Abstract
Power mini-grids are being transformed from locally automated electrical systems into cyber-physical ecosystems in which heterogeneous distributed energy resources, storage, converters, flexible demand and uncertain external conditions must be coordinated. Existing surveys commonly treat microgrid control, artificial intelligence (AI), multi-agent systems, communications, digital twins and cybersecurity as separate research streams. In this survey, the cognitive power mini-grid is introduced as a unifying paradigm in which physical and social contexts are perceived by distributed agents, task-relevant semantic information is exchanged, auditable coordination readiness is checked and proposed actions are subject to independent safety checks. A corpus of 247 scholarly publications, standards and technical sources is synthesized across microgrid engineering, distributed AI, semantic communication, language models, federated learning, neuro-symbolic AI, digital twins, causal reasoning, runtime assurance, cybersecurity and community energy markets. A six-layer architecture is proposed in which fast deterministic control is separated from semantic coordination, distributed learning, agentic deliberation and assurance. Representative studies are compared by problem, method, control horizon, information assumptions, validation environment, hardware-in-the-loop (HIL) status, reported outcome, limitations and architectural relevance. Applications are organized into balancing, resilience, demand-response, maintenance and inter-mini-grid markets. Cross-layer challenges are identified in stability under asynchronous interaction, semantic interoperability, hallucination, common-knowledge failure, edge resources, privacy and cyber-physical security constraints. A research agenda is developed around proof-carrying actions, causal digital twins, edge small language models, federated multimodal foundation models, neuromorphic semantic control and human-agent governance. Cognition is therefore positioned as a safety-gated coordination capability above verified physical control loops rather than as a replacement for established control.