Numerical approach regarding functional and design optimization for a residential building heating system composed by heat pump and auxiliary

In this paper is presented the physical model and mathematical approach which describe the equation system used in system calibration and design optimization. The system proposed for study is built from heat pump, for energy demand delivery, together with auxiliary heating source to face in all low temperature days, when heat pump work at maximum load but the required demand by the building is higher. The paper present few of the common used systems in market for which the mathematical equation system will be proposed to come in help designers for in simulation and cost optimization. Simulation of proposed design is realized and results are delivered. The system construction, is optimized by comparison study of design and simulation data for each system type proposed. The comparison study is used for cost estimation of system and energy balance.


Introduction
Building heating and cooling research domain encounter no limits today, being a used subject in design, simulation or experimental study or together [1][2][3][4]. Methodologies to evaluate [5] and optimise [6] exist today. Agents for heating purpose are prepared by a wide diversity of individual heating equipment or hybrid systems [7][8][9]. Even the subject make part of multiple numbers of studies, the domain give more and more interesting direction for research and design. Newly types of heating equipment are also a research pillar due to high level of innovation and uncertainness when are designed by engineers. More and more tools for this type of design are available today to engineering and research. Basically, empiric technics in digital instruments, are mathematics and physics modelling of real equipment. Mechanical engineering has developed a wide range of equipment modelling which today results in a high efficiency heating equipment components with high accurate mathematical models. Comparative studies are done, results and discussions give a good direction in terms of design and optimisation. For those studies, geothermal heat pumps are driven the lower running costs in Europe, or, secondly, diesel oil fired boilers, used for electric heating [10]. On the other hand, an interesting study show the increasing of 33% in primary energy usage, respectively, 26% greenhouse gas emissions of geothermal heat pump compared with district heating system [11]. For heat pumps, experimental researches were driven to see the performances of different types of heat pumps. For two twin houses, an experimental investigation was launched, between a geothermal and air to water heat pumps. The results shown relatively constant performances for geothermal heat pump comparing air to water [12]. In practice, are found more and more complex heating systems, which are composed by at least two types of heating equipment. Hybrid systems, for heating, are generally built for delivery the necessary demand in worst conditions, or to improve the old equipment. Also, to decrease the overall primary heating demand and increase performances, hybrid systems are suitable to candidate. Therefore, will give the opportunity, to research field, to develop new methods of evaluation or to use separate methods for each systems and link them, by correlation. Literature, is giving numerous types of strategies to be used for evaluation regarding performances or optimisation of the heat pump. Wet bulb temperature and entering output temperature in evaporator, as input parameters for regressive curves are used to simulate the behaviour of the heat pump with EnergyPlus [13]. In this paper, the condensing waste heat recovery was evaluated by model. Energy savings encountered values between 47% and 64%, in cooling, comparing system with no heat recovery. Bi-Linear interpolation, of performances data, were used as modelling technique to evaluate heating and cooling capacities, heating and cooling electrical power demands, or heating and cooling coefficients of performance, using finite element design of a ground source heat pump (GSHP) boreholes transfer elements. Results are plotted for installation in London, for an building with total area of 10,500 m 2 [14]. Results of simulation shows decreasing in temperature of deep ground elements by a period of 30 years, which reveal the susceptibility of underground heat to decrease by time. Air source heat pump (ASHP) compressor performances, drive in general, the global performances of the heat pump. A parametric study, concentrate on compressor evaluation for efficiency, tacking into account pressure ratio, was done to evaluate dependency [15]. Cycle parameters are extracted from refrigerant state diagrams. In this study, it was shown an interesting influence of compressor isentropic efficiency by refrigerant state pressures, corresponding to temperatures at evaporator and condenser units. Two refrigerants were considered and tree types of compressors were simulated. Isentropic efficiency interval were found to be 0.53 to 0.77, corresponding to pressure ratios of 7.5 respectively 2.5 in case of R410 refrigerant with a scroll compressor.
In case of a water source heat pump (WSHP), with an exterior lake as heat source, an exponential dependent heat pump COPs, by water temperature, were used for heating and cooling demands [16]. This model consist by knowing the regressive coefficients of historical data, from experiments. Equations feet the curves of COP in heating and cooling, and electrical power demand has been evaluated with. Some of results conduct to an interval of 6˚C to 10˚C of source water temperature, in heating season, respectively 22˚C to 31˚C for cooling season.
By simulation, for an ASHP installed in Beijing, China, a maximum electrical power of 800W was measured for a maximum heating load of 30kW when outside temperature is -15˚C, in case of a residential building [17]. For those values, the electrical power of compressor is the 2.7% of maximum heating load demands.
By sizing, in case of 42.631kW maximum load power for domestic hot water production, was used a heat pump with maximum electrical power equals 8.2kW [20]. This conduct to 19.24% percentage of heat pump electrical power comparing maximum heat demand. Hot water demand is based calculated by a 10˚C inlet system temperature with 60˚C as set temperature value of daily hot water.
For cooling purpose, two WSHPs used as water to water configuration, register a maximum electrical power of 8.00 kW to 9.00 kW. For the building where system is installed, two heat pumps provide 32,8kW of the cooling needs. Heat pump return the heat into a recirculated water from a ground loop using heatexchangers. The study was done for Sydney weather. The heat pumps maximum instant power consumption, represent 24.3% -27.4% of maximum building cooling heat demand [19]. Data delivered by study was estimated with DesignBuilder software, used in modelling of energy demands, heating and cooling space and systems modelling.
For different system configurations and multiple weather conditions, the heat pumps electrical power consumption reported to maximum heat load, in heating or cooling, is not overpass a 30% for case studies presented.
This paper will propose a mathematical model to be used for energy demands evaluation of building heating system. Optimisation of heat pumps systems, based on energy demand and heat pump configuration will be made using model parameters evaluation. Two types of heat pump, ASHP and WSHP are evaluated for 5 different cities of Romania, based on ISO weather data for this country through Meteonorm database.

Mathematical model
Water source heat pump considered for modelling, is based on relative quasi-constant temperature of underground or surface lakes water. Heat pump extract the heat from the water using different types of equipment such heat-exchangers or indirect immersed evaporators with respect of refrigerant pressure for unfreezing purpose. A schematic of the system configuration, for building heating demands, and water source based on lake water is presented in figure 1.
The system considered take into account the all elements, from the heat source to delivery plugs of the heating agent. The building is generally presented to reveal the internal design temperature set point. time, didn't lose the capacity of providing heat, as was