Solar and wind power are potential carbon-free energy solutions for urban areas, but they are also subject to large variability. At the same time, urban areas offer promising flexibility solutions for balancing variable renewable power. This paper presents models for optimal control of power-to-heat conversion to heating systems and shiftable loads in cities to incorporate large variable renewable power schemes. The power-to-heat systems comprise heat pumps, electric boilers, and thermal storage. The control strategies comprise optimal matching of load and production, and cost-optimal market participation with investment analysis. All analyses are based on hourly data. The models are applied to a case study in Helsinki, Finland. For a scheme providing ca. 50% of all electricity in the city through self-consumption of variable renewables, power-to-heat with thermal storage could absorb all the surplus production. A significant reduction in the net load magnitude was obtained with shiftable loads. Investments to both power-to-heat and load shifting with electric heating and commercial refrigeration have a positive net present value if the resources are controlled cost-optimally. (C) 2016 Elsevier Ltd. All rights reserved.