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.