Front Cover -- Affine Arithmetic-Based Methods for Uncertain Power System Analysis -- Copyright -- Contents -- Preface -- Acknowledgments -- 1 Uncertainty management in power systems -- 1.1 Sampling methods -- 1.2 Analytical methods -- 1.3 Approximate methods -- 1.4 Non-probabilistic methods -- References -- 2 Elements of reliable computing -- 2.1 Interval arithmetic -- 2.2 Affine arithmetic -- 2.3 Solving uncertain equations by AA -- 2.4 Reliable solution of non-linear equations -- 2.5 Reliable solutions of constrained optimization problems -- References -- 3 Uncertain power flow analysis
3.1 Problem formulation -- 3.2 Affine arithmetic based solution of the power flow equations -- 3.3 Numerical results -- 3.3.1 IEEE 30-bus network -- 3.3.2 IEEE 57-bus network -- 3.3.3 IEEE 118-bus network -- 3.3.4 Discussion -- 3.4 Robust formulation of the power flow equations -- 3.4.1 Solving the power flow equations -- 3.5 Case study -- References -- 4 Uncertain optimal power flow analysis -- 4.1 Mathematical background -- 4.1.1 Uncertain power dispatch analysis -- 4.1.2 Reactive power dispatch -- 4.2 Numerical results -- 4.2.1 Uncertain power dispatch analysis -- 4.2.2 Reactive power dispatch
4.2.3 Discussion -- 4.3 Robust formulation of optimal power flow problems -- 4.4 Case study -- 4.5 Remarks -- References -- 5 Unified AA-based solution of uncertain PF and OPF problems -- 5.1 Theoretical framework -- 5.2 Applications -- 5.2.1 Solving power flow problems -- 5.2.2 Solving optimal power flow problems -- 5.3 Numerical results -- 5.3.1 Power flow analysis -- 5.3.2 Optimal power dispatch -- 5.3.3 Optimal voltage regulation -- 5.4 Computational requirements -- 5.5 Remarks -- References -- 6 Uncertain power system reliability analysis -- 6.1 Markov Chains
6.1.1 Discrete-Time Markov Chains -- 6.1.2 Continuous-Time Markov Chains -- 6.1.3 Effects of data uncertainties -- 6.1.4 Matrix notation -- 6.2 Uncertain Markov Chains analysis by AA -- 6.3 Case studies -- 6.3.1 Case Study 1: resilience analysis -- 6.3.2 Case Study 2: energy storage system modeling -- 6.3.3 Computational effort -- References -- 7 Uncertain analysis of multi-energy systems -- 7.1 Optimal scheduling of an energy hub -- 7.1.1 Energy hub modeling -- 7.1.2 Deterministic optimal dispatch -- 7.2 Case study -- References
8 Enabling methodologies for reducing the computational burden in AA-based computing -- 8.1 PF analysis -- 8.2 OPF analysis -- 8.3 AA-based computing -- 8.4 Numerical results -- 8.4.1 IEEE 30-bus system PF -- 8.4.2 2383-bus Polish power system PF -- 8.4.3 118 bus network OPF -- 8.4.4 AA analysis -- 8.5 Remarks -- References -- 9 Uncertain voltage stability analysis by affine arithmetic -- 9.1 AA-based calculation of PV curves -- 9.2 Numerical results -- 9.2.1 5 bus test system -- 9.2.2 2383 bus test system -- 9.2.3 Computational burden and sources of error -- 9.3 Remarks -- References
