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2022-05-05
Raab, Alexander, Mehlmann, Gert, Luther, Matthias, Sennewald, Tom, Schlegel, Steffen, Westermann, Dirk.  2021.  Steady-State and Dynamic Security Assessment for System Operation. 2021 International Conference on Smart Energy Systems and Technologies (SEST). :1—6.

This contribution provides the implementation of a holistic operational security assessment process for both steady-state security and dynamic stability. The merging of steady-state and dynamic security assessment as a sequential process is presented. A steady-state and dynamic modeling of a VSC-HVDC was performed including curative and stabilizing measures as remedial actions. The assessment process was validated by a case study on a modified version of the Nordic 32 system. Simulation results showed that measure selection based on purely steady-state contingency analysis can lead to loss of stability in time domain. A subsequent selection of measures on the basis of the dynamic security assessment was able to guarantee the operational security for the stationary N-1 scenario as well as the power system stability.

2022-03-22
Jiang, Xin, Yang, Qifan, Ji, Wen, Chen, Yanshu, Cai, Yuxiang, Li, Xiaoming.  2021.  Smart grid data security storage strategy based on cloud computing platform. 2021 6th International Conference on Smart Grid and Electrical Automation (ICSGEA). :69—74.
Aiming at the security problems of traditional smart grid data security storage strategy, this paper proposes a smart grid data security storage strategy based on cloud computing platform. Based on the analysis of cloud computing and cloud storage, the security storage of smart grid data is modeled to improve the security storage performance of power system. The dynamic key mechanism is introduced to obtain the initial key information in the key chain and generate the dynamic secret key. The hyperchaotic system is used to obtain the modified bit plane code in the key chain to form the context and decision of data storage. MQ arithmetic encoder is used for entropy coding to generate the corresponding data storage compressed code stream, and the smart grid data storage key is improved. Combined with encryption processing and decryption processing, the secure storage of smart grid data is realized. The experimental results show that the smart grid data security storage strategy based on cloud computing platform increases the security of smart grid data storage.
2022-03-14
Kummerow, André, Rösch, Dennis, Nicolai, Steffen, Brosinsky, Christoph, Westermann, Dirk, Naumann, é.  2021.  Attacking dynamic power system control centers - a cyber-physical threat analysis. 2021 IEEE Power Energy Society Innovative Smart Grid Technologies Conference (ISGT). :01—05.

In dynamic control centers, conventional SCADA systems are enhanced with novel assistance functionalities to increase existing monitoring and control capabilities. To achieve this, different key technologies like phasor measurement units (PMU) and Digital Twins (DT) are incorporated, which give rise to new cyber-security challenges. To address these issues, a four-stage threat analysis approach is presented to identify and assess system vulnerabilities for novel dynamic control center architectures. For this, a simplified risk assessment method is proposed, which allows a detailed analysis of the different system vulnerabilities considering various active and passive cyber-attack types. Qualitative results of the threat analysis are presented and discussed for different use cases at the control center and substation level.

Lingaraju, Kaushik, Gui, Jianzhong, Johnson, Brian K., Chakhchoukh, Yacine.  2021.  Simulation of the Effect of False Data Injection Attacks on SCADA using PSCAD/EMTDC. 2020 52nd North American Power Symposium (NAPS). :1—5.
Transient simulation is a critical task of validating the dynamic model of the power grid. We propose an off-line method for validating dynamic grid models and assessing the dynamic security of the grid in the presence of cyberattacks. Simulations are executed in PowerWorld and PSCAD/EMTDC to compare the impact on the grid of cyber-attacks. Generators in the IEEE 14-bus system have been modified to match the need of adjustment in modern power system operation. To get effective measurements for state estimation, SCADA polling model is reproduced in PSCAD/EMTDC by providing controlled sampling frequency. The results of a tripped line case and injecting false data to the loads caused by cyberattacks is presented and analyzed.
2021-11-29
Braun, Sarah, Albrecht, Sebastian, Lucia, Sergio.  2020.  A Hierarchical Attack Identification Method for Nonlinear Systems. 2020 59th IEEE Conference on Decision and Control (CDC). :5035–5042.
Many autonomous control systems are frequently exposed to attacks, so methods for attack identification are crucial for a safe operation. To preserve the privacy of the subsystems and achieve scalability in large-scale systems, identification algorithms should not require global model knowledge. We analyze a previously presented method for hierarchical attack identification, that is embedded in a distributed control setup for systems of systems with coupled nonlinear dynamics. It is based on the exchange of local sensitivity information and ideas from sparse signal recovery. In this paper, we prove sufficient conditions under which the method is guaranteed to identify all components affected by some unknown attack. Even though a general class of nonlinear dynamic systems is considered, our rigorous theoretical guarantees are applicable to practically relevant examples, which is underlined by numerical experiments with the IEEE 30 bus power system.
2021-05-13
Chen, Ziyu, Zhu, Jizhong, Li, Shenglin, Luo, Tengyan.  2020.  Detection of False Data Injection Attack in Automatic Generation Control System with Wind Energy based on Fuzzy Support Vector Machine. IECON 2020 The 46th Annual Conference of the IEEE Industrial Electronics Society. :3523—3528.
False data injection attack (FDIA) destroys the automatic generation control (AGC) system and leads to unstable operation of the power system. Fast and accurate detection can help prevent and disrupt malicious attacks. This paper proposes an improved detection method, which is combined with fuzzy theory and support vector machine (SVM) to identify various types of attacks. The impacts of different types of FDIAs on the AGC system are analyzed, and the reliability of the method is proved by a large number of experimental data. This experiment is simulated on a single-area LFC system and the effects of adding a wind storage system were compared in a dynamic model. Simulation studies also show a higher accuracy of fuzzy support vector machine (FSVM) than traditional SVM and fuzzy pattern trees (FPTs).
2020-08-03
Nakayama, Kiyoshi, Muralidhar, Nikhil, Jin, Chenrui, Sharma, Ratnesh.  2019.  Detection of False Data Injection Attacks in Cyber-Physical Systems using Dynamic Invariants. 2019 18th IEEE International Conference On Machine Learning And Applications (ICMLA). :1023–1030.

Modern cyber-physical systems are increasingly complex and vulnerable to attacks like false data injection aimed at destabilizing and confusing the systems. We develop and evaluate an attack-detection framework aimed at learning a dynamic invariant network, data-driven temporal causal relationships between components of cyber-physical systems. We evaluate the relative performance in attack detection of the proposed model relative to traditional anomaly detection approaches. In this paper, we introduce Granger Causality based Kalman Filter with Adaptive Robust Thresholding (G-KART) as a framework for anomaly detection based on data-driven functional relationships between components in cyber-physical systems. In particular, we select power systems as a critical infrastructure with complex cyber-physical systems whose protection is an essential facet of national security. The system presented is capable of learning with or without network topology the task of detection of false data injection attacks in power systems. Kalman filters are used to learn and update the dynamic state of each component in the power system and in-turn monitor the component for malicious activity. The ego network for each node in the invariant graph is treated as an ensemble model of Kalman filters, each of which captures a subset of the node's interactions with other parts of the network. We finally also introduce an alerting mechanism to surface alerts about compromised nodes.

2020-07-16
Kërçi, Taulant, Milano, Federico.  2019.  A Framework to embed the Unit Commitment Problem into Time Domain Simulations. 2019 IEEE International Conference on Environment and Electrical Engineering and 2019 IEEE Industrial and Commercial Power Systems Europe (EEEIC / I CPS Europe). :1—5.

This paper proposes a software framework to embed the unit commitment problem into a power system dynamic simulator. A sub-hourly, mixed-integer linear programming Security Constrained Unit Commitment (SCUC) with a rolling horizon is utilized to account for the variations of the net load of the system. The SCUC is then included into time domain simulations to study the impact of the net-load variability and uncertainty on the dynamic behavior of the system using different scheduling time periods. A case study based on the 39-bus system illustrates the features of the proposed software framework.

2020-06-26
Jaiswal, Prajwal Kumar, Das, Sayari, Panigrahi, Bijaya Ketan.  2019.  PMU Based Data Driven Approach For Online Dynamic Security Assessment in Power Systems. 2019 20th International Conference on Intelligent System Application to Power Systems (ISAP). :1—7.

This paper presents a methodology for utilizing Phasor Measurement units (PMUs) for procuring real time synchronized measurements for assessing the security of the power system dynamically. The concept of wide-area dynamic security assessment considers transient instability in the proposed methodology. Intelligent framework based approach for online dynamic security assessment has been suggested wherein the database consisting of critical features associated with the system is generated for a wide range of contingencies, which is utilized to build the data mining model. This data mining model along with the synchronized phasor measurements is expected to assist the system operator in assessing the security of the system pertaining to a particular contingency, thereby also creating possibility of incorporating control and preventive measures in order to avoid any unforeseen instability in the system. The proposed technique has been implemented on IEEE 39 bus system for accurately indicating the security of the system and is found to be quite robust in the case of noise in the measurement data obtained from the PMUs.

2020-02-17
Al-Eryani, Yasser, Baroudi, Uthman.  2019.  An Investigation on Detecting Bad Data Injection Attack in Smart Grid. 2019 International Conference on Computer and Information Sciences (ICCIS). :1–4.
Security and consistency of smart grids is one of the main issues in the design and maintenance of highly controlled and monitored new power grids. Bad data injection attack could lead to disasters such as power system outage, or huge economical losses. In many attack scenarios, the attacker can come up with new attack strategies that couldn't be detected by the traditional bad data detection methods. Adaptive Partitioning State Estimation (APSE) method [3] has been proposed recently to combat such attacks. In this work, we evaluate and compare with a traditional method. The main idea of APSE is to increase the sensitivity of the chi-square test by partitioning the large grids into small ones and apply the test on each partition individually and repeat this procedure until the faulty node is located. Our simulation findings using MATPOWER program show that the method is not consistent where it is sensitive the systems size and the location of faulty nodes as well.
2020-02-10
Niu, Xiangyu, Li, Jiangnan, Sun, Jinyuan, Tomsovic, Kevin.  2019.  Dynamic Detection of False Data Injection Attack in Smart Grid using Deep Learning. 2019 IEEE Power Energy Society Innovative Smart Grid Technologies Conference (ISGT). :1–6.
Modern advances in sensor, computing, and communication technologies enable various smart grid applications. The heavy dependence on communication technology has highlighted the vulnerability of the electricity grid to false data injection (FDI) attacks that can bypass bad data detection mechanisms. Existing mitigation in the power system either focus on redundant measurements or protect a set of basic measurements. These methods make specific assumptions about FDI attacks, which are often restrictive and inadequate to deal with modern cyber threats. In the proposed approach, a deep learning based framework is used to detect injected data measurement. Our time-series anomaly detector adopts a Convolutional Neural Network (CNN) and a Long Short Term Memory (LSTM) network. To effectively estimate system variables, our approach observes both data measurements and network level features to jointly learn system states. The proposed system is tested on IEEE 39-bus system. Experimental analysis shows that the deep learning algorithm can identify anomalies which cannot be detected by traditional state estimation bad data detection.
2019-05-01
Konstantelos, I., Jamgotchian, G., Tindemans, S., Duchesne, P., Cole, S., Merckx, C., Strbac, G., Panciatici, P..  2018.  Implementation of a Massively Parallel Dynamic Security Assessment Platform for Large-Scale Grids. 2018 IEEE Power Energy Society General Meeting (PESGM). :1–1.

This paper presents a computational platform for dynamic security assessment (DSA) of large electricity grids, developed as part of the iTesla project. It leverages High Performance Computing (HPC) to analyze large power systems, with many scenarios and possible contingencies, thus paving the way for pan-European operational stability analysis. The results of the DSA are summarized by decision trees of 11 stability indicators. The platform's workflow and parallel implementation architecture is described in detail, including the way commercial tools are integrated into a plug-in architecture. A case study of the French grid is presented, with over 8000 scenarios and 1980 contingencies. Performance data of the case study (using 10,000 parallel cores) is analyzed, including task timings and data flows. Finally, the generated decision trees are compared with test data to quantify the functional performance of the DSA platform.

2019-04-05
Shu, H., Shen, X., Xu, L., Guo, Q., Sun, H..  2018.  A Validity Test Methodfor Transmission Betweens and Transmission Sections Based on Chain Attack Analysisand Line Outage Distribution Factors. 2018 2nd IEEE Conference on Energy Internet and Energy System Integration (EI2). :1-6.

The identification of transmission sections is used to improve the efficiency of monitoring the operation of the power grid. In order to test the validity of transmission sections identified, an assessment process is necessary. In addition, Transmission betweenness, an index for finding the key transmission lines in the power grid, should also be verified. In this paper, chain attack is assumed to check the weak links in the grid, thus verifying the transmission betweenness implemented for the system. Moreover, the line outage distribution factors (LODFs) are used to quantify the change of power flow when the leading line in transmission sections breaks down, so that the validity of transmission sections can be proved. Case studies based on IEEE 39 and IEEE 118 -bus system proved the effectiveness of the proposed method.

2018-09-05
Zhong, Q., Blaabjerg, F., Cecati, C..  2017.  Power-Electronics-Enabled Autonomous Power Systems. IEEE Transactions on Industrial Electronics. 64:5904–5906.

The eleven papers in this special section focus on power electronics-enabled autonomous systems. Power systems are going through a paradigm change from centralized generation to distributed generation and further onto smart grid. Millions of relatively small distributed energy resources (DER), including wind turbines, solar panels, electric vehicles and energy storage systems, and flexible loads are being integrated into power systems through power electronic converters. This imposes great challenges to the stability, scalability, reliability, security, and resiliency of future power systems. This section joins the forces of the communities of control/systems theory, power electronics, and power systems to address various emerging issues of power-electronics-enabled autonomous power systems, paving the way for large-scale deployment of DERs and flexible loads.

2018-05-24
Dey, A. K., Gel, Y. R., Poor, H. V..  2017.  Motif-Based Analysis of Power Grid Robustness under Attacks. 2017 IEEE Global Conference on Signal and Information Processing (GlobalSIP). :1015–1019.

Network motifs are often called the building blocks of networks. Analysis of motifs is found to be an indispensable tool for understanding local network structure, in contrast to measures based on node degree distribution and its functions that primarily address a global network topology. As a result, networks that are similar in terms of global topological properties may differ noticeably at a local level. In the context of power grids, this phenomenon of the impact of local structure has been recently documented in fragility analysis and power system classification. At the same time, most studies of power system networks still tend to focus on global topo-logical measures of power grids, often failing to unveil hidden mechanisms behind vulnerability of real power systems and their dynamic response to malfunctions. In this paper a pilot study of motif-based analysis of power grid robustness under various types of intentional attacks is presented, with the goal of shedding light on local dynamics and vulnerability of power systems.

2018-05-09
Salles-Loustau, G., Garcia, L., Sun, P., Dehnavi, M., Zonouz, S..  2017.  Power Grid Safety Control via Fine-Grained Multi-Persona Programmable Logic Controllers. 2017 IEEE International Conference on Smart Grid Communications (SmartGridComm). :283–288.

Trustworthy and safe operation of the power grid critical infrastructures relies on secure execution of low-level substation controller devices such as programmable logic controllers (PLCs). Currently, there are very few security protection solutions deployed on these devices to ensure provenance control: to execute controller code on the device that is developed by trusted parties and complies with safety/security policies that are defined by the code developer as well as the power grid operators. Resource-limited PLC controllers have been becoming increasingly popular among not only legitimate system operators, but also malicious adversaries such as the most recent Stuxnet and BlackEnergy malware that caused various damages such as unauthorized infrastructural safety and integrity violations. We present PLCtrust, a domain-specific solution that deploys virtual micro security-perimeters, so-called capsules, and the corresponding device-level runtime power system-safety policy enforcement dynamically. PLCtrust makes use of data taint analysis to monitor and control data flow among the capsules based on data owner-defined policies. PLCtrust provides the operators with a transparent and lightweight solution to address various safety-critical data protection requirements. PLCtrust also provides the legitimate third-party controller code developers with a taint-aware programming interface to develop applications in compliance with the dynamic power system safety/security policies. Our experimental results on real-world settings show that PLCtrust is transparent to the end-users while ensuring the power grid safety maintenance with minimal performance overhead.

2018-03-05
Shelar, D., Sun, P., Amin, S., Zonouz, S..  2017.  Compromising Security of Economic Dispatch in Power System Operations. 2017 47th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN). :531–542.

Power grid operations rely on the trustworthy operation of critical control center functionalities, including the so-called Economic Dispatch (ED) problem. The ED problem is a large-scale optimization problem that is periodically solved by the system operator to ensure the balance of supply and load while maintaining reliability constraints. In this paper, we propose a semantics-based attack generation and implementation approach to study the security of the ED problem.1 Firstly, we generate optimal attack vectors to transmission line ratings to induce maximum congestion in the critical lines, resulting in the violation of capacity limits. We formulate a bilevel optimization problem in which the attacker chooses manipulations of line capacity ratings to maximinimize the percentage line capacity violations under linear power flows. We reformulate the bilevel problem as a mixed integer linear program that can be solved efficiently. Secondly, we describe how the optimal attack vectors can be implemented in commercial energy management systems (EMSs). The attack explores the dynamic memory space of the EMS, and replaces the true line capacity ratings stored in data regions with the optimal attack vectors. In contrast to the well-known false data injection attacks to control systems that require compromising distributed sensors, our approach directly implements attacks to the control center server. Our experimental results on benchmark power systems and five widely utilized EMSs show the practical feasibility of our attack generation and implementation approach.

Shelar, D., Sun, P., Amin, S., Zonouz, S..  2017.  Compromising Security of Economic Dispatch in Power System Operations. 2017 47th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN). :531–542.

Power grid operations rely on the trustworthy operation of critical control center functionalities, including the so-called Economic Dispatch (ED) problem. The ED problem is a large-scale optimization problem that is periodically solved by the system operator to ensure the balance of supply and load while maintaining reliability constraints. In this paper, we propose a semantics-based attack generation and implementation approach to study the security of the ED problem.1 Firstly, we generate optimal attack vectors to transmission line ratings to induce maximum congestion in the critical lines, resulting in the violation of capacity limits. We formulate a bilevel optimization problem in which the attacker chooses manipulations of line capacity ratings to maximinimize the percentage line capacity violations under linear power flows. We reformulate the bilevel problem as a mixed integer linear program that can be solved efficiently. Secondly, we describe how the optimal attack vectors can be implemented in commercial energy management systems (EMSs). The attack explores the dynamic memory space of the EMS, and replaces the true line capacity ratings stored in data regions with the optimal attack vectors. In contrast to the well-known false data injection attacks to control systems that require compromising distributed sensors, our approach directly implements attacks to the control center server. Our experimental results on benchmark power systems and five widely utilized EMSs show the practical feasibility of our attack generation and implementation approach.

Shelar, D., Sun, P., Amin, S., Zonouz, S..  2017.  Compromising Security of Economic Dispatch in Power System Operations. 2017 47th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN). :531–542.
Power grid operations rely on the trustworthy operation of critical control center functionalities, including the so-called Economic Dispatch (ED) problem. The ED problem is a large-scale optimization problem that is periodically solved by the system operator to ensure the balance of supply and load while maintaining reliability constraints. In this paper, we propose a semantics-based attack generation and implementation approach to study the security of the ED problem.1 Firstly, we generate optimal attack vectors to transmission line ratings to induce maximum congestion in the critical lines, resulting in the violation of capacity limits. We formulate a bilevel optimization problem in which the attacker chooses manipulations of line capacity ratings to maximinimize the percentage line capacity violations under linear power flows. We reformulate the bilevel problem as a mixed integer linear program that can be solved efficiently. Secondly, we describe how the optimal attack vectors can be implemented in commercial energy management systems (EMSs). The attack explores the dynamic memory space of the EMS, and replaces the true line capacity ratings stored in data regions with the optimal attack vectors. In contrast to the well-known false data injection attacks to control systems that require compromising distributed sensors, our approach directly implements attacks to the control center server. Our experimental results on benchmark power systems and five widely utilized EMSs show the practical feasibility of our attack generation and implementation approach.
2018-02-21
Overbye, T. J., Mao, Z., Shetye, K. S., Weber, J. D..  2017.  An interactive, extensible environment for power system simulation on the PMU time frame with a cyber security application. 2017 IEEE Texas Power and Energy Conference (TPEC). :1–6.

Power system simulation environments with appropriate time-fidelity are needed to enable rapid testing of new smart grid technologies and for coupled simulations of the underlying cyber infrastructure. This paper presents such an environment which operates with power system models in the PMU time frame, including data visualization and interactive control action capabilities. The flexible and extensible capabilities are demonstrated by interfacing with a cyber infrastructure simulation.

2017-11-27
Parate, M., Tajane, S., Indi, B..  2016.  Assessment of System Vulnerability for Smart Grid Applications. 2016 IEEE International Conference on Engineering and Technology (ICETECH). :1083–1088.

The smart grid is an electrical grid that has a duplex communication. This communication is between the utility and the consumer. Digital system, automation system, computers and control are the various systems of Smart Grid. It finds applications in a wide variety of systems. Some of its applications have been designed to reduce the risk of power system blackout. Dynamic vulnerability assessment is done to identify, quantify, and prioritize the vulnerabilities in a system. This paper presents a novel approach for classifying the data into one of the two classes called vulnerable or non-vulnerable by carrying out Dynamic Vulnerability Assessment (DVA) based on some data mining techniques such as Multichannel Singular Spectrum Analysis (MSSA), and Principal Component Analysis (PCA), and a machine learning tool such as Support Vector Machine Classifier (SVM-C) with learning algorithms that can analyze data. The developed methodology is tested in the IEEE 57 bus, where the cause of vulnerability is transient instability. The results show that data mining tools can effectively analyze the patterns of the electric signals, and SVM-C can use those patterns for analyzing the system data as vulnerable or non-vulnerable and determines System Vulnerability Status.

2015-05-06
Sanandaji, B.M., Bitar, E., Poolla, K., Vincent, T.L..  2014.  An abrupt change detection heuristic with applications to cyber data attacks on power systems. American Control Conference (ACC), 2014. :5056-5061.

We present an analysis of a heuristic for abrupt change detection of systems with bounded state variations. The proposed analysis is based on the Singular Value Decomposition (SVD) of a history matrix built from system observations. We show that monitoring the largest singular value of the history matrix can be used as a heuristic for detecting abrupt changes in the system outputs. We provide sufficient detectability conditions for the proposed heuristic. As an application, we consider detecting malicious cyber data attacks on power systems and test our proposed heuristic on the IEEE 39-bus testbed.
 

Zhen Jiang, Shihong Miao, Pei Liu.  2014.  A Modified Empirical Mode Decomposition Filtering-Based Adaptive Phasor Estimation Algorithm for Removal of Exponentially Decaying DC Offset. Power Delivery, IEEE Transactions on. 29:1326-1334.

This paper proposes a modified empirical-mode decomposition (EMD) filtering-based adaptive dynamic phasor estimation algorithm for the removal of exponentially decaying dc offset. Discrete Fourier transform does not have the ability to attain the accurate phasor of the fundamental frequency component in digital protective relays under dynamic system fault conditions because the characteristic of exponentially decaying dc offset is not consistent. EMD is a fully data-driven, not model-based, adaptive filtering procedure for extracting signal components. But the original EMD technique has high computational complexity and requires a large data series. In this paper, a short data series-based EMD filtering procedure is proposed and an optimum hermite polynomial fitting (OHPF) method is used in this modified procedure. The proposed filtering technique has high accuracy and convergent speed, and is greatly appropriate for relay applications. This paper illustrates the characteristics of the proposed technique and evaluates its performance by computer-simulated signals, PSCAD/EMTDC-generated signals, and real power system fault signals.

2015-05-04
Shaobu Wang, Shuai Lu, Ning Zhou, Guang Lin, Elizondo, M., Pai, M.A..  2014.  Dynamic-Feature Extraction, Attribution, and Reconstruction (DEAR) Method for Power System Model Reduction. Power Systems, IEEE Transactions on. 29:2049-2059.

In interconnected power systems, dynamic model reduction can be applied to generators outside the area of interest (i.e., study area) to reduce the computational cost associated with transient stability studies. This paper presents a method of deriving the reduced dynamic model of the external area based on dynamic response measurements. The method consists of three steps, namely dynamic-feature extraction, attribution, and reconstruction (DEAR). In this method, a feature extraction technique, such as singular value decomposition (SVD), is applied to the measured generator dynamics after a disturbance. Characteristic generators are then identified in the feature attribution step for matching the extracted dynamic features with the highest similarity, forming a suboptimal “basis” of system dynamics. In the reconstruction step, generator state variables such as rotor angles and voltage magnitudes are approximated with a linear combination of the characteristic generators, resulting in a quasi-nonlinear reduced model of the original system. The network model is unchanged in the DEAR method. Tests on several IEEE standard systems show that the proposed method yields better reduction ratio and response errors than the traditional coherency based reduction methods.