Modeling of Energy Management Systems for Commercial Parks with Thermodynamic Equipment

Commercial park energy management systems (CPEMS) can reasonably plan appliances’ schedule of commercial tenants (CT) and lower their electricity purchasing cost. However, in the existing models, thermodynamic equipment like air conditioners and water heaters are not precise enough, failing to reflect the actual operating characteristics of the equipment. This paper presents an energy management system model including thermodynamic equipment. By coordinating the electricity consumption schedule of multiple CTs, CPEMS can reduce CTs’ electricity purchase costs. In the demonstration example, electricity purchase costs of CTs are reduced and operators of CPEMS gain profit, proving the feasibility of the model.


Introduction
A commercial park (CP) has a function combining eating, accommodation, transportation, shopping and entertainment. With the development of China's economy, CPs' electricity consumption grow rapidly. On the one hand, various smart appliances usually controlled by smart devices like smart phones are being used gradually. On the other hand, with the development of photovoltaic and other distributed power technology together with cost reduction, more and more distributed photovoltaic power used by CTs (like restaurants, hotels, etc.) apply for access to the grid [1]. The importance of intelligent CP power consumption and demand side response technology are arousing scholars' attention.
In traditional power systems, user side is usually deemed as a simple power consumer. However, after the energy crisis in the 1970s, Europe and the United States launched a variety of electricity price systems, and began a research about demand side management (DSM) [2][3][4][5]. As the power demand grows, many scholars start to study energy management system (EMS) [6][7][8][9][10]. Through monitoring and collecting users' power consuming information, EMS can analyse users' consumption habits and add overall management and optimization to their power consumption. A user's load optimization model based on consumption efficiency was proposed in [6], which analysed the influence of different consumption habits in the model. Under the background of day-ahead and real-time power markets, a kind of mixed integer programming algorithm was proposed in [7], which focused on charging modes of electromobile with energy storing devices. The general model of EMS with changing electricity prices is discussed in [8], which compares the effects of solving high-dimensional optimization problems using heuristic algorithm and Q-learning algorithm respectively. The power's continuity and discreteness, transferability and intransferability, interruptibility and non-interruptibility of appliances are analysed in [10], which studied the modeling and optimization of EMS including appliances such as PVs, energy storing devices and electromobiles. Papers above concluded that through optimizing users' power consumption, the peak-valley difference of power systems can be reduced effectively, and so does users' power costs. The existing researches achieved the modeling of CT appliances, but it's focused on electrical appliances (electromobiles, storage batteries, PV batteries, etc.). Actually, the behaviour of the thermodynamic equipment such as air conditioners and water heaters has played an important role in the whole CP's electricity consumption characteristics. More detailed model research should be carried out.
This paper presents an energy management model with multiple CTs in a CP. Models of the transferable appliances; energy storage devices and thermodynamic equipment in CTs are built. The model is applied to a four-CT demonstration example, which shows that the model can achieve an optimal management of CT load, and the validity and feasibility of the model are verified.

Classifications and Characteristics of Appliances in Commercial Parks
According to the operating characteristics of CTs' appliances and control methods, CT appliances can be divided into four categories.
 Non-transferable Appliances: When the user gives a work order, the uncontrollable appliances must respond immediately without delay. Such appliances' start/stop and operating power are not controlled by the CPEMS. Such appliances are mostly lighting and entertainment appliances, whose start/stop has a strong randomness, varying with user's habits. Typical representatives are incandescent lamps, televisions and so on.  Transferable Electrical Appliances: Users can set the working time of such electrical appliances in advance. In the time range set by the user, the CPEMS can be free to arrange the working time of electrical appliances. Further, such appliances can be divided into two categories as interruptible and uninterruptible. The difference between these two categories is whether the appliance can be interrupted when it's working. For example, the dishwasher can be set to work in a period of time between 19:00 and 22:00, but once the dishwasher starts to work, it cannot be interrupted until the dishwasher completes the job. On the contrary, take electromobiles for example, the user can set to finish the charging between 20:00 and 7:00, and the charging process can be interrupted for many times.  Energy Storage Devices: Because the peak-valley hours and peak-valley generation amount of distributed power is different to that of CPs' load, clients can buy energy storage devices which will store or release electric power to take full advantage of distributed power. For CTs, considering that the typical peak value of CTs' load is of kW level, usually lithium batteries and lead batteries can be used as energy storage devices  Thermodynamic Equipment: It can be seemed as a special kind of transferable appliances.
Because of thermodynamic equipment like refrigerator, air conditioner and water heater has a temperature property, the change of internal and external temperature should be taken into consideration while modeling, and heat exchange process should be modeled. To ensure users' comfort, thermodynamic equipment is often set to work in a temperature range, which is usually set by users and varied with different living habits of users.

Modeling of CPEMS
In CPEMS, appliances' operation constraint conditions should be concluded according to different types of appliances' operation characteristics. The object is to minimize the cost of electricity purchase, and the optimal operation schedule of CTs' appliances should be made. In this paper, the time interval of CTs' appliances' working schedule is 15 minutes.
Among the equation above, Equation (2) indicates that transferable appliance can only complete its work within the time period specified by the user. s i t and e i t is specified by the user according to his or her own habits, and the user can change them at any time according to the need. For example, the user can take the washing machine as a transferable appliance which is opened to the operators of CPEMS, and specify the time that the washing machine can work between 18:00 to 22:00 every day. This schedule is informed to the CPEMS operator at the planning stage before day. One day the user needs to complete the laundry work between 10:00 to 12:00 for some reason. Then he needs to notify the CPEMS operators at realtime adjustment stage. The CPEMS operators will adjust the work plan to meet the user's demand for electricity. Equation (3) indicates that the start-up time of the transferable appliance in one day is equal to the time required to complete the work, thus ensuring the completion of the task. The value of i D is determined by the appliance itself. Equation (4)  Equation (6) is a constraint on the charge state of the energy storage system. For chemical battery type energy storage systems, the larger the depth of discharge will generally shorten the battery life, which is particularly evident for lithium-ion batteries. Therefore, the general battery type energy storage system usually set the maximum and minimum state of charge to protect the battery. min i soc / max i soc will be provided by the energy storage system manufacturer. Equation (7) ensures that at the end of the optimization period, the energy storage device maintains a certain amount of energy to ensure the ability to adjust for the next optimization period. Equation (8) constrains that a system with multiple energy storage systems cannot be in a state of charge and discharge at the same time. If part of the energy storage device is in the charging state, and the other part of the energy storage device is also in the discharge equipment, this is also a behavior of energy wasting. However, the formula (8) is essentially a quadratic constraint with multiple cross terms. This type of constraint will destroy the convexity of the problem and cause the problem to be difficult to solve. To solve this problem, flag variables ch t f is set. ch t f indicates whether the energy storage device can be recharged in the th i time period. A value of 0 means that it can be recharged , while value of 1 means not. Equation (8) can be re-expressed as:

Thermodynamic Equipment.
The key to the modelling of thermodynamic equipment is how to describe the heat exchange process. Take air conditioning as an example, assume that the internal temperature of the room is r T (ignoring the room temperature difference), outdoor temperature is out T .
The heat change in the room is caused by the heat exchange between the air conditioner and the room as well as the heat exchange between the room and the outside. The whole process can be described as: Similar results have been reported in [9] [10], but they do not distinguish the heating and cooling power of air-conditioning equipment, which limits the application of the model. Generally, in order to ensure the comfort of the user, the user can set the upper and lower limits of the indoor temperature, the CPEMS operator will keep the indoor temperature within the range:

Operational Strategy of CPEMS
The user's distributed power generation system will meet the user's own needs of electricity preferentially, and the extra electricity can be selling to the power grid to gain more profit. If the PVs equipment and energy storage devices are not sufficient to meet the CT electricity demand, users need to purchase electricity from the grid. CPEMS operators need to ensure the power balance of CTs' smart grid by selling and buying electricity from the grid. Constraint condition of it can be described as: Exposed to the sunlight, solar panel's generation data and outdoor temperature conditions is shown in Figure 2. The outdoor temperature can be obtained from the local meteorological bureau, and the PV power can be calculated from the daylighting condition data. The electricity purchasing price is different in peak and valley hours. The time between 6:00 and 22:00 is peak hours, and the price is 0.56 Yuan/kWh. The time between 22:00 to 6:00 of the next day is valley period, and the price is 0.28 Yuan/kWh.  The demonstration examples use MATLAB 2014a and YALMIP [12] to complete the calculations, where the solution for mixed integer programming is done using IBM ILOG CPLEX 12.6. All calculations are done on a personal laptop with a 2.6G clock speed and 8G of memory with a processor model i5-4219M.

Result Analysis
In order to verify the effectiveness of the proposed energy management model, the following two situations are demonstrated and compared.  Situation 1: No CPEMS participates. All the transferable load can begin to work at allowed working time. When the PV power is supplied to the user, the excess electricity is sold to the power grid. The electricity price is 0.3 Yuan/kWh for peak hours and 0.15 Yuan/kWh for valley period.  Situation 2: The users make an agreement with the CPEMS operators and the operators will arrange the transferable load's and energy storage devices' operation. On the basis of purchasing power and selling electricity, the operators can reduce 7% of the electricity purchasing cost and give a subsidy of 7% of the electricity sales to the users, and subsidize the users' energy storage capacity according to 0.02 Yuan/(kWh· day). In the two situations, the CTs' electricity costs are shown in Table 1. The operation of CPEMS in situation 2 is shown in Table 2. It can be seen that in Situation 2 where the CPEMS participates, most of the users' electricity purchasing costs are significantly lower than that in Situation 1 due to the subsidy given by the CPEMS operator. In this case, CTs are willing to sign agreement with the CPEMS operator to obtain the subsidy. Also, in this situation, the CPEMS can reduce the total cost of purchasing power by optimizing the electricity plan of the four CTs, in spite that subsidizing the user increases the operating costs. Generally speaking, CPEMS is profitable. This shows that the operating mode in this paper can help users and CPEMS achieve a win-win situation. consumed locally and users' costs are reduced. At the same time, the CPEMS operator gains profit, achieving a win-win situation. In this model, the effect of the uncertainty of the renewable energy is not taken into account. Using the mathematic tools such as robust optimization and stochastic programming to quantitatively consider the influence of PV forecast error on the specified electricity plan, and improving the robustness of the electricity plan is the direction of next research.

Acknowledgments
We thank the support by State Grid Technology Program (52094016000F).

Appendix
Appendix