Abstract
A necessary condition for monitoring and control of a Power System (PS) is possessing a credible model of this system. The PS model for a need of dispatchers in national control centre is created in real time. An important element of such a model is a topology model. PS Topology Verification (PSTV) is an important problem in PS engineering. Often this problem is solved together with PS state estimation (Lukomski, & Wilkosz, 2000; Mai, Lefebvre, & Xuan, 2003). Methods, that enable such a solution of the problem, are sophisticated and usually time consuming. They require successful state estimation performance but convergence problems may occur in the case of certain Topology Errors (TEs). Thus, a robust method for PSTV before a state estimation is desired.
TopDescription Of The Considered Solution
To ensure that in the described method a larger knowledge on PS will be utilized than it is in other methods for PSTV, so-called unbalance indices are introduced. Taking into account the nature of the solved problem and to accomplish the best features of the PSTV, Radial Basis Function Networks (RBFNs) are utilized.
Power System Model
Elements of the PS topology model are nodes (representing electrical nodes) and branches (representing power lines, transformers, loads etc.). The assumption, that every branch in a PS model is modeled as the π -equivalent circuit (Fig. 1), is adopted. It is assumed that there is an accessible credible measurement data set of such quantities as: active and reactive power flows at the ends of each branch, power injections, loads and voltage magnitudes at each node. Usually, if a branch is not included in PS model the measurement data related to the branch are not taken into account in carried out analyses.
Figure 1. The assumed π model of the branch, Zkl = Rkl + j Xkl, Yk = jBkl, Yl = jBlk, Bkl = Blk = B. B is a half of the capacitive susceptance of the branch.
Key Terms in this Chapter
Power System Topology Model: A description of the physical connections in a power system.
Orthogonal Least Squares (OLS) Algorithm: Algorithm describing a Gram-Schmidt orthogonalisation process which ensures that each new column added to the result matrix of the growing subset is orthogonal to all previous columns. This considerably simplifies the equation for the change in learning error and results in a more efficient algorithm.
Neutral Decision: In fact, the lack of any decision.
Power System Topology Error: Inconsistency among the real power network connectivity and the power system topology model.
Unbalance Index: The left-hand side of the appropriate relationship, considered in the form in which its right-hand side is equal to zero. The mentioned relationship is a balance of active (reactive) powers at a node or a relationship among active (reactive) power flows at the ends of a branch.
Power System Topology Verification: Proving or disproving the correctness of a power system topology model.
Radial Basis Function Network: A type of artificial neural network which uses radial basis functions as activation functions. Typically, it consists of one hidden layer of Radial Basis Function (RBF) neurons (units). RBF hidden layer units have a receptive field which has a centre: that is, a particular input value at which they have a maximal output. Their output tails off as the input moves away from this point. Generally, the hidden unit function is a Gaussian. They are used in classification and approximation problems.
Power System State Estimation: A process, which leads to calculation of a power system state vector using incoming measurement data and a mathematical power system model. A power system state vector fully specifies any state in which a power system can be.