A Decision-Making Model for Optimized Energy Plans for Buildings Considering Peak Demand Charge—A South Korea Case Study

Abstract

The energy industry has been trying to reduce the use of fossil fuels that emit carbon and to proliferate renewable energy as a way to respond to climate change. The attempts to reduce carbon emissions resulting from the process of generating the electric and thermal energy needed by a building were bolstered with the introduction of the concept of nZEB (nearly zero-energy building). In line with such initiatives, the South Korean government made it mandatory for new buildings to have an nZEB certificate as a way to promote the supply of renewable energy. The criteria for Energy Independence Rate, which is one of the nZEB certification criteria in South Korea, is to maintain the share of renewable energy as at least 20% of the primary energy sources for the building. For a new building in South Korea to have an nZEB certificate, it is required to establish an energy plan that would allow the building to meet the Energy Independence requirement. This optimally reflects the cost of installation for renewable energy facilities and the cost of purchasing energy from external sources, such as the national grid or district heating companies. In South Korea, the base retail rate of energy is calculated based on the peak demand per hour over the year, rather than the contracted energy. This has produced difficulties in standardizing the process with a mathematical model; in addition, there have not been many preceding studies that could be used as a reference. In this regard, this paper analyzed a modeling strategy for developing a realistic yet optimized energy plan in consideration of the unique conditions of the retail energy rates of South Korea, and analyzed the impact of the rates based on peak demands upon the total energy plan. In this study, our research team analyzed the electric billing system, conducted a case study, and analyzed the impact of the billing system that is based on the peak demand upon the optimal cost. By utilizing the restrictions for reaching the 20% Energy Independence goal, this paper calculated the proper energy supply facility capacity for renewable energy. Then, the cases in which the maximum demand modeling was used and the cases without one were compared to confirm the cost benefits observable when the suggested model is added or implemented.

1. Introduction

Across the world, there are more people living in cities than those living in non-urban areas. According to a report by the UN, 30% of the world’s total population lived in a city as of 2018, and, based on this fact, it was expected that 68% of the world’s total population would be doing so as of 2050 [1]. There are a good number of reports which argue that rapid urbanization is further aggravating climate change issues. According to these reports, the number of energy consumers in a city was correlated with the carbon emission volume, and they have proposed that issues such as the energy consumption patterns of consumers due to urbanization and the power plants that generate electricity through the traditional methods of consuming fossil fuel to emit carbon, etc., must be considered in a comprehensive manner [2]. The rise of sea levels due to climate change will make human populations more vulnerable to natural disasters such as floods [3,4]. Additionally, the reduced level of thermal comfort due to the increased average temperature will lead to an increased demand for cooling and heating, which will further push up the consumption of fossil fuels [5,6]. To address the issue of climate change, the Paris Agreement postulated a goal of limiting the change in temperature to no more than 2° above the level prior to industrialization. To meet this goal, it is necessary to connect the urbanization phenomenon, which is at the center of climate change issues, and the paradigm of a sustainable energy supply plan. It is now time to consider a shift in the urban energy system so that the energy consumed by the urban population, which is expected to grow by 30% in the future, will not result in reckless emissions of carbon [7,8].

The reason why the concept of nZEB (nearly zero-energy building) is gaining attention in the construction industry these days is connected to the purpose of solving climate change issues resulting from urbanization. The ideal model that could be presented as a zero-energy building at the moment is where the entirety of the energy demands of the building users is satisfied through the renewable energy sources established within the building. This will eliminate the need to obtain energy from external sources generated by traditional means [9]. By reducing the sources of energy that emit carbon in this way, it would be possible to make the buildings in a city themselves contribute to the solution of climate change. However, if you look at this issue from the perspective of property owners, the facility investments and fuel costs involved in providing sustainable energy are very likely a key factor in the decision-making process related to the economic feasibility of a building.

Therefore, some transitional technologies have been suggested, such as the nearly zero-energy building (nZEB), that can be realized with current technology [10]. The key characteristic of nZEB is to enhance the energy efficiency of a building in terms of its structure and enable the supply of renewable energy sources so that the dependency upon fossil fuels can be reduced when it comes to the building energy demands [11]. The South Korean government is beefing up its support policies as a means to address climate change issues. From now on, it will be mandatory for a new building or an expanded building to have an nZEB certificate issued. This nZEB certification program has the minimum requirement that at least 20% of the total energy demand must be met by the energy generated using sustainable resources [12,13]. Additionally, the program provides various benefits, such as grants for the installation of renewable energy sources in the buildings to which the certificate has been issued, with the aim of encouraging building owners to participate in the program.

If such nZEB policies of the South Korean government are to be put into practice and realized, there must be a method that can be used to evaluate the economic effect of the program on the investors of a new building. The starting point of this study was to try out an optimized energy plan in the South Korean energy industry and construction industry, in view of realizing the nZEB. Here, the optimal energy plan for a building has been defined as the minimization of the energy supply cost of a building while satisfying the nZEB certification criteria of South Korea. Since there have been many existing studies that have addressed this topic, it was possible for this research to refer to the optimization algorithm and modeling methodologies. Refs. [14,15,16] suggested a method for optimizing the factors for developing an energy plan, in which a renewable energy source (RES) and a battery storage system (ESS) are to be installed in a building, included in the initial investment amount, etc., in a cost function. The method suggested herein can be used to calculate the optimal equipment capacity for the RES and the battery storage system in order to achieve nZEB. Refs. [17,18] covered the methodologies for applying various billing structures provided by the power companies to establish a building energy supply plan. Energy storage equipment is shown as a resource that can be used proactively in billing plans such as the Time-of-Use tariff (ToU). If you combine solar power and the ESS, it is possible to store the energy in the ESS during the daytime and use it during the night [19,20]. It was also possible to refer to a study when developing an optimal plan by modeling a machine that can convert the form of the energy, such as converting electricity into heat or generating heat and electricity at the same time [21,22].

However, our research team became aware that there are factors to be considered in order for such existing studies to be applied along with the billing plans of the South Korean power companies. The commercial and industrial electricity billing plans are composed of the base rate, which is based on the peak demand per unit time, and the usage rate, which changes by the season and the time of the day. The base rate is calculated by applying maximum demand per hour of the month to the basic billing rate. The maximum demand is also based on the maximum demand per hour of the month that belongs to the winter season and summer season over the past twelve months, as well as the current month. The usage rate includes nine different usage ranges, which are based on three time zones (light load, moderate load, and peak load time zones) and three seasonal zones (summer, spring/autumn, and winter) [23]. To apply this model to the optimized cost function, our research team reviewed existing similar studies. Ref. [24] included the case studies applicable to the contracts with fixed usage rates and basic rates. The usage rate was set based on the average rate of 2019 by the ELsport. The base rate was based on the rates suggested by the power companies in accordance with the allowable limits of supply voltages and currents at the distribution panel of the user. Ref. [25] considered the seasonal and hourly electricity rates to calculate the energy supply cost of a building. The billing plans provided by the power companies are composed of the base rate that changes by the seasons, while the usage rate is based on the critical peak pricing (CPP). The base rate is fixed for the month and updated according to the season. However, in the equation that was used in the methodology, it is set as a fixed value that is not proportionate to the capacity of the electric facilities of the user or the contracted power. In other studies, a single rate or a ToU billing plan was considered to develop an energy plan that can minimize the supply cost, while the methodology did not consider the fees at the peak load or the base rate [26,27].

Comparing the external energy billing plans applied to the existing studies above, it was found that the basic rate was set by each electric company, but there was no model applied with the basic rate linked to the maximum power usage per month, such as the Korea Electric Company. Therefore, it was necessary to evaluate the differences that originated from the methodology when it was simplified without applying the billing plan of a South Korean power company to the energy plan. To achieve this, the first study topic of this study was to model and add the base billing plan of the power company that is calculated using the peak demand during the current month and the winter and summer peak demand within the past 12 months to the cost function of the building energy plan. The second topic of this study is to analyze the impact of the addition of the said billing plan by the power company to the optimal building energy plan. Additionally, the suggested methodology models the nZEB certificate of South Korea to assess the results of the energy plan that meets the renewable energy supply ratio criteria.

2. Boundary of the Research

This paper applied the characteristics of the retail billing plans of a South Korean power company and the energy independence equation to the model to develop an intra-building energy plan in consideration of nZEB when designing a new building in South Korea.

2.1. The Retail Power Billing System of South Korea

Normally, a power company considers the risks due to the volatility of energy prices when they design a retail power billing system. Such risks of volatility can materialize under various energy market environments that the electricity companies find themselves in. European countries have individual grids connected to a single network. Therefore, a strategy of purchasing energy from outside is reflected in the retail rates. The power wholesale market of the PJM includes the costs for the backup capacity of the grids, the cost of accessing the network, and the high traffic surcharge for the power transmission lines in their market prices, which makes it possible to consider various options as they design their retail prices. The countries with rich hydropower resources, such as Chile, include the estimation of the annual rainfall into their risk management factors.

In the case of the South Korean power grid, it forms an independent network of energy that does not have any connections with any external grids [28]. Therefore, it is completely dependent upon the primary energy sources, which are entirely import dependent, and such a risk must be considered by the power companies as they design retail billing plans [29]. The two

Table 1. The characteristics of the retail billing plans of the power companies in each country.

Power Company	Base Rate	Usage Rate
Enedis, France	Based on the seasonal contract capacities	ToU
E.ON, Germany	Based on the contract capacity	Flat rate, progressive rate, ToU
Ausgrid, Australia	Based on the monthly peak demand per hour	Flat rate, ToU
Korea Electric Power Corporation (KEPCO), South Korea	Based on the highest monthly peak demand per hour over past 12 months	Progressive rate, ToU

and

Table 2. The risk factors of the South Korean power companies.

The Origin of the Risks	Risk Control Factors
Isolated power network Most of the primary energy sources are import dependent. Mid-altitude temperate climate, with a temperature gap between summer and winter of 30 to 40 degrees. Manufacture-dominant industrial environment	The importation of primary energy sources is being controlled by public corporations. Retail billing plans are designed to encourage end users to control their demands voluntarily. Partial government subsidies

below compare the power billing plan of the power companies of various countries and that of South Korea, along with a summary of the factors the South Korean power companies must consider to manage their supply risks. Retail power rates reflect various factors for the purpose of services, the costs for energy, as well as the network access costs, tax, and environmental burdens, to name a few. Power companies design their power billing plans of various structures to be provided to the end users based on the costs incurred in such wholesale markets [30]. The simplest of all plans is the fixed-rate plan, which makes it easier to estimate the cost, making it more accessible and less prone to disputes. However, since the price of energy can be volatile, the rates so determined are typically conservative. A contrasting example is a billing plan that is designed to allow the strategic utilization of a part of the price volatility of energy, so that during certain hours of the day, a lower rate than the fixed rate can be provided, while a higher rate may apply during the hours with higher demands. In this scheme, the billing plan becomes more complicated, as there are more conditions that can be utilized in the operation of the end users. As shown in the second table below, there are not so many cards that the utility company can utilize in South Korea to manage energy volatility.

Based on such factors, the power companies of South Korea provide significantly more complicated retail billing plans that is summarized in

Table 3. The general and industrial power billing structure of the KEPCO.

Item	Description
Base rate	The highest demand among the peak hourly demands of the current month and December, January, February, July, August, and September of the past 12 months, as well as the current month, is defined as the demand to be applied as the basis of the rate. Monthly payment amounts are calculated by multiplying the contract rate with the demand to be applied as the basis of the rate. If the peak demand of the unit time is higher than the contract demand, a surcharge for the excess amount shall be imposed.
Usage rate	Three seasons, which are spring/autumn, summer, and winter, and the three time zones, which are the light load, moderate load, and peak load time zones, are defined as segments. Each segment is subject to a different usage rate. The time zone segments are the same from spring to autumn. However, during the winter, the time zones of the moderate load and the peak load are different (in consideration of the heating load during the evening hours of the winter).

to their end users so that they are partially exposed to price volatility. The base fee in particular, unlike other examples of billing plans, is calculated by multiplying the monthly peak hourly demand with the base rate. This is made possible by the installation of electronic power meters in commercial and industrial buildings, which record the power consumption over a 15-min period. Additionally, the seasonal difference is reflected, such that a rational incentive to discourage the demands for heating and cooling is also included in the design of the billing plan. The usage plan is based on the ToU plan, which has different rates depending on the season and the time of the day, and the applicable time zones also vary depending on the season. For the base rate, the peak hourly demand in January, February, July, August, September, and December, when there are high demands for heating and cooling, is applied over one year from the occurrence of the peak demand, and an updated value is used to calculate the power bill if there is a higher peak demand during said period.

2.2. Calculating the Energy Independence Rate of a Building

In South Korea, all new buildings are required to be certified with the nZEB certification program and have a certificate issued. This certificate is issued based on the assessment of whether the result of the ECO2 (building energy analysis program) analysis of the drawing of the building during the designing phase meets the criteria for certificate issuance. The assessment criteria are classified into the three categories in the following

Table 4. South Korea’s nZEB certification program criteria.

Criteria	Description
Building energy efficiency grade 1++ or higher	Less than 90 kWh/(m2yr) for residents and 140 kWh/(m2yr) for non-residents, as per the building energy analysis program (ECO2). Primary energy consumption(kWh/(m2yr)) = sum of the energy consumption × primary energy conversion coefficient
Energy independence at least 20%	The share of the renewable energy among the energy consumed by the building as per the building energy analysis program (ECO2) analysis result must be at least 20%. Energy independence rate(%) = 100 × $\frac{\mathrm{Primary}\mathrm{renewable}\mathrm{energy}\mathrm{generation}\mathrm{output}\mathrm{per}\mathrm{unit}\mathrm{area}}{\mathrm{Primary}\mathrm{energy}\mathrm{consumption}\mathrm{per}\mathrm{unit}\mathrm{area}}$
BEMS or remote power meter installation	(BEMS) Nine evaluation items, including data gathering and display, information monitoring, control system sync, etc. (Remote meter reading) Six evaluation items, including data gathering and display, meter management, data management, etc.

. The criterion that can be applied to the model that is included in this study is criterion No. 2, which is the energy independence assessment item. The energy independence assessment criteria is basically the ratio between the renewable energy generation output versus the energy consumption of the building. In this process, each energy source must be converted to primary energy for the calculation. Since it is difficult to apply the mathematical modeling within the internal logic of the ECO2 program, this paper designed an equation that is relevant to the situation of the model, which is suggested based on the premise for the definition of energy independence (13). The case study shows the results of the cases in consideration of the energy independence criterion of 20%. The internal discussion on the findings within the research team has been summarized and included in the Section 5.

3. The Proposed Methodology

3.1. Building Energy System Structure

The system assumed in this study has a structure in which the system receives energy from the external energy network, such as the national grid, while generating energy for itself and supplying the energy to the end user utilizing the power and heating network within the building. A PV system converts the solar energy into electric energy and is usually installed on rooftop or walls. Since most of the power-consuming appliances of the power users within a building use AC power, the power is converted into energy using the inverter located within a PV system. Likewise, an ESS system also converts the energy into AC power utilizing an inverter installed within the system. The electric energy, once converted into AC power, goes through the electric distribution panels of the building, and the energy is delivered to the end user within the building, along with the energy supplied by an external grid.

During the winter season, the amount of heat energy used in a building increases due to the heating needs, etc. The heat energy that can be provided from outside is delivered to each residential unit through the district heating pipeline. Using a heat pump, which can convert the energy stored in heat using electricity back and forth, can be considered as well. In such a case, the heating and the cooling air heat pump that can convert the thermal energy for heating and cooling at the same time can be considered for the model. Yet another option is to use a secondary boiler, which can convert gas into heat energy. In such a case, the cost of purchasing the gas must be taken into account. If the waste heat of fuel cells is to be used, a waste heat recovery system can be used as an additional source of heat energy.

3.2. Energy Balance

If the inside of a building is divided into small network systems such as microgrids, it is subject to a requirement that the supply and consumption of energy within the network must be equal at every moment. To model this phenomenon, it is necessary to match the total amount of energy provided to the end user with the energy consumption in all-time units. The methodology suggested here sets a restriction of equivalence so that the energy balance of the electric and thermal energy can be maintained.

$$\begin{array}{cc}\hfill & D_t^{elec}+Q_t^{hp-cooler}/c^{hp-cooler}+Q_t^{hp-heater}/c^{hp-heater}+Q_t^{ess-charge}\hfill \\ \hfill & =Q_t^{bapv-rooftop}+Q_t^{bipv-facade}+Q_t^{fuelcells}+Q_t^{ess-discharge}+E_t^{elec}\forall t\in \mathbf{T}\hfill \end{array}$$

(1)

$$D_t^{heat}=Q_t^{fuelcells-hr}+Q_t^{hp-heater}+Q_t^{boiler}+E_t^{district-heat}\forall t\in \mathbf{T}$$

(2)

$$D_t^{cooling}=Q_t^{hp-cooler}+E_t^{district-cooling}\forall t\in \mathbf{T}$$

(3)

In the case of electricity, the model is designed in such a way that the electricity demands for all the lightings, heating devices, driving mechanisms, or electronics in use in a building are satisfied by the power network that has been established within the building. Therefore, the hourly power demand for each hour can be simplified into a single value, and the power that is to be provided can also be calculated as the sum of these elements. Here, the electricity that is used in the process where the electric energy used in charging an energy storage device such as an ESS, and the electricity used in the process where a heat pump converts electricity into heat can be added to the demand side.

The thermal energy network is modeled in the same way as the power network. However, since it is difficult to construct a device that converts heat energy into electricity within a building, a heat pump is designed in such a way that the energy balance can be achieved on the energy supply side. A machine that couples electricity and heat in such a way must be modeled to ensure that the generation and consumption at the applicable time unit match.

3.3. Installed Capacity Modeling

Energy equipment can generate energy in each time unit. If the model assumes that there is no limitation in the energy generation, it would be possible to fill all the demands using the cheapest energy. However, there are capacity limits for the energy amount that can be generated by the equipment. For this reason, the model sets the capacity limit for each piece of equipment, limiting the amount of energy that can be generated by each one over the given time unit.

$$\begin{array}{cc}\hfill \forall t& \in \mathbf{T}\hfill \\ \hfill & Q_t^{fuelcells}\le I^{fuelcells}\hfill \\ \hfill & Q_t^{hp-heater}\le I^{hp-heater}\hfill \\ \hfill & Q_t^{hp-cooler}\le I^{hp-cooler}\hfill \\ \hfill & Q_t^{boiler}\le I^{boiler}\hfill \\ \hfill & Q_t^{ess-charge}\le I^{ess}\hfill \\ \hfill & Q_t^{ess-discharge}\le I^{ess}\hfill \end{array}$$

(4)

The energy generated by a piece of energy equipment over the unit time cannot exceed the capacity of the equipment. For the whole time index t, the energy generation amount Q is set to be lower than the installed capacity of I, according to the restrictions. This will make it possible to realize a model that is limited by the amount of energy generated over the time unit.

3.4. PV Modeling

The equipment that generates energy using natural energy sources such as solar photovoltaic energy or wind energy has an advantage in its ability to generate energy without emitting pollutants or carbon. However, it is normally difficult to control the output artificially with these types of energy equipment. For PV equipment, therefore, a pattern of the hourly solar irradiation amount is prepared, and the electricity generated by the PV system per solar irradiation is used as the input data. This can be realized by using the solar irradiation data and the sunshine time data from the weather stations in the area for every hour in each year in the area, and by and the direction and angle of the panels.

The amount of power generated by a PV system can be scaled as per the following equation, based on the unit capacity calculated by the recurrence relation above and the energy output pattern per unit capacity of the equipment.

$$\begin{array}{cc}\hfill \forall t& \in \mathbf{T}\hfill \\ \hfill & Q_t^{bapv-rooftop}=W_t^{bapv-rooftop}{I}^{bapv-rooftop}\hfill \\ \hfill & Q_t^{bipv-facade}=W_t^{bipv-facade}{I}^{bipv-facade}\hfill \end{array}$$

(5)

Depending on the location and arrangement of the PV installations, there can be differences in the amount of solar irradiation that arrives at the horizontal surface. Therefore, this paper prepared two different classes for the modeling. The BAPV units (building-applied photovoltaic systems) are installed on the sloped surfaces of the roof or on a support structure that is installed on a flat rooftop area, with different angles or directions as desired to secure the highest amount of solar irradiation. Considering the longitudinal and latitudinal location of South Korea, these systems are installed at 36° facing 10° off due south in most cases. On the other hand, the Building Installation Photovoltaic Systems (BIPV) that are installed as a part of the exterior wall surface of the building have fixed installation directions and angles. Therefore, the amount of solar irradiation reaching the vertical surfaces of these panels is less than that of the BAPVs. Therefore, different solar output patterns, W, for the BAPV and the BIPV separately, were set in the proposed methodology.

3.5. Energy Storage Unit Modeling

For the devices that store and discharge energy when needed, such as the ESS, one must consider two factors. One of them is the limitations on the energy storage. When energy is discharged, there must be stored energy within the energy storage. When energy is stored, there must be a capacity limit for storing energy, which cannot be exceeded.

$$\begin{array}{cc}\hfill \forall t& \in \mathbf{T}\hfill \\ \hfill & S_t^{ess}\le {ϵ}^{maximum}{I}^{ess}\hfill \\ \hfill & S_t^{ess}\ge {ϵ}^{minimum}{I}^{ess}\hfill \end{array}$$

(6)

Most energy storage devices manage the maximum and minimum level of stored energy for the sake of seamless operation and safety. The input parameters, such as ${ϵ}^{maximum}\mathrm{and}{ϵ}^{minimum}$, can be applied to the capacity of an energy storage device so that the model can reflect such a condition.

Secondly, it is necessary to maintain the time series continuity for the storage and discharge of the energy. When storing energy, it is modeled as accumulating energy in the amount of energy stored in the previous unit time, and when releasing energy in reverse, the energy storage level is reduced compared to the previous unit time.

$$\begin{array}{cc}\hfill \forall t& \in \left\{x\right|x\in \mathbf{T}\wedge x\notin \left\{1\right\}\}\hfill \\ \hfill & S_t^{ess}=S_{t-1}^{ess}+\frac{1}{{\eta }^{ess}}{Q}_t^{ess-charge}-{\eta }^{ess}{Q}_t^{ess-discharge}\hfill \end{array}$$

(7)

Here, η, which is the loss occurring in the process of storing or releasing energy, must be considered as well in order to prevent unrealistic results where an abnormal amount of energy storage or discharge happens.

3.6. Heat Pump Unit Modeling

Heat travels from a high temperature to a low temperature until a thermal equilibrium is reached. A heat pump uses electricity and coolant to transfer heat from a low temperature to a high temperature. By using either the heat-absorbing side or the heat-releasing side, it is possible to provide cooling or heating. Therefore, a heat pump is basically modeled with the generalization that it uses electricity to generate heat energy.

$$\begin{array}{cc}\hfill \forall t& \in \mathbf{T}\hfill \\ \hfill & D_t^{hp-heater}=Q_t^{hp-heater}/c^{hp-heater}\hfill \\ \hfill & D_t^{hp-cooler}=Q_t^{hp-cooler}/c^{hp-cooler}\hfill \end{array}$$

(8)

As shown in the equations above, the model includes the variables that are used in the electricity side and the heat energy side in the energy balance model. Such restrictions maintain the coupling between the heat energy supply and consumption balance and the electricity supply and consumption balance.

3.7. Delivered Energy Price Modeling

This paper defined the restricting conditions and recurrence relations in order to model the retail billing plan of the South Korean power companies mentioned in the Section 1 and Section 2. For a model, an energy network that is outside a building is assumed to be capable of providing a limitless amount of energy at a cost corresponding to the amount of energy incoming, so that the optimal balance between the incoming energy from outside and the energy generated within the building can be identified.

The price of using the external energy is calculated as the sum of the base rate, which is calculated using the peak demand during the given time window, and the usage rate, which is in proportion to the energy consumption. Each factor has a relationship with the time unit; therefore, the model endows properties to the time units, and they are converted into a mapping table within the model. The key values of the mapping table are composed of the indexes that are assigned in chronological order of time units within the model, and each of these indexes is given a value that is used to identify the property of time, such as the monthly index, month of year, etc.

The base rate of KEPCO that was referred to in the model is charged on a monthly basis and the previous 12 months, including the current month, are set in the period window. With this, a group that allows definition of a time window for each month is formed to search for the appropriate time period within the model. As shown in the following model, ${\mathbf{MT}}_m$ is defined as the group of the time indexes, t, during the search period for the base rate for the month index, m. To define an equation for ${\mathbf{MT}}_m$, the starting time of the month index, $Y^{start-index}$ and the ending time index, $Y^{end-index}$, are registered as input parameters in advance. Here, the group of months during which the peak demand can be updated in each year—that is, January, February, July, August, September, and December—is defined as $\mathbf{SM}$.

$$\begin{array}{cc}\hfill \forall m& \in \mathbf{M}\hfill \\ \hfill & {\mathbf{ToM}}_m=\{Y_m^{start-index}...Y_m^{end-index}\}\hfill \\ \hfill & {\mathbf{K}}_m=\left\{x\right|x\in \left\{m\right\}\wedge \mathbf{SM}\}\hfill \\ \hfill & {\mathbf{K}}_m^{*}=\{(m-12)...m\}\cap {\mathbf{K}}_m\hfill \\ \hfill & {\mathbf{MT}}_m={\cup }_{x\in {\mathbf{K}}_m^{*}}{\mathbf{ToM}}_x\hfill \end{array}$$

(9)

Using the group of the time indexes defined with the above-mentioned equations, the maximum demand that is to be applied to the base rate is calculated.

$$P_m^{elec}\ge Q_t^{elec}\forall m\in \mathbf{M},\forall t\in \mathbf{T}\cap {\mathbf{MT}}_m$$

(10)

In order to implement a non-linear function equal to the maximum value in a linear programming, this research designated a unilateral inequality condition in the proposed methodology (10). With this, and due to the nature of a linear program that tries to minimize the cost of the target function, the applicable control variable is always limited to the maximum demand.

3.8. Energy Independence Modeling

The methodology suggested here includes a function to calculate the share of the energy that is self-generated out of the total energy demand for the building. Here, the share of the self-generated energy is defined as the energy independence rate, and it is used as the criterion to determine how close a building is to becoming a true ZEB building. The South Korean government made it mandatory to have an nZEB certificate issued for every new building. One of the criteria to have a certificate issued is that the energy independence rate must be 20% or higher. Therefore, in order to establish an optimal energy plan for a building under the energy and construction environment of South Korea, it is necessary to apply the model suggested herein. The basic concept for calculating the energy independence rate is to assess the ratio of the demand addressed by renewable energy out of the total energy demand of the building converted to the primary energy.

$$\mathrm{Energy}\mathrm{independence}\mathrm{rate}(\%)=100\times \frac{\mathrm{Annual}\mathrm{primary}\mathrm{renewable}\mathrm{energy}\mathrm{generation}}{\mathrm{Annual}\mathrm{primary}\mathrm{energy}\mathrm{consumption}}$$

(11)

To realize such a model, the energy generated by the building itself and the total demand of the building are converted into the primary energy caloric values. The nZEB certification program of South Korea, which was used as the reference for the model, defines the following conversion coefficients in the

Table 5. The conversion coefficient table of the primary energy.

Division	Primary Energy Conversion Factor
Fuel	1.1
Electricity	2.75
District Heating	0.728
District Cooling	0.937

for each type of energy.

There are the conversion coefficients calculated as a part of the program in order to consider the loss of energy during the generation of power and transportation of fuel, etc., while converting the primary energy units to kWh. Therefore, it should be noted that the results may vary depending on the efficiency of the energy generation facilities within the building or the composition of the power generation sources outside the building.

In the model suggested herein, the conversion coefficients mentioned above are used to form an equation to calculate the energy independence rate. According to the criteria for the nZEB certification program in South Korea, a building must meet the 20% independence rate requirement to be certified for the nZEB. If the energy plan in the model is to be found in conformity with the nZEB certification program, the following conditions must be observed.

$$\begin{array}{cc}\hfill & B^{delivered}=\sum _{t\in \mathbf{T}}2.75D_t^{elec}+0.728E_t^{district-heat}+0.937E_t^{district-cooling}\hfill \\ \hfill & B^{hp-consumption}=\sum _{t\in \mathbf{T}}2.75(Q_t^{hp-heater}/c^{hp-heater}+Q_t^{hp-cooler}/c^{hp-cooler})\hfill \\ \hfill & B^{fuel-consumption}=\sum _{t\in \mathbf{T}}1.1(Q_t^{boiler}/{\eta }^{boiler}+Q_t^{fuelcells}/{\eta }^{fuelcells})\hfill \\ \hfill & B^{pv}=\sum _{t\in \mathbf{T}}2.75(Q_t^{bapv-rooftop}+Q_t^{bipv-facade})\hfill \\ \hfill & B^{fuelcells}=\sum _{tin\mathbf{T}}2.75Q_t^{fuelcells}+Q_t^{fuelcells-hr}\hfill \end{array}$$

(12)

$$0.2(B^{delivered}+B^{hp-consumption}+B^{fuel-consumption})\le B^{pv}+B^{fuelcells}$$

(13)

As you can see in the equations mentioned above, the energy demand of the building is converted to kWh, followed by the calculation of the primary energy consumption amount using the conversion coefficients introduced in the zero-energy building program. Then, the energy generated by the building itself is converted to a primary energy amount using the applicable conversion coefficient, and, based on this rate, the building is assessed to determine whether it qualifies for certification.

3.9. Cost Modeling

3.9.1. Variable Cost Modeling

In traditional nation-wide or province-wide energy supply plans, most of the variable cost originates from the fossil fuel cost used for the generation of the energy. Therefore, in order to secure the economic feasibility of the energy supply for the entire region, a scenario for the fuel cost became an important part of the plan. However, in a simulated environment that is run by a relatively smaller network and with a tendency to refrain from the use of fossil fuel, the range of the variable cost to be considered must be adjusted. Therefore, in the suggested model, most of the variable cost is composed of the costs that are incurred due to the use of the energy supplied from external sources, such as the power bill costs or heating bill costs.

The monthly base rate is calculated by applying the base rate price to the maximum demand to be applied to the base rate of the month.

$$V_m^{basic-elec}={\gamma }^{basic-elec}{P}_m^{elec}\forall m\in \mathbf{M}$$

(14)

The usage rate of the energy includes some elements of the ToU billing system. Therefore, by mapping the proper energy usage unit rate ${\gamma }_t^{usage-*}$, this is modeled. By using the time property of the applicable index on the mapping table, the unit price of the ToU plan is determined, and this is applied to the consumption of the external energy to calculate the usage energy fare per unit time.

$$\begin{array}{cc}\hfill \forall t& \in \mathbf{T}\hfill \\ \hfill & V_t^{usage-elec}={\gamma }_t^{usage-elec}{E}_t^{elec}\hfill \\ \hfill & V_t^{usage-district-heat}={\gamma }_t^{usage-district-heat}{E}_t^{district-heat}\hfill \\ \hfill & V_t^{usage-district-cooling}={\gamma }_t^{usage-district-cooling}{E}_t^{district-cooling}\hfill \end{array}$$

(15)

As shown in the following equation, the variable cost for fuel purchase at the time index t is defined as the energy purchasing price at the time as well as the amount of fuel used.

$$\begin{array}{cc}\hfill \forall t& \in \mathbf{T}\hfill \\ \hfill & V_t^{boiler}={\gamma }_t^{boiler}{Q}_t^{boiler}/{\eta }^{boiler}\hfill \\ \hfill & V_t^{fuelcells}={\gamma }_t^{fuelcells}{Q}_t^{fuelcells}/{\eta }^{fuelcells}\hfill \end{array}$$

(16)

3.9.2. Fixed Cost Modeling

The energy equipment installation cost is determined as follows for the installation capacity of I. $\Gamma$ means the investment cost per unit.

$$\begin{array}{cc}\hfill F=& {\Gamma }^{bapv-rooftop}{I}^{bapv-rooftop}+{\Gamma }^{bipv-facade}{I}^{bipv-facade}\hfill \\ \hfill +& {\Gamma }^{fuelcells}{I}^{fuelcells}+{\Gamma }^{hp-heater}{I}^{hp-heater}+{\Gamma }^{hp-cooler}{I}^{hp-cooler}\hfill \\ \hfill +& {\Gamma }^{boiler}{I}^{boiler}+{\Gamma }^{ess}{I}^{ess}\hfill \end{array}$$

(17)

3.9.3. Overall Cost Modeling

The overall energy supply cost of a building is calculated as the sum of the variable costs and the fixed costs. As mentioned before, this paper defined a group of indexes, as follows, to organize the time series units of the related equations.

$$\mathbf{T}=\{1...\mathrm{the}\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{the}\mathrm{time}\mathrm{units}\mathrm{during}\mathrm{the}\mathrm{simulated}\mathrm{period}\}$$

(18)

$$\mathbf{M}=\{1...\mathrm{the}\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{the}\mathrm{months}\mathrm{during}\mathrm{the}\mathrm{simulated}\mathrm{period}\}$$

(19)

Equation (18) is the group of time indexes over the entirety of the simulated period, while Equation (19) is the group of the monthly indexes incremented without regard to the year over the entire simulated period. Using these equations, it is possible to sum up the base fares calculated by the month as well as the variable costs calculated by the hours over the entirety of the simulated period. By summing up the elements mentioned above, the total energy supply cost of a building can be calculated as follows:

$$\begin{array}{cc}\hfill \forall t\in \mathbf{T}& \\ \hfill O_t=& V_t^{usage-elec}+V_t^{usage-district-heat}+V_t^{usage-district-cooling}\hfill \\ \hfill +& V_t^{fuelcells}+V_t^{boiler}\hfill \end{array}$$

(20)

$$\underset{Q_t\in \mathbf{T},E_t\in \mathbf{T},I}{\mathrm{minimize}}F+\sum _{t\in \mathbf{T}}{O}_t+\sum _{m\in \mathbf{M}}{V}_m^{basic-elec}$$

(21)

4. Case Study

4.1. Case Setting

To get an energy plan result using the suggested methodology, Korea Electric Power Research Institute (KEPRI), which is supporting this study, provided the annual energy consumption data and energy operation equipment performance data, which are obtained based on the BEMS control point measurement data of many buildings. The data so provided are divided into four groups (office, public, educational, and medical facilities) depending on the purpose of the facilities. Here, this paper selected the BEMS data of office buildings as the data to be utilized in the case study. The general information on the building was obtained from one building that was registered as an office building in the open public construction data system of South Korea. This information, in turn, was used as the basis to calculate the annual energy demand and the hypothetical energy supply facilities to be installed. As such, the information assumed for the performance of this case study was as shown in the following

Table 6. The building setting information for the case study.

Item	Description	Remarks
Purpose of the building	Office	-
Site area	4062 m2	-
Building coverage	2777 m2	-
Gross floor area	45,829 m2	-
Energy unit	140 kWh/(m2yr)	As per the end energy consumption
Annual energy demand	6.4 GWh	Energy use intensity (EUI) for office building multiplied by gross floor area
Unit time energy demand pattern	Based on the BEMS data of an office building	-
Area available for BAPV installation	1944 m2	70% of the total building coverage
Area available for BIPV installation	704 m2	About 30% of one side of the exterior walls of the building

.

The energy operation data of an actual building are not available due to the Privacy Protection Act. Therefore, the general information of existing buildings and the energy unit statistics data of South Korean buildings, as well as the energy demand pattern data obtained from the BEMS information, were utilized to form a set of time series demand data during the simulated energy plan period. The form of the building was simplified as an assumed cuboid, which allowed the assumption of the area available for the installation of BAPV on the rooftop of the building based on the building coverage area. Additionally, the area covered by the BIPV installed on the exterior wall of the building depends on the direction, shade, and structure of the exterior walls of the building. Therefore, as a conservative estimation, this research assumed that about 30% of a single side (facing south) of the building was all that was available for the installation.

The installation cost for the supplied equipment per unit capacity was set based on statistics and data from related studies [31,32]. The capacity factor of the PV was calculated based on the energy generation pattern per unit area used in the modeling. The BIPV installed on the wall of the building had a tilt of 90°, so the solar irradiation on the surface of the panel was calculated to be lower than the case of the PV units installed on a flat surface [33]. The CoP of the heat pump, the charging and discharging loss rate of the ESS, and the efficiency of boilers and fuel cells were all assumed conservatively, and it is expected that they would perform better in reality. As for the recovery of the waste heat of fuel cells, 60% of the waste heat from these fuel cells would be recovered to generate heat energy, according to the configurations of this model. In this paper, it was not specified where exactly these devices would be installed in the building. However, it was assumed that the BAPV units would be installed on the slope of the roof or the rooftop, while the BIPV would be installed as an exterior wall finishing material. Based on the rated output of the PV panels that are widely available in South Korea, it was believed that about 5.4 m² of area was necessary to install a PV panel of 1 kW capacity. Due to the limitations in the installation areas, there are limitations regarding the installed capacity that would allow us to search for the optimal solution. The calculation results were, respectively, about 360 kW for BAPV and 130 kW for BIPV, and each of these was set as the optimization input condition. The configurations of the heat pump and the boiler were based on the availability of these facilities, as well as the energy demands in the BEMS data. As for the ESS, it was assumed that they would search up to 10% of the average energy demand, referring to the current construction regulation requiring that the capacity be at least 5% of the contract power. However, due to the lack of available data regarding fuel cells, it was configured that the optimal solution would be sought at a capacity of 10% of the average demands. The

Table 7. The information on the energy supply equipment to be installed in the building.

Item	Equipment	Value	Remarks
Installation cost per kW	PV	$1137/kW	-
	BIPV	$1698/kW	-
	ESS	$343/kWh	Per battery size
	Heat pump	$133/kW	-
	Fuel cells	$5410/kW	-
	Boiler	$250/kW	-
Performance factors	PV	14.2%	Capacity factor
	BIPV	7.9%	Capacity factor
	ESS	10%	Charge and discharge loss
	Heatpump	3.18, 2.59	CoP (heating, cooling)
	Fuel cells	50%	Efficiency
	Boiler	80%	Efficiency
Space requirement to installation	BAPV	5.4 m2/kW	On rooftop
	BIPV	5.4 m2/kW	On building facade
Maximum range of searching space in optimization	BAPV	360 kW	Consider the area of the rooftop
	BIPV	130 kW	Consider the area of the exterior wall
	ESS	73 kWh	battery size
	Heatpump (heating)	772 kW	Air heat pump for heating
	Heatpump (cooling)	638 kW	Air heat pump for cooling
	Fuel cells	73 kW	-
	Boiler	29 kW	-

shows the details of the energy supply equipment to be installed in the building.

In consideration of the purpose of the building in this case study and its annual energy demand, the billing plan provided by the South Korean power company is assumed to be the ‘General Service(A)II High Voltage A Option I’ plan that is shown in

Table 8. The energy charging plans with external suppliers for district heat and power.

Energy Type	Divisions		Price
Power	Base Charge		$5.975/kW
	Summer	Off-Peak	$0.048/kWh
		Mid-Peak	$0.091/kWh
		On-Peak	$0.110/kWh
	Spring, Fall	Off-Peak	$0.048/kWh
		Mid-Peak	$0.054/kWh
		On-Peak	$0.064/kWh
	Winter	Off-Peak	$0.055/kWh
		Mid-Peak	$0.081/kWh
		On-Peak	$0.093/kWh
District Heat	On-Peak (Dec., Jan., Feb.)		$0.072/kWh
	Off-Peak (the others)		$0.059/kWh
District Cooling	On-Peak (Jul., Aug.)		$0.097/kWh
	Mid-Peak (Jul., Aug.)		$0.075/kWh
	Off-Peak (the rest others)		$0.045/kWh

. The electricity bill is composed of the base rate and the usage rate. The formula to calculate the base fare is the same as the one introduced in the Section 1 and Section 2. The usage rate is a billing system that reflects the different seasons of the year and time of the day. District heating or district cooling are, respectively, designed with differentiated rates, which reflect the energy use, season, and time of day. The base rates of district heating and district cooling were not separately considered, and only the usage rates were considered, because, unlike electricity bills, their rates are fixed regardless of the energy operations.

4.2. Results of Case Study

A simulated environment was established based on the suggested methodology, and the optimized solution for it was calculated to develop an optimal building energy plan in consideration of the buildings and energy environments of South Korea. The optimal solution was simulated using the LP algorithm. The modeling equation was converted to a question that can be analyzed by an LP solver using the ZIMPL [34] tool. After calculating the optimal solution, the data for each of the control variables were extracted to summarize the optimal plan. The LP solver tool used was the CBC [35] tool that was provided by the Coin-OR project. The optimization simulation period was set to five years, in consideration of the calculation method for the base rate of electricity, which has a searching time window of the preceding 12 months. The changes in the occupancy rate after the completion of the building were ignored, assuming that the amount of annual energy demand during the simulated period remained unchanged.

To analyze the results of the case study, some additional cases were developed with some of the conditions modified. Case 1 is where the suggested methodology was applied unchanged so that the intended optimal energy plan could be identified. Case 2 identified the energy plan after removing the modeling for the base rate from the suggested methodology, for the purpose of evaluating the model for calculating the base rate based on the peak demand, which was addressed in the Section 1. The

Table 9. Composition of the case studies.

Cases	Description
Case 1	The default case with the suggested methodology applied as is.
Case 2	A case to analyze the effect of the base rate modeling based on the peak demand per unit time An energy plan is identified excluding the formula in (10).

lists the objectives to be derived from each case.

Case 1 summarized the simulation results over five years to plot a chart of energy supply in the Figure 1. The total energy demand per year was 6.4 GWh, which was composed of the power, cooling, and heating demands. Each energy demand was based on the power, heating, and cooling demands, respectively, from the time-series operation information extracted from the BEMS data of an office building. The analysis results based on the annual averages of these were 58%, 26% and 16%. To obtain a balance in the supply and demand of energy, a total of 7.0 GWh of power was supplied each year. The 0.6 GWh in excess was used to operate heat pumps or charge the ESS. The energy delivered from outside of the building was 61% of the total energy supply, while the remaining 39% was generated by the building itself. Seven percent was the renewable energy generated by the BAPV or the BIPV. The share of the energy converted by the heat pumps to heating or cooling energy was 25%, while the share of the heat generated from the recovered waste heat and the power from fuel cells was 7%.

Of the energy supply cost results of Case 1 in the Figure 2, 80% was spent purchasing energy from the power company or the district heating company. Some of these costs were used in operating heat pumps or charging the ESS. However, most of it was allocated to the fulfillment of the energy demands of the building. The cost of installing energy supply equipment was 15% when the total service life of it was divided by the year. Here, the installation cost for PV panels was 8%, which was the highest and followed by the installation cost of fuel cells, which was 5%. The fuel cost accounted for 5%, which was spent on purchasing the fuel to operate the fuel cell.

To check the effectiveness of the base rate modeling, the electricity purchase costs in Case 1 and Case 2 were compared separately for the base fare and the usage fare. In the Figure 3, case 2 had a 7% increase compared to Case 1, and this was because of a 30% increase in the base fare. Case 2 did not include model (10), so it did not consider the peak demand that was applicable to the base rate.

The Figure 4 below shows the plots of the unit time peak demand applied to the base rates in Case 1 and Case 2, for the two years starting from the starting year of the simulation period. The base fare calculation formula used in this study maintains the peak demand calculated in the current month for the next twelve months. Therefore, as shown in the results for Case 2, the peak demand in the first year stays the same until the end of the second year. On the other hand, Case 1 is modeled so that the formula concerning the base rate is to be included in the cost. Therefore, the peak demand in the January of the first year remains virtually untouched.

The total equipment capacity of the energy supply equipment calculated in Case 1 and Case 2 was, respectively, 2046 kW and 1946 kW. In both cases, the BAPV and BIPV installed matched the total limit of the available capacities for installation, and the reason for this can be found in (13). The primary energy conversion coefficient for electricity was 2.75, which is higher than the coefficient for other primary energies. To meet the requirement of getting 20% of the total primary energy consumption from renewable energies, using a renewable energy source with a higher conversion coefficient is more advantageous. Therefore, even though the installation cost was high and the capacity factor was relatively low, the equipment capacity was allocated to the fullest. The

Table 10. Equipment capacity results for each case.

Item	Case 1	Case 2
BAPV	360 kW	360 kW
BIPV	130 kW	130 kW
Fuel cells	73 kW	47 kW
ESS	73 kWh	Not installed
Air heat pump for heating	772 kW	772 kW
Air heat pump for cooling	638 kW	638 kW

shows the details of equipment capacity results for each case.

The same goes for fuel cells, as the generation of electricity and generating heat using waste heat, basically, are considered the provision of renewable energy. Therefore, despite the high installation cost, they were still, in the end, included in the energy plan. In Case 2, fuel cells were allocated with a proper equipment capacity, while Case 1 installed fuel cells to the maximum available limit, while the ESS, which was not included in Case 2, was also installed. This indicates that it is closer to an optimal plan to use fuel cells and the ESS to reduce the peak demand than to reduce the installation cost. Figure 5 shows the energy operation for each item at the time of the peak demand in each month over the two years of the simulated period. In Case 2, heat pumps are used proactively to provide heating and cooling energy during the peak hours. On the other hand, Case 1 had reduced heat pumps in operation but used district heating and fuel cells as the replacement for the heating and the cooling energy. The reason for these results is that, in Case 1, the base rate based on the peak demand is included in the model. If an unlimited amount of external energy is provided at the peak hours, as in Case 2, it will update the peak demand that is applied to the twelve-month period. This will, eventually, increase the energy bill. In the end, it is now obvious that reducing the external energy by utilizing a relatively expensive energy source only during peak hours would be closer to an optimal plan. Therefore, the effect of the billing plan that is provided by the South Korean electricity company could be confirmed by the comparison between Case 1 and Case 2.

5. Discussion

As this research analyzed the simulated results of the case studies, the meaningfulness of the addition of the modeling of billing plans that are based on peak demands on the building energy plan was confirmed. Additionally, such a retail billing plan was shown to reduce the peak demand of the end user through a comparison between Case 1 and Case 2. As this paper mentioned in the Introduction, the power industry in South Korea has an isolated national grid and almost the entirety of the primary energy is import dependent. Therefore, there is a strong need to manage the risks of the power company meticulously.

One of the implications of Case 2 is that the result of the case where this study was not conducted and the retail billing was simplified in an energy plan and the simulated results of Case 2 would be similar. Especially in Case 2, the ESS, which can shift the peak demand, is not installed. If this was the case in a real designing process of a building, additional power cost would be incurred after the completion of the construction or an additional space would have be secured, and therefore paid for, to add an ESS.

According to the nZEB certification criteria of South Korea, it is very important to reduce the use of electricity or replace it with renewable energy to secure energy independence. This also makes using electricity to run a heat pump for heating or cooling less attractive. Regarding this, some believed that the role of district heating and cooling would increase in the nZEB environment of South Korea. A CHP, which is capable of generating electricity and heat at the same time, can be a good way to provide a large amount of heat to an area that is densely populated with new buildings. Additionally, one may consider developing a demand management program that can shift the load of the ESS. Utilizing studies on the right types of incentives and obtaining cooperation from the users of buildings, it might be possible to reduce the peak demand without adding more equipment.

6. Conclusions

The purpose of this study is to establish the optimal energy plan for new buildings in the construction and energy environment of South Korea. Since there are already many outstanding existing studies, it was possible for this research to prepare the modeling of energy supply equipment and estimate the load. However, since the peak demand affects the calculation of the base rate in the retail billing system of South Korea, there is a need for a methodology that can model this and evaluate its impact. To this end, this paper developed a model that affects the base rate over the next twelve months once the peak demand per unit hour is updated and collated with the South Korean power billing system, nZEB certification program, and BEMS operation pattern data for office buildings to conduct a case study. In the case study, the case where the base rate modeling was applied and the case without one were compared to verify the impact on the base fare. Additionally, a discussion on the impact of the building energy plan that does not include such a model showed that it could result in the omission of the equipment that is necessary for an optimal energy plan.