Summary |
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1 | (6) |
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1 Physical Structure of the Existing Grid and Current Trends |
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7 | (25) |
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7 | (1) |
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8 | (8) |
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Interconnected Alternating Current Power Grids |
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8 | (2) |
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10 | (1) |
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Basic Circuits---Quasi-Steady-State Time Frame |
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11 | (2) |
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Three-Phase Power Systems and Per-Phase Analysis |
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13 | (3) |
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Illustrative Types of Analysis Needed for the Grid |
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16 | (14) |
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Power Flow---Steady-State Analysis |
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16 | (4) |
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Interconnected Power System Steady-State Operations |
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20 | (4) |
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Longer-Term Power System Planning |
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24 | (1) |
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25 | (4) |
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29 | (1) |
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Organization of the Report |
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30 | (1) |
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31 | (1) |
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2 Organizations and Markets in the Electric Power Industry |
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32 | (12) |
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32 | (1) |
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History of Federal and State Regulation with Regional Standards Development |
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32 | (3) |
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33 | (1) |
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Reliability Organization Development |
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33 | (1) |
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North American Regional Entities |
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34 | (1) |
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34 | (1) |
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U.S. Wholesale Power Markets |
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35 | (2) |
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Common Features of Electric Markets |
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37 | (1) |
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Electricity Market Co-optimization |
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37 | (1) |
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37 | (3) |
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38 | (1) |
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38 | (1) |
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38 | (2) |
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40 | (1) |
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40 | (1) |
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40 | (1) |
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Examples of International Markets |
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41 | (1) |
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Australian National Electricity Market |
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41 | (1) |
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German Electricity Market |
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41 | (1) |
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42 | (1) |
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42 | (2) |
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3 Existing Analytic Methods and Tools |
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44 | (17) |
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44 | (1) |
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44 | (4) |
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Steady-State Contingency Analysis |
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48 | (1) |
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Optimal Power Flow and Security-Constrained Optimal Power Flow |
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49 | (1) |
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50 | (2) |
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Transient Stability and Longer-Term Dynamics |
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52 | (3) |
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55 | (1) |
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Electromagnetic Transients |
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55 | (1) |
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56 | (1) |
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56 | (2) |
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Modeling High-Impact, Low-Frequency Events |
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58 | (1) |
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59 | (2) |
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4 Background: Mathematical Research Areas Important for the Grid |
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61 | (23) |
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61 | (2) |
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63 | (2) |
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65 | (6) |
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General-Purpose Optimization Methods and Software |
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65 | (2) |
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Grid-Related Continuous Optimization |
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67 | (1) |
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Mixed-Integer Linear Programs |
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67 | (2) |
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69 | (2) |
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71 | (2) |
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71 | (1) |
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71 | (1) |
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72 | (1) |
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73 | (1) |
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Risk Analysis, Reliability, Machine Learning, and Statistics |
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73 | (6) |
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74 | (1) |
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Classification and Hazard Modeling |
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74 | (1) |
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75 | (1) |
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76 | (1) |
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Reliability Modeling with Physical Models |
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77 | (1) |
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78 | (1) |
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78 | (1) |
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Complexity and Model Reduction in the Time of Big Data |
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79 | (2) |
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Uncertainty Quantification |
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81 | (1) |
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82 | (2) |
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5 Preparing for the Future |
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84 | (9) |
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84 | (1) |
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Uncertainty in What Lies Ahead |
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84 | (1) |
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Technologies That Will Enhance the Observability of the Grid |
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85 | (2) |
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Technologies That Will Enhance the Controllability of the Grid |
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87 | (1) |
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Effects of Climate Change |
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88 | (1) |
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Mathematical and Computational Challenges in Grid Architectures |
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88 | (1) |
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Mathematical and Computational Challenges in Local Distribution Grid Architectures |
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89 | (2) |
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Mathematical and Computational Challenges in Managing Interdependencies Between the Transmission and Local Distribution Grids/Microgrids |
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91 | (1) |
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92 | (1) |
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6 Mathematical Research Priorities Arising from the Electric Grid |
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93 | (18) |
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93 | (1) |
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Synthetic Data for Facilitating the Creation, Development, and Validation of New Power System Tools for Planning and Operations |
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94 | (3) |
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96 | (1) |
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Data-Driven Models of the Electric Grid |
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97 | (2) |
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The Role of Control Theory in the Changing Electric Energy Systems |
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99 | (1) |
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Physics-Based Simulations for the Grid |
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100 | (3) |
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Data-Driven Approaches for Improving Planning, Operations, and Maintenance and for Informing Other Types of Decision Making |
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103 | (2) |
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Creating Hybrid Data/Human Expert Systems for Operations |
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103 | (1) |
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Machine-Learning Models for Hazard Modeling and Reliability |
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103 | (1) |
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Visualization Tools for Understanding Data |
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104 | (1) |
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Detecting Who Has No Power |
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104 | (1) |
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Machine Learning for Long-Term Planning |
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104 | (1) |
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105 | (3) |
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Convex Relaxation in Grid-Related Optimization |
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105 | (1) |
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Robust and Chance-Constrained Optimization |
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106 | (2) |
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Challenges in Modeling the Electric Grid's Coupling with Other Infrastructures |
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108 | (1) |
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109 | (2) |
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111 | (17) |
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111 | (1) |
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Case Study in Optimization: PJM's Daily Operations |
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111 | (5) |
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112 | (2) |
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114 | (1) |
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Capacity Market---Reliability Pricing Model Optimization |
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115 | (1) |
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Financial Transmission Rights |
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115 | (1) |
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Challenges for the Day-Ahead Unit Commitment Formulation |
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115 | (1) |
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Case Study in Mathematical Needs for the Modeling and Mitigation of Low-Frequency Events |
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116 | (3) |
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Interdisciplinary Modeling |
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118 | (1) |
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118 | (1) |
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Resilience Control Center Design |
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118 | (1) |
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Resilience Power System Design |
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119 | (1) |
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Case Study in Data-Centered Asset Maintenance: Predicting Failures in Underground Power Distribution Networks |
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119 | (3) |
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120 | (1) |
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Handling Unstructured Text |
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121 | (1) |
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121 | (1) |
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121 | (1) |
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Visualization and Interpretation of Results |
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121 | (1) |
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Machine-Learning Methods Comprehensible to Human Experts |
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121 | (1) |
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Case Study in Synchrophasors |
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122 | (3) |
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Overview of Synchrophasors |
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122 | (2) |
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Application of Synchrophasors |
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124 | (1) |
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Mathematical Challenges to Improve Synchrophasor Measurements |
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124 | (1) |
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Case Study in Inverter-Based Control for Stabilizing the Power System |
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125 | (1) |
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126 | (2) |
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8 Building a Multidisciplinary Research Community |
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128 | (11) |
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128 | (1) |
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Example of a Multidisciplinary Team: PSERC |
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129 | (1) |
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Example of a Multidisciplinary Effort: Markets |
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129 | (2) |
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Examples from Other Disciplines |
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131 | (1) |
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Recommendation for Synthetic Data Libraries |
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132 | (1) |
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Recommendation for Software Libraries |
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132 | (1) |
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Recommendation for Increased R&D Coordination |
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133 | (1) |
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Recommendation for a National Center |
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134 | (1) |
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135 | (4) |
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139 | (2) |
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141 | (4) |
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145 | |