• Pavel S. Pankratev, Bratsk state university (Bratsk, Russia)

Optimal distribution of electric loads between energy sources is a crucial process enabling the minimization of financial costs for the energy supplier at the current demand level. This process, internationally known as economic dispatch, is traditionally built on the principle of equality of incremental fuel costs, which allows for determining the optimal power allocation in terms of achieving economic efficiency. However, the modern state of the energy sector, characterized by global ESG transformation and the implementation of Corporate Social Responsibility (CSR) principles, requires considering not only direct economic indicators but also socio-environmental ones. The latter are often hard to formalize or entirely non-formalizable, introducing significant complexity to the optimization process. These conditions necessitate the involvement of a Decision Maker (DM) with their inherent internal value system. Under these circumstances, the traditional cost-minimization approach becomes insufficient, dictating the need for new hybrid methods. This article proposes a hybrid method for power allocation based on the synthesis of the classical Lagrange multiplier method, generalized by Karush–Kuhn–Tucker (KKT) conditions, and Multi-Attribute Utility Theory (MAUT). The scientific novelty of the approach lies in the direct integration of a multi-attribute value function, reflecting the DM's subjective preferences, into the structure of the optimization problem. To validate the developed hybrid method, an isolated power system with a total load of 500 MW was modeled. The optimization problem in a static formulation was solved for two scenarios: a baseline scenario (minimizing fuel costs) and a socially-oriented scenario (considering DM participation with an active constraint on the value function level V ≥ 0.60). The results showed that meeting the DM requirements at a value level of 0.60 leads to a substantial reconfiguration of the energy balance, substituting 43% of base-load coal generation with gas power capacity. It is demonstrated that the resulting cost increase (by 22%) is compensated by achieving the required level of social value. The calculated values of dual variables (Lagrange multipliers) are interpreted as "shadow prices" of non-formalizable constraints, reflecting the marginal cost of improving the socio-environmental situation.

optimal load distribution, economic dispatch, system analysis, Multi-Attribute Utility Theory (MAUT), Lagrange multiplier method, Karush-Kuhn-Tucker conditions, shadow price, decision making

2026-09-03