On the Impacts of Different Consistency Constraint Formulations for Distributed Optimal Power Flow

Analyzing Malicious Data Injection Attacks on Distributed Optimal Power Flow Algorithms

“…To use ADMM algorithm (6) to solve OPF problems (1), consider the case when there are multiple agents defined by the set A, each of which operates a partitioned subset of the buses N i ⊂ N , i ∈ A along with the corresponding connected elements, i.e., generators G j , loads L j , and shunts H j , ∀j ∈ N i . While OPF problem's objective function (1a) is separable, the variables and constraints are coupled.…”

“…Each agent has a copy of the coupled constraints and variables in addition to consistency constraints between the coupled variables and the corresponding auxiliary variables. The consensus OPF problem thus has the form of ( 5) with X i = Ω i , ∀i ∈ A, i.e., the set of OPF constraints in (1), and can therefore be solved using the ADMM algorithm (6). However, the ADMM convergence guarantee is limited to convex problems, which is not the case for the OPF problem in (1).…”

“…ADAs solve large problems by iteratively solving smaller subproblems associated with each area a ∈ A. There are several decomposition strategies with differing implications for the number of variables and the convergence rate [11]. PowerModelsADA decomposes the OPF problem by introducing fictitious buses and generators, with zero-cost unbounded active and reactive power outputs, at branch terminals connecting two areas as shown in Fig.…”

“…We previously presented and analyzed various data manipulation strategies that drive distributed optimization algorithms for OPF problems to suboptimal solutions [6]- [8]. We consider a more stealthy attack model in [7] that uses a feedback loop to reduce the deviation of the manipulated data from the expected value.…”

“…Using neural network (NN) models for anomaly detection is a promising approach for detecting data manipulation [9]. Our prior work in [7], [8] shows that NN detection models have the potential to detect a variety of data manipulation strategies in the context of distributed optimization algorithms. However, using NN models for anomaly detection is challenging due to the nature of anomalies, as they are rare and heterogeneous, and hence difficult to collect on a large scale for training [9].…”