E. Barocio

A Dynamic Mode Decomposition Framework for Global Power System Oscillation Analysis

A global multiscale method based on a dynamic mode decomposition (DMD) algorithm to characterize the global behavior of transient processes recorded using wide-area sensors is proposed. The method interprets global dynamic behavior in terms of both, spatial patterns or shapes and temporal patterns associated with dynamic modes containing essentially single-frequency components, from which the mode shapes, frequencies and growth and decay rates of the modes can be extracted simultaneously. These modes are then used to detect the coherent and dominant structures within the data. The technique is well suited for fast wide-area monitoring and assessment of global instability in the context of modern data fusion-based estimation techniques. Results of the application of the proposed method to large, high-dimensional data sets are encouraging.

Normal form analysis of stressed power systems: incorporation of SVC models

In this paper a comprehensive analytical technique based on normal form theory and symbolic computer algebra is proposed for the analysis of non-linear inter-area oscillations in stressed power systems that incorporate the operation of Static VAR Compensators (SVCs). A second-order representation of the power system is derived that considers the explicit representation of synchronous machines and multiple SVCs in the state representation. On the basis of this model, normal form theory is used to study non-linear power system behaviour following large disturbances. The proposed approach is general and may be extended to include other FACTS devices. A simplified 4-machine, 11-bus test system is used to study the effect of SVC voltage support on system damping.

Scaling of normal form analysis coefficients under coordinate change

Power system normal form analysis has developed coefficients and indices in modal coordinates to quantify nonlinear modal interactions. We study the changes in the coefficients and indices when the power system equations are expressed in different coordinates or units and show that they can be normalized to be invariant to coordinate changes and thus intrinsic to the power system. The results are illustrated on a 4-generator system. An example shows that the coefficients and indices not only detect nonlinear interactions but also can become very large near a strong resonance in the system linearization.

Analysis of nonlinear modal interaction in stressed power systems with SVCs

This paper discusses the application of normal form theory to study nonlinear modal interaction in stressed power systems that include static VAr compensators (SVCs). A second-order representation of the power system is developed wherein static compensation and synchronous machines interact through the linear representation of the transmission system. Then, a modified normal form method is used to study nonlinear modal interaction between inertial modes and control modes. The proposed approach is general and may be extended to include other FACTS devices. A simplified 4-machine, 11-bus test system is used to study the effect of SVC voltage support on system damping.

Detection and visualization of power system disturbances using principal component analysis

In this paper, a multivariate statistical projection method based on Principal Component Analysis (PCA) is proposed for detecting and extracting unusual or anomalous events from wide-area monitoring data. The method combines PCA with statistical test to detect and analyze anomalous dynamic events from measured data. Simulations based on a transient stability model of the New England Test System are used to demonstrate the ability of the method to detect and extract system events from wide-area data.

A real normal form approach to the study of resonant power systems

A novel formulation for computing real normal forms of resonant vector fields is presented. Making use of a special real-valued nonlinear transformation of coordinates in physical space, a general technique for the computation of real normal forms is proposed. Symbolic and numerical calculations are presented to illustrate the effectiveness and applicability of the proposed analytic technique.

Analysis of modal interaction in power systems with FACTS controllers using normal forms

In this paper, an analytical procedure based upon normal form (NF) theory and the Kronecker product, is proposed for the analysis of second-order modal interaction in power systems with multiple static VAR compensators (SVCs). The approach used is based on a flexible representation of the power system and may be used to study higher-dimensional systems. First, an analytical derivation is developed which is utilized to investigate the effects of nonlinear modal interaction on system dynamic performance. Next, analytical expressions are derived that provide approximate solutions near a singularity and techniques for interpreting these solutions in terms of modal functions are given. The analysis methodology is demonstrated on a practical 46-machine, 189-bus test system in which several SVCs are used to support system voltage. Results of the second-order normal form study are presented and techniques for implementing each phase of the method are discussed. The analysis results are compared with the detailed step-by-step time-domain simulations (SBSS) of the system to test the validity of the analysis.

Coordinated application of FACTS controllers to damp out inter-area oscillations

Abstract This paper proposes a systematic analysis and design procedure for simultaneously determining the best locations and input signals of flexible AC transmission system (FACTS) devices in order to damp out inter-area oscillations. First, a modified modal power flow oscillation flow method is developed to determine the nature of the energy exchange over the transmission network in the presence of FACTS devices. With this method, the modal distribution along critical system paths is identified, and the contribution of each machine and network device is computed. Controllability and observability studies are then used to assess the effect of existing FACTS controllers on system damping as well as to identify optimal locations for new devices. The proposed procedure is demonstrated on a 46-machine, 190-bus reduced-order equivalent model of the Mexican interconnected system that includes several static VAR compensators.

Perturbations of weakly resonant power system electromechanical modes

It is not uncommon for oscillatory electric power system modes to move close to a resonance in which eigenvalues coincide. In a weak resonance, the modes are decoupled and the eigenvalues do not interact. We analyze general perturbations of a weak resonance and find two distinct behaviors, including interactions near strong resonances in which the eigenvalues quickly change direction. The possible perturbations are illustrated with interactions between electromechanical modes in a 4-generator power system. Some of the interactions are similar to subsynchronous resonance and can lead to oscillatory instability.

Assessment of non-linear modal interaction in stressed power networks using the method of normal forms

Abstract This paper reports on the experience in the analysis of non-linear effects arising from the interaction between the fundamental modes of oscillation in power systems. The approach used is based on a flexible representation of the power system derived from the utilisation of a modified normal form approach. First, a brief introduction to the method of normal forms is presented; then a non-linear model of the power system that includes the representation of second-order effects is proposed for the analysis of non-linear effects in a classical model of the power system. This approach is general and can be extended to allow for the analysis of higher dimensional non-linear systems. Based on this formulation, approximate closed form time-domain solutions are utilised to evaluate the influence of non-linear modal interaction on system behaviour. The procedures developed are tested on a 46-machine, 190-bus practical system.