Prof. Dongdong Li, Mengxian Sun (Presenter)

Shanghai University of Electric Power, Shanghai, China

18/07/2023

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Dynamic Short Circuit Ratio for Stability Assessment of Grid Connected VSC-HVDC Systems Involving Wide-band Oscillatory Behaviors

System with PEDs Implemented

Generator: 50 Hz or 60 Hz AC is created from a rotating electro-magnet. Its dynamic is described by

The dynamic behaviors of power system are dominated by controls of PEDs.

Power electronic device (PED): Its dynamic is set by software （digital control). Besides, it behaves differently from a traditional generator.

The dynamic behaviors of power system are dominated by rotors of the generators.

The Wide-band Oscillations in Real World

For the past few years, the wide-band oscillation is a concerned stability issue which stems from the complicated interaction between power electronic devices (PEDs) and weak receiving-end AC grid.

Introduction of the Short Circuit Ratio

Definition: Short Circuit Ratio (SCR) is a metric index which can be used to quantify the strength of nonlinear system which is relative to system stability. Its expression is given by

V_thi and Z_thi are respectively Thevenin equivalent voltage and impedance seen from the Bus i。

Will it be okay If I connect it with experienced criterion？

Larger SCR, Stronger System Strength

• SCR>3: Strong, much more stable
• 2<SCR<3: Weak, stable.
• SCR<2: Very weak, unstable.

SCR? Wide-band Oscillation?

Two modification of SCR:

• Composite short circuit ratio by GE
• Weighted short circuit ratio by ERCOT

Motivations of Our Recent Research Work

K_pll^I ：1400 →4500

K_pll^P：60→600

Detailed model of the VSC-HVDC system in Simulink Library

SCR：1.9999→0.9905

L_g：0.42095H→0.85H

• The relationship between SCR and wide-band oscillations is ambiguous.
• The critical value of SCR is not clear (not a fixed value).

RTDS simulation of SCR changing^[1]

[1] Y. Qi, H. Ding, Y. Zhang, X. Shi and A. M. Gole, “Identification of Sub-Synchronous Interaction in MMC Systems using Frequency Scanning,” 2020 IEEE Power & Energy Society General Meeting (PESGM), 2020, pp. 1-5.

Dynamic Short Circuit Ratio (DSCR)

The DSCR is defined as the following equation.

The diagram of grid-connected VSC-HVDC system and its control loops

where ρ_co is a correction factor which is relative to the system parameters.

DSCR is a modification of SCR by the correction factor.

A sensitivity factor is defined with the DSCR.

If SF_DSCR >0, system stability is improved.

What is the physical meaning of DSCR?

What is the critical value of DSCR?

The relation between DSCR and Stability

Whether the system is stable or not

The stability criterion:

DSCR>1, the system is stable. Otherwise, the system is unstable.

There exist a finite-step Lyapunov function such that

Whether the general asymptotic gain matrix (GAGM) is a non-negative matrix which has shrinking property or not

Lyapunov Stability criterion: If

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is satisfied, the system is stable.

• The sufficiency and necessity of the proposed stability criterion have been demonstrated^[2].
• The critical value of DSCR is a fixed value.

[2] D. Li, M. Sun, Y. Mi, Y. Zhao and Y. Gao, “Dynamic Short Circuit Ratio for Stability Assessment of Grid Connected VSC-HVDC Systems Considering the Impact of Time-Varying Phase Shift,” in IEEE Transactions on Power Systems, doi: 10.1109/TPWRS.2023.3244788.

The relation between DSCR and Stability

The system is stable

[3] N. Noroozi and B. S. Rüffer, “Non-conservative dissipativity and small-gain theory for ISS networks,” 53rd IEEE Conference on Decision and Control, Los Angeles, CA, USA, 2014, pp. 3131-3136, doi: 10.1109/CDC.2014.7039872.

Spectral radius of Γ:

Take a two order system^[3] as an example

By iterating above equation in one step, there is no one positive matrix P satisfying

The positive function V cannot be found.

By iterating the two order system in three steps and taking infinite norm as a measurement function, we can get

Is the system unstable?

The Description of the Test System

RT-LAB Platform

TABLE I

Key System Parameters of Grid connected VSC-HVDC System

The Verification of effectiveness of DSCR

DSCR(P₁)：1.1805 → 1.1786；

DSCR(P₂)：1.1786 → 0.9339。

DSCR(P₃)： 1.1805 → 1.1439；

DSCR(P₄)： 1.1439 → 0.9909。

DSCR(P₅)： 1.1805 → 1.053；

DSCR(P₆)： 1.053 → 0.7763。

The Comparison between DSCR and SCR

The expression of the sensitivity factor of SCR is given by

Table II

The Computation Results of SF_DSCR and SF_SCR under Different System Conditions

• SCR is only sensitive to L_g.
• Because the impacts of system parameters can be taken into account by the correction factor ρ_co, the value of SF_DSCR changes as all system parameters varies, which means DSCR is sensitive to L_g, K_i^P and K_i^I_.

The Relationship between the DSCR and Oscillation Frequency

• If the increment of inductor parameter of the receiving-end AC grid results in the value of DSCR being less than one, the dominated oscillation frequency is the sup-synchronous frequency。
• If the variation of the current control’s parameters causes the value of DSCR to be less than one, the magnitude of current corresponding to the medium frequency has non-negligible influence on the system stability。

The DFT analysis of A phase instantaneous current injected into receiving-end grid under different values of L_g.

The DFT analysis of A phase instantaneous current injected into receiving-end grid under different values of K_i^P.

The DFT analysis of A phase instantaneous current injected into receiving-end grid under different values of K_i^I.

The Impacts of Outer-loops on Validation

of DSCR

K_oI^Q：0.1→10

K_oP^DC：0.1→10

K_oI^DC：5→20

K_oP^P：0.1→5

K_oI^P：5→200

K_oP^Q：0.1→3

TABLE III

The Computation Results of DSCR with Changes of Parameters of Various Outer-Loop Controls

Concluding Remarks

What we have done:

• The relationship between DSCR and dynamic stability has been established.
• The critical value of DSCR is a fixed value, one, unaffected by the system parameters. It can distinguish between the stable and unstable margin effectively.
• The relationship between DSCR and oscillation frequency is preliminary investigated. If the increment of inductor parameter of the receiving-end AC grid results in the value of DSCR being less than one, the dominated oscillation frequency is the sup-synchronous frequency. If the variation of the current control’s parameters causes the value of DSCR to be less than one, the magnitude of current corresponding to the medium frequency has non-negligible influence on the system stability..

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Some issues need to be solved in the future:

• The mathematical relation between DSCR and oscillation modes has not been established well.
• The computed method of the correction factor is complicated, making it difficult to be used in the real industry engineering compared with impedance method.
• The influence of interaction between different kinds of PEDs is ignored.

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