Constraint relaxation by definition means that certain security, operational, or financial constraints are allowed to be violated in the energy market model for a predetermined penalty price. System operators utilize this mechanism in an effort to impose a price-cap on shadow prices throughout the market. In addition, constraint relaxations can serve as corrective approximations that help in reducing the occurrence of infeasible or extreme solutions in the day-ahead markets. This work aims to capture the impact constraint relaxations have on system operational security. Moreover, this analysis also provides a better understanding of the correlation between DC market models and AC real-time systems and analyzes how relaxations in market models propagate to real-time systems. This information can be used not only to assess the criticality of constraint relaxations, but also as a basis for determining penalty prices more accurately.

Constraint relaxations practice was replicated in this work using a test case and a real-life large-scale system, while capturing both energy market aspects and AC real-time system performance. System performance investigation included static and dynamic security analysis for base-case and post-contingency operating conditions. PJM peak hour loads were dynamically modeled in order to capture delayed voltage recovery and sustained depressed voltage profiles as a result of reactive power deficiency caused by constraint relaxations. Moreover, impacts of constraint relaxations on operational system security were investigated when risk based penalty prices are used. Transmission lines in the PJM system were categorized according to their risk index and each category was as-signed a different penalty price accordingly in order to avoid real-time overloads on high risk lines.

This work also extends the investigation of constraint relaxations to post-contingency relaxations, where emergency limits are allowed to be relaxed in energy market models. Various scenarios were investigated to capture and compare between the impacts of base-case and post-contingency relaxations on real-time system performance, including the presence of both relaxations simultaneously. The effect of penalty prices on the number and magnitude of relaxations was investigated as well.

Recent changes in the energy markets structure combined with the conti-nuous load growth have caused power systems to be operated under more stressed conditions. In addition, the nature of power systems has also grown more complex and dynamic because of the increasing use of long inter-area tie-lines and the high motor loads especially those comprised mainly of residential single phase A/C motors. Therefore, delayed voltage recovery, fast voltage collapse and short term voltage stability issues in general have obtained significant importance in relia-bility studies. Shunt VAr injection has been used as a countermeasure for voltage instability. However, the dynamic and fast nature of short term voltage instability requires fast and sufficient VAr injection, and therefore dynamic VAr devices such as Static VAr Compensators (SVCs) and STATic COMpensators (STAT-COMs) are used. The location and size of such devices are optimized in order to improve their efficiency and reduce initial costs. In this work time domain dy-namic analysis was used to evaluate trajectory voltage sensitivities for each time step. Linear programming was then performed to determine the optimal amount of required VAr injection at each bus, using voltage sensitivities as weighting factors. Optimal VAr injection values from different operating conditions were weighted and averaged in order to obtain a final setting of the VAr requirement. Some buses under consideration were either assigned very small VAr injection values, or not assigned any value at all. Therefore, the approach used in this work was found to be useful in not only determining the optimal size of SVCs, but also their location.