Heat Production Costs Research Articles

Operational optimization in a district heating system

We consider the problem of selection of supply temperatures in a district heating (DH) network. The problem is formulated as a mathematical model which incorporates the consumers, the district heating network and the production plant; the objective is to minimize the operational costs. The dynamics of the DH consumers and the dynamics of the distribution network usually affect the operation of the DH system heavily. This is both due to the time delays in the DH network, which are usually large compared with the time delays in other parts of the DH system, and due to heat storage in and heat loss to the surrounding ground. For operational planning and operational optimization, it is therefore vital to have appropriate simulation models of the consumers and the DH network available. We give a discussion of the two elements and describe the principle of the so-called node method. This method can be applied to simulate the flow and temperature development of a given DH system as a consequence of the consumers' heat loads and supply temperatures from the plant. We present models of the production system under various assumptions of its constitution. We consider one production plant, i.e. one geographical location. Three types of production units are considered: boiler units, back pressure units and extraction units. The objective function, which is to be minimized, consists of a sum of contributions, one for each time period, for each production unit, and for each pump. In each time period, there are fuel costs and also costs for the electrical power consumption of the pumps. If there is a CHP unit, then there is also, in time period t, an income (i.e. negative cost) associated with the sale of the produced electrical power to the electrical network. The strategy for solution of the mathematical model is to establish an interplay between the node method and a standard optimization package. Computational experiences with several real-world cases are extensively discussed. It is demonstrated that it is possible to solve the model and thereby obtain the optimal supply temperatures. The cases demonstrate that minimization of the cost of district heating calls for a very active control of the supply temperatures from the plant, in the case that the heat production costs either depend on the time of day or on the load level. This is explained by the dynamic and complex nature of the district heating system. Our method appears to be easy to use and flexible. It is, for instance, very easy to incorporate models for different heat production principles and to include different restrictions. As implemented, the model is suited for off-line analysis due to its long computation time. However, there are large potentials for substantial reduction of computation time by more careful implementation. This way, it appears that the method could indeed be applied in on-line operational planning at regular time intervals, e.g. every hour.

On flow and supply temperature control in district heating systems

This paper discusses how the control of the flow and the supply temperature in district heating systems can be optimized, utilizing stochastic modelling, prediction and control methods. The main objective is to reduce heat production costs and heat losses in the transmission and distribution net by minimizing the supply temperature at the district heating plant. This control strategy is reasonable, in particular, if the heat production takes place at a combined heat and power (CHP) plant. The control strategy is subject to some restrictions, e.g. that the total heat requirement for all consumers is supplied at any time, and each individual consumer is guaranteed some minimum supply temperature at any time. Another important restriction is that the variation in time of the supply temperature is kept as small as possible. This concept has been incorporated in the program package, PRESS, developed at the Technical University of Denmark. PRESS has been applied and tested, e.g. at Vestkraft in Esbjerg, Denmark, and significant saving potentials have been documented. PRESS is now distributed by the Danish District Heating Association.

Relative values of coals for electric power generation

A model has been developed to estimate the value of steam coals. Relative values are established by equating the total costs of producing electric power with each of the coals. The model can be used by mine operators to estimate the value of their coal to a targeted utility user in comparison with any other competitive coals available to the user. The model also provides guidance to utility users in arriving at competitive estimates for available coals. The total cost of power generation includes the price of coal at the mine-mouth and transportation cost from mine to users, net boiler heat production cost, plant-investment costs, maintenance and operating costs, and insurance and taxes, with economic parameters characteristic of utility financing. Taken into account is the impact of the physical and chemical properties of each coal on its combustion properties and on the plant investment needed for its use. The model involves the use of spreadsheet techniques and incorporates 34 separately specifiable parameters that are fully interactive. Execution times are of the order of 1 sec. Examples are provided in which several coals in four user locations are compared in both new and older power plants.

The effect of dietary protein and energy restriction on heat production and growth costs in the young rat.

1. The effect of dietary protein and energy restriction on heat production and growth costs has been examined in rats fed on a marginal (MP) or high (HP) protein diet, containing 9.2% or 22% respectively of the gross energy content as casein. Diets were given either ad lib. or at approximately 25, 50 or 75% of the ad lib. intake. 2. Heat production (kJ/kg body-weight (W)0.75 per d) was increased by 23% in rats fed on the MP diet ad lib., as compared with their HP controls (P less than 0.01). 3. Factorial analysis of the data showed that the overall cost of energy deposition (kJ/kJ; Ee) was elevated on the MP diet (MP 1.7, HP 1.28; P less than 0.001). Maintenance requirements (kJ/kg W0.75 per d) for zero energy balance were unchanged (MP 562, HP 573). 4. The partial energy cost of protein deposition (Ep) varied with dietary manipulation. If the partial energy cost of fat deposition (Ef) was assumed constant at 1.25 kJ/kJ, and maintenance requirements were assumed to vary with metabolic body size (W0.75), Ep was elevated on the MP diet. On both diets, Ep was reduced at low energy intakes. 5. The significance of these results is discussed in the context of current approaches to the analysis and interpretation of findings describing dietary induced changes in the rate of heat production.