  Power grid frequency control is a demanding task requiring expensive idle
power plants to adapt the supply to the fluctuating demand. An alternative
approach is controlling the demand side in such a way that certain appliances
modify their operation to adapt to the power availability. This is specially
important to achieve a high penetration of renewable energy sources. A number
of methods to manage the demand side have been proposed. In this work we focus
on dynamic demand control (DDC), where smart appliances can delay their
switchings depending on the frequency of the system. We introduce a simple
model to study the effects of DDC on the frequency of the power grid. The model
includes the power plant equations, a stochastic model for the demand that
reproduces, adjusting a single parameter, the statistical properties of
frequency fluctuations measured experimentally, and a generic DDC protocol. We
find that DDC can reduce small and medium size fluctuations but it can also
increase the probability of observing large frequency peaks due to the
necessity of recovering pending task. We also conclude that a deployment of DDC
around 30-40\% already allows a significant reduction of the fluctuations while
keeping the number of pending tasks low.
