15-02-2017 17:30  Graduate Seminar

An Analytic Solution for State Estimation and Observability Analysis in Power Systems

This research thesis addresses the problem of observability analysis and state estimation in power systems. State estimation is one of the most important tools for network monitoring and control. Its purpose is to process available measurements to estimate the voltage phasors of all buses in the network. Observability analysis is a procedure taking place prior to the state estimation process, to determine whether the given measurement set is sufficient for a unique state estimation. A central challenge in state estimation problems is to minimize a highly nonlinear and non-convex objective function. This function is mostly formulated according to the Weighted Least Squares (WLS) criterion, and solved using iterative optimization algorithms. However, when the objective function is non-convex, such algorithms are not guaranteed to converge or to detect the global optimum of the problem. Therefore an open challenge remains to develop state estimation algorithms that are guaranteed to converge to the global solution and are numerically robust. Observability analysis is performed under the DC approximation. This means that all voltage magnitudes are assumed to be close to one, the voltage phases are assumed to be close to zero, the conductance part of the network is approximated as zero and shunt admittances are ignored. This fact produces an observability conclusion that may not be sufficiently accurate in case the network operates in conditions that are highly different from the approximations. Therefore an additional open challenge is to develop exact observability analysis algorithms that do not make any assumptions about the network state and topology. To meet these open challenges, we propose an efficient algorithm to solve both observability analysis and state estimation problems. The advantages of this algorithm are as follows: 1) it is non iterative and is guaranteed to provide the state estimation in a closed formula. 2) it is numerically stable and is able to integrate pseudo measurements along with noisy measurements. 3) it can detect all observable islands directly without making any assumptions on the systems state and topology. The main idea behind the proposed method is the network characteristic matrix $L$. This matrix incorporates measurements and topological data, and provides detailed information about the power network. A main theoretical result is that the true network state is a member of this matrix null space. By calculating a null space basis of $L$ the voltage solution can be expressed as a linear transformation of this basis with unknown coefficients. The problem now becomes finding the coefficients that fit all voltage constraints. We then show that it is sufficient to recover the cross products of this vector to calculate the voltages. The cross products are simpler to recover because they satisfy a linear equation set. Numerical simulations were conducted on 9,14,30,57,118,300 bus test cased. Observability analysis was tested on the 14 bus test case in three scenarios. In the first two cases the network was unobservable and in the third case the network was observable. Results show a successful detection of the observable islands in all cases. The computation time per island was tested on all network sizes, presenting low calculation times. State estimations performance was illustrated in several cases. The precision of the proposed method was compared to WLS-NR. The average voltage mismatch was tested over several network sizes and SNR values. Results show significant decrease in voltage mismatch as SNR increases. Finally, the proposed state estimation solution was tested as a starting point for WLS-NR algorithm. Results show a significant increase in convergence rate compared to a random starting point.

Location: 1061
Speaker: Yehuda Barel
Affiliation: Dept. of Electrical Engineering Technion Back