Jiří Fink

Long cycles in hypercubes with optimal number of faulty vertices

Let f(n) be the maximum integer such that for every set F of at most f(n) vertices of the hypercube Qn, there exists a cycle of length at least 2n−2|F| in Qn−F. Castañeda and Gotchev conjectured that

Minimizing costs is easier than minimizing peaks when supplying the heat demand of a group of houses

f(n)=\binom{n}{2}-2

Central model predictive control of a group of domestic heat pumps case study for a small district

. We prove this conjecture. We also prove that for every set F of at most (n2+n−4)/4 vertices of Qn, there exists a path of length at least 2n−2|F|−2 in Qn−F between any two vertices such that each of them has at most 3 neighbors in F. We introduce a new technique of potentials which could be of independent interest.

House thermal model parameter estimation method for Model Predictive Control applications

This paper studies planning problems for a group of heating systems which supply the hot water demand for domestic use in houses. These systems (e.g. gas or electric boilers, heat pumps or microCHPs) use an external energy source to heat up water and store this hot water for supplying the domestic demands. The latter allows to some extent a decoupling of the heat production from the heat demand. We focus on the situation where each heating system has its own demand and buffer and the supply of the heating systems is coming from a common source. In practice, the common source may lead to a coupling of the planning for the group of heating systems. On the one hand, the external supply of the energy for heating up the water may have to be bought by an energy supplier on e.g. a day-ahead market. As the price of energy varies over time on such markets, this supplier is interested in a planning which minimizes the total cost to supply the heating systems with energy. On the other hand, the bottleneck to supply the energy also may be the capacity of the distribution system (e.g. the electricity networks or the gas network). As this has to be dimensioned for the maximal consumption, in this case it is important to minimize the maximal peak. The two mentioned coupling constraints for supplying the energy for producing the heat, lead to two different objectives for the planning of the group of heating systems: minimizing cost and minimizing the maximal peak. In this paper, we study the algorithmic complexity of the two resulting planning problems. For minimizing costs, a classical dynamic programming approach is given which solves the problem in polynomial time. On the other hand, we prove that minimizing the maximal peak is NP-hard and discuss why this problem is hard. Based on this, we show that this problem becomes polynomial if all heating systems have the same consumption of energy when turned on. Finally, we present a Fix Parameter Tractable (FPT) algorithm for minimizing the maximal peak which is linear in the number of time intervals.

Connectivity of Matching Graph of Hypercube

In this paper we investigate optimal control of a group of heat pumps. Each heat pump provides space heating and domestic hot water to a single household. Besides a heat pump, each house has a buffer for domestic hot water and a floor heating system for space heating. The paper describes models and algorithms used for the prediction and planning steps in order to obtain a planning for the heat pumps. The optimization algorithm minimizes the maximum peak electricity demand of the district. Simulated results demonstrate the resulting aggregated electricity demand, the obtained thermal comfort and the state of charge of the domestic hot water storage for an example house. Our results show that a model predictive control outperforms conventional control of individual heat pumps based on feedback control principles.

Soft-islanding a group of houses through scheduling of CHP, PV and storage

In this paper we investigate thermal network models with different model orders applied to various Dutch low-energy house types with high and low interior thermal mass and containing floor heating. Parameter estimations are performed by using data from TRNSYS simulations. The paper discusses results in relation to model order and the order which yields a sufficient level of accuracy is determined. The paper presents a semi-physical estimation method which is used to improve correlation of model parameters with physical determined values. The thermal network model can be used for various simulation studies or for Model Predictive Control (MPC) of house heating or cooling systems. The paper investigates accuracy of the model for MPC by comparing MPC-results with results from TRNSYS simulations, including ventilation heat losses.

Thermal storage in a heat pump heated living room floor for urban district power balancing - effects on thermal comfort, energy loss and costs for residents

The matching graph

Some remarks on inverse Wiener index problem

\mathcal{M}(G)

Matchings Extend into 2-Factors in Hypercubes

of a graph

Gray codes with bounded weights

G