A Probabilistic Multi-Objective Model for Phasor Measurement Units Placement in the Presence of Line Outage

Abstract

Optimal phasor measurement units (PMU) placement was developed to determine the number and locations of PMUs on the premise of full observability of the whole network. In order to enhance reliability under contingencies, redundancy should also be considered beside the number of PMUs in optimal phasor measurement units placement problem. Thus, in this paper, a multi-objective model was established to consider the two conflicting components simultaneously, solved by ε-constraint method and the fuzzy satisfying approach. The redundancy here was formulated as average possibility of observability including random component outages, and full possibility formula was applied to calculate the average possibility of observability in the case of single line outage. Finally, the model was employed to the IEEE-57 bus system, and the results verified that the developed model could provide a placement scheme with higher reliability.Sustainability 2019, 11, 7097 2 of 12 bee colony (ABC) algorithm, modified binary cuckoo optimization algorithm (MBCOA), weighted method, multi-objective evolutionary algorithm-based, were adopted to solve the multi-objective model in [11][12][13][14][15], respectively. In addition, to obtain the final solution from the Pareto front quickly and accurately, the fuzzy satisfying approach was applied in [16,17] and sparse neighborhood surroundings in [18]. Furthermore, the accuracy of state estimation was taken into consideration, subject to the constraint of supervisory control and data acquisition (SCADA) measurement data in [19] and the uncertainties of power system conditions in [20].Literatures aforementioned analyzed the system observability from a deterministic view, including two contrary states, i.e., observable or unobservable. However, it was investigated in a probabilistic manner in [21][22][23][24]. In [21], to obtain a PMU placement scheme with unobservable probability resulted from 1st-order and 2nd-order failures of PMUs and line less than the pre-defined threshold, the unobservable probability was calculated iteratively by increasing PMU numbers gradually on the basis of initial PMU placement scheme, until the requirements were met. A multi-objective model was proposed, simultaneously minimizing the PMU cost and unobservable probability under PMU or line failures in [22]. However, random component outages were not taken into consideration in [21] and [22]. In [23], a probabilistic manner was adopted to differentiate the multiple solutions and showed significant priority comparing to measurement redundancy. A solution with maximum observable probability considering random component outages was selected as the final optimal scheme. In addition, when considering multistage PMU placement, the observable probability was regarded as the objective to optimize at each stage [24].In this paper, firstly, APO of all buses in the network was calculated under two different cases, i.e., with and without consideration of single line outages. It is noticeable to consider the effect of single line outag...

A robust state estimation by optimal placement of measurement units considering loads/renewable generations and measurements uncertainty

“…The main objective of them is to keep the observability of the power system during normal and contingency conditions. References [6][7][8][9][10] proposed an optimal MUs placement approach to keep network observability under normal and contingency conditions.…”

“…Reference [10] took only the transmission lines outage into account in the optimal PMUs placement problem considering the redundancy to enhance the reliability under the mentioned contingencies. The redundancy was defined as the average possibility of observability, in the case of the single-line outage.…”

“…The Cholesky decomposition method combined with the Nataf transformation technique can be efficiently used to make the correlated uncertain variables by independently producing samples of X i . The desired covariance matrix 𝜌 X for an Ndimensional random vector, X can be decomposed according to (10).…”

“…References [6–10] proposed an optimal MUs placement approach to keep network observability under normal and contingency conditions.…”

An Optimal DF Based Method for Transient Stability Analysis

“…Furthermore, the trained classification model is used to conduct online evaluation of the newly received power grid sampling data to meet the requirements of real-time transient stability evaluation [26][27][28][29]. Compared with the traditional physical model-driven transient stability evaluation method, the data-mining-based transient stability evaluation method is data-driven and has higher evaluation accuracy while satisfying the rapidity of evaluation [30][31][32][33][34][35].…”