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The dynamic non-linear state-space model of a power-system consisting of synchronous generators, buses, and static loads has been linearized and a linear measurement function has been considered. A distributed dynamic framework for estimating the state vector of the power system has been designed here. This framework employs a type of distributed Kalman filter (DKF) known as a Kalman consensus filter (KCF) which is located at distributed control centers (DCCs) that fuse locally available noise ridden measurements, state vector estimates of neighboring control centers, and a prediction obtained by the linearized model to obtain a filtered state vector estimate. Further, the local residual at each control center is checked by a median chi-squared detector designed here for bad data/Gaussian attack detection. Simulation results show the working of the KCF for an 8 bus 5 generator system, and the efficacy of the median chi-squared detector in detecting the DCC affected by Gaussian attacks. 

Most of the traditional state estimation algorithms are provided false alarm when there is attack. This paper proposes an attack-resilient algorithm where attack is automatically ignored, and the state estimation process is continuing which acts a grid-eye for monitoring whole power systems. After modeling the smart grid incorporating distributed energy resources, the smart sensors are deployed to gather measurement information where sensors are prone to attacks. Based on the noisy and cyber attack measurement information, the optimal state estimation algorithm is designed. When the attack is happened, the measurement residual error dynamic goes high and it can ignore using proposed saturation function. Moreover, the proposed saturation function is automatically computed in a dynamic way considering residual error and deigned parameters. Combing the aforementioned approaches, the Kalman filter algorithm is modified which is applied to the smart grid state estimation. The simulation results show that the proposed algorithm provides high estimation accuracy. 

Gaining money and high profit is the dream of electricity market investors; however, it requires accurate financial knowledge and price forecasting ability. Most of the investors are used the electricity market historical information for forecasting power generation, consumption, and utility price. Unfortunately, electricity market time-series profile is high volatility and change over time, so the factual data cannot accurately reflect the electricity market states such as power consumption and generation. In the literature, there is no systematic way or suitable models that can fit, analyze, and predict electricity market system states over time. Interestingly, this paper proposes an electricity market state-space model which is obtained by a set of electricity market differential equations. After simplifying of these equations, the continuous-time electricity market state-space model is derived. Using discrete-time step size parameter, the continuous-time system is discretised. Furthermore, the noisy measurements are obtained by a set of smart sensors. Finally, the Kalmna filter based electricity market state forecasting algorithm is developed based on noisy measurements. Simulation results show that the proposed algorithm can properly forecast the electricity market states. Consequently, this kind of model and algorithm can help to develop the electricity market simulator and assist investor to participate/invest electricity market regardless of the world economic downtown.