Adaptive on-load tap-changing voltage control for active distribution networks

Abstract

The basic prerequisites for the correct operation of the classic on-load tap-changing voltage control (CVC) are that the distribution network (DN) is passive. However, by installing distributed generators (DGs), today's DNs become increasingly active. Consequently, by measuring only the current and voltage magnitudes at the on-load tap-changing transformer secondary side, its automatic voltage regulator receives a false image of the DN load. In such a case, it is impossible to determine the optimal voltage value at the transformer secondary side in all possible states. Therefore, the CVC must be adapted to the new situation. This paper presents a simple, efficient, and inexpensive adaptive on-load tap-changing voltage control (AVC) for active DN with DGs and customers placed on different feeders. The adaptation refers only to the false image of DN load correction, based on the DN load assessment without the influence of DG. Practically, this correction is realized by minimal investment into the existing equipment and infrastructure. Thus, complicated methods requiring an expensive upgrade of DN in terms of communication infrastructure expansion, installation of new sensors and control devices, their coordination, and integration with modern IT/OT systems are avoided. The verification of the AVC is performed in real-life in the real-world active DN.

Appendix

A feeder with DG is considered, Fig. 

Fig. 14

Feeder with DG

14. Currents and voltages phasors at the feeder with DG are shown in Fig. 

Fig. 15

Currents and voltages phasors at the feeder with DG

15. For easy execution, the voltage phasor at the end of the feeder with DG is declared as the reference phasor $\hat{U}_{{\text{G}}}^{{\prime}} = U_{{\text{G}}}^{{\prime}} \angle 0^{ \circ }$.

The complex current at the beginning of the feeder with DG, Fig. 14, is:

$$ \hat{I}_{{\text{G}}} = \hat{I}_{{\text{G}}}^{{\prime}} + \hat{I}_{01} + \hat{I}_{02} = \hat{I}_{G}^{{\prime}} + j0.5 \cdot B \cdot \left( {\hat{U}_{{{\text{Tr}}}}^{{\prime\prime}} + \hat{U}_{{\text{G}}}^{{\prime}} } \right). $$

(21)

For the consideration that follows, an innocuous approximation is introduced:

$$ \hat{I}_{01} \approx \hat{I}_{02} = j0.5 \cdot B \cdot U_{{{\text{Tr}}}}^{{\prime\prime}} . $$

(22)

Based on the phasors diagram, Fig. 15 follows the equality of the real parts of the current phasors at the beginning and the end of the feeder:

$$ {\text{Re}} \{ \hat{I}_{{\text{G}}} \} \approx {\text{Re}} \{ \hat{I}_{{\text{G}}}^{{\prime}} \} \;, $$

(23)

$$ I_{{\text{G}}} \cdot \cos (\pi - \varphi_{{\text{G}}}^{{\prime}} - \alpha ) \approx I_{{\text{G}}}^{{\prime}} \cdot \cos (\pi - \varphi_{{\text{G}}}^{{\prime}} ), $$

(24)

that is:

$$ - I_{{\text{G}}} \cdot \cos (\varphi_{{\text{G}}}^{{\prime}} + \alpha ) \approx - I_{{\text{G}}}^{{\prime}} \cdot \cos \varphi_{{\text{G}}}^{{\prime}} . $$

(25)

Based on the law of the cosines and the trigonometric shifts follow:

$$ [B \cdot U_{{{\text{Tr}}}}^{{\prime\prime}} ]^{2} = I_{{\text{G}}}^{2} + I_{{\text{G}}}^{{\prime} 2} - 2 \cdot I_{{\text{G}}} \cdot I_{{\text{G}}}^{{\prime}} \cdot \cos \alpha , $$

(26)

$$ \cos (\varphi_{{\text{G}}}^{{\prime}} + \alpha ) = \cos \alpha \cdot \cos \,\varphi_{{\text{G}}}^{{\prime}} - \sin \alpha \cdot \sin \,\varphi_{{\text{G}}}^{{ ^{\prime}}} . $$

(27)

By replacing Eq. (27) into Eq. (25), the current magnitude at the end of the feeder with DG is as follows:

$$ I_{{\text{G}}}^{{\prime}} = I_{{\text{G}}} \cdot \left[ {\cos \alpha - \sin \alpha \cdot tg\varphi_{{\text{G}}}^{{\prime}} } \right]. $$

(28)

By replacing Eq. (28) into Eq. (26) follows:

$$ \begin{aligned} \left[ {B \cdot U_{{{\text{Tr}}}}^{{\prime\prime}} } \right]^{2} & = I_{{\text{G}}}^{2} \cdot \left[ {1 - \cos^{2} \alpha - \sin^{2} \alpha \cdot tg^{2} \varphi_{{\text{G}}}^{{\prime}} } \right] \\ & = I_{{\text{G}}}^{2} \cdot \sin^{2} \cdot \left[ {1 + tg^{2} \varphi_{{\text{G}}}^{{\prime}} } \right] = I_{{\text{G}}}^{2} \cdot \sin^{2} \alpha \cdot \cos^{ - 2} \varphi_{{\text{G}}}^{{\prime}} . \\ \end{aligned} $$

(29)

From Eq. (29), the value of the angle α, between the current phasors at the beginning and the end of the feeder, is defined:

$$ \sin^{2} \alpha = \frac{{B^{2} \cdot U_{{{\text{Tr}}}}^{{\prime\prime} 2} }}{{I_{{\text{G}}}^{2} \cdot \left[ {1 + tg^{2}\varphi{\prime}_{{\text{G}}}} \right]}} = \frac{{B^{2} \cdot U_{{{\text{Tr}}}}^{{\prime\prime} 2} }}{{I_{{\text{G}}}^{2} }} \cdot \cos^{2} \varphi_{{\text{G}}}^{{\prime}} . $$

(30)

Mathematically, the previous equation has two solutions, $\pm \alpha$. Practically, the current at the beginning of the feeder, with DG and no customers, is the leading one over the current at its end. So, there is only one physically applicable solution:

$$ \alpha = \arcsin \;\left[ {\frac{{B \cdot U_{{{\text{Tr}}}}^{{\prime\prime}} }}{{I_{{\text{G}}} }} \cdot \cos \varphi_{{\text{G}}}^{{\prime}} } \right]. $$

(31)

Based on the phasors diagram, Fig. 15, Eq. (24) and the known value of the angle α, a current phasor at the beginning of the feeder with DG is defined:

$$ \hat{I}_{{\text{G}}} = - I_{{\text{G}}} \cdot \cos (\varphi_{{\text{G}}}^{{\prime}} + \alpha ) + jI_{{\text{G}}} \cdot \sin (\varphi_{{\text{G}}}^{{\prime}} + \alpha ). $$

(32)

Based on Fig. 15 and Kirchhoff's current and voltage laws:

$$ \hat{U}_{{{\text{Tr}}}}^{{\prime\prime}} - U_{{\text{G}}}^{{\prime}} - \hat{Z} \cdot \hat{I}_{12} = 0, $$

(33)

$$ \hat{I}_{12} = I^{{\text{Re}}} + jI^{{\text{Im}}} = \hat{I}_{{\text{G}}} - j0.5 \cdot B \cdot U_{{{\text{Tr}}}}^{{\prime\prime}} , $$

(34)

follows a system of two equations with two unknown values $\theta$ and $U_{{\text{G}}}^{{\prime}}$:

$$ {\text{Re}}:\quad U_{{{\text{Tr}}}}^{{\prime\prime}} \cdot \cos \theta - R \cdot I_{12}^{{{\text{Re}}}} + X \cdot I_{12}^{{{\text{Im}}}} = U_{{\text{G}}}^{{\prime}} , $$

(35)

$$ {\text{Im}}:\quad U_{{{\text{Tr}}}}^{{\prime\prime}} \cdot \sin \theta - X \cdot I_{12}^{{{\text{Re}}}} - R \cdot I_{12}^{{{\text{Im}}}} = 0. $$

(36)

Equation (36) gives the value of the phase shift of the voltage at the end of the feeder θ, related to the voltage at its beginning:

$$ \theta = - \arcsin \;\left[ {\frac{{X \cdot I_{12}^{{\text{Re}}} + R \cdot I_{12}^{{\text{Im}}} }}{{U_{{{\text{Tr}}}}^{{\prime\prime}} }}} \right]. $$

(37)

The value of the voltage at the end of the feeder with DG $U_{{\text{G}}}^{{\prime}}$ is defined based on Eq. (35).

The previous equations and Fig. 15 are in accordance with $\hat{U}_{{\text{G}}}^{{\prime}} = U_{{\text{G}}}^{{\prime}} \angle 0^{ \circ }$. To correctly processed the current phasors at the beginning of the feeders with DG and the transformer secondary side, it is necessary for them to be expressed in relation to a common reference phasor. If a voltage phasor at the transformer secondary side is declared as the reference phasor $\hat{U}_{{{\text{Tr}}}}^{{\prime\prime}} = U_{{{\text{Tr}}}}^{{\prime\prime}} \angle 0^{ \circ }$, then the current phasor at the beginning of the feeder with DG is defined as:

$$ \hat{I}_{{\text{G}}} = - I_{{\text{G}}} \cos (\varphi_{{\text{G}}}^{{\prime}} + \alpha - \theta ) + jI_{{\text{G}}} \sin (\varphi_{{\text{G}}}^{{\prime}} + \alpha - \theta ), $$

(38)

$$ \psi_{{\text{G}}} \approx \pi - \varphi_{{\text{G}}}^{{\prime}} - \alpha + \theta . $$

(39)