Double Loop Network for Combined Heating and Cooling in Low Heat Density Areas

This study investigated a double loop network operated with ultra-low supply/return temperatures of 45/25 °C as a novel solution for low heat-density areas in Denmark and compared the proposed concept with a typical tree network and with individual heat pumps to each end-users rather than district networks. It is a pump-driven system, where the separate circulation of supply and return flow increased the flexibility of the system to integrate and displace heating and cooling energy along the network. Despite the increased use of central and local water pumps to operate and control the system, the simulated overall pump energy consumption was 0.9% of the total energy consumption. This was also an advantage at the design stage as the larger pressure gradient, up to 570 Pa/m, allowed minimal pipe diameters. In addition, the authors proposed the installation of electrically heated vacuum-insulated micro tanks of 10 L on the primary side of each building substation as a supplementary heating solution to meet the comfort and hygiene requirements for domestic hot water (DHW). This, combined with supply water circulation in the loop network, served as a technical solution to remove the need for bypass valves during summer periods with no load in the network. The proposed double loop system reduced distribution heat losses from 19% to 12% of the total energy consumption and decreased average return temperatures from 33 °C to 23 °C compared to the tree network. While excess heat recovery can be limited due to hydraulic issues in tree networks, the study investigated the double loop concept for scenarios with heat source temperatures of 30 °C and 45 °C. The double loop network was cost-competitive when considering the required capital and operating costs. Furthermore, district networks outperformed individual heat pump solutions for low-heat density areas when waste heat was available locally. Finally, although few in Denmark envisage residential cooling as a priority, this study investigated the potential of embedding heating and cooling in the same infrastructure. It found that the return line could deliver cold water to the end-users and that the maximum cooling power was 1.4 kW to each end-user, which corresponded to 47% of the total peak heat demand used to dimension the double loop network.

Some new optimal and suboptimal infinite families of undirected double-loop networks

International audience Let n, s be positive integers such that 2 ≤ s < n and s = n/2 . An undirected double-loop network G(n; 1, s) is an undirected graph (V,E), where V =Zn={0, 1, 2, . . . , n−1} and E={(i, i+1 (mod n)), (i, i+s (mod n)) | i ∈ Z}. It is a circulant graph with n nodes and degree 4. In this paper, the sufficient and necessary conditions for a class of undirected double-loop networks to be optimal are presented. By these conditions, 6 new optimal and 5 new suboptimal infinite families of undirected double-loop networks are given.

DIAMETER FORMULAS FOR A CLASS OF UNDIRECTED DOUBLE-LOOP NETWORKS

An n-node network, with nodes numbered 0 to n-1, is an undirected double-loop network with chord lengths 1 and s(2≤s<n/2) when each node i(0≤i<n) is connected to each of the four nodes i±1 and i±s via an undirected link; all node-index expressions are evaluated modulo n. Let n=qs+r, where r(0≤r<s) is the remainder of dividing n by s. Furthermore, let s=ar+b, where b(0≤b<r) is the remainder of dividing s by r. In this paper, we provide closed-form formulas for the diameter of a double-loop network for the case q>r and for a subcase of the case q≤r when b≤aq+1. In the complementary subcase of q≤r, when b>aq+1, network diameter can be derived by applying the O(log n)-time algorithm of Zerovnik and Pisanski (J. Algorithms, Vol. 14, pp. 226-243, 1993). Obtaining a closed-form formula for diameter of the double-loop network in the latter subcase remains an open problem.

SOME COMBINATORIAL PROPERTIES OF MIXED CHORDAL RINGS

We propose a new network called the mixed chordal ring where the amount of hardware and its structure are very comparable to the (directed) double-loop network, and yet can achieve a better diameter. We also investigated other combinatorial properties such as connectivity and hamiltonian circuits in the mixed chordal ring.