# University of Twente Student Theses

## An approximate dynamic programming approach to the micro-CHP scheduling problem

Vinke, Maarten
(2012)
*An approximate dynamic programming approach
to the micro-CHP scheduling problem.*

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Abstract: | Due to environmental issues such as the greenhouse effect, and the fact that the earth’s oil and gas reserves are slowly depleting, the electricity supply chain is slowly transforming toward novel methods of energy generation. One of these methods consists of using micro-CHPs in households to satisfy part of the electricity demand. A micro- CHP is an installation that simultaneously generates heat and electricity, replacing the traditional boiler. In this setting, the electricity production is essentially a by-product of the heat production, so that there is no heat loss during the electricity production process. The micro-CHP comes with a heat buffer, in which hot water can be stored, so there is some flexibility in the time for this production. Still, as electricity is dependent on the heat demand, the electricity generation from a single house can become erratic. Therefore, in this thesis we consider a group of houses, for which the goal is to obtain a more or less constant electricity production. To enforce this, we assume that there are fixed upper and lower bounds on the total electricity production. The goal in this thesis is to find a production schedule for the different micro-CHPs, so that both these total electricity bounds and the houses’ individual heat demands are satisfied. Within these constraints, the objective is to maximize the revenue gained by selling this electricity, whereby these electricity prices are time-dependent, with peaks during the hours when electricity demand is higher. This micro-CHP problem has already been investigated by Bosman [4], where multiple heuristics were used to find such a schedule, using a discretized time scale. In this thesis, we have attempted to solve the scheduling problem mentioned above using the technique of Approximate Dynamic Programming (ADP). For this the problem was first modelled as a Dynamic Program, which was too large to solve exactly. After this technique is introduced by considering the taxicab problem, it is used on the actual micro-CHP problem. As a decision here consists of determining which micro-CHPs are turned on and off in the following time interval, often the number of possible decisions is too large to consider them all. Therefore, first the decision space is reduced by using a strict priority list. Then an approximation function for every state is defined, which uses a weighted sum of basis functions. These basis functions are numerical values based on certain features of a state. Then, the approximation function and the reduced decision space can be used to find to find paths through the state space, each resulting in a production schedule for the micro-CHPs. After such a schedule has been found, the values found in this schedule are used to update the weights in the approximation function, to increase the quality of the approximation. This is repeated for multiple iterations. This algorithm is applied to a data set, after which the results were compared to those of Bosman [4]. The results are generally better than his results from the local search heuristic, and comparable with those of the column generation method. Only in the cases where the planning intervals were so small that the production behaviour of the micro-CHP had to be taken into account, the ADP algorithm did not perform as well. |

Item Type: | Essay (Master) |

Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |

Subject: | 31 mathematics |

Programme: | Applied Mathematics MSc (60348) |

Link to this item: | https://purl.utwente.nl/essays/62262 |

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