In this paper, we consider the problem of optimal precooling of thermostatic loads by a load serving entity (LSE) under time varying electricity prices. Specifically, we propose a low complexity dynamic programming based algorithm for controlling the switching of HVAC units such that the cost of cooling is minimized while ensuring that the resultant temperatures do not violate the comfort constraints of consumers. Specifically, our algorithm makes use of two facts: (i) the price of electricity vary discretely in time and (ii) the cost-optimal state trajectory under fixed electricity price and ambient temperature, with given initial and final states, can be characterized explicitly in closed-form. We validate our algorithm with a set of numerical simulation studies using real market prices of electricity from the New York and Texas electricity markets. In addition, we also provide an approximation mechanism to implement this optimization algorithm in HVAC systems that have ON-OFF switching constraints.

District Heating (DH) networks are complex thermal grids wherein a centrally heated fluid is circulated through a network of pipes and heat exchangers to meet the heating needs of residential and commercial buildings. Several factors can lead to inefficient and unfair energy distribution among consumers in these networks. These include varying levels of building insulation, distance of individual buildings from the central energy source, and thermal losses in network pipes. Moreover, shortage of energy at the central energy source and extreme weather conditions can exacerbate these issues, leading to differing levels of thermal comfort and customer disgruntlement in the long run. In this paper, we propose and study a demand response scheme that attempts to ensure thermal fairness among energy consumers in modern thermal grids. We develop optimization formulations based on thermodynamic models of DH networks, which determine optimal energy flow for individual buildings in order to achieve thermal fairness across the network. Our numerical results using physics based models for DH networks show that it is indeed possible to achieve network level thermal fairness based objectives by controlling network parameters such as mass flow rates of water to the consumer premises and the supply water temperature.

The load profiles of most commercial and industrial consumers are characterized by brief periods of very high power consumption followed by intervals of lower demand. To encourage such consumers to flatten their load profiles, power utilities around the world often levy a monthly demand charge (DC) on the peak demand measured over brief intervals. In this work, we consider the joint optimization of energy costs (EC) and the instantaneous peak power of a multi-unit building which uses a hydronic heating, ventilation and air-conditioning (HVAC) system and responds to a demand response (DR) program. Despite the apparent non-convexity of the control framework, we show how it may be transformed into a convex optimization problem. Next, we study the power demand patterns resulting from our proposed strategy for thermostatically controlled loads (TCLs), and evaluate the strategy’s performance for various climate zones in the US under both typical and atypical weather conditions. The results show that, depending on the ambient conditions and the tariff structure, our strategy can result in utility bill savings of up to nearly 19% compared to the baseline. The results also indicate that our power control strategy can significantly reduce the instantaneous peak power consumption in commercial TCLs.

Modern-day energy systems are evolving to be complex, interconnected, and transactive systems without clear demarcation between energy “producers” and “consumers”. This is aided by the large-scale proliferation of renewables (at a centralized scale and in more distributed settings, such as rooftop solar) and the growing potential for demand-side flexibility. In this paper, we propose a mathematical framework that considers the interaction of energy flexibility and renewable generation in a transactive power system, where a grid operator can secure both generation and flexibility (storage) from centralized and/or distributed assets. Our results, derived under network-abstracted settings, mathematically relate the system operating cost to the available flexibility capacity. In addition, our proposed framework also characterizes the inflection point beyond which further addition of flexibility capacity does not affect the cost of system operation. Furthermore, the relationship between the price spread in the grid, i.e., the difference between maximum and minimum prices over the time horizon under consideration, and the available flexibility is also commented upon. Finally, we demonstrate our findings on a modified IEEE 30 bus test network.