Leveraging Modal Analysis for Multi-scenario Power System

A Proposal for Allocating PMUs for Monitoring Critical Oscillation Modes in the Mexican System

The interconnected European power system is evolving due to the new extensions and to the systematic integration of Power Park Modules, i.e., unit or ensemble of units generation electricity (Renewable Energy (RE), Distributed Generation (DG), etc), which is connected to the grid by power electronics and FACTS (STATCOM, HVDC,…). As a consequence, the increase of the size and the emergence of the new oscillatory modes which involve distant dynamic devices, i.e., of coupling modes (modes associated to generator/turbine inertia, and modes associated to Power Park Modules), and of modes related to various regulations. In this paper, a full scan of European power system is given. An exhaustive method that determines all oscillatory modes independently of the system’s order, of the topology and without a priori knowledge about the system, is used. The exhaustive method is fully analytic. Indeed, it is based only on the state-space realisation of any given power system and does not require operator manipulation like dynamic simulations. To this end, we quantify and analyse the interaction between the different inputs/outputs of a given system. This leads to the identification of classes of coupled dynamic devices of the power system. Next, starting from a reduced number of classes, a selective modal analysis method is applied to each class to put into evidence a good approximation of all oscillatory modes. Finally, a complete classification of the oscillatory modes found at the previous stage is provided in terms of the types (interarea, electrical,…) and their characteristics (oscillation frequency, damping, participation,…). 2900 oscillatory modes were found for the studied model of the European system.

A steady state analysis is applied to study the voltage collapse problem. The modal analysis method is used to investigate the stability of the power system. Q-V curves are used to confirm the obtained results by modal analysis method and to predict the stability margin or distance to voltage collapse based on reactive power load demand. The load characteristics are considered in this research. Different voltage dependent loads are proposed in order to be used instead of the constant load model. The effect of induction machine load is considered in this study. The load is connected to several selected buses.;The analysis is performed for three well-known system; Western System Coordinating Council (WSCC) 3-Machines 9-Bus system, IEEE 14 Bus system and IEEE 30 Bus system. The modal analysis technique is performed for all systems using the constant load model, the voltage dependent load models and induction machine load model. Then, the most critical mode is identified for each system. After that, the weakest buses, which contribute the most to the critical mode, are identified using the participation factor. The Q-V curves are generated at specific buses in order to check the results obtained by the modal analysis technique and to estimate the stability margin or distance to voltage collapse at those buses.

A parameterized modal analysis is proposed to evaluate power system small-signal stability and a simulation procedure using DIgSILENT programming language (DPL) is presented for this purpose. Modal analysis, or small-signal stability analysis, refers to the ability of a system to withstand small perturbations around an equilibrium point without reaching instability or displaying sustained oscillations. This is an important problem in real systems as sustained oscillations may cause mechanical failures in generating units and make the system vulnerable to the point of losing stability. In order to define the most critical scenario, the standard approach employed by the industry is to consider the system at its maximum loading. This chapter proposes that critical scenarios should be further sought as in even lighter loading conditions, low-frequency oscillations may dangerously appear. Using DPL, the system modal analysis is parameterized in order to search for critical operating points. To validate the importance of employing a parameterized modal analysis, a real case is studied: the Northern Chile Interconnected System. The obtained results applying parameterized modal analysis show that the system in a real operation only requires minor deviations from the programmed operating points to incur in dangerous low-frequency oscillations. These results validate the importance of searching for critical scenarios and DPL scripting is used to program the steps of the proposed analysis. The scripts and applications presented in this chapter set the basis for additional development to identify critical scenarios for modal analysis in other real systems.

Voltage stability is a challenging issue for a power system with high penetration level. Two voltage stability indices are proposed in this paper to quantitatively evaluate the steady-state voltage stability and the short-term voltage stability respectively. The steady-state voltage stability metric is based on voltage collapse proximity indicator (VCPI) and considers the priorities of different transmission lines. The short-term voltage stability index evaluates not only the extent of the voltage deviation, but also the voltage recovery time, which is critical to the wind-penetrated power system. Complex load model is also considered in this paper to address the adverse impact of the induction motor loads on the power system. The New England 39-bus test system is used to demonstrate the effectiveness of the proposed indices in PSSE.

Direct stability analysis using an energy function has recently been widely used for angular and voltage stability analysis in electric power systems. Considerable efforts have concentrated on seeking energy functions for lossy power systems, accomplished only for the simple two-bus system. A new approach is presented to derive an energy function by using the complex integral of bus current equations with respect to bus voltages. Under an assumption that all transmission lines have a uniform R/X ratio, it is shown that the energy function can be developed for multimachine power systems with losses. The proposed energy function is tested on sample systems by comparing the time simulation method, which shows the validity of the proposed method.

In this paper, an investigation into the use of Flexible ac Transmission Systems (FACTS) devices to aid damping of low-frequency inter-area oscillations in longitudinal power systems is presented. A linear model of VSC-based FACTS devices that takes into account the dynamics of dc links is developed and incorporated into a production-grade software for small signal analysis of large power systems. Based on this representation, a unified framework for modal power oscillation flow studies is then developed to analyze the sensitivity of modal behavior to FACTS control action. With this method, the transmission corridors and system parameters having a large contribution to critical system oscillations modes are determined. The method is particularly well suited for investigating inter-system oscillations in large-scale power systems with embedded FACTS controllers The utilized methodology is tested on a practical 45-machine Mexican system that includes several major static VAR compensators. Control mode implementations are discussed and tested and comparisons with existing technologies are presented.

This chapter presents the small‐signal stability of power systems operating in “steady state,” that is, the system stability of an equilibrium point. The ability of the power system to track the load changes requires the power system to be small‐signal stable, that is, a power system can stably move from one operating condition to a slightly different operating condition. The chapter discusses electromechanical modes in power systems and techniques to compute and identify the frequency and damping of these modes. The approach used is to develop linearized system models that are valid in a region about the equilibrium operating point. Electromechanical modes in a practical power system can be divided into three types: intraplant modes; local modes; and interarea modes. The chapter provides an overview of the development of linear models for nonlinear systems. There are two methods commonly used for generating linearized models: using analytical expressions, and using a numerical perturbation method.

The authors propose here a new low‐frequency oscillatory (LFO) modes estimation scheme by applying Karhunen–Loeve transform (KLT) with total least square estimation of signal parameter employing rotational invariance technique (TLS‐ESPRIT). The proposed KLT provides the perfect decorrelation of the signal from the noise at low signal‐to‐noise ratio and for both white and coloured noise. KLT also maximally compress the energy of the estimated signal. KLT helps to estimate the signal subspace perfectly for any non‐stationary ambient power signal with the fastest computational time. First, the authors applied the KLT denoise to the filtered signal buried with highly correlated coloured Gaussian noise through the first eigenvectors of the correlation matrix and estimated the signal subspace. Finally, TLS‐ESPRIT is applied to estimate the modes of the power system. A comparative analysis of the KLT‐TLS‐ESPRIT with the modified TLS‐ESPRIT, multi‐channel wavelet transform, data driven‐stochastic subspace identification, TLS‐ESPRIT, Root‐MUSIC, and improved Prony method is presented. To explore the real‐time application of the KLT‐TLS‐ESPRIT, the authors considered Kundur's two‐area test system and 16‐machine 68‐bus system using 50,000 Monte‐Carlo simulations. The obtained results show that the KLT‐TLS‐ESPRIT accurately estimates the LFO with least mean and standard deviation as compared to the remaining six methods.

This paper reports experiences on voltage stability assessment for the Alberta interconnected power system with respect to the WSCC criteria. The WSCC criteria are first reviewed. The system transfer capability is then assessed under normal operating conditions and with credible contingencies. Modal analysis is performed on critical contingencies to identify their impacts and associated voltage collapse areas. The paper demonstrates a practical engineering approach to assess the voltage stability and reactive power reserve conditions of a real power system. In addition, methods for identifying critical voltage collapse mode and to measure the severity of contingencies are proposed.

Small-signal stability analysis of power system oscillations is a well-established field within power system analysis, but not much attention has yet been paid to systems with a high penetration of wind turbines (WTs) and with large wind power plants (WPPs). A comprehensive analysis is presented, which assesses the impact of full-load converter interfaced WTs on power system small-signal stability. The study is based on a seven-generator network with lightly damped inter-area modes. A detailed WT model with all grid relevant control functions is used in the study. The WT is, furthermore, equipped with a park-level WPP voltage controller and comparisons are presented. The WT model for this work is a validated dynamic model of the 3.6 MW Siemens wind power WT. The study is based on modal analysis which is complemented with the time-domain simulations on the non-linear system.

This paper proposes a method of selecting and/or locating phasor measurement unit (PMU) signals for monitoring critical oscillation modes in large power systems. A robust indicator, modal participation ratio, is introduced to identify critical PMU locations and signal channels, in order to monitor modes of interest to power system operators. This indicator is easy to compute in practice, and is theoretically rigorous based on linear control theory and spectral analysis. This indicator can suggest location and/or selection of PMUs in order to most effectively observe modes of interest to power system operators. The effectiveness and robustness of the algorithm is illustrated in both modified 68-bus system and 140-bus system.

The impact of converter-based loads on the power system is evaluated based on stability studies. This requires adequate load models. This paper deals with a time-domain model of an electric vehicle battery charger with grid support functionality (so-called controllable load). The dynamic properties of the components of a unidirectional 1,2 kW battery charger with input diode rectifier are discussed with respect to transients and oscillatory modes in power systems. Simulation results are shown for the battery charger model for a low-frequency oscillation. These results are compared to an induction motor load, which is directly connected to the mains.

Voltage stability is a vast subject, which covers a substantial area in power system analysis, such as uniform voltage profile, reactive power balance, and feasible operation of the power system. The study and understanding of voltage stability are not only crucial but also very helpful in the safe operation of a power system. This paper presents an implementation of modal analysis in voltage stability. Here, we propose to use of voltage-reactive power relations from the load flow jacobian matrix to establish a V-Q sensitivity relationship and study the unstable modes in a real-time power system of Nepal. This paper also describe a heuristic approach to bring back an unstable system to a stable operating regime using the results of modal analysis, and further analyze the root cause behind the instability inherent in the first place.

This paper proposes a power system multimode generator energy loss factor (GELF) based on energy flow method under environmental excitation. This index can evaluate generator damping changes in different oscillation modes in power systems, timely discover the damping deterioration of the generator, and track the source of low‐frequency oscillation. A signal expression method for electrical frequency domain under environmental excitation is derived. This method is combined with dissipated energy flow method to obtain a new type of GELF. In terms of signal processing, dynamic mode decomposition and Morlet wavelet filter extraction system mode components are used to improve computing accuracy. The proposed index enables online calculation with the support of phasor measurement unit and wide area measurement system. Simulation analysis is conducted in a standard 39 node system and wind‐integrated power system. Test results show the effectiveness and generality of the proposed index and method.