Vol. 4 No. 1 (2026)

The number of photovoltaic installations at residential level has risen to a marked extent; this has led to the development of microgrids powered mainly by photovoltaic. Motivated by these technologies, particularly with smart grids and IoT-enabled devices, this paper explores the first main stochastic control method—the dynamic programming principle—for enhancing flexibility from the demand side. This is brought about by adjusting the demand for electricity to better match generation from solar energy over the course of each hour, day or longer timeframe. The proposed method is applied to household appliances which exhibit spontaneous cycling, called thermostatically controlled loads, and can manage uncertainty related to weather by employing the technique of shaping filter for modeling ambient temperature as diffusion processes. A stochastic control problem has henceforth been established, and we have come through with a quite novel flexibility Markov model. Accordingly, in theory, the Hamilton–Jacobi–Bellman equation provides the only closed-form exact solutions. Even if the existence of solutions to Bellman’s equation is assured, it is often difficult to compute or characterize optimal controls from Bellman’s equation. Our substantial contribution in this work consists of a systematic method for approximating the exact solutions, inspired from the Taylor-Young formula of second-order in the continuous component of the state. Some of our computational experiences are provided in the context of behind-the-meter solar power with simulated scenarios: step function-like random functions and periodic functions. Monte-Carlo method is employed to study the impact of stochastic versus open-loop control. We believe that the comparative study reveals the breadth of flexibility control, namely, to convert the social benefit of mitigating the consequences of renewables uncertainty to a private benefit for users.

The paper is focused on the relevant risk and uncertainty evaluation of Slovak nuclear power policy. There are considerations about cost estimations for decommissioning and radioactive waste management in Slovakia. Results were incorporated into the actualization of Slovak national policy and program for spent nuclear fuel and radioactive waste management, which was sent for acceptance to the Government of Slovak Republic for the next 6 years period. The most significant risks in Slovakia are connected to build of deep geological repository, and too much consider new projects, which will probably influent human resources in decommissioning. Nevertheless, the nuclear optimism declared in political support of Slovak government should be balanced via real investment to improvement of nuclear infrastructure in Slovakia/Europe/world-wide including substantial investment in nuclear knowledge and human resources. The paper can be inspirative also for other countries with developed nuclear program as Slovak lessons learned.