There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The smart grid is conceived of as an electric grid that can deliver electricity in a controlled, smart way from points of generation to active consumers. Demand response (DR), by promoting the interaction and responsiveness of the customers, may offer a broad range of potential benefits on system operation and expansion and on market efficiency. Moreover, by improving the reliability of the power system and, in the long term, lowering peak demand, DR reduces overall plant and capital cost investments and postpones the need for network upgrades. In this paper a survey of DR potentials and benefits in smart grids is presented. Innovative enabling technologies and systems, such as smart meters, energy controllers, communication systems, decisive to facilitate the coordination of efficiency and DR in a smart grid, are described and discussed with reference to real industrial case studies and research projects.

Demand response and smart grids—A survey

Optimal electrical and thermal energy management of a residential energy hub, integrating demand response and energy storage system

The proliferation of technologies such as combine heat and power systems has accelerated the integration of energy resources in energy hubs. Besides, the advances in smart grid technologies motivate the electricity utility companies toward developing demand response (DR) programs to influence the electricity usage behavior of the customers. In this paper, we modify the conventional DR programs in smart grid to develop an integrated DR (IDR) program for multiple energy carriers fed into an energy hub in smart grid, namely a smart energy (S. E.) hub. In our model, the IDR program is formulated for the electricity and natural gas networks. The interaction among the S. E. hubs is modeled as an ordinal potential game with unique Nash equilibrium. Besides, a distributed algorithm is developed to determine the equilibrium. Simulation results show that in addition to load shifting, the customers in the S. E. hubs can participate in the IDR program by switching the energy resources (e.g., from the electricity to the natural gas) during the peak hours. Moreover, the IDR program can increase the S. E. hubs’ daily payoff and the utility companies’ daily profit.

From Demand Response in Smart Grid Toward Integrated Demand Response in Smart Energy Hub

Innovations in the residential sector are required to reduce environmental impacts, as the sector is a contributor to greenhouse gas emissions. The increasing demand for electricity and the emergence of smart grids have presented new opportunities for home energy management systems (HEMS) in demand response markets. HEMS are demand response tools that shift and curtail demand to improve the energy consumption and production profile of a dwelling on behalf of a consumer. HEMS usually create optimal consumption and productions schedules by considering multiple objectives such as energy costs, environmental concerns, load profiles and consumer comfort. The existing literature has presented several methods, such as mathematical optimization, model predictive control and heuristic control, for creating efficient operation schedules and for making good consumption and production decisions. However, the effectiveness of the methods in the existing literature can be difficult to compare due to diversity in modelling parameters, such as appliance models, timing parameters and objectives. The present chapter provides a comparative analysis of the literature on HEMS, with a focus on modelling approaches and their impact on HEMS operations and outcomes. In particular, we discuss a set of HEMS challenges such as forecast uncertainty, modelling device heterogeneity, multi-objective scheduling, computational limitations, timing considerations and modelling consumer well-being. The presented work is organized to allow a reader to understand and compare the important considerations, approaches, nomenclature and results in prominent and new literary works without delving deeply into each one.

Home energy management systems: A review of modelling and complexity

This paper presents mathematical optimization models of residential energy hubs which can be readily incorporated into automated decision making technologies in smart grids, and can be solved efficiently in a real-time frame to optimally control all major residential energy loads, storage and production components while properly considering the customer preferences and comfort level. Novel mathematical models for major household demand, i.e., fridge, freezer, dishwasher, washer and dryer, stove, water heater, hot tub, and pool pumps are formulated. Also, mathematical models of other components of a residential energy system including lighting, heating, and air-conditioning are developed, and generic models for solar PV panels and energy storage/generation devices are proposed. The developed mathematical models result in Mixed Integer Linear Programming (MILP) optimization problems with the objective functions of minimizing energy consumption, total cost of electricity and gas, emissions, peak load, and/or any combination of these objectives, while considering end-user preferences. Several realistic case studies are carried out to examine the performance of the mathematical model, and experimental tests are carried out to find practical procedures to determine the parameters of the model. The application of the proposed model to a real household in Ontario, Canada is presented for various objective functions. The simulation results show that savings of up to 20% on energy costs and 50% on peak demand can be achieved, while maintaining the household owner's desired comfort levels.

S. A. Hashmi

Papers

Optimal Operation of Residential Energy Hubs in Smart Grids