Recently, the power system has begun to grow very largely and more complex, so real time monitoring and control become very important in order to fulfill a reliable operation. Energy Management System (EMS) is responsible for this mission, and it forms the basis for efficient operating and control. State Estimation (SE) forms the spine of the EMS by providing the information of the real time state of the system which can be used in other EMS functions. Hence, an accurate and efficient state estimation is necessary for a reliable and efficient operation of the power system [1] [2] .

The state estimator computes the voltage magnitudes and voltage angles at the buses of the power system. We know that, power system is not a static system, but it changes very slowly with time and continuously. That means, when the load on the buses changes, the generations also have to change to overcome these changes in load. This in turn causes the change in power flows and injections at the buses, also leads to change in voltage angular at the buses and perhaps change in voltage magnitude at some buses depending on the size of this change; therefore, change the nature of the power system from static state to dynamic state nature. These dynamic behaviors of the power system are difficult to overcome by the conventional Static State Estimation (SSE). This led to the development of a new algorithm called Dynamic State Estimation (DSE) [1] -[5]. The DSE technique possesses a mathematical model for the time variation of the power system. The DSE uses this mathematical model depending on the previous state of the system at time (t), to predict the state vectors at the next state of the system (one step ahead) at time (t + 1). This capability of predicting the state one step ahead is a very important advantage in the control center, because the state forecasting gives a longer decision time to the system operator, and because the security assessment, economic dispatching and the other functions can be performed in advance. So, Dynamic State Estimation has the ability to represent an important role in the modern-day control center [1] .

In this paper, we will not only describe the dynamic model for the time behavior of the system state, but will show more details about the DSE, mainly the state predicting and state filtering. When the state variables are estimated at time k by state estimation technique, we will use these state variables to forecast the state vectors at time k + 1 using linear exponential smoothing. The state vectors are filtered based on Extended Kalman Filter and weighted least squares method. The proposal is tested using IEEE 14 bus test system. The test includes normal and abnormal operations.

The measurement vector consists of active power and reactive power flows and injection’s power as well as some voltage magnitudes, is denoted by an m-dimensional vector z. The power equation s is expressed by [6] [7] .

The measurement and state variable and at time instant k are given by equation

where is measurement vector m-dimensional, is state variables dimensioned, is nonlinear function relating measurement to the state vector .dimensioned and is the measurements error with zero mean and standard deviation of R.

where, σ is the standard deviation of error.

where is Jacobian matrix dimensional (m´n), m is number of measurements and n is number of state vectors.

The general model for DSE is given by.

where x_k and x_k+1 are the state vector at instants k and k+1 respectively, F_k is nonzero diagonal matrix dimensioned (n ´ n), a function represent the state transition between two instant of time, G_k is nonzero vector associated with trend behavior of the state trajectory dimensional (n ´ 1) and w_k is white Gaussian noise with zero mean and covariance matrix Q [1] -[4].

The steps of the dynamic state estimation algorithm are described above. The covariance matrix R of the measurement error is assumed to be calculated online.

where

where a_m & b_m are the manufacture factors. s_t represents the real value of the measurement. s_f is the maximum value of the measurement. As mentioned before, for predicting state we used Holt’s 2-exponential smoothing, the values of the smoothing parameters α and β, are fixed at 0.7 and 0.45, and for the filtering state we used Extended Kalman Filter. The elements of the covariance matrix Q of the system, is set at 10^‒6. The load curve at each bus was composed of a linear trend and random fluctuation (jitter).

In this paper, the Dynamic State simulation is studied over a period of 20 time sample intervals. with increasing of constant value 5% of the load at all the buses at each period. Once the load is changed the load flow is ready to update all the real and reactive power and injection power on the lines, voltage magnitudes and angles on the system. In this paper, the actual values of the state vectors are obtained from the 14-bus IEEE standard data for the base case and load flow for rest of the time samples [11] . The test cases and their results are shown in tables and figures in the next sections.

The dynamic state estimator technique has been made based on Holt’s exponential smoothing and Extended Kalman Filter for forecasting and filtering state respectively. The system dynamic was simulated over 20 time samples, with increasing the load at all busbars 5% during any time sample. The algorithm of DSE has been simulated through these 20 time intervals used standard IEEE 14_bus test system under normal and abnormal operation. In this paper, the algorithm gave very good performance results through the normal operation and abnormal operation (bad data and sudden load change) conditions. The error per bus for voltage magnitude and voltage angle has been calculated over these 20 time intervals in both predicted and filtered states.