Towards a low carbon energy future, the interest in Renewable Energy Sources (RES) as sources of electrical energy in the grid has increased significantly. As most RES are converter based, the electric power system is currently undergoing a drastic transition from synchronous generators (SG) dominated to converter-based generation units dominated. As a result, the network is losing its precious SG inertia used for instant frequency response after a contingency in the network. Low SG inertia in the network leads to rapid and significant frequency fluctuations becoming considerable challenges to address. As a result of low SG inertia in the network, the introduction of control strategies of some RES to provide the so-called synthetic inertia (SyI) are becoming popular. However, due to the stochastic nature and physical characteristics of RES, the provided SyI may be a time-varying and tradeable quantity in the contemporary network. Therefore, it is crucial to understand the values of network inertia in the time ahead to avoid rapid and significant frequency fluctuations in the network due to low and time-varying inertia. Prior knowledge of the system inertia values is essential to help operators plan and apply appropriate measures and suitable control schemes to mitigate stability issues.

Therefore, this study aims to monitor and optimise inertia values in modern networks with high penetration of RES. The monitoring part of the research is further subdivided into three subparts presented in separate independent Chapters. The three subparts are offline inertia estimation, online inertia estimation, and long-range inertia forecasting. The inertia optimisation part is discussed in a separate Chapter as well.

In addition to Chapter 1 which gives a general introduction to this thesis, Chapter 2 provides a comprehensive literature review on inertia's role for grid flexibility under the high penetration of variable renewables. Chapter 2 reviews the challenges and solutions related to the role of inertia in maintaining frequency stability in the network. Further, a comprehensive literature survey on the need for inertia estimation, monitoring, forecasting, and optimisation is presented in Chapter 2. This part of the study reveals the research gaps that need attention in modern networks. The subsequent Chapters further cover the identified gaps by developing techniques to fill up the research gaps.

The proposed methods start with the offline inertia estimation method presented in Chapter 3. This part of the study develops a data-driven method to estimate the time-changing inertia in the network based on the frequency gradient of an estimated model of the network. This approach uses phasor measurement units (PMUs)-measured network data to estimate a network's dynamic model. Next, a system identification approach is applied to estimate the power system model, from which the estimated inertia can be extracted. The benefits of the proposed method include, i) reduction of a high order model to a low order model to avoid computation burden, ii) extraction of the inertia from the low order model using the gradient mapping on RoCoF of the system response, and iii) estimation of the inertia constant of the network using normal operating conditions.

Then, Chapter 4 proposes an online method to estimate the inertia in the network based on the recursive least-squares approach. The proposed method uses network measurements with a non-recursive system identification approach to estimate the network's hypothesis model. Then, the recursive method is used together with time changing measurements to recursively estimate model parameters and extract online estimates of the inertia in the network. During estimation, the technique does not need to store previous data after each sample step; therefore, significantly reducing the computation burden. More importantly, the method incorporates the use of available electromechanical oscillation modes in the system, which are linked with system parameters to determine the estimates of the network's inertia.

After establishing the offline and online inertia estimation methods, Chapter 5 gives the long-range forecasting of inertia in modern and future power networks. Due to quick inertial responses, there is practically a short time for control actions in real-time that is difficult to be addressed by online approaches. Therefore, system operators need to understand the inertia values in advance to plan, control, and operate the network securely. Unlike short-range forecasting methods, long-range forecasting of inertia values in the network can identify when the network is likely to be potentially at risk in a reasonable time ahead. Thus, this Chapter proposes an improved ARIMA model (i-ARIMA) approach to long-range forecast inertia values in a modern network. The i-ARIMA uses strong periodic and seasonality patterns of historical time series data to long-range forecast future inertia values.

Finally, the participation of SyI in the market of RES-rich networks to provide instant frequency support when required proposes an increase in the operation cost of modern networks. Consequently, depreciation of operation costs by optimising the required SyI in the network is inevitable. The provided optimal values of SyI should also ensure stability resilience of the network is retained. Therefore, Chapter 6 proposes a flexible SyI optimisation method to address these issues. The algorithm developed in the proposed technique minimizes the operation cost of the network by giving flexible SyI at a given SG inertia and different sizes of contingency events.