Balanced Truncation Approach to Power System Model Order Reduction

Abstract

This article demonstrates the application of balanced truncation based model order reduction to the task of dynamic reduction of power systems. The entire power system is separated into an external area and a study area; dynamic reduction of the external area is conducted. The benefit of applying the balanced truncation technique is that key input-output relationships between these areas are retained during the reduction process. For perturbations originating in the study area, patterns in the dynamic behavior of the external area, such as generator coherency, are well captured by the reduced equivalent. The efficiency of the balanced truncation algorithm is also explored in the context of changing system conditions. Illustrative applications using a test system representative of the northern grid of India have led to some key findings on the coherency of the generators in this grid.

PSO Based reduced order modelling of autonomous AC microgrid considering state perturbation

“…BT involves large matrix computations while analyzing larger power systems, for evaluating the controllability and observability of system. DC offset may occur while evaluating lower order approximations due to its inefficiency in following the original system's steady-state behaviour [4].…”

“…Several methods have been explored to reduce the dimensionality of large power systems in the literature [1][2][3][4][5][6][7][8]. Aggregation, balanced realization, truncation, and certain mixed methods have been discussed to reduce the order of these power systems in [3].…”

“…Aggregation, balanced realization, truncation, and certain mixed methods have been discussed to reduce the order of these power systems in [3]. Balanced Truncation (BT) technique has been applied to large power systems in [4] using a number of matrix calculations. But the main drawback lies in the frequent occurrence of a steady-state error in BT-reduced order model.…”

Vector Fitting-Based Reduced Order Modelling Method for Power Cables

“…In addition, the order of the fitted state space model/ transfer function of power cable can be very high, since the parasitic capacitance exists along the power cable [7,8,12]. There are numerous classical model order reduction (MOR) methods for linear time invariant (LTI) systems [6,7,10,11,[13][14][15][16][17], among which the singular value decomposition (SVD)-based approximation method has been gained much population [11,14]. SVD-based MOR methods mainly consist of proper orthogonal decomposition (POD) technique, balanced truncation (BT) approach.…”

“…However, the obtained reduced order model is not the same once the inputs and initial conditions change. BT approach first uses a transformation matrix to transform the original state space model to an internally balanced system, which means the controllability Gramian and the observability Gramian are the same and are diagonal [17]. The elements of the balanced diagonal matrix are the Hankel singular values (HSVs) representing the importance of the state variables on the input-output behavior [15].…”