Power electronic converters in both AC and DC microgrids are controlled using different approaches: AC grid-forming control enables integration of renewable energy sources, while DC droop control regulates decentralized DC-bus voltage. These control strategies share similarities but their similarities remain largely unexplored due to the distinct physical domains in which they operate. Theoretical analysis reveals isomorphism between AC grid-forming and DC I--V droop control in several aspects.

A two-stage stochastic optimization framework is proposed for virtual power plants (VPPs) that integrates detailed device-level constraints and network limitations into a scheduling model. The model jointly optimizes bidding across energy and reserve markets, incorporating conditional value-at-risk to represent risk preferences, and dynamic network tariffs are used to unlock local flexibility. Risk aversion reduces profit volatility through closer alignment with physical dispatch, but strong tariff signals reduce expected profitability by up to 65%.

A shifted passivity analysis of the single-machine infinite-bus system was presented, which showed local asymptotic stability of a synchronous steady state under specific conditions. The analysis used a port-Hamiltonian representation to construct a local shifted passivity condition and derived a dissipation inequality that leads to a sufficient stability condition in terms of various machine parameters. This provides a compact passivity-based stability certificate for the stationary-frame model, preserving the periodic structure of the rotor angle.

A new complex-vector power formulation for three-phase systems has been developed to explicitly represent cross-phase unbalance in phase asymmetry. This representation supplements the classical dot-product expression of complex power with a cross product of voltage and current phasors, making it possible to capture antisymmetric interphase relations. The formulation preserves the norm of apparent power under the Fortescue transformation and provides a compact phasor-based descriptor of unbalance that complements established apparent-power theories.

Electricity price forecasting models achieved varying performance across Norway's five bidding zones, with LightGBM yielding the best results and a linear benchmark remaining competitive in northern zones. The use of external features like reservoir levels and gas prices was crucial to stratify forecast errors, which increased under stressed market regimes. A unified benchmark evaluating feature contributions across all zones remains lacking despite robust testing methods being employed.