Coherency-Independent Structured Model

Reduction of Power Systems

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Paper No: 15PESGMXXX

Christopher SturkLuigi Vanfretti

Yuwa Chompoobutrgool Henrik Sandberg

KTH Royal Institute of Technology, Sweden

Background (What ?) We propose a new model reduction

algorithm for power systems based on an extension of balanced truncation. A method for model reduction of non-coherent power

system areas which retains some nonlinearities is presented.

The method is an adaptation of a control-theoretic structure-preserving model reduction algorithm to a power systems setting.

(Why ?) The division of the power system can be made arbitrarily and does not rely on the identification of coherent generators.

(Expected outcome?) A reduced order system with a full nonlinear description of the study area and a reduced linear model of the external area. Algorithm demonstrated on the Klein-Rogers-Kundur 2-area

system and the KTH-NORDIC32 system. Various modes captured by varying the approximation order, which is relevant for distributed damping control.

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Structured Model ReductionObjective: Find the reduced order system such thatis made as small as possible and

where

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N(s) G(s)

G

Divide system into a study area N (where the nonlinearity will be retained) and an external area G (where it will be linearized and reduced).

Four-Step Algorithm1. Define the

model 2. Linearize the

model3. Apply model

reduction to the external area

4. Reconnect to the nonlinear model of the study area

Results

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Structured Model Reduction vs. Balanced Truncation

Responses after an initial perturbation to the machine angle δ1

Linear vs. Nonlinear Model Reduction

Responses after an initial perturbation Vref of the G1

Conclusions

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A model reduction algorithm based on an extension of balanced truncation, which is applicable to power systems, has been shown to be feasible for both small and large power systems. The algorithm takes the behavior of the full power system

into account when reducing the external area. If certain frequency ranges are amplified more by the

study area, the reduced model of the external area will be more accurate in those frequency ranges.

Validity and sensitivity of the reduced model have been demonstrated. For small disturbances, the reduced model is capable of

matching the responses of the full model nearly well, For larger disturbances, the reduced model is sufficient to

model the transients following a perturbation.