Optimal Comfort with Limited Power
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Electricity consumption is growing and with more efficient equipment introducing larger power peaks. Reducing the power peaks can substantially reduce the electricity expenses for a building. In 2015 it was presented that 60-70% of the grid tariff cost was the power-dependant part for commercial buildings in Norway. There are several different power-dependant billing practices which increase expenses based on a buildings monthly power peaks. Some practices only focus on the single highest peak of the month. This means that one day can heavily increase the electricity expenses for the whole month. A fair amount of work has been done to reduce the power peaks for buildings. Many of the solutions suggest some sort of optimal control theory, with the use of building models. However, modelling the dynamics of a building can be very cost and time consuming. This paper presents a solution for reducing power peaks, by utilizing neural networks and optimal control. Where neural networks will identify the system dynamics, which will be utilized by the optimal control to guide the processes towards optimal values for distributing comfort with limited power. Identifying suitable models to describe the input-output behaviour of dynamic systems is not directly suited for novel neural networks. This is due to their inability to represent the recurrence of connections through time. However, Recurrent Neural Networks (RNN) incorporate feedback connections, giving them the ability to tackle many complex system identification problems. By combining RNN architecture and linear systems theory we create a Linear Recurrent Neural Network (LRNN) which approximates individual process dynamics directly to a second order state-space. This paper suggests two different ways of limiting power and fairly distributing comfort. First using the well established Model Predictive Control (MPC). Second using a custom optimization algorithm that utilizes steady-state and pole-placement, which is named Steady State Control (SSC) in this paper. Using the MPC is not viable due to our inability to formulate a convex optimization. Using the SSC is viable given approximated steady-state gains and bias values provided via the LRNN, with online-learning correcting for disturbances and dynamical changes. However, pole-placement with online-learning has the risk of causing instability, which is why we should rather get control parameters from an initial tuning procedure and keep them constant. In conclusion, this paper provides a proof of concept for limiting power and fairly distributing comfort using a custom optimization algorithm with neural network system identification. However, it does need to be tested in a real building to prove its validity.