REAL TIME ENERGY MANAGEMENT : CUTTING ENERGY COSTS AND THE CARBON FOOTPRINT

Qi Luo and Kartik B. Ariyur∗ School of Mechanical Engineering Purdue University West Lafayette, Indiana 47907 Email: [email protected], [email protected]

ABSTRACT This article provides an analysis of the effect on the overall energy bill of a commercial facility of active energy management. We first show the benefits of pure hedging, hedging when the facility has its own power source–we consider the use of co generation in winter and the use of solar power in summer. We next show how active control of facility temperature set points augments the benefits of the hedging and use of local power. Our studies are based on real consumption data of a large commercial facility, the corresponding real time prices of grid power, prices of natural gas, intensity of solar radiation, and temperature history of the period under consideration. We show that the combination of hedging, local power generation and active control can reduce facility energy bills by up to 30%, and bill variance by up to 80%. Thus, we have a scenario where consumers save significantly while using power sources with a smaller carbon footprint. 1 Introduction

In recent years, there has been increasing support among economists for real time prices of electricity (RTP) that reflect the instantaneous balance between supply and demand. New York has had the system for three years. Real time prices can potentially increase the efficiency of electricity usage and thus reduce overall emissions and carbon footprint. But factors such as the volatility of bills may prevent the large scale adoption of RTP. Pioneering work by Borenstein, [1] has shown that bill volatility can reduced by means of a simple hedging strategy based on past usage-a futures contract based on combining usage at agreed upon prices and real time prices. In this work, we explore two novel ideas: estimating bills and their variances using a combination of local and grid power; estimating bills and variances using grid and local power in conjunction with active energy management. Both methods yield substantial reduction in bills and ∗

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Anoop Mathur Terrafore Inc., 1420 Iowa Avenue, Suite 220 Riverside, California 92507 Email: [email protected]

positive bill variation. The use of local sources of power with a low carbon footprint effectively reduces the overall carbon footprint. We perform our studies using data from a large commercial facility in New York. We show that the use of co-generation in winter and concentrating solar power (CSP) plants in summer in conjunction with hedging and active energy management reduces the overall energy bill by up to 30% and bill variance by up to 80%. The paper is organized as follows: Section 2 presents pure hedging to minimize bill volatility; Section 3 and 4 presents results when a local power source is used, specifically, solar power in summer and co generation in winter; Section 5 presents the results when the active power management, or adjustment of the thermostat is done in along with the hedging and use of local power.Section 5 concludes with the several problesm this work opens up.

2 Hedging

The real time price of electricity used in this paper is from Con Edison electricity company [2]. The electric consumption history is from by a large commercial building in New York . With these data, it is possible to construct a monthly bill of the building by combining power consumption data with the real time pricing data of that period. The cost formula used in [1] for the futures contract is Ccost = q¯ × p¯ + (qt − q) ¯ × PRT P ,

(1)

where q¯ is the target quantity and p¯ is the hedging price, qt is the consumption at that time and PRT P is the real-time-price of the electricity at that time. This equation indicates that the consumers may buy a fixed amount of electricity at a fixed price. And then if the amount needed exceeds the fixed amount, the consumers may buy extra electricity at real-time prices, and if the amount needed is less than the fixed electricity consumption contracted for, the consumers can sell electricity back at real time prices to the power company. The bill volatility is evalutuated by the coefficient of deviation. For the volatility with no hedging, we calculate the standard deviation of the

monthly bill as well it’s mean. Figure 1 shows the monthly bill of the commercial building from Jun-2007 to May-2008. And Figure 2 shows

the sum of predicted electricity purchase and that produced by cogeneration. 0

0

Dt = Delectricity (t) + Dcoge (t) = Delectricity +Vgas β 1.4

x 10

1.3

Qheat = Qgas + Qelectric = Vgas r + Qelectric ,

the bill($)

1.2

(3)

where r is the transfer coefficient of gas to heat while producing the electricity and typically 40%. The gross heat of combustion of one normal cubic meter of commercial quality natural gas is around 39 megajoules (≈10.8 kWh).As the heat generated from the gas must do not exceed the capacity of the gas heater, we can get the equation as

1.1

1

0.9

0.8

2

4

6 8 the monthly bill

10

0 ≤ Qgas ≤ 10.8 ×Vgasmax β

12

Figure 1. Electricity bill(monthly) of a commercial building in New York from Jun-2007 to May-2008

the mean hedging of the monthly bill.It shows that the optimal hedging might be around 130%, which means to buy 130% of average electricity consumption at prearranged price. and the corresponding coefficient of deviation is 0.2786, and the bill’s variation has been decreased more than 50%.

(4)

The electricity generated by consuming the gas cannot exceed the capacity of the co-generation plant. Dcoge ≤ Dcogemax

(5)

Therefore the cost of the consumer is the sum of electricity and natural gas costs, co-generation maintenance cost Bill = ∑ D0electric Pelectric + ∑ Vgas Pgas + ∑ Dcoge Plantvarcost + Plant f ixcost

3.1

(6)

Case study

Generally, for the or the typical commercial building in NY mentioned above the conventional heating efficient of directly burning the gas is always 90%. While for the gases consumed by co-generation, 40% converts to heat, while 40% converts to electricity. Figure 3 is the plot of the natural gas prices from 2001 to 2008, these data are from the Energy Information Administration [5]. Usually,

0.65

0.6

0.55 coefficient of deviation

(2)

whereβ is the transfer coefficient of gas to electricity and is normally 40%. And the heat loads, must be met instantaneously by the sum of electricity purchase, and that of the on site generation,

5

0.5

0.45

0.4

0.35

0.3

0.25

Figure 2.

0

5

10 15 20 hedging percentage (in decade)

25

30

The effect of hedging on the coefficient of deviation( monthly

bill)

Figure 3.

3 Cost Analysis with Co-generation

Based on the previous work done by Stadler and Marnay [3], and Siddiqui, Maribu [4], electricity loads must be met instantaneously by

Monthly gas prices from 2001 to 2008

people consume the gas for heating in winter, like November, December and January, assume the building have a heat capacity equal to 1000kw,

Table 1. Gas+electricity bill when combined with co generation

5

1.4

x 10

units

1.35

efficiency for heating

1.3

the bill($)

1.25 original−bill bill−with−250kwcoge bill−with−500kwcoge bill−with−1000kwcoge

1.2 1.15

original 250Kw 0.9

efficiency for electricity

1.1

500Kw

1000Kw

0.4

0.4

0.4

0.4

0.4

0.4

1.05 1

1

1.5

2

the monthes

2.5

3

3.5

Figure 4. Monthly bill of the commercial Building with co generation of various capacity

the bill analysis for co-generation of various capacity in Nov-2007, Dec 2007 and Jan-2008 is in Figure 4. And next we take Jan-2007 for detailed analysis of the effect of the hedging and co generation on the gas+electricity bill. In Table 3, the daily cost contains two parts when the co generation is in usage. The first part the daily gas consumption cost, and the second part is the daily installation and maintenance cost ( installation/maintenance cost divided by the life time of the co generation( in days)). And the detailed gas+electricity bill analysis for Jan-2008 is shown in Figure 5. Next we will apply the various hedging

gas prices in Nov-2007

$/cubic meter

0.4195

0.4195

0.4195

0.4195

gas prices in Dec-2007

$/cubic meter

0.3899

0.3899

0.3899

0.3899

gas prices in Jan-2008

$/cubic meter

0.4476

0.4476

0.4476

0.4476

life time

year

20

20

20

monthly bill average

1000$

130.1

125.03

119.0

106.7

standard deviation of the monthly bill

1000$

13.988

11.274

8.645

4.23

0.1075

0.0902

0.0726

0.0396

coefficient of deviation the original bill.

4 Cost Analysis with Solar Concentrator

Electricity loads must be met instantaneously by the sum of predicted electricity purchase and the solar concentrator generation. 0

Figure 5. The electricity+gas bill in Jan-2008 for a commercial building in NY with co generation

strategy to the combined bill of co-generation for 250 Kw, 500Kw and 1000Kw. The different hedging percentage is just percentage times the mean consumption, and the contract price is the mean price. It can be seen from the Figure 6 that the 190% hedging is the optimal hedging for reducing the bill violation without changing the bill significantly for co-generation of 1000kW. And Figure 7 is the combined bill under optimal hedging and with 1000kW co-generation, and at this level, the bill variance decreased for about than 80% compared to

Dt = Delectricity (t) + Dsolar (t)

(7)

Therefore the cost of the consumer is the sum of electricity purchased and the Solar Concentrator maintenance cost: Bill = ∑ D0electric Pelectric +CSPf ixcost + ∑ DsolarCSPvarcost

4.1

Case Study:

(8)

The monthly solar radiation in New York is from National Solar Radiation Data Base [6], and shown in Figure 8. And Figure 9 shows the monthly bill when combining with the CSP. And the mean of the bill as well as the bill volatility for CSP of various capacity are in Table 4. And next we take Jun-2007 for detailed analysis of the predicted

Table 2. Co-generation of various capacity in

units

250kw

500kW

1000kW

efficiency for heating

0.4

0.4

0.4

efficiency for electricity

0.4

0.4

0.4

20

20

20

year

gas consumption cubic for comegeneration+furnace ter/day

3240.7

4012.3

5555.5

$/cubic meter

0.4476

0.4476

0.4476

gas price bill for gas

1

daily cost when in usage 2

$/day

1450.6

1795.9

Figure 7. The combined bill of 190% hedging(optimal hedging) for the commercial building with co-generation of 1000kw in Jan-2008

5

3.5

2486.6

x 10

3

$/day

bill (electricity+gas)variance decrease average

1492.7

18%

bill(electricity+gas) decrease $/day average

1846.3

2546.7

40%

73%

the monthly solar radiation(w/m2)

life time

2.5

2

1.5

1

0.5

174.32

376.67

831.02 Figure 8.

2

4

6 the monthes

8

10

12

Monthly solar radiation(w/mˆ2) in New York (average of 2000-

2005) the mean hourly bill

180

and it can be obviously seen that the

160 150 140

coefficient of deviation

hedging−250kw hedging−500kw hedging−1000kw

170

0

5

10 15 20 hedging percentage (in decade)

25

30

q predicted = 1756.9 × T − 92880

(9)

0.4 hedging−250kw hedging−500kw hedging−1000kw

0.35 0.3

Bill predicted = ∑(1756.9 × T − 92880 − Dsolar )Pelectric

0.25

CSPf ixcost + ∑ DsolarCSPvarcost

0.2 0.15

0

5

10 15 20 hedging percentage (in decade)

25

(10)

30

Figure 6. The optimal hedging for the commercial building with cogeneration of various capacity in Jan-2008

bill, the effect of the hedging and CSP on the real bill. For the typical commercial building in NY mentioned above , the electricity load in the hot season vs temperature is shown below in Jun-2007. It is reasonable for the temperature and the load to have positive relation because in summer, the major electricity consumption is due to the air conditions. Therefore the energy consumption of the building can be expressed as

And Figure 10 is the detailed temperature and solar radiation history from Temperature Data Archive [7] and National Solar Radiation Data Base [6] respectively. And from these data we can discuss the hourly bill of the building in Jun-2007. Next we will apply the various hedging strategy to bill of solar concentrator of 250Kw, 500Kw and 1000Kw. The different hedging percentage is just percentage times the mean consumption, and the contract price is the mean price. It can be seen from the Figure 13 that the 180% hedging is the optimal hedging for reducing the bill violation without changing the bill significantly. And Figure 14 is the bill under optimal hedging and with 1000KW solar concentrator, and at this level, the bill variance decreased for more than 50%.

5

1.5

x 10

bill−with−250kwCSP bill−with−500kwCSP bill−with−1000kwCSP original−bill

1.4 1.3

the bill($)

1.2 1.1 1 0.9 0.8 0.7

2

4

6 the monthes

8

10

12

Figure 9. Monthly Bill of The Commercial Building from Jun-2007 to

Figure 10. Electricity consumption versus temperature in summer

May-2008 with CSP of various capacity 78 76

units original 250Kw 500Kw 1000Kw 25%

25%

25%

availability factor

95%

95%

95%

5

3.5

3.5

72 70 68 66

the installment and maintain Price

$/w

life time

year

64 62 60

20

20

20

monthly bill average

1000$ 105.40 105.59 106.21 106.46

standard deviation of the monthly bill

1000$ 15.769 16.201 16.649 17.587

coefficient of deviation

0.1496 0.1523 0.1573 0.1655

Table 3.

74

temperature(F)

capacity factor

0

Figure 11.

5

10

15 the time(days)

20

25

30

Temperature in New York in Jun(average from 2000-2005)

therefore we can develop the control equation as mCp

dθin 1 = 1 (θout − θin ) + Q˙ L dt ( hin A + kA + hout1 A )

(12)

and finally we got mCp

dθin ˙ = UA(θout − θin ) + Q, dt

(13)

where the parameters are defined as

The bill and its volatility when combined with CSP

5 Simulation Results for Specific Scenarios When Combined With controller 5.1 The dynamic model And based on the data analysis, we will build up a controller of the building with the control equation expressed as dθin = hinside A(θinsidewall − θin ) + Q˙ dt θ − θoutsidewall hinside A(θinsidewall − θin ) = −k insidewall L θinsidewall − θoutsidewall k = houtside A(θoutsidewall − θout ) L mCp

(11)

thermal mass m the heat capacity C p the air temperature inside the building θin the air temperature outside the building θout the inside temperature of the building brick θinsidewall the outside temperature of the building brick θoutsidewall the conduction coefficient of the brick k the convection coefficient of the inside air hinside the convection coefficient of the outside air houtside heating Q˙ the overall hear transfer coefficient U In the steady state , the inside air temperature should be controlled within 20−30deg, therefore the air density can be treated as constantρ =

Figure 12.

Solar radiation(w/mˆ2) in New York in Jun(average from

2000-2005) Figure 13. The electricity bill in Jun-2007 for a commercial building in NY with solar concentrator

units

250kw

500kw

1000kw

capacity factor

25%

25%

25%

availability factor

95%

95%

95%

the installment and maintain Price

$/w

the installment and maintain cost

million$

5

3.5

3.5

150 the mean hourly bill

Solar concentrators of various capacity in Jun-2007

140

1.25

1.75

3.5

life time

year

20

20

20

daily cost

$/day

171.24

239.7

497.45

bill variance decrease average

%

46.52

42.81

37.21

bill decrease average

$/day

183.09

274.48

423.1

1.205kg/m3 , and so does the heat capacity C p = 1.005kJ/kgK. And the data is available at the Engineering tool box [8]. And the overall heat transfer coefficient can be expressed as UA = Udoors Adoors +Uwalls Awalls +Uroo f ling Aroo f ling +Uwindows Awindows

(14)

hedging−250kw hedging−500kw hedging−1000kw

130 120

coefficient of deviation

Table 4.

0

5

10 15 20 hedging percentage (in decade)

25

30

0.5 hedging−250kw hedging−500kw hedging−1000kw

0.4 0.3 0.2

0

5

10 15 20 hedging percentage (in decade)

25

30

Figure 14. The optimal hedging for the commercial building with 1000kw solar concentrator in Jun-2007

and therefore we can get the controller equation series as following β ˙ θin (T ) = γθin (0) + (1 − γ)θout (0) + (1 − γ) Q(0) α β ˙ θin (2T ) = γθin (T ) + (1 − γ)θout (T ) + (1 − γ) Q(T ), α where γ = e−αT .

(17) (18)

and we can get the result θin (t) = e−αt θin (0) +

Zt

5.2 ˙ eα(τ−t)(αθout (t) + βQ(t))dτ

(15)

0

whereα = UA/mCP ,β = 1/mCp and when divided the time into equivalent time interval and assuming that T0 and Q˙ are constant from the time kTime − (k + 1)Time,we can get the discretized equation as θin ((k + 1)T ) = e−αTime θin (kT ) β ˙ +(1 − e−αTime )θout (kT ) + (1 − e−αTime ) Q(kT ) α

Control Strategy for Co-generation in Cold Weather

For the specific commercial building in New York, we apply the on-off strategy in the co generation control.That is  Qmax θset − θin > δ θset − θold < δ Qin = (19) 0 |θin − θset | < δ and in order to maintain the temperature inside the building at a conform level to human, there are more constrains on the set temperature Tset .

(16)

287K < θset < 307K

(20)

16 is the combined bill of the electricity and gas. It can be seen that the combined bill decreases slightly compared to the one without the controller, it is mainly because although the controller can reduce the heating consumption Q˙ in ,it also reduce the electricity generated by consuming the gas as well, therefore the net effect is that the bill is increased by 4.2%.

Figure 15. The combined bill of 180% hedging(optimal hedging) for the commerical building with co-generation of various capacity in Jun-2008

And in order to limit the gas bill in a certain amount, there should be further constrains on the setting temperature θset = θset + min(0, 3600/UA/gascost ∗ (expvol ∗ gascost − cost)) (21) And the parameters for this equations are as following: the cost of gas per time unit cost; heat transfer coefficient UA; the volume of gas expected to be consumed expvol; and the cost per volume unit of gas gascost. From this equations, we can set different expected volume based on the instant gas prices to maintain the bill at a low level. With constraints above, we build up the thermal model of that commercial building. Figure 15 is the gas bill when applied the control strategy. The inside temperature varies in the range of |θset − θin | < δ, and the co-generation furnace runs 200 seconds and then turned off for 1000 seconds. Figure

Figure 17.

The gas+electricity bill when applied the hedging, co-

generation and also the controller strategy in Jan-2008

5.3

Control Strategy for solar plant in hot Weather

For the specific commercial building in New York, we apply the on-off strategy in the cooling control as well.That is Qin =



Qmax θin − θset > δ θold − θset < δ , 0 |θset − θin | < δ

(22)

where Q˙ max is the maximum cooling capacity, and in order to maintain the temperature inside the building at a conform level to human, there are more constrains on the set temperature Tset . 287K < θset < 307K

(23)

And in order to limit the electricity bill in a certain amount, there should be further constrains on the setting temperature θset = θset + min(0, 3600/UA/elecost ∗ (exp − cost))

Figure 16.

The gas bill of the 1000kw co-generation combined with con-

troller in Jan-2008

(24)

And the parameters for this equations are as following: the cost of electricity per time unit cost; the expected electricity to be consumed exp; the cost per unit of electricity elecost. Figure 17 is electricity bill especially for cooling when applied the control strategy. The inside temperature varies in the range of |θset − θin | < δ. Figure 18 is the electricity bill when apply CSP, hedging and controller strategy.And we assume that the maximum cooling load Q˙ in is 500kw. It can be seen that the combined bill decreases compared to the one without the controller, therefore the net effect is that the bill is decreased by 8.6%.

Figure 18. The electricity(only the cooling consumption part) bill when applied controller strategy in Jun-2007

Figure 19.

The electricity bill when applied the hedging, CSP and also

the controller strategy in Jun-2007

6 Conclusions and Future Work What policies will help the use of renewable or co-generation? What level of feed-in tariffs will make solar power economical? The avoidance of the upside costs and the possibility to reap significant profit when the costs in real time are lower will benefit the company in the eyes of analysts–as costs are lower than expected and profits are therefore higher! Better hedging will be possible with higher fidelity data on the environmental parameters (egg solar, wind, temperature) –memory is cheap and lots of offline data and pre-processed information can easily be used for both hedging and real time control.

REFERENCES

[1] Borenstein, S., 2006. Consumer Risk from Real-Time Retail Electricity Pricing: Bill Volatility and Hedgability. Tech. rep., University of California Energy Institutee, July. See also URL http://www.ucei.org. [2] The real time price of electricity. The ConEdison Company. URLhttps://m020-w5.coned.com/

CimsWebServ/RTP/NYRtp.asp. [3] Firestone, R., and Marnay, C., 2007. Distributed Generation Dispatch Optimization under Various Electricity Tariff. Tech. rep., Lawrence Berkeley National Lab, July. See also URL http://eetd.lbl.gov/ea/EMS/EMS_pubs.html. [4] Siddiqui, A. S., and Maribu, K., 2009. “Investment and upgrade in distributed generation under uncertainty”. Energy Economics, 31(1), pp. 25–37. [5] Natural gas price data. Energy Information Administration. URL http://tonto.eia.doe.gov/dnav/ng/hist/ n3035ny3m.htm. [6] Solar radiation data. National Solar Radiation Database. URL http://rredc.nrel.gov/solar/old_data/ nsrdb/1991-2005/tmy3/. [7] Temperature data archive. University of Dayton. URL http://www.engr.udayton.edu/faculty/ jkissock/gsod/NYALBANY.txt. [8] The density and heat capacity of air. Engineering Toolbox. URL http://www.engineeringtoolbox.com/ air-properties-d_156.html.