on the design and placement of a supplementary damping ... · omar kotb. elkraft 2017. chalmers...

On the Design and Placement of a Supplementary Damping Controller in an Embedded VSC-MTDC

NetworkOmar Kotb*, Mehrdad Ghandhari*, Robert Eriksson**, Javier Renedo***, Luis Rouco***,

*Department of Electric Power and Energy Systems, KTH, Stockholm, Sweden**Svenska Kraftnät (Swedish National Grid), Sundbyberg, Sweden

***Institute for Research in Technology, Comillas Pontifical University, Madrid, Spain

Presented by:Omar Kotb

Elkraft 2017Chalmers University of TechnologyGothenburg, Sweden2017-05-18

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Presentation Outline

• Introduction• Motivation• Power System Model• Controller Design• Conclusions


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Introduction: Embedded VSC-MTDC Network


Embedded VSC-MTDC: locatedwithin one synchronous AC grid.

Segmented AC system: VSC-MTDC connecting more thanone asynchronous AC grids.

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AC/DC Power System Model:

• One slack bus

• VSC representedby average model

• Master-slave DC voltage control


MTDC Control Imperatives in AC/DC Power System

• Primary control: active&reactive power, DC voltage, AC voltage

• Supplementary control: Power Oscillation Damping (POD), frequency support

• Control coordination: PSS, other FACTS POD

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Motivation

Supplementary (POD) control not sufficiently investigated as comparedto primary control in VSC-MTDC

Multiple damping controllers: adverse control interactions

Control coordination problem through nonlinear optimization:- Complex objective functions- Time-consuming solutions

Strategic placement of supplementary controller(s)


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MLQG-MISO control allows damping of targeted modes of interest, other modes are not affected

Assumptions:

• Negligible time delays

• PMUs readily available

Motivation


SISO control structure

MISO control structure

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Power System Model

( , , )0 ( , , )x f x y u

g x y u==

- Nonlinear DAE system model:

- Linearized system model:

Linearization conducted around the equilibrium point of the DAE system.

0x y u

x y u

x f x f y f ug x g y g u

∆ = ∆ + ∆ + ∆

= ∆ + ∆ + ∆


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Eigenvalue sensitivity to controller parameter (q):

( )2

( , ) 1|1 ( , )i

Tii s i i

i

F s qR w B Cvq q F qλλ

λ=

∂ ∂= =

∂ ∂ −

Power System Model


::

i

i

wv

Mode’s left eigenvector

Mode’s right eigenvector

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x Ax Bu wy Cx υ= + + Γ= +

- Linearized state-space system model:

Process noise measurement noise:w :υ

- Modal variables:

( ) ( )z t Mx t=

Power System Model


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- Cost function:

( )( )0

limT

T T Tk mT

J E x M Q M x u Ru dt→∞

= +

∫

:mQ:R

Weighting matrix for modal variables

Weighting matrix for controller output

:M Mapping matrix

Feedback control law given by: ˆ( ) (t)u t Kx= −

MLQG Control Design


:K MLQG controller gain

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Constant estimation error feedback matrix, obtained by the solution of Algebraic Ricccati Equation (ARE):

ARE solution is according to cost function for Kalman filter:

( )0

limT

T TL T

J E x Wx u Vu dt→∞

= +

∫

MLQG Control Design


obtained using Kalman filter:ˆ(t)x ( )ˆ ˆ ˆ(t)x Ax Bu L y Cx Lυ= + + − +

:L

( )ˆ ˆ ˆ(t)x Ax Bu L y Cx Lυ= + + − +

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, , , ,,

A B C MW V

Γ

Model

LQG

,mQ R

Results

MLQG Control Design

MLQG POD supplementary controller design merits:

- Enhanced robustness- Targeted damping of specific oscillatory modes

(weighting matrices)- Linear control strategy

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Results


Inter-area modes’ observabilities (normalized).

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Results


Inter-area modes’ locations in complex plane.

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Results


Disturbance: 10% load increase for 100 ms.

Power flow over inter-area AC tie line.

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Conclusions & Future Work

Research theme: AC/DC power system stability enhancement & controlthrough MTDC supplementary controls

Strategic positioning of a single damping controller within an embedded VSC-MTDC network

Investigation of supplementary (POD) control in case of droop controlused for DC voltage regulation.


Thank you! Questions?

18Elkraft 2017Chalmers University of TechnologyGothenburg, Sweden2017-05-18

on the design and placement of a supplementary damping ... · omar kotb. elkraft 2017. chalmers...

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