# Analysis of Electrical Circuits with Variable Load Regime by A. Penin

By A. Penin

This booklet introduces electrical circuits with variable so much and voltage regulators. It permits to outline invariant relationships for varied parameters of regime and circuit sections and to turn out the recommendations characterizing those circuits. Generalized identical circuits are brought. Projective geometry is used for the translation of alterations of working regime parameters. Expressions of normalized regime parameters and their alterations are awarded. handy formulation for the calculation of currents are given. Parallel voltage resources and the cascade connection of multi-port networks are defined. The two-value voltage rules features of lots with constrained strength of voltage resource is taken into account. The booklet offers the basics of electrical circuits and develops circuit theorems. it really is worthwhile to engineers, researchers and graduate scholars who're attracted to the fundamental electrical circuit idea and the legislation and tracking of energy offer systems.

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Additional info for Analysis of Electrical Circuits with Variable Load Regime Parameters: Projective Geometry Method

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22) as ( 1 10 1 0 I11 ¼ ÀY11 DR10 L1 I1 þ Y12 DRL2 I2 þ I1 1 10 1 0 I21 ¼ Y12 DR10 L1 I1 À Y22 DRL2 I2 þ I2 : Then, we get ( À Á1 10 1 0 1 þ Y11 DR10 L1 I1 À Y12 DRL2 I2 ¼ I1 À Á : 1 10 1 0 ÀY12 DR10 L1 I1 þ 1 þ Y22 DRL2 I2 ¼ I2 ð1:23Þ The solution of Eq. 23) gives the subsequent currents À Á 0 0 I10 þ DR10 L2 Y22 I1 þ Y12 I2 ¼ ; D10 À Á 0 0 I 0 þ DR10 L1 Y11 I2 þ Y12 I1 I21 ¼ 2 D10 I11 ð1:24Þ where the determinant 2 10 10 10 D10 ¼ ð1 þ Y11 DR10 L1 Þð1 þ Y22 DRL2 Þ À ðY12 Þ DRL1 DRL2 : Let us carry out the analysis of these relationships.

Y11 a12 V1 Á ¼ YD10Y a22 I1 Y 10 1 Y10 Y00 Y10 # Á ! V1 : I1 Introduction ð1:29Þ Using the attenuation coefﬁcient c [2], we may rewrite Eq. 29) V0 I0 YIN:C ! # ! " pYL:C ﬃ V1 ﬃﬃﬃﬃ chc shc DY ¼ Á : 1 ﬃ pIﬃﬃﬃﬃ shc chc D ð1:30Þ Y In turn, the admittance transformation has the view YL YIN Y þ thc ¼ L:C YL : YIN:C 1 þ Y thc L:C ð1:31Þ We have the relative values YIN =YIN:C , YL =YL:C . 31) is not a pure relative because contains the value thc. This value is diverse for twoports with different losses.

10. The equation of the load straight line of the ﬁrst active two-pole in Fig. 3) take place; that is, ~I1 I1 ¼ SC ; SC ~I1 I1 ~1 V1 V ¼ : ~0 V0 V The equation of the load straight line of the second active two-pole in Fig. 10b is given by I1 ¼ y0N y1N ðV0 À V1 Þ; y0N þ y1N where conductivity y1N corresponds to the conductivity of voltage regulator. (a) y01 (b) I1 V1 V0 + − YL1 y01 V0 + − N I1 + V1N − y1N V1 YL1 Fig. 10 a Active two-pole without a voltage stabilization. b Stabilization of a load voltage 12 1 Introduction It is possible to carry out the normalization by the SC current I1SC if there is an access to this source at an experimental investigation.