.
