Coordinated operation of district heating networks and electric power systems offers significant potential to reduce operational costs and improve grid flexibility by leveraging thermal storage capabilities. However, most scheduling approaches today rely on simplified discrete-time models that fail to capture the complex spatiotemporal thermal dynamics occurring within heating distribution networks.
Researchers have developed an advanced optimization framework that explicitly incorporates continuous-time thermal dynamics into integrated heat-power scheduling. The innovation centers on a Bernstein-Galerkin transform method, which converts the governing partial-differential equations representing thermal dynamics into a finite set of algebraic constraints suitable for standard optimization solvers.
This mathematical transformation preserves the essential dynamic characteristics of the heating system while eliminating the computational intractability typically associated with continuous-domain optimization problems. Rather than forcing thermal behavior into rigid time-step intervals, the method represents system dynamics through polynomial approximations, capturing the smooth evolution of temperature and pressure throughout the distribution network.
Comparison with conventional discretization approaches reveals meaningful advantages. The proposed framework achieves superior economic performance by more accurately estimating the flexibility available from thermal inertia—the ability of the heating medium and pipes to store and release energy. This improved accuracy reduces over- or under-estimation of heat storage capacity, leading to more reliable and cost-effective schedules.
For power system operators, particularly those managing hybrid heat-electricity systems common in northern Europe and other regions with extensive district heating infrastructure, this approach offers practical benefits. More precise modeling enables operators to use thermal mass strategically during peak electricity demand periods or when renewable generation fluctuates, reducing reliance on expensive peaking generation or energy imports.
The work addresses a genuine gap in optimization literature, where most commercial scheduling tools treat heating systems as secondary appendages to power grid operations. By elevating thermal dynamics to equivalent importance in the optimization framework, the research provides a blueprint for utilities seeking competitive advantage through sophisticated multi-energy system coordination.
