Electricity prices are calculated based on several variables. Electrical power is traded on the spot market by wholesalers, and a spot price is determined on when and how
much is traded. A residential consumer has the choice of entering into a various set of pricing models, and they can decide on which service provider to buy from. Nord Pool provides statistics for spot prices. [9]
In addition to the variable spot price provided by a service provider, a consumer will have to connect to the local electrical grid. The local power supplier will charge a fixed price for connection to the grid, then a variable price for consumption of MWh, and a consumption fee based on MWh consumed. Equation 2.23 shows how to calculate the total cost of electricity. [43]
Ctot =GRf ixed + (GRvar·E) + (GRf ee·E) +SP ·E[NOK] (2.23) In this equation, total cost,Ctot [NOK], is dependent on the energy consumed,E [kWh], the fixed grid rent,GRf ixed [NOK], the variable grid rent,GRvar[NOK/kWh], the variable grid fee,GRf ee [NOK/kWh], and the spot price, SP [NOK/kWh].
Trondheim has a local district heating system, and prices are set by Statkraft and calculated similarly. Prices are based on spot price, in addition to system connection price. Both are dependent on consumption. According to the Energy Law in Norway,§5-5, district heating cost are not allowed to be higher than the electricity cost. [8]
A district heating system using a heat pump and excess heat from e.g. cooling of a ice rink, will demand less power than using electricity as sole energy source. This will provide savings which must be compared to the investment cost of a district heating system.
Creduced =Celec−Ccomp [NOK] (2.24)
The equation 2.24, shows the possible savings, Creduced [NOK] when comparing the cost of space heating using electricity,Celect[NOK], and the energy cost of using a heat pump for space heating,Ccomp [NOK].
The same equation can be used to find savings for using a heat pump to heat DHW compared to only using electrical power to heat DHW.
To find the today’s value of the future savings, Net Present Value is the most common formula to use. The net present value, N P V [NOK], is the today’s value of future cash flows, so in this thesis it will show today’s value of the future savings.
The calculation of NPV is shown in equation 2.25 N P V =
NPV is dependent on the time periods, t [−], the discounting rate of return on an alternative investment,i[−], and the net inflows and outflows for a single period, Rt [NOK].
Chapter 3 Method
This chapter begins with presenting the programs used in this thesis. Then, the building project at Tungaveien 1 at Leangen in Trondheim will be introduced, and the different options for the energy system that will be evaluated will be presented.
Further, the method for evaluating the energy demands will be presented. The next sections will go through the different heat sources that could be used, and how the heat pump will be simulated. Finally, the cost analysis will be presented.
3.1 Programs
SIMIEN
SIMIEN is a simulation program used to generate accurate energy profiles for build-ings. The model is simplified so all areas, zones, within the building are treated alike, e.g. variations from bathrooms, internal loads, temperature profiles are not separately considered. Other specifications like construction details and energy sys-tems are also included in the tool. Through a simulation of the building, SIMIEN is able to pull an energy profile, presenting energy demands and yearly usages of the different energy suppliers. In this thesis, SIMIEN is used to estimate the energy profile and the thermal comfort profile. These estimates are used in the calculations and dimensioning of the heat pump. SIMIEN is downloaded through RemoteApp from NTNU.
Dymola
Dymola is a collection of modeling and simulation tools used to visualize complex computerized version of real life systems under different conditions. The program can be used to build heat pumps in a detailed manner, with specifications for all components within it, and simulate and investigate its behavior with different set points, limitations and other conditions. The simulation gives an accurate represen-tation of different variables, including water flows, pressure states and temperatures.
Dymola uses the language Modelica, and the TIL library is used as an additional component package. Dymola is a program that have different functions with dif-ferent licenses. The license provided by NTNU makes the TIL library possible to implement. The program can be downloaded from their website [14].
DaVE
DaVE is an additional application that interacts with Dymola. It uses simulation results from Dymola to design detailed diagrams. In this thesis, pressure points from Dymola is used to make diagrams like ph-diagrams. DaVE is a complimentary program that works with Dymola and is licensed based. The license used for this thesis is provided by NTNU.
CoolPack
Coolpack is a simple simulation tool for refrigeration systems where operations of a heat pump can be evaluated at a detailed level. The tool uses inputs for some of the values, and calculates the remaining values. It also presents a ph-diagram, as well as other state values. The program is run on RemoteApp from NTNUs servers.
Visio
Visio is a drawing program used in this thesis to make figures. Every figure which is not referenced from another source or simulation tool, was drawn in Visio. The program is downloaded through NTNUs RemoteApp function.
COMSOL Multiphysics
COMSOL Multiphysics is a simulation tool used for anticipating the workflow of different scientific problems, like fluid or heat flow. The tool uses the finite element method to solve complex mathematical problems. The finite element method in-volves dividing the physical domain into a finite number of smaller parts, a mesh, and reduce the problem of fluid flow and heat transfer into simpler mathematical equations related to the boundaries between these parts. COMSOL Multiphysics is used to simulate heat transfer and fluid flow in the gray water tank. Both 2D and 3D representations of the problem are simulated. The program can be downloaded from their website [5].