## Forschungszentrum Energie

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Load shifting of resistive domestic hot water heaters has been done in Europe since the 1930s, primarily to ease the power supply during peak times. However, the pursued and already commenced energy transition in Europe changes the requirements for the underlying logic. In this more general context, demand side management is considered a viable approach to utilize the flexibility of thermal and electrochemical storage systems for buffering energy generated from renewables. In this work, an autonomous approach for demand side management of energy storage systems is developed, which is based on unidirectional communication of an incentive. This concept is then applied to the specific problem of resistive domestic hot water heaters.
The basic algorithms for an optimized operation are developed and evaluated based on simulation studies. The optimization problem considered, maps the search for the optimal heating schedule, while ensuring the temperature limits defined: Firstly, a maximum, which is defined by the hysteresis set point temperature; Secondly, during hot water draw offs, the outlet temperature should not fall below a set minimum. To establish this, the time series of hot water usage has to be predicted.
Depending on the complexity of the hot water heater model used, the formulation of the problem ranges from a linear to non-linear optimization with discontinuous constraints. The simulation studies presented, comprise a formulation as binary linear optimization problem, as well as a solution based on a heuristic direct method to solve the non-linear version. In contrast to the first linear approach, the latter takes stratification inside the tank into account. One-year simulations based on realistic hot water draw profiles are used to investigate the potentials with respect to load shift and energy efficiency improvements. Additional to assuming perfect prediction of user behavior, this work also considers the k-nearest neighbors algorithm to predict the time series. If compared to usual night-tariff switched operation, assuming perfect prediction shows 30 % savings on the electricity market when stratification is taken into account. The user prediction proposed leads to 16 % cost savings, while 6 % of the electric energy is conserved.
Based on the linear approach, a prototype is developed and used in a field test. A micro computer processes the sensor information for local data acquisition, receives electricity spot market prices up to 34 hours in advance, solves the optimization problem for this time horizon, and switches the power supply of the resistive heating element accordingly. Beside the temperature of the environment, the inlet and outlet temperatures, the temperature inside the tank is measured at five points, as well as the water volume flow rate and the electric power recorded. Two test runs of 18 days each, compare the night-tariff switched operation to the price-based optimization in a real-world environment. Results show a significant increase of 6 % in thermal efficiency during the operation based on the algorithm developed, which can be contributed to the optimization accounting for the usage expected.
To facilitate the technical and economic feasibility for retrofit-able implementations of the method proposed for autonomous demand side management, the sensors used must be kept to a minimum. A sufficiently accurate state estimation of the storage has to be achieved, to facilitate a useful model predictive control. Therefore, the last part of this work focuses on the aspect of automated system identification and state estimation of resistive domestic hot water heaters. To that end, real hot water usage profiles and schedules gathered in a field test are used in a lab setup, to collect data on the temperature distribution inside the tank during realistic operating conditions. Four different thermal models, common in literature, are considered for state estimation and system identification. Based on the data collected in the lab, they are evaluated with respect to robustness, computational costs, and estimation accuracy. Based on the observations made in the experiments, an extension of the one-node model by a single additional parameter is proposed. By this adaption, a linear temperature distribution in the lower part of the tank can be modeled during heating. The resulting model exhibits improved robustness and lower computational costs, when compared to the original model. At the same time, the average temperature in the storage tank is estimated nearly as accurate (6 % mean average percentage error) as in the case of the about 50 times more computationally expensive multi-layer model (4 % mean average percentage error).

In contrast to fossil energy sources, the supply by renewable energy sources likewind and photovoltaics can not be controlled. Therefore, flexibilities on the demandside of the electric power grid, like electro-chemical energy storage systems, are usedincreasingly to match electric supply and demand at all times. To control those flex-ibilities, we consider two algorithms that both lead to linear programming problems.These are solved autonomously on the demand side, i.e., by household computers.In the classic approach, an energy price signal is sent by the electric utility to thehouseholds, which, in turn, optimize the cost of consumption within their constraints.Instead of an energy price signal, we claim that an appropriate power signal that istracked in L1-norm as close as possible by the household has favorable character-istics. We argue that an interior point of the household’s feasibility region is neveran optimal price-based point but can result in a L1-norm optimal point. Thus, pricesignals can not parametrize the complete feasibility region which may not lead to anoptimal allocation of consumption.We compare the price and power tracking algorithms over a year on the base ofone-day optimizations regarding different information settings and using a large dataset of daily household load profiles. The computational task constitutes an embarrassingly parallel problem. To this end, the performance of the two parallel computation frameworks DEF [1] and Ray [2] are investigated. The Ray framework is used to run the Python applications locally on several cores. With the DEF frameworkwe execute our Python routines parallelly in a cloud. All in all, the results providean understanding of when which computation framework and autonomous algorithmwill outperform the other.