Assuming that the simulated family members are an office worker, a homemaker, and two children, we simulate each member’s daily activity schedules by using the Markov chain model. The concept of the model is presented in Figure 2. First, a member’s activity at 0:00 is decided according to the member’s ratio from a time use survey [12] . Table 1 shows activity classifications and examples. Next, according to the transition probabilities of

activity from 0:00 to 0:03, his or her activity at 0:03 is decided. The above processing is repeatedly performed and the activity after 3 minutes is stochastically decided from the current activity. The activity transition probabilities are also estimated from the time use survey [12] . Figure 3 shows an example of the simulation results of the daily activity schedules of a family.

Then, we estimate 3-minute demand profiles of electricity and hot water corresponding to the simulated living activities. Table 2 and Table 3 show the unit consumptions of electricity and hot water. For instance, when some family members watch TV from 8:00 to 10:00, 107 W electric power consumed by the TV occurs from 8:00 to 10:00. We assume that the whole demand for space heating and cooling is provided by electrical air conditioners, and the electric consumption for space heating and cooling is calculated separately by a household

heating and cooling simulation model¹. The house where the family lives is assumed to be a detached house in Tokyo. Figure 4 shows the estimated electric power and hot water profiles of a typical household and the average of 200 households on a summer weekday. The demand estimation every 3 minutes successfully reproduces

spikes from using high-energy appliances, such as a hair dryer and microwave oven.

The generated power from PV, , can be estimated by:

where: Global solar radiation (kW);

: Transformation coefficient of global solar radiation into solar irradiance on a roof in each season (summer: 1.022, winter: 1.389, mid-season: 1.146);

: Capacity of PV (kW);

: Power factor of PV (0.7);

: Solar radiation intensity (1.0 kW/m³).

We use 1-minute global solar radiation data observed at the Tokyo District Meteorological Observatory [13] and estimate the 3-minute electric power from the 3.0 kW PV system in summer, winter, and mid-season. Figure 5 shows the estimated PV electric output profile on July 27^th and the average profile in summer. As shown, the PV output profile draws a smooth curve on average, whereas the electric power fluctuates greatly.

We simulate energy supply-demand profiles every 3 minutes by using mixed integer programming. The target function of this programming minimizes the household energy cost. The household energy cost is composed of the initial cost of the energy apparatus (), electricity charge (), gas charge (), and benefit from selling PV electricity ():

Monthly amortized initial costs to purchase the energy apparatus can be derived by:

where: Price of energy apparatus(JPY);

: Subsidy of energy apparatus (JPY);

: Lifespan of energy apparatus (year);

: Discount rate (0.01).

The price, subsidy, and lifespan of each energy apparatus are shown in Table 4.

Both electricity and gas charges are the sum of the basic charge and the commodity charge, as shown in the following equations:

where: Grid electricity consumption at time on day (kWh);

: Gas consumption at time on day (m³);

: Monthly basic charge of electricity (JPY/month);

: Commodity charge rate of electricity (JPY/kWh);

: Monthly basic charge of gas (JPY/month);

: Commodity charge rate of gas (JPY/m³).

Basic charges and commodity charge rates of electricity and gas follow TEPCO and Tokyo Gas’s pricing.

The selling benefit depends on the electricity from PV back to the grid. It is obtained by:

where: Selling unit price of electricity from PV (42 JPY/kWh);

: Electricity from PV back to the grid at time on day (kWh).

CO₂ emissions by energy consumption are also calculated by setting the CO₂ emission basic units as below:

where: CO₂ emission basic unit of electricity (0.69 kg-CO₂/kWh);

: CO₂ emission basic unit of electricity (2.21 kg-CO₂/m³).

This mixed integer programming consists of 461,432 equations and 389,462 variables about cost, CO₂ emissions, energy balance, and household energy apparatus (fuel cell, PV, and battery). Table 5 shows performances of our assumed household energy apparatus.

Figure 6 shows the annual electricity consumptions in each case. Here, the electricity self-sufficiency rate is calculated by:

where: Annual electricity generated from the fuel cell (kWh/year);

: Annual electricity generated from the PV (kWh/year);

: Annual electricity demand (kWh/year).

In the base case, the total electricity consumption of 6487 kWh is supplied from the grid. When a fuel cell is installed into the household, about 4000 kWh of electricity is generated from the fuel cell, and it provides for about 60% of the total electricity consumption in each household. When the residential PV system is introduced, surplus electricity from the PV goes back to the grid. More electricity can be reversely transmitted when the

household has the hybrid generation system and battery. In the case of HB and HB + BT, electricity back to the grid is more than the purchased electricity, and thus the electricity self-sufficiency rates are over 100%. This result indicates that a household with a fuel cell and a PV system is a net-zero energy house (NZEH).

Figure 7 shows the annual energy costs in each case. First, we assess the economic effect of the fuel cell by comparing the energy cost in the FC case to that in the base case. The total energy cost is 294.9 thousand JPY/ year in the base case and 392.7 thousand JPY/year in the FC case, and the annual cost increases by 97.8 thousand JPY/year when a fuel cell is installed. The cost increase is caused by the additional amortized initial cost for the fuel cell (+163.8 thousand JPY/year) and exceeds the energy charge saving (−66.0 thousand JPY/year). Next, we appraise the economic effect of using a battery with a fuel cell by comparing energy costs in the FC case and the FC + BT case. The annual energy cost is 392.7 thousand JPY/year in the FC case and 570.1 thousand JPY/year in the FC + BT case, which is about 1.5 times greater. The initial cost difference of 177.4 thousand JPY/year directly influences the total energy cost. The energy charges saved are very low because peak- load pricing is not considered. Finally, we assess the influence on the energy cost by installing a residential PV system. As a result of the comparison between the base and the PV case, or between the FC case and the HB case, we find that the energy cost slightly decreases by introducing the PV system into the household. This is mainly due to the benefit of selling surplus electricity from the PV. Although the energy charge in the HB+BT case is relatively high, this is offset by the selling benefit.

Figure 8 shows annual CO₂ emissions by household energy use in each case. First, we evaluate the environ-

mental effect of the fuel cell by comparing CO₂ emission in the FC case to that in the base case. In the base case, 4.03 t CO₂ is emitted every year; on the other hand, 3.12 t CO₂ is emitted in the FC case. Introducing a fuel cell reduces CO₂ emission by 22.4%, and its marginal cost is 108.5 thousand JPY/t CO₂. Second, we assess the environmental impact of installing the PV system. The annual CO₂ emission is 2.88 t CO₂ and a reduction of 1.95 t CO₂ emission is enabled by the residential PV system. This reduction is equivalent to 28.4% of the CO₂ emission in the base case. The marginal cost for CO₂ reduction is 34.8 thousand JPY/t CO₂, when the selling benefit is not considered. Third, we evaluate the reduction of CO₂ emission by installing the hybrid generation system. The comparison between the base case and the HB case suggests that 2.00 t CO₂, or 49.5% of CO₂ emission, can be reduced each year by the household fuel cell and the PV system. The social marginal cost excluding the selling benefit is 100.0 thousand JPY/t CO₂.