Application of Volterra Equations to Solve Unit Commitment Problem of Optimised Energy Storage and Generation

Development of reliable methods for optimised energy storage and generation is one of the most imminent challenges in modern power systems. In this paper an adaptive approach to load leveling problem using novel dynamic models based on the Volterra integral equations of the first kind with piecewise continuous kernels. These integral equations efficiently solve such inverse problem taking into account both the time dependent efficiencies and the availability of generation/storage of each energy storage technology. In this analysis a direct numerical method is employed to find the least-cost dispatch of available storages. The proposed collocation type numerical method has second order accuracy and enjoys self-regularization properties, which is associated with confidence levels of system demand. This adaptive approach is suitable for energy storage optimisation in real time. The efficiency of the proposed methodology is demonstrated on the Single Electricity Market of Republic of Ireland and Northern Ireland.

Enteric methane emissions and nitrogen utilisation efficiency for two genotype of hill hoggets offered fresh, ensiled and pelleted ryegrass

Thirty-six 12-month-old hill hoggets were used in a 2 genotype (18 Scottish Blackface vs. 18 Swaledale×Scottish Blackface)×3 diet (fresh vs. ensiled vs. pelleted ryegrass) factorial design experiment to evaluate the effects of hogget genotype and forage type on enteric methane (CH4) emissions and nitrogen (N) utilisation. The hoggets were offered 3 diets ad libitum with no concentrate supplementation in a single period study with 6 hoggets for each of the 6 genotype×diet combinations (n=6). Fresh ryegrass was harvested daily in the morning. Pelleted ryegrass was sourced from a commercial supplier (Aylescott Driers & Feeds, Burrington, UK) and the ryegrass silage was ensiled with Ecosyl (Lactobacillus plantarum, Volac International Limited, Hertfordshire, UK) as an additive. The hoggets were housed in individual pens for at least 14 d before being transferred to individual respiration chambers for a further 4 d with feed intake, faeces and urine outputs and CH4 emissions measured. There was no significant interaction between genotype and forage type on any parameter evaluated. Sheep offered pelleted grass had greater feed intake (e.g. DM, energy and N) but less energy and nutrient apparent digestibility (e.g. DM, N and neutral detergent fibre (NDF)) than those given fresh grass or grass silage (P<0.001). Feeding pelleted grass, rather than fresh grass or grass silage, reduced enteric CH4 emissions as a proportion of DM intake and gross energy (GE) intake (P<0.01). Sheep offered fresh grass had a significantly lower acid detergent fibre (ADF) apparent digestibility, and CH4 energy output (CH4-E) as a proportion of GE intake than those offered grass silage (P<0.001). There was no significant difference, in CH4 emission rate or N utilisation efficiency when compared between Scottish Blackface and Swaledale × Scottish Blackface. Linear and multiple regression techniques were used to develop relationships between CH4 emissions or N excretion and dietary and animal variables using data from sheep offered fresh ryegrass and grass silage. The equation relating CH4-E (MJ/d) to GE intake (GEI, MJ/d), energy apparent digestibility (DE/GE) and metabolisability (ME/GE) resulted in a high r2 (CH4-E=0.074 GEI+9.2 DE/GE−10.2 ME/GE−0.37, r2=0.93). N intake (NI) was the best predictor for manure N excretion (Manure N=0.66 NI+0.96, r2=0.85). The use of these relationships can potentially improve the precision and decrease the uncertainty in predicting CH4 emissions and N excretion for sheep production systems managed under the current feeding conditions.