This thesis develops an optimisation formulation for the efficient procurement of reserve. The formulation explicitly accounts for delay and ramp rates in reserve response, and the effect they have on keeping the grid frequency above minimum limits. This research is conducted as a part of GREEN Grid project, which is seeking to understand the impacts of Variable Renewable Energy (VRE), such as wind and solar, and other distributed resources on the New Zealand power system. After considering the impacts of wind generation on reserve requirements, a method is developed to compare reserve resources for contingencies more accurately, which can be applied to the scheduling and dispatch processes.

In a power system, contingencies like the loss of a generator or transmission circuit can create an imbalance, where generation is insufficient to supply load. Reserve is required to increase power output to stop the declining grid frequency, otherwise the system collapses. The amount of time available for reserve to respond is dependent on three factors: the size of the largest credible contingency, the inertia of the power system, and allowable frequency range. To increase the available time to respond, the size of the contingency is to be small, inertia should be maximised, and the allowable frequency range is to be wider. However, with increased penetrations of VRE, it is expected that the size of the largest credible contingency can increase and the inertia can decrease, thereby requiring greater response speed from reserve.

In electricity markets across the world, for the most part only capacity and price of reserve feature into decisions of optimal dispatch. Any transient features of reserve responses are considered too difficult for MILP methods. The literature, recognising the importance of response speed, has provided means of incorporating transient features, but have suffered from a lack of generality or insufficient computational performance. Therefore a new approach is developed that allows a wider range of responses to be optimised while being solved in a practical amount of time. It comes at the cost of greater complexity, and deviates from MILP. However it retains convexity like LP, which is beneficial for practical solve times. Further development is required for the inclusion of mixed integer variables and towards achieving its full potential of being implemented in real-time electricity markets.

The new formulation introduces the swing equation, which defines frequency dynamics, into the optimisation formation. Reserve is limited to step and ramp responses that can be delayed. Frequency limits are applied at critical times and quadratic constraints are formed on account of ramped reserve that typifies responses from conventional power stations. This problem cannot be purely classified as a Quadratically Constrained Programming (QCP) problem, as the constraints change between being quadratic and linear depending on the location in the feasible solution space. Therefore this solution method is more accurately called Piecewise Quadratically Constrained Programming.