**Utility Scale Solar Power with Minimal Energy Storage**

Qi Luo and Kartik B. Ariyur *Purdue University USA* 

#### **1. Introduction**

378 Solar Radiation

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Smart grid functionality creating an internet of energy has been a topic of increasing interest. It is opening up several real time functions: pricing, network and consumption tracking, and integration of solar and wind power. The report from Department of Energy (DOE, 2008; 2009) supplies accessible details. At the present time, utilities run coal thermal power plants and nuclear plants as base load (Srivastava & Flueck, 2009) and use land based gas turbine plants to absorb unexpected demand surges (Nuqui, 2009). Solar energy, though envisioned as one of the panaceas to power from fossil fuels, suffers from two deficiencies: the density of energy available, and the unreliability of power production. Density limits mean solar power will never quite replace coal and nuclear plants for base load. However, the factor that limits penetration of solar power is the unreliability of supply that stems from uncertainty in incident solar radiation. A 100MW plant can produce much less power output in a matter of minutes if a cloud passes over it. It can also jump the other way. This can potentially result in large and undesirable transients being introduced into the grid. Large currents can damage grid equipment, such as power lines or transformers, in a very short period of time. This means that solar power needs backup power in the grid in the form of polluting coal or expensive gas. This is the main reason that grid operators and utilities are reluctant to integrate solar energy into their systems. This also means that solar or wind power at present may actually be contributing to greater use of fossil fuels in some regions. In this paper, we focus on solutions to three approaches to avoid the usage of grid storage: Distributing solar production to minimize its variance, correlation of solar power production to power consumption in air conditioning to determine the upper limits of solar penetration possible without storage, and grid failure probability with different levels of solar penetration.

The paper is organized as follows: Section 2 introduces the method of reducing supply uncertainty via geographic distribution of solar plants; Section 3 introduces the idea of matching solar output with air conditioning consumption and matching wind/solar power output with the consumption of electrical appliances; Section 4 demonstrates the probability of grid failure with different levels of solar penetration; Section 5 supplies concluding remarks.

#### **2. Reducing supply uncertainty via geographic distribution**

#### **2.1 Solar power production**

We consider a solar thermal system to produce electricity, in which the solar radiation is first absorbed by the receiver—a tube filled with working fluid (eg. molten salt, 150 <sup>−</sup> <sup>350</sup>*oC* ) and then the absorbed thermal energy is used as a heat source for a power generation system. Our analysis can be easily extended to PV systems – only the constants of proportionality will be different, yielding qualitatively similar results.

We assume flat plate solar collectors for analysis, which can be easily extended to cylindrical parabolic collectors (Singh & Shama, 2009).

$$P = A \cdot I \cdot \eta\_1 \cdot \eta\_2 \cdot r\_\prime \tag{1}$$

where *A* is the total area of collectors, *I* is the solar radiation intensity, and *η*<sup>1</sup> is energy transfer efficiency from solar radiation to thermal energy, *η*<sup>2</sup> is the Carnot Cycle energy transfer efficiency from thermal to mechanical energy, and *r* is the ratio of efficiency of real heat engine compared to the Carnot Cycle efficiency. We assume that conversion from mechanical to electrical energy is 100%.

The solar-thermal transfer efficiency *η*<sup>1</sup> can be calculated as:

$$
\eta\_1 = \tau \alpha - \mathcal{U}\_L \frac{T\_H - T\_a}{I},
\tag{2}
$$

where *τ* is the transmissivity, *α* is the absorptivity listed in Tables 1 and 2. *TH* is the average temperature of heat transfer fluid (usually melted salt or oil), and *Ta* is the ambient temperature.


Table 1. Typical flat-plate solar collector (Black) properties


Table 2. Typical flat-plate solar collector(Selective) properties

The Carnot efficiency *η*<sup>2</sup> in equation (1) is calculated :

$$
\eta\_2 = 1 - \frac{T\_L}{T\_H} \tag{3}
$$

where *TL* is the lowest cycle temperature (which is slightly greater than ambient temperature *Ta*), *TH* is the highest cycle temperature.

#### **2.2 The idea of distributed solar power plant**

Solar power plants can produce significant swings of power supply. A cloud passing over a 100MW plant can reduce its output to 20MW, and when it passes over, the output will again swing to 100MW. We develop here the idea of a distributed solar power plant which can ameliorate these swings. Similar work on distribution of wind plants has shown significant

then the absorbed thermal energy is used as a heat source for a power generation system. Our analysis can be easily extended to PV systems – only the constants of proportionality will be

We assume flat plate solar collectors for analysis, which can be easily extended to cylindrical

where *A* is the total area of collectors, *I* is the solar radiation intensity, and *η*<sup>1</sup> is energy transfer efficiency from solar radiation to thermal energy, *η*<sup>2</sup> is the Carnot Cycle energy transfer efficiency from thermal to mechanical energy, and *r* is the ratio of efficiency of real heat engine compared to the Carnot Cycle efficiency. We assume that conversion from mechanical

where *τ* is the transmissivity, *α* is the absorptivity listed in Tables 1 and 2. *TH* is the average temperature of heat transfer fluid (usually melted salt or oil), and *Ta* is the ambient

> Number of covers *τα UL*(*kW*/*m*<sup>2</sup> *K*) 0 0.95 34 1 0.9 5.7 2 0.85 3.4

> Number of covers *τα UL*(*kW*/*m*<sup>2</sup> *K*) 0 0.90 28.5 1 0.85 2.8 2 0.80 1.7

> > *<sup>η</sup>*<sup>2</sup> <sup>=</sup> <sup>1</sup> <sup>−</sup> *TL*

where *TL* is the lowest cycle temperature (which is slightly greater than ambient temperature

Solar power plants can produce significant swings of power supply. A cloud passing over a 100MW plant can reduce its output to 20MW, and when it passes over, the output will again swing to 100MW. We develop here the idea of a distributed solar power plant which can ameliorate these swings. Similar work on distribution of wind plants has shown significant

*TH*

*TH* − *Ta*

*η*<sup>1</sup> = *τα* − *UL*

*P* = *A* · *I* · *η*<sup>1</sup> · *η*<sup>2</sup> · *r*, (1)

*<sup>I</sup>* , (2)

, (3)

different, yielding qualitatively similar results.

The solar-thermal transfer efficiency *η*<sup>1</sup> can be calculated as:

Table 1. Typical flat-plate solar collector (Black) properties

Table 2. Typical flat-plate solar collector(Selective) properties

The Carnot efficiency *η*<sup>2</sup> in equation (1) is calculated :

*Ta*), *TH* is the highest cycle temperature.

**2.2 The idea of distributed solar power plant**

parabolic collectors (Singh & Shama, 2009).

to electrical energy is 100%.

temperature.

benefits (Archer & Jacobin, 2007). The difficulty here is that correlation of solar intensity in locations less than 100 miles from each other will make our quantitative results very different. In the analysis below we assume negligible correlation between solar intensity at multiple locations.

The construction of 10 plants of 10MW each will cause additional capital and maintenance costs. However these may be offset by the benefit of a steadier power supply and less damage to grid equipment. We show how this distribution may be systematically performed.

The power production of the distributed plant *PT* is the sum of power produced in individual location *Pi*,:

$$P = \sum P\_{\text{i}\nu} \tag{4}$$

The variance of power production in the distributed plant is

$$
\sigma\_p^2 = \sum\_{i=1}^n f\_i^2 \sigma\_i^2 \tag{5}
$$

where *fi* = *Pi PT* , *<sup>σ</sup>*<sup>2</sup> *<sup>i</sup>* is the variance of *Pi*, and

$$\sum\_{i=1}^{n} f\_i = 1,\tag{6}$$

*σ*2 *<sup>p</sup>* is minimized by the following solution:

$$f\_i = \frac{1}{\sigma\_i^2} \frac{1}{\sum\_{i=1}^n \frac{1}{\sigma\_i^2}},\tag{7}$$

#### **2.3 Hypothetical New York example**

We use the historical data of solar intensity of twenty four candidate places within New York state from National Solar Radiation Data Base (NSRDB, 2005), and the corresponding temperature data from the United States Historical Climatology Network (USHCN, 2005). Then we choose four places of maximum annual solar intensity: Islip Long Island Macarthur Airport, John F Kennedy Intl Airport, New York Laguardia Airport and Republic Airport, and label them as area A, B, C and D. Fig. 1 shows the hourly average solar radiation of a typical day within each month. To construct synthetic time series of solar data, we proceeded as follows: Use random samples *xk* from the data of solar intensity distribution between 2001-2005 every *T* = 36 seconds and use a low pass filter with a time constant *τ* = 180 seconds. A valid question that may be asked here is – what is the benefit if solar intensity is strongly correlated between different locations? Our calculation of the covariance matrix of solar intensity for June, 2005 using hourly observations each day yields 30 difference covariance matrices for 30 days in June, 2005. The ratio of standard deviation to mean solar intensity of the corresponding eigenvalues of these 30 matrices range from 0.4681 to 0.8283 indicates a varying solar intensity distribution for different days. The ratio of the difference between eigenvalues and diagonal elements over diagonal elements range from -2.6496 to 0.9858 indicates a strong correlation of these four cites. However, in this discussion, we just neglect the correlation among these four cites. This opens up problems for future work which we discuss in the conclusions.

Fig. 1. Radiation intensity

The low pass filter smooths out jumps in intensity so they mimic what the motion of a cloud produces. The X axis in Fig. 1 is formed by one day from each month (24*hr* · 12*month*).

The data of hourly average temperature of a typical day within each month is acquired from United States Historical Climatology Network (USHCN, 2005). Fig. 2, 3 and 4 show respectively the electric power outputs of the central plants in one location (16000*m*<sup>2</sup> <sup>×</sup> 1), evenly in two locations (8000*m*<sup>2</sup> <sup>×</sup> 2), and evenly in four locations (4000*m*<sup>2</sup> <sup>×</sup> 4). Fig. 5 shows the power output of the optimally distributed plants. Fig. 6 gives the relationship between the coefficient of deviation and the installment cost. *Y*<sup>1</sup> axis represents the natural log of coefficient of deviation, *Y*<sup>2</sup> axis represents the natural log of setup cost. We can see from the figure that as the number of locations increases, the coefficient of deviation decreases, while the setup cost increases.

#### **3. Supply-demand matching mechanisms**

#### **3.1 Matching solar production to air conditioner consumption**

The electricity load in the hot season vs temperature for a large commercial facility in New York (Luo et al, 2009) in June, 2007 is shown in Fig. 7. The X axis is the temperature in *oF*, and Y axis is the electricity consumption in kWh. It is reasonable for the temperature and the load to have positive relation because in summer, the great portion of electricity consumption is due to air conditioning. Therefore the energy consumption of the building from the plot can be expressed as:

$$
\mathfrak{q}\_p = \mathfrak{a}\_1 \times T + \mathfrak{a}\_2 \tag{8}
$$

2

)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Radiation intensity (kW/m

The low pass filter smooths out jumps in intensity so they mimic what the motion of a cloud

The data of hourly average temperature of a typical day within each month is acquired from United States Historical Climatology Network (USHCN, 2005). Fig. 2, 3 and 4 show respectively the electric power outputs of the central plants in one location (16000*m*<sup>2</sup> <sup>×</sup> 1), evenly in two locations (8000*m*<sup>2</sup> <sup>×</sup> 2), and evenly in four locations (4000*m*<sup>2</sup> <sup>×</sup> 4). Fig. 5 shows the power output of the optimally distributed plants. Fig. 6 gives the relationship between the coefficient of deviation and the installment cost. *Y*<sup>1</sup> axis represents the natural log of coefficient of deviation, *Y*<sup>2</sup> axis represents the natural log of setup cost. We can see from the figure that as the number of locations increases, the coefficient of deviation decreases, while the setup cost

The electricity load in the hot season vs temperature for a large commercial facility in New York (Luo et al, 2009) in June, 2007 is shown in Fig. 7. The X axis is the temperature in *oF*, and Y axis is the electricity consumption in kWh. It is reasonable for the temperature and the load to have positive relation because in summer, the great portion of electricity consumption is due to air conditioning. Therefore the energy consumption of the building from the plot can

produces. The X axis in Fig. 1 is formed by one day from each month (24*hr* · 12*month*).

2

)

Radiation intensity (kW/m

Jan. Mar. May July Sep. Nov. <sup>0</sup>

Jan. Mar. May July Sep. Nov. <sup>0</sup>

Time (hour)

*qp* = *a*<sup>1</sup> × *T* + *a*<sup>2</sup> (8)

Time (hour)

Jan. Mar. May July Sep. Nov. <sup>0</sup>

Jan. Mar. May July Sep. Nov. <sup>0</sup>

**3. Supply-demand matching mechanisms**

**3.1 Matching solar production to air conditioner consumption**

Time (hour)

Time (hour)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Radiation intensity (kW/m

Fig. 1. Radiation intensity

increases.

be expressed as:

2

)

Radiation intensity (kW/m

2

)

Fig. 2. Electricity output by CSP of area 16000*m*<sup>2</sup> <sup>×</sup> <sup>1</sup>

Fig. 3. Electricity output by CSP of area 8000*m*<sup>2</sup> <sup>×</sup> <sup>2</sup>

Fig. 4. Electricity output by CSP of area 4000*m*<sup>2</sup> <sup>×</sup> <sup>4</sup>

Fig. 5. Optimal electricity output by CSP of area located in four places

Jan. Mar. May July Sep. Nov. <sup>0</sup>

Jan. Mar. May July Sep. Nov. <sup>0</sup>

Fig. 5. Optimal electricity output by CSP of area located in four places

Time (month)

Time (hour)

Only one location Two locations Four locations

200

200

400

600

800

1000

Output electricity (kW)

1200

1400

1600

1800

2000

Fig. 4. Electricity output by CSP of area 4000*m*<sup>2</sup> <sup>×</sup> <sup>4</sup>

400

600

800

1000

Output electricity (kW)

1200

1400

1600

1800

Fig. 6. Coefficient of deviation vs cost

Fig. 7. Electricity consumption versus temperature in summer

$$\mathcal{C}\_{p} = \sum (a\_1 \times T + a\_2 - D\_s) P\_\varepsilon + \mathcal{C}SP\_f + \sum D\_s \mathcal{C}SP\_{\overline{\upsilon}} \tag{9}$$

$$a\_1 = 1756.9, a\_2 = -92880\tag{10}$$

Where *qp* is the predicted energy consumption, *Cp* is the predicted bill, *Ds* is the solar energy output, *Pe* is the electricity price, *CSPf* is the fixed CSP maintenance cost, and *CSPv* is the CSP cost that may vary according to the solar energy output. The reason the correlation of power consumption to temperature is not very strong in Fig. 7 is that, for the commercial facility , air conditioning consumption is a large but not the dominant part of consumption.

This idea comes from the simple fact that as the solar intensity increases, both the CSP output and the air conditioner consumption increase, so we can match them to achieve an energy balance. The advantage of this matching may include: reduce the need for base load plants, and integrating solar power stably into the grid base.

Fig. 8 gives the electricity consumption of air conditioner of 10000 families (with room area uniformly distributed within 80*m*<sup>2</sup> <sup>−</sup> <sup>160</sup>*m*<sup>2</sup> and power of air conditioner uniformly distributed within 0.8*kW* − 1.6*kW*). It is calculated using active energy management described in previous work (Luo et al, 2009). We can see by comparing Fig. 5 and Fig. 8 that in summer, they have similar envelopes. The AC consumption flattens out because of the on-off nature of the control through thermostats.

Fig. 8. AC consumption of 10000 families

Where *qp* is the predicted energy consumption, *Cp* is the predicted bill, *Ds* is the solar energy output, *Pe* is the electricity price, *CSPf* is the fixed CSP maintenance cost, and *CSPv* is the CSP cost that may vary according to the solar energy output. The reason the correlation of power consumption to temperature is not very strong in Fig. 7 is that, for the commercial facility , air

This idea comes from the simple fact that as the solar intensity increases, both the CSP output and the air conditioner consumption increase, so we can match them to achieve an energy balance. The advantage of this matching may include: reduce the need for base load plants,

Fig. 8 gives the electricity consumption of air conditioner of 10000 families (with room area uniformly distributed within 80*m*<sup>2</sup> <sup>−</sup> <sup>160</sup>*m*<sup>2</sup> and power of air conditioner uniformly distributed within 0.8*kW* − 1.6*kW*). It is calculated using active energy management described in previous work (Luo et al, 2009). We can see by comparing Fig. 5 and Fig. 8 that in summer, they have similar envelopes. The AC consumption flattens out because of the on-off nature of

<sup>0</sup> <sup>50</sup> <sup>100</sup> <sup>150</sup> <sup>200</sup> <sup>250</sup> <sup>300</sup> <sup>0</sup>

Time (hour)

conditioning consumption is a large but not the dominant part of consumption.

and integrating solar power stably into the grid base.

the control through thermostats.

2000

Fig. 8. AC consumption of 10000 families

4000

6000

Energy consumption (kWh)

8000

10000

12000

*Cp* = ∑(*a*<sup>1</sup> × *<sup>T</sup>* + *<sup>a</sup>*<sup>2</sup> − *Ds*)*Pe* + *CSPf* + ∑ *DsCSPv*, (9)

*a*<sup>1</sup> = 1756.9, *a*<sup>2</sup> = −92880 (10)


Table 3. Weekly energy consumption of home appliances
