Simulation of a ZEB Electrical Balance with aHybrid Small Wind/PV

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1.1. Battery Storage

Electrical storage battery is a needful part of renewable power systems particularly, small wind turbines and photovoltaic and is defined as a device which allows electricity to flow in both directions: inside and outside.

In the ZEB approach, battery storage is an essential component of the standby, emergencybackup services and electric vehicles which is the concept known as vehicle-to-building (V2B) and vehicle-to-home (V2H) technology. They are able to provide beneficial storage capacity to both vehicle and the building owners by lowering cost of the electric vehicles, reducing building’spurchased energy and enabling reliable emergency power systems.

The State of Charge (SOC) of a rechargeable battery (also, known as secondary battery) at any time is defined as

(1)

where is the remaining capacity and is the rated capacity both measured in Ampere-hours () which means delivering Amperes in k hours ^[4].

1.2. Photovoltaic & Small Wind

The efficient solar to electrical energy conversion using photovoltaic (PV) cells is one of the promising solutions for the global future energy demand. Solar cells are capable of converting the solar radiation into the electrical direct current (DC) through the so-called effect called photovoltaic. Photovoltaic modules or photovoltaic panels are made of the multiple interconnected solar cells. Owing to its low output power to meet the requirement of the house demands, photovoltaic arrays are usually utilized which are the linked collection of photovoltaic modules. To be applicable for household devices, the array output DC power should be converted to an alternative current (AC) via a device called inverter. Solar arrays electrical power are generally measured in watts (W), kilowatts (kW) and sometimes megawatts (MW) ^[5]. As illustrated in Figure 2, the array power generation varies from zero to its maximum value throughout the day.

Arotational flow driven machine which converts the kinetic energy from the moving air (wind) into the mechanical energy is called a wind turbine. Using a generator, the output mechanical energy is converted into the useful electricity. The relationship between the extracted mechanical power and the wind speed can be shown by a plot called a power curve. Figure 3 illustrates an idealized wind turbine power curve. The operating limits of a wind turbine is characterized by cut-in and cut-out speeds.

Figure 2. Typical electricity PV generation profile [6]

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Figure 3. Idealized wind turbine power curve [7]

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It can be seen from Figure 3 that the power curve is divided into four distinct zones:

• Before cut-in wind speed consists of low wind speeds which there is not sufficient torque exerted by the wind on the turbine blades to make them rotate so no power can be extracted.

• Between cut-in and rated wind speed is a transition region mainly concerned with keeping rotor torque and noise low and can be expressed as

(2)

where is the extracted power (W), is the rated turbine power (W), is the wind speed (), is the cut-in speed () and is the cut-out speed ().

• Between rated and cut-out wind speed which is relevant to higher wind speeds, the turbine design limit the output power to a maximum level (rated output power) and no further rise will happen in the extracted power.

• After cut-out speed (storm protection shut-down) there is a risk of damage to turbine structure and the control system stops the rotor.

1.3. Smart Meter

During the day, the smart meter has the option of charging various rates which are split into three separate periods according to demand for electricity: off-peak (low demand), mid-peak (moderate demand) and on-peak (high demand). The lowest prices are usually at night, on weekends and on holidays and are different throughout summertime and wintertime. Figure 4 shows a typical time-of-use price periods and is used in the model of the current study. Table 1 shows the assumed electricity rates in the current study.

Figure 4. Hourly separate periods of electricity demand for weekdays (up) and weekends (down) [8]

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Table 1. Rates of electricity in different periods (values of B_i) [9]

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2. Model Equations

At each point of the time (here, we consider each point as an hour) where , we can write the energy balance on the building system boundary as

(3)

where is the energy exchanged during 1 hour and the subscripts , , , and stand for wind turbine, photovoltaic panel, electrical grid, battery and the home energy demand, respectively. For the case of the battery, the exchanged energy is identical to its charging when and discharging when , in other words

(4)

where and denotes charging and discharging, respectively.

Taking the battery capacity into account, we can associate the state of the charge (SOC) and the exchange energy as following

(5)

where the value of is always between its minimum and maximum levels.

(6)

The battery fault can be a reason for not assigning the values 0 and 1 to the minimum and maximum values of the . As the second reason, the system owner probably like to ensure that there is always a charge remnant left in the battery. Eq. (2) is the simple case in which the battery efficiency considered to be 100% during charging and discharging. The more typical case can be written as (5).

(7)

where and are the battery efficiencies in charging and discharging modes, respectively.

The daily price of purchased electricity can be calculated using

(8)

where is the rate of electricity at the time . Values of can be found in Table 1. Assuming a constant daily trend throughout a month, the monthly electricity bill is calculated. The aim of the current simulation is to find the minimum value of B denoted by .

Assumed value for the two first terms in Eq. (2) is depicted in Figure 5 and Figure 6. The PV array has a nominal power output of and the small wind turbine specifications can be found in Table 2.

Figure 5. Distribution of daily wind speed at turbine height used for the turbine power output [11]

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Figure 6. Distribution of hourly photovoltaic energy generation [12]

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Figure 7. Distribution of hourly energy consumption for a typical family [13]

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Table 2. Small wind turbine characteristics [10]

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Table 3. Battery specifications

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In this study we considered a typical family which consumes electricity similar to what can be seen in Figure 8. more information about load profile patterns can be found in ref. (14).The values of constants in Eqs. (5) and (6) in the model can be found in Table 3.

Figure 8. Distribution of daily wind turbine power used in the model

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3. General Algebraic Modeling System

Equations (3) to (8) comprise a linear system of equations which can be solved using the General Algebraic Modeling System (GAMS) which is a high level modeling system ^[15] and is very similar to fourth generation programming systems. The procedure is carried out according to the defined algorithm by the software. It is capable to globally solve linear programs as well as finding local optima of nonlinear programs. In this software, the programmer can build models which are expressed in simple and concise algebraic statements to find the optimum value of a predefined function. Here, the statements are very similar to the model equations (3) to (8) except for its initial condition is required by the software to solve the problem more efficiently. We put the value of at o be as can be seen in Figure 11. The available input data for wind, PV and the energy consumption along with the rate periods are imported to the system defining tables which pertains to each energy supplies/demands.

4. Results

The hourly wind turbine output power is calculated using Eq. (2) and Figure 5. The output power is shown in Figure 8 and is used in the model equations. Modeling the equation systems in GAMS, the monthly electricity bill B is calculated in three cases:

• Case I: In presence of RET (renewable energy technology) with battery storage. In this case, there is a minimum value of B.

• Case II: In presence of RET without battery storage. Here, no minimum value of B exist.

• Case III: In absence of RET.

It is assumed that the daily trend of energy consumption depicted in Figure 7 continues for all the other days throughout a month. Figure 9, Figure 10, Figure 11 illustrates the simulation results. As Table 4 shows, using all elements can save 96% in electricity cost while 22% of this reduction owes to the battery storage. The more the battery storage capacity was used the more the improvement is seen in the energy saving through shifting high amount of energy from off-peak to the on-peak hours.

Table 4. Simulation results for daily prices for different cases

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5. Conclusion

Zero Energy Building(ZEB) is a modern concept which deals with providing the electrical or thermal energy from renewable energy resources to supply the buildings’ annual energy demands. However ZEBs have different aspects, current research investigated them with electrical approach as the part of building balance boundary.

A simple model was developed to encompass the balance boundary aspect of a nearly zero energy building and the electricity cost was optimized to its minimum level using the GAMS software. Three different modes (RET with storage, RET without storage, conventional non-ZEB) were simulated to show how each element affect the monthly electricity bill. Electricity bill were calculated to be 2’377, 18’240 and 66’960 dollars per month for each of the previous cases, respectively. Hourly variations of each energy flow were shown in different graphs. Besides free resources of renewable energies, the electrical energy storage which shifts the high-cost hours to the low-cost ones, is the main reason for this reduction.

Figure 9. Simulation results for hourly variations of power flow into the balance boundary of the building through battery storage in case I

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Figure 10. Simulation results for hourly variations of power flow into the balance boundary of the building through electricity grid in cases I and II

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Figure 11. Simulation results for hourly variations of battery state of charge (SOC) in case I

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