Affine Arithmetic-Based Methods for Uncertain Power System Analysis

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
10 Reliable microgrids scheduling in the presence of data uncertainties
	10.1 Deterministic optimization
	10.2 Robust optimization
	10.3 Affine arithmetic-based optimization
	10.4 Numerical results and discussion
	10.5 Remarks
	References
Index