Chia-Chi Chu

Model-order reductions for MIMO systems using global Krylov subspace methods

This paper presents theoretical foundations of global Krylov subspace methods for model order reductions. This method is an extension of the standard Krylov subspace method for multiple-inputs multiple-outputs (MIMO) systems. By employing the congruence transformation with global Krylov subspaces, both one-sided Arnoldi and two-sided Lanczos oblique projection methods are explored for both single expansion point and multiple expansion points. In order to further reduce the computational complexity for multiple expansion points, adaptive-order multiple points moment matching algorithms, or the so-called rational Krylov space method, are also studied. Two algorithms, including the adaptive-order rational global Arnoldi (AORGA) algorithm and the adaptive-order global Lanczos (AOGL) algorithm, are developed in detail. Simulations of practical dynamical systems will be conducted to illustrate the feasibility and the efficiency of proposed methods.

MIMO Interconnects Order Reductions by Using the Multiple Point Adaptive-Order Rational Global Arnoldi Algorithm

We extend the adaptive-order rational Arnoldi algorithm for multiple-inputs and multiple-outputs (MIMO) interconnect model order reductions. Instead of using the standard Arnoldi algorithm for the SISO adaptive-order reduction algorithm (AORA), we study the adaptive-order rational global Arnoldi (AORGA) algorithm for MIMO model reductions. In this new algorithm, the input matrix is treated as a vector form. A new matrix Krylov subspace, generated by the global Arnoldi algorithm, will be developed by a Frobenius-orthonormal basis. By employing congruence transformation with the matrix Krylov subspace, the one-sided projection method can be used to construct a reduced-order system. It will be shown that the system moment matching can be preserved. In addition, we also show that the transfer matrix residual error of the reduced system can be derived analytically. This error information will provide a guideline for the order selection scheme. The algorithm can also be applied to the classical multiple point MIMO Pade approximation by the rational Arnoldi algorithm for multiple expansion points. Experimental results demonstrate the feasibility and the effectiveness of the proposed method.

Nonlinear STATCOM Controller using Passivity-Based Sliding Mode Control

The passivity-based sliding mode (PBSM) approach has been used on designing static synchronous compensator (STATCOM) controller aimed at reactive power compensation and voltage regulation. The energy-dissipative properties of the proposed model derived in the synchronous d-q rotating frame are fully retained. The proposed controller design is separated into the inner loop and the outer loop controller. In the inner loop, passivity-based control is employed by using energy shaping and damping injection techniques to produce the proper switching function for voltage source converter (VSC)-based STATOCM. The load terminal voltage and the DC-side voltage dynamics are regulated via the outer loop controller cascaded to the inner loop controller. The outer loop control is employed by two sliding mode controllers to determine the appropriate current command. Simulation results are presented to show efficacy of the resulting PBSM controller with regard to voltage regulation and reactive power compensation

The Multiple Point Global Lanczos Method for Multiple-Inputs Multiple-Outputs Interconnect Order Reductions

The global Lanczos algorithm for solving the RLCG interconnect circuits is presented in this paper. This algorithm is an extension of the standard Lanczos algorithm for multiple-inputs multiple-outputs (MIMO) systems. A new matrix Krylov subspace will be developed first. By employing the congruence transformation with the matrix Krylov subspace, the two-side oblique projection-based method can be used to construct a reduced-order system. It will be shown that the system moments are still matched. The error of the 2q-th order system moment will be derived analytically. Furthermore, two novel model-order reduction techniques called the multiple point global Lanczos (MPGL) method and the adaptive-order global Lanczos (AOGL) method which are both based on the multiple point moment matching are proposed. The frequency responses using the multiple point moment matching method have higher coherence to the original system than those using the single point expansion method. Finally, simulation results on frequency domain will illustrate the feasibility and the efficiency of the proposed methods.

Boundary properties of the BCU method for power system transient stability assessment

The BCU method has been confirmed as an important on-line tool for direct transient stability assessment of power systems. The boundary property, which guarantees the controlling UEP of the original model and that of the reduced-state model, is a key issue in the BCU method. Instead of one-parameter transversality conditions proposed earlier, analytical results on the boundary property will be explored. We have applied the self-indexing energy function and the structural stability to analyze boundary properties of simple power systems. We have shown that, under certain mild conditions, the original system and the reduced-state system share the same UEPs on stability boundaries. Numerical studies confirm theoretical developments.

Robust consensus-based droop control for multiple power converters in isolated micro-grids

In order to provide autonomous power sharing of the conventional droop-control scheme for multiple power converters in isolated micro-grids, two consensus-based droop-control schemes will be examined. Since the conventional uniform droop gain ratio scheme requires identical droop gain ratio settings among all converters, applications to large-scale systems are restricted. An alternative scheme with the non-uniform droop gain ratio is proposed in this paper to simplify the droop gain setting while maintaining the perfect power sharing. Also, this new scheme is more robust since it is independent of particular gain settings. Real-time simulations of a micro-grid system are conducted to validate the effectiveness of this robust consensus-based droop control method.

Moment computations of nonuniform distributed coupled RLC trees with applications to estimating crosstalk noise

A novel method is proposed to compute moments of nonuniform distributed coupled RLC transmission lines. Recursive formulae of moments of coupled RC trees are extended to those of coupled RLC trees by considering both self inductances and mutual inductances. It can be observed that moment computations of distributed lines outperform those of lumped ones. The inductive crosstalk noise waveform can be accurately and efficiently estimated using the moment computation technique in conjunction with the projection-based order reduction method. Fundamental developments of the proposed approach are described in detail. Experimental results demonstrate the improved accuracy of the proposed method over that of the traditional lumped methods.

Multi-point model reductions of VLSI interconnects using the rational Arnoldi method with adaptive orders (RAMAO)

This work proposes the rational Arnoldi method with adaptive orders for high-speed VLSI interconnect reductions. It is based on an extension of the classical multi-point Pade approximation by using the rational Arnoldi iteration approach. Given a set of expansion points, the transfer function error at each expansion point is derived first. In each iteration of the proposed algorithm, the expansion frequency corresponding to the maximum output moment error is chosen. The corresponding reduced-order model yields the greatest output moment improvement.

Applications of tree/link partitioning for moment computations of general lumped RLC networks with resistor loops

A new moment computation technique for general lumped circuits with resistor loops is proposed. Using the concept of tearing, a lumped network can be portioned into a spanning tree and several resistor links. The contributions of network moments from each tree and the corresponding links can be determined independently. By combining the conventional moment computation algorithms and the reduced ordered binary decision diagram (ROBDD), the proposed method can compute system moments efficiently.

Energy function based neural networks UPFC for transient stability enhancement of network-preserving power systems

An energy function based unified power flow controller (UPFC) is developed for improving transient stability of network-preserving power systems. In order to consider model uncertainties, we also propose a forward neural networks controller to deal with such model uncertainties. This controller can be treated as neural network approximations of energy function control actions and provides online learning ability. Simulations on two power systems demonstrate that the proposed control strategy is very effective for suppressing power swing even under severe system conditions.