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Optimization to controllability measure of the POD in DFIG-integrated power systems to improve small-signal stability margin considering the impact of pre-fault slip

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Abstract

The power oscillation damper (POD) at the doubly-fed induction generator (DFIG) helps to damp the low-frequency oscillation (LFO) in the power system, but the damping effect is affected by the pre-fault slip (s|0|) under the overspeed mode. This paper investigates the relationship among the damping effect of the POD, the transfer function (TF) of the POD, and s|0|, and proposes a new optimization scheme to extend the allowable range of s|0|. At first, the controllability measure (CM) is introduced to quantify the damping effect of the POD, and the sensitivity model of the CM is newly derived to analyze the influence of s|0| and the TF on the damping effect. Then, the small-signal stability margin (SSSM) is defined by the allowable range of s|0| and applied to quantify the system stability influenced by both s|0| and the POD. By adding a new constraint to the eigenvalue sensitivity, the sensitivity model of the SSSM is derived. Lastly, based on the proposed sensitivity model, the interior point method is applied to solve the proposed optimization scheme to POD’s parameters and extend the allowable range of s|0|. Simulation results show that the CM of the POD is more sensitive to s|0| than the TF of the POD. Compared with the existing eigenvalue sensitivity-based optimization scheme, the proposed scheme has a better effect on the SSSM.

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Data availability

The datasets used or analysed during the current study are available from the corresponding author on reasonable request.

Abbreviations

CM:

Controllability measure

DFIG:

Doubly-fed induction generator

LFO:

Low frequency oscillation

MPPT:

Maximum power point tracking

POD:

Power oscillation damper

PSS:

Power system stabilizer

RSC, GSC:

Rotor-side and grid-side converters

SG:

Synchronous generator

SSSM:

Small-signal stability margin

TF:

Transfer function

WT:

Wind turbine

A :

State matrix

B, C, D :

Input, output, and feed-forward matrices

E :

Identity matrix

F, X :

Imbalanced term and unknowns of power flow

f, g :

Differential and algebraic equations

G :

Transfer function of the POD

J :

Jacobian matrix

K POD, T d, T h :

Parameters of the POD

M :

Controllability measure

P, Q :

Active and reactive powers

p :

Laplace operator

R, X :

Resistance, reactance

s :

Slip

υ w :

Wind speed

I, V, θ :

Current, magnitude and angle of voltage

x, h :

State and algebraic variables

y :

Output vector

α :

Parameter of interest

μ :

Coefficient of the pre-fault slip variation

δ, ω :

Power angle, angular speed

ρ :

Electromechanical loop participation ratio

λ, ξ, φ :

Eigenvalue, damping ratio, participation factor

Ψ, Φ :

Left and right eigenvectors

Δ:

Increment

Ref:

Reference value

• :

Differential

n:

Iteration number

T:

Transpose

d, q, x, y:

Axis in direct/quadrature and x/y frames

In:

Input signal

M:

Mechanical parameter

M:

Magnetizing circuit

min, max:

Minimum and maximum values

S:

Stability margin

s, r, g:

Stator, rotor (or RSC), GSC

sys:

Power system except for DFIGs

*:

Critical mode

|0|:

Initial value

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Funding

This study was funded by the National Natural Science Foundation of China (grant number 51877061).

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, 230009, Anhui, China

    Shenghu Li & Diwen Tao

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  1. Shenghu Li
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Shenghu Li developed the idea of the study and analysed the data. Diwen Tao completed the mathematical modelling and wrote the paper.

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Correspondence to Diwen Tao.

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Li, S., Tao, D. Optimization to controllability measure of the POD in DFIG-integrated power systems to improve small-signal stability margin considering the impact of pre-fault slip. Electr Eng (2024). https://doi.org/10.1007/s00202-024-02335-6

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