NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

The Relationship between Wind 

Generation and Balancing-Energy 

Market Prices in ERCOT: 2007–2009 

E. Nicholson, J. Rogers, and K. Porter

Exeter Associates, Inc.

Columbia, Maryland

Subcontract Report

NREL/SR-5500-49415

November 2010
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

National Renewable Energy Laboratory

1617 Cole Boulevard

Golden, Colorado 80401

303-275-3000 • www.nrel.gov

Contract No. DE-AC36-08GO28308

The Relationship between Wind 

Generation and Balancing-Energy 

Market Prices in ERCOT: 2007–2009

E. Nicholson, J. Rogers, and K. Porter

Exeter Associates, Inc.

Columbia, Maryland

NREL Technical Monitor: Erik Ela

Prepared under Subcontract No. LAM-9-99431-01

Subcontract Report

NREL/SR-5500-49415

November 2010
This publication received minimal editorial review at NREL.

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iii

TABLE OF CONTENTS

PAGE

Introduction................................................................................................................................................... 1

Balancing-Energy Market in ERCOT........................................................................................................... 2

Generation in ERCOT................................................................................................................................... 3

Wind Generation in ERCOT..................................................................................................................... 5

Wind Penetration ...................................................................................................................................... 8

Balancing-Energy Market Prices.............................................................................................................. 9

Negative Balancing-Energy Prices ......................................................................................................... 11

Wind Generation and Balancing-Energy Prices ..................................................................................... 14

Modeling Electricity Prices..................................................................................................................... 17

Estimation Strategy................................................................................................................................. 17

Estimation Results .................................................................................................................................. 19

Conclusion .................................................................................................................................................. 22

Appendix A – Additional Figures and Graphs........................................................................................... A1

Appendix B – The ARIMA Model ............................................................................................................ B1

LIST OF TABLES

PAGE

1 ERCOT Wind Generation by Month; 2007-2009................................................................................. 6 

2 2007 Average Balancing-Energy Prices in ERCOT ($/MWh)............................................................. 9 

3 2008 Average Balancing-Energy Prices in ERCOT ($/MWh)........................................................... 10

4 2009 Average Balancing-Energy Prices in ERCOT ($/MWh)........................................................... 11

5 Pair-wise Correlations Between Balancing-Energy Prices and Generation by Fuel Type ................. 16 

6 ARMAX Model Specifications .......................................................................................................... 19 

7 ARMAX Model Coefficients on Wind Generation ............................................................................ 19

B1 Hour-by-Hour ARMAX Models Coefficient on Wind Generation ................................................... B2 

B2 ARMAX Models by Hour – Coefficient on Wind Generation.......................................................... B3 
iv

LIST OF FIGURES

PAGE

1 ERCOT Wind Capacity and Output; 2007-2009 .................................................................................. 1

2 ERCOT Percent of Energy Generation by Fuel Type; 2009 ................................................................ 4

3 2009 ERCOT Capacity by Zone........................................................................................................... 4

4 Average Hourly Wind Generation Duration Curves in ERCOT .......................................................... 5 

5 2008 Average Hourly ERCOT Load, Net Load, and Wind Generation ............................................... 7 

6 ERCOT Wind Generation and Penetration; 2007-2009 ....................................................................... 8 

7 Count of Negative Balancing-Energy Prices in ERCOT by Hour and Zone...................................... 13

8 The Merit Order Effect of Wind Power.............................................................................................. 14

A1 ERCOT Zones ................................................................................................................................... A1

A2 2007 ERCOT Balancing-Energy Market Price Percentiles by Zone................................................. A1

A3 2008 ERCOT Balancing-Energy Market Price Percentiles by Zone................................................ A2

A4 2009 ERCOT Balancing-Energy Market Price Percentiles by Zone................................................. A3
1 

Introduction

Texas has more installed wind capacity than any other state in the United States, with nearly nine

gigawatts (GW) of wind. Installed wind capacity in the Electric Reliability Council of Texas (ERCOT) 

nearly tripled between 2007 and 2009, increasing from approximately 2.8 GW at the beginning of 2007 to 

over 8.9 GW by the end of 2009.1

Figure 1

This paper attempts to measure the average marginal effects of wind 

generation on the balancing-energy market price in ERCOT with the help of econometric analysis. The 

econometric approach employed in this paper differs from other studies of the effects of wind on 

electricity markets because those studies, most of which focused on Europe, used production cost 

modeling. Rather than simulating market outcomes, this paper uses historical data from the ERCOT 

balancing market and attempts to quantify the average marginal effects of price on wind generation. 

presents a graph of the installed wind capacity in ERCOT as well as the monthly output. Both 

increased significantly over the 2007-2009 period.

Figure 1 - ERCOT Wind Capacity and Output; 2007-2009

Sources: ERCOT System Planning Division, “Monthly Status Report to Reliability and Operations 

Subcommittee” (Jan 2007 – Nov 2008), http://www.ercot.com/committees/board/tac/ros/; Kent Saathoff, “Grid 

Operations and Planning Report,” ERCOT Board of Directors, (Dec 2008 – Dec 2009), 

http://www.ercot.com/committees/board/. 

 

 

1 ERCOT System Planning Division, “Monthly Status Report to Reliability and Operations Subcommittee” (Jan. 

2007 – Nov. 2008), http://www.ercot.com/committees/board/tac/ros/; Kent Saathoff, “Grid Operations and Planning 

Report,” ERCOT Board of Directors, (Dec. 2008 – Dec. 2009), http://www.ercot.com/committees/board/. 

0

1

2

3

4

5

6

7

8

9

0

250

500

750

1,000

1,250

1,500

1,750

2,000

Jan-07

Mar-07

May-07

Jul-07

Sep-07

Nov-07

Jan-08

Mar-08

May-08

Jul-08

Sep-08

Nov-08

Jan-09

Mar-09

May-09

Jul-09

Sep-09

Nov-09

Installed Wind Capacity (GW)

Wind Generation (GWh)

Wind Capacity (GW) Wind Generation (GWh)
2 

The ERCOT market is comprised of four congestion zones (“zones”) and five key constraints. The zonal 

balancing-energy prices are equal when there is no congestion between the zones and zonal balancingenergy prices differ in the presence of inter-zonal congestion. A map of the ERCOT system and 

congestion zones is presented in Figure A1 of Appendix A. ERCOT uses the balancing-energy market to 

manage inter-zonal congestion. However, ERCOT will convert to a nodal market in late 2010, after 

which congestion will be managed at the nodal, rather than zonal, level. 

Balancing-Energy Market in ERCOT

The balancing-energy market represents a small portion of total transactions in ERCOT, usually less than 

5% of the total energy sold in ERCOT.2

 The majority of electricity in ERCOT is sold through bilateral 

transactions. However, balancing-energy market prices are important because they affect real-time 

dispatch in ERCOT and influence ERCOT’s bilateral market. According to ERCOT’s independent 

market monitor, the balancing energy market serves the following functions: balance supply and demand

in real time; manage inter-zonal congestion, and displace higher-cost energy with lower-cost energy given 

the energy offers of Qualified Scheduling Entities (QSEs).

3

 All parties that participate in the balancing 

market, such as load serving entities and generators, must be represented by a QSE. QSEs submit their 

load forecasts and resource schedules to ERCOT, who aggregates the schedules for planning purposes. 

ERCOT permits QSEs to submit unbalanced schedules, which means that QSEs can overstate (or 

understate) their load schedules with the expectation of selling (or purchasing) the difference in the 

balancing-energy market. 

Balancing-energy market prices are determined by the QSE resource offers and ERCOT’s scheduling and 

dispatch software, which develops zonal balancing energy prices. QSEs submit bids into the balancingenergy market that are essentially stepped supply curves that indicate the output level (in megawatt hours, 

“MWh”) and price (in $/MWh) that the QSE is willing to supply the balancing-energy market. The 

balancing-energy market has two components – “Inc” or “up balancing” energy and “Dec” or “down 

balancing” energy. When a QSE submits an Inc bid for up balancing service, it agrees to increase its 

production up to the quantity indicated in its supply schedule if the balancing-energy market price is 

greater than or equal to its Inc bid. A QSE can also submit Dec bids, where it agrees to decrease its own 

level of generation and purchase its requirements from ERCOT instead when the balancing-energy price 

is less than or equal to its Dec offer.

 

2 Potomac Economics, Ltd, “2008 State of the Market Report for the ERCOT Wholesale Electricity Markets,” 

(August 2009), 16, http://www.puc.state.tx.us/wmo/documents/annual_reports/2008annualreport.pdf. 3 Ibid., ii. 
3 

In real-time, ERCOT uses the balancing-energy market to balance supply and demand. When real-time 

load differs from forecasted load or when scheduled resources differ from actual resources, which is 

possible given relaxed balanced schedules, ERCOT makes up the difference by purchasing “up 

balancing” or “down balancing” energy. If the scheduled energy resources are insufficient to satisfy realtime load, ERCOT will purchase up balancing-energy services from QSEs that submitted Inc bids that 

cleared the balancing-energy market. When load is below expected levels, ERCOT reduces the level of 

electricity generated by purchasing down balancing-energy services. In such cases, QSEs with Dec offers 

that ERCOT accepts will purchase energy from ERCOT at the balancing-energy market clearing price 

rather than generate electricity themselves. 

According to Potomac Economics, ERCOT’s independent market monitor, ERCOT’s demand for 

balancing-energy is also affected by load patterns because ERCOT’s demand for balancing-energy is 

positive in the morning when loads ramp up and negative when load ramps down in the evening.4

Generation in ERCOT

 This is 

an artifact of ERCOT scheduling practices because QSEs mostly schedule generation in ERCOT on an 

hourly basis and bilateral contracts are frequently based on 6 AM – 10 PM blocks. Load typically ramps 

up and down at a faster pace than the scheduled generation, so ERCOT uses the balancing-energy market 

to fill in the gaps. Finally, unexpected transmission outages and unplanned generator outages also affect 

ERCOT’s demand for balancing energy. 

Generation resources in ERCOT produced 305,432 gigawatt-hours (GWh) of energy in 2009. Electricity

generation in ERCOT is dominated by natural gas and coal, with natural gas generally serving as the 

marginal fuel. Natural gas plants produce the most energy in the summer months (May – September), 

while coal plants produce the most energy during the rest of the year.5

 

Forty-two percent of the energy generated in ERCOT in 2009 came from natural gas and 37% from coal, 

as seen in Figure 2. Wind facilities produced 6.2% of energy in ERCOT in 2009. 6

 Wind generation 

constituted between 4% and 5% of total generation between May and September, and between 6% and 

9% during the rest of the year.

 

4 Ibid., 23. 5 ERCOT, “ERCOT 2009 Demand and Energy Report,” (January 2010), 

http://www.ercot.com/content/news/presentations/2010/ERCOT_2009_Demand_and_Energy.xls. 6 Ibid.
4 

Figure 2 - ERCOT Percent of Energy Generation by Fuel Type; 2009

Source: ERCOT, “ERCOT 2009 Demand and Energy Report,” (January 2010), 

http://www.ercot.com/content/news/presentations/2010/ERCOT_2009_Demand_and_Energy.xls. 

The resource mix within ERCOT varies across zones and Figure 3 shows how generation capacity was 

distributed across the zones in 2009. The vast majority of wind capacity – 90% – is located in the West 

zone.7

Figure 3 - 2009 ERCOT Capacity by Zone

 The North zone contains the most total generation capacity, while the West zone contains the least.

Source: Potomac Economics, Ltd, “2009 State of the Market Report for the ERCOT Wholesale Electricity 

Markets,” (August 2009), 16, http://www.puc.state.tx.us/WMO/documents/annual_reports/2009annualreport.pdf. 

 

7 Potomac Economics, Ltd, “2009 State of the Market Report for the ERCOT Wholesale Electricity Markets,” 

(August 2010), 45, http://www.puc.state.tx.us/WMO/documents/annual_reports/2009annualreport.pdf. 

Natural Gas 

42%

Coal

37%

Nuclear

14%

Wind

6%

Other

1%
5 

Wind Generation in ERCOT 

ERCOT has more than twice the wind capacity of any other organized wholesale electricity market – 

independent system operator (ISO) or regional transmission organization (RTO) – in North America.8

 

The wind capacity expansion from 1,385 megawatts (MW) in 2004 to 8,916 MW in 2009 corresponds to 

a compound average annual growth rate of 45.1%. The wind generation duration curves for 2007, 2008, 

and 2009 presented in Figure 4 demonstrate that increased wind capacity over the period resulted in 

higher levels of wind generation. 

Figure 4 - Average Hourly Wind Generation 

Duration Curves in ERCOT 

 

 

8

 The RTO/ISOs in North America are: Alberta, CAISO, ERCOT, Ontario IESO, ISO New England, Midwest ISO, 

New Brunswick SO, New York ISO, PJM Interconnection, and the Southwest Power Pool. 

1,000

2,000

3,000

4,000

5,000

6,000

MW

2,000 4,000 6,000 8,000

Hours

2007 2008 2009
6 

Table 1 summarizes the monthly wind generation dispatched in ERCOT (“wind generation”) between 

2007 and 2009. Annual wind generation increased almost 73% between 2007 and 2008, from 8.8 GWh 

to 15.2 GWh. The rate of increase in wind generation slowed to 23% between 2008 and 2009, when 18.8 

GWh of wind generation was produced. The maximum hourly wind generation in ERCOT rose by 32% 

between 2007 and 2008 from 3,407 MW to 4,491 MW, while the maximum hourly wind generation in 

ERCOT increased an additional 33% between 2008 and 2009 to 5,984 MW.

Table 1 - ERCOT Wind Generation by Month; 2007-2009

2007 2008 2009

Mean

(MW)

Max

(MW)

Total

(MWh)

Mean

(MW)

Max

(MW)

Total

(MWh)

Mean

(MW)

Max

(MW)

Total

(MWh)

Jan 638 2, 82 470,651 1,520 3,449 1,131,144 2,118 4,454 1,575,861

Feb 985 2,339 661,733 1,663 3,474 1,157,666 2,450 4,150 1,646,223

Mar 1,000 2,399 743,974 2,009 3,536 1,492,376 2,499 4,619 1,854,612

Apr 1,156 2,347 821,014 1,959 4,190 1,410,164 2,809 4,722 2,022,367

May 770 2,617 572,858 2,082 3,923 1,548,914 1,892 4,428 1,407,312

Jun 855 2,592 615,690 2,264 4,431 1,629,991 2,084 4,217 1,500,351

Jul 535 2,388 397,113 1,536 3,799 1,142,435 1,713 4,206 1,274,166

Aug 1,090 2,881 810,672 788 3,337 586,040 1,903 4,270 1,415,890

Sep 986 3,064 708,094 869 3,011 624,534 1,549 3,806 1,115,325

Oct 1,411 3,334 1,049,755 1,787 3,785 1,329,219 2,346 5,984 1,745,723

Nov 1,294 3,184 932,007 1,906 4,172 1,372,623 2,248 5,117 1,618,898

Dec 1,395 3,407 1,037,958 2,432 4,491 1,809,107 2,186 5,848 1,626,285

Total 1,009 3,407 8,821,520 1,735 4,491 15,234,213 2,147 5,984 18,803,013

 %

Change 72.0% 31.8% 72.7% 23.7% 33.2% 23.4% 
7 

Figure 5 shows the average hourly load, net load, and wind output in ERCOT in 2008. The average wind 

generation profile is almost the inverse of the average daily load pattern. While the wind patterns vary 

from year to year, wind output is lowest during the day and in the summer months, when load is highest. 

Figure 5 - 2008 Average Hourly ERCOT Load,

Net Load, and Wind Generation

25,000

30,000

35,000

40,000

Load and Net-Load (MW)

1,400

1,600

1,800

2,000

2,200

Wind Generation (MW)

1 3 5 7 9 11 13 15 17 19 21 23

Hour

Wind Generation Load Net Load
8 

Wind Penetration

Wind penetration, defined as the ratio of wind generation to total generation, depends on several factors 

including installed wind capacity, wind speeds, and transmission capacity. Figure 6 shows the wind 

generation duration curves and the wind penetration curves, ranked independently, for 2007, 2008, and 2009. 

The maximum wind penetration was 12.9% in 2007, increased to 17.6% in 2008, and to 24.4% in 2009.

Figure 6 - ERCOT Wind Generation and Penetration; 2007-2009

 

Hourly Wind Penetration Rate

Average (%) Maximum (%)

2007 3.13

12.93

2008 5.13 17.55

2009 6.17 24.43

 

 Note: wind penetration and generation are ranked independently 

 

 

Wind penetration in ERCOT was above 5% for 2,200 hours in 2007. In contrast, wind penetration was 

greater than 5% for over 4,200 hours in 2008. While penetration levels increased between 2007 and

2008, transmission constraints limited the level of wind that ERCOT could dispatch from the West zone 

to the rest of ERCOT at any given time. ERCOT’s market monitor attributed these constraints to 

increased installed wind capacity in the West.

9

 

 

9 Potomac Economics, Ltd, “2008 State of the Market Report for the ERCOT Wholesale Electricity Markets,” 

(August 2009), 87, http://www.puc.state.tx.us/wmo/documents/annual_reports/2008annualreport.pdf. 

5%

10%

15%

20%

25%

30%

Penetration (%)

1,000

2,000

3,000

4,000

5,000

6,000

Generation (MW)

0 2,000 4,000 6,000 8,000

Hours

Wind Generation Wind Penetration

ERCOT Wind Generation and Penetration 2007

5%

10%

15%

20%

25%

30%

Penetration (%)

1,000

2,000

3,000

4,000

5,000

6,000

Generation (MW)

0 2,000 4,000 6,000 8,000

Hours

Wind Generation Wind Penetration

ERCOT Wind Generation and Penetration 2008

5%

10%

15%

20%

25%

30%

Penetration (%)

1,000

2,000

3,000

4,000

5,000

6,000

Generation (MW)

0 2,000 4,000 6,000 8,000

Hours

Wind Generation Wind Penetration

ERCOT Wind Generation and Penetration 2009
9 

In 2008, ERCOT could dispatch up to 4 GW of wind from West to the other zones before the interface 

limit was binding.

10 Additionally, a double-circuit 345-kilovolt (kV) transmission line was out of service 

for much of February and March 2008, which further reduced the West-to-North transfer capability

during those months.

11 The West-to-North transmission constraint limits the wind generation that 

ERCOT can accommodate and was binding in 60.6% of the 15-minute intervals in 2008 and 35.6% in 

2009.

12 ERCOT’s independent market monitor found that wind curtailment caused by inter-zonal 

congestion on the West-to-North interface decreased from 604 GWh in 2008 to 442 GWh in 2009. 

However, intra-zonal, or “local” congestion in the West zone increased over the same period, and wind 

curtailment rose from 812 GWh in 2008 to 3,400 GWh in 2009.13

Balancing-Energy Market Prices

The three main functions of ERCOT’s balancing market are to balance supply and demand, manage interzonal congestion, and displace high-cost energy with lower-cost energy when possible.

14

Table 2

 Balancingenergy market-price drivers include natural gas prices, the time of day, and system conditions (e.g., line 

outages, generator de-ratings, etc). displays the average price by month and zone for balancing 

energy in 2007.

Houston North South West

Jan 50.05 50.06 50.09 51.01

Feb 52.49 52.51 52.36 53.29

Mar 54.36 54.27 54.08 54.30

Apr 58.23 54.72 56.22 53.65

May 56.38 52.04 54.21 53.19

Jun 56.35 54.99 55.25 56.13

Jul 48.68 49.14 47.79 49.78

Aug 57.75 56.70 57.26 55.68

Sep 61.18 60.89 61.07 60.40

Oct 49.83 47.23 46.36 46.87

Nov 50.88 46.88 48.53 41.05

Dec 49.69 49.68 49.77 51.44

 

10 Ibid., 88. 11 Ibid., 90. 12 Potomac Economics, Ltd, “2009 State of the Market Report for the ERCOT Wholesale Electricity Markets,” 

(August 2010), 85, http://www.puc.state.tx.us/WMO/documents/annual_reports/2009annualreport.pdf. 13 Ibid., 87. 14 Potomac Economics, Ltd, “2008 State of the Market Report for the ERCOT Wholesale Electricity Markets,” 

(August 2009), ii, http://www.puc.state.tx.us/WMO/documents/annual_reports/2008annualreport.pdf. 

Table 2 - 2007 Average Balancing-Energy Prices

in ERCOT ($/MWh)
10

Figure A2 in Appendix A plots the 10th, 25th, 50th, 75th, and 90th percentiles of hourly balancing-energy prices 

by zone in 2007. The price percentile graphs give an indication of the distribution of balancing-energy prices 

in each hour. For example, the 75th percentile represents the price level (per hour) that 75% of the balancingenergy prices were below. Note that balancing-energy prices increase in the morning shoulder period when 

load starts to ramp up, and decrease in the evening shoulder period when load falls. 

Table 3 shows the average balancing-energy prices by month and zone in 2008. In contrast to 2007, the 

2008 zonal balancing-energy prices are more divergent, particularly in April, May, and June of 2008. The 

ERCOT market monitor attributed one-quarter of the 2007-2008 price increase in April, May and June to 

transmission congestion.15 

Houston North South West

Jan 58.70 59.09 58.12 50.98

Feb 58.59 56.46 60.32 56.45

Mar 65.90 65.67 61.41 36.50

Apr 91.59 70.09 76.69 56.41

May 127.44 76.20 142.12 54.80

Jun 119.66 98.61 133.70 79.10

Jul 91.04 90.54 91.30 86.80

Aug 79.98 79.74 80.12 79.21

Sep 42.25 39.94 41.78 40.08

Oct 50.36 43.06 48.04 37.77

Nov 39.16 39.00 39.07 34.28

Dec 40.70 40.52 40.39 27.80

The increase in balancing-energy prices in 2008 relative to 2007 is also attributed to natural gas prices, 

which increased dramatically in the summer of 2008.

16 ERCOT also increased the offer cap in the 

balancing market from $1,500/MWh to $2,250/MWh in March 2008.

Unlike the other three zones, balancing-energy prices in the West zone decreased in 2008 relative to 2007. 

According to ERCOT’s independent market monitor, part of the 2007-2008 decrease in West balancingenergy prices can be attributed to the significant increase in installed wind capacity in that zone.

17

 

15 Ibid., 2.

 As 

16 Ibid. 17 Ibid., 8. 

Table 3 - 2008 Average Balancing-Energy Prices

in ERCOT ($/MWh)
11

Figure A3 in Appendix A shows, the 10th percentile of hourly balancing-energy prices in the West zone 

are below zero in hours zero to nine and 19 to 23 in 2008. Balancing-energy prices in the 90th percentile 

reached much higher levels in 2008 than experienced in 2007, especially in the South and Houston zones. 

The monthly average balancing-energy prices for 2009 are presented in Table 4. Balancing-energy prices

fell in 2009 to levels well below 2008, which is attributed to a decrease in natural gas prices. Average 

natural gas prices fell by 56% between 2008 and 2009.18 

Houston North South West

Jan 31.54 30.78 32.31 23.23

Feb 26.48 26.86 26.28 19.66

Mar 28.28 29.86 25.62 24.04

Apr 23.90 24.10 23.45 12.91

May 30.63 30.61 30.58 23.45

Jun 51.28 31.69 66.89 30.57

Jul 33.07 32.92 32.99 31.90

Aug 30.44 29.90 30.16 28.07

Sep 28.66 25.11 28.32 23.28

Oct 29.55 28.74 29.24 27.06

Nov 26.65 26.59 26.68 26.58

Dec 39.20 39.54 38.97 37.69

In 2009, balancing-energy prices across zones were also closer to each other than they were in 2008

because inter-zonal congestion was less frequent. The hourly balancing-energy price percentiles by zone 

in 2009 are displayed in Figure A4 of Appendix A. 

Negative Balancing-Energy Prices

Under normal circumstances, when ERCOT wants to take generation off the grid (i.e., purchase downbalancing-energy services), QSEs that submit Dec offers that clear the balancing-energy market ramp 

down their units and purchase energy from ERCOT (at a price below its marginal cost) instead. This 

price is almost always positive because generators avoid marginal fuel costs when they ramp their units 

down. However, this is not always true for wind generators. Wind generators receive a production tax 

credit for each MWh of electricity they generate, and they also sell renewable energy credits (RECs). 

These revenues are in addition to the revenues they earn in the ERCOT balancing-energy market. With

 

18 Potomac Economics, Ltd, “2009 State of the Market Report for the ERCOT Wholesale Electricity Markets,” 

(August 2010), 2, http://www.puc.state.tx.us/WMO/documents/annual_reports/2009annualreport.pdf. 

Table 4 - 2009 Average Balancing-Energy Prices

in ERCOT ($/MWh)
12

these additional payments, wind generators have an incentive to produce energy even when the price is 

negative, i.e., they are willing to pay ERCOT for the right to produce electricity.19 Wind generators can 

make a profit with negative balancing-energy prices provided that the value of the production tax credits 

and the RECs exceed the price (in $/MWh) that they pay ERCOT for the right to produce electricity.

20 

Figure 7 plots the number of hours when the balancing-energy price was negative by year and zone. In 

2007, the balancing-energy price was negative in 89 hours in the West zone and was rarely negative in the 

other three zones. The number of hours in the West with negative balancing-energy prices in 2008 

increased almost 13-fold to 1,150 hours. The North, South, and Houston zones also had negative 

balancing-energy prices in 2008, but only in a few hours in the early morning when wind generation tends 

to be higher. The number of hours in the West with negative balancing-energy prices decreased by 39% 

to 704 in 2009 because inter-zonal congestion was less frequent and hence ERCOT used zonal congestion 

management during fewer hours in 2009 compared to 2008.

21 However, as in prior years, the West had

the greatest number hours with negative balancing-energy prices.

 

19Potomac Economics, Ltd, “2009 State of the Market Report for the ERCOT Wholesale Electricity Markets,” 

(August 2010), xxviii, http://www.puc.state.tx.us/WMO/documents/annual_reports/2009annualreport.pdf. 20 Some wind generators may have a power purchase agreement with load-serving entities that specify a particular 

power purchase rate per MWh, and are therefore not directly affected by negative prices. 

21Potomac Economics, Ltd, “2009 State of the Market Report for the ERCOT Wholesale Electricity Markets,” 

(August 2010), 87, http://www.puc.state.tx.us/WMO/documents/annual_reports/2009annualreport.pdf. 
13

 

Figure 7 - Count of Negative Balancing-Energy Prices in ERCOT by Hour and Zone

Number of hours with negative balancingenergy prices

Zone 2007 2008 2009

Houston 5 30 26

North 8 32 30

South 6 33 26

West 89 1,150 704

Total 108 1,245 784

0

10

20

30

40

50

60

70

80

1 3 5 7 9 11 13 15 17 19 21 23

Number of Hours Hour

Number of Hours with Negative Prices

ERCOT 2007

Houston North South West

0

10

20

30

40

50

60

70

80

1 3 5 7 9 11 13 15 17 19 21 23

Number of Hours Hour

Number of Hours with Negative Prices 

ERCOT 2008

Houston North South West

0

10

20

30

40

50

60

70

80

1 3 5 7 9 11 13 15 17 19 21 23

Number of Hours Hour

Number of Hours with Negative Prices 

ERCOT 2009

Houston North South West
14 

Wind Generation and Balancing-Energy Prices 

This section examines the relationship between wind generation and the balancing-energy market price in 

ERCOT, frequently referred to as the merit order effect of wind energy. European studies of Denmark and 

Germany found that wind generation decreased the spot price for electricity.22 Additionally, ERCOT’s 

independent market monitor found that increased wind generation likely lowered the average price in the West 

zone.23 We generally expect wind generation will decrease the balancing-energy prices. 

Figure 8 presents a European Wind Energy Association (EWEA) graphic that explains the merit order effect. 

The hatched and solid supply schedule represents the supply slack without and with wind, respectively. 

Figure 8 - The Merit Order Effect of Wind Power 

 Source: EWEA, The Economics of Wind Energy, (March 2009), 18, 

http://www.ewea.org/fileadmin/ewea_documents/documents/00_POLICY_document/Economics_of_Wind_Energy__March_2009_.pdf. 

Wind generation has zero marginal cost so it is located near nuclear generation in the resource stack. An 

increase in wind generation in a given hour constitutes an increase in the supply of generation, 

represented by a rightward shift in the supply curve. The merit order effect is the price change resulting 

from such a supply curve shift. 

 

22 Pöyry, “Wind Energy and Electricity Prices: Exploring the ‘Merit Order Effect’,” Literature Review for the 

European Wind Energy Association, (April 2010), 

http://www.ewea.org/fileadmin/ewea_documents/documents/publications/reports/MeritOrder.pdf. 23 Potomac Economics, Ltd, “2008 State of the Market Report for the ERCOT Wholesale Electricity Markets,” 

(August 2009), 8, http://www.puc.state.tx.us/wmo/documents/annual_reports/2008annualreport.pdf; The market 

monitor noted that higher levels of wind generation might also increase variability and cause price spikes. While 

important, the variability of prices is beyond the scope of this paper. 
15

Figure 8 contains three demand curves representing three different levels of electric demand: Night, Day, 

and Peak. The three demand curves intersect the supply curve at different points. The Night demand 

curve crosses the relatively flat and low-price portion of the supply curve, while the Peak demand curve 

crosses the supply curve at the steeper and higher-priced portion. The merit order effect in Figure 8 

during the Peak period equals the difference between Price A and Price B. Since the slope of the supply 

curve is relatively flat during the night and steeper during the day, the merit order effect during the night 

should be lower than the merit order effect in hours with regular and peak load. 

The EWEA commissioned a review of studies that estimated the merit order effect and estimates ranged 

from 3-23€/MWh.24 The relationship between wind generation and the balancing-energy market price in 

ERCOT likely differs from the relationships estimated in Europe because ERCOT did not have a fullfledged real-time electricity market in the 2007-2009 period. A first step in examining the relationship 

between the level of wind generation and zonal balancing-energy prices is to examine the simple 

correlation between the two variables. A pair-wise correlation coefficient is a basic statistic that 

indicates, in a rough way, the sign and strength of the relationship between two variables. Table 5 

presents the pair-wise correlations between the zonal balancing-energy prices and generation by fuel type 

for the three study years. The correlation coefficient ranges between negative one and positive one, 

where the further the coefficient is from zero, the stronger the co-movement between the two variables. If 

the correlation coefficient is negative, the two variables tend to move in opposite directions (i.e., variable 

A is generally above its average when variable B is below its average). If the two variables tend to move 

in the same direction, the correlation coefficient will be positive.

 

24 Pöyry, “Wind Energy and Electricity Prices: Exploring the ‘Merit Order Effect’,” Literature Review for the 

European Wind Energy Association, (April 2010), 

http://www.ewea.org/fileadmin/ewea_documents/documents/publications/reports/MeritOrder.pdf. 
16

Houston North

2007 2008 2009 2007 2008 2009

Wind -0.149 -0.045 -0.124 -0.168 -0.113 -0.133

Coal 0.084 0.154 0.144 0.095 0.222 0.158

Natural Gas 0.369 0.373 0.252 0.367 0.400 0.222

Nuclear -0.023 -0.006† 0.002† -0.024 0.032 0.007†

Hydro 0.134 0.263 0.168 0.136 0.258 0.154

Other 0.286 0.247 0.130 0.278 0.278 0.115

South West

2007 2008 2009 2007 2008 2009

Wind -0.157 -0.028 -0.104 -0.216 -0.300 -0.262

Coal 0.087 0.153 0.115 0.095 0.249 0.216

Natural Gas 0.367 0.351 0.225 0.303 0.356 0.269

Nuclear -0.027 0.028 0.007† -0.017† 0.013† -0.020†

Hydro 0.133 0.235 0.151 0.117 0.221 0.165

Other 0.283 0.230 0.113 0.223 0.241 0.142

†

Insignificant from zero at the 5% level

The correlations in Table 5 suggest, but by no means prove, that wind generation is negatively correlated 

with price. The negative sign means that on average when the level of wind generation is above its 

average level, the price is below its average level. The balancing-energy prices are correlated with all

fuel types, but wind generation levels are negatively correlated with the balancing-energy price in each 

zone and year. Nuclear generation levels are also negatively correlated with price in some instances; 

however, nuclear units essentially operate at all hours regardless of the balancing-energy prices, except 

when they are brought offline for scheduled maintenance. Furthermore, the nuclear correlation

coefficients are close to zero and many are statistically insignificant (signified with a † in Table 6), while

the wind coefficients are all significant.

The wind correlation coefficients are the strongest (in this case, the most negative) in the West zone, 

which contains 90% of ERCOT’s wind capacity. We expect that higher levels of generation from any 

fuel type with increasing marginal cost will increase the balancing-energy price because QSEs dispatch 

their cheap resources before their expensive ones. Hence, it is not surprising to see positive correlations 

between coal and natural gas and the balancing-energy price. Natural gas has the strongest positive 

correlation with price, which is consistent with the fact that natural gas is frequently the marginal fuel in 

ERCOT. The marginal cost of wind is zero, so wind and price are not expected to have a positive 

correlation coefficient. However, the negative correlation between wind generation and price is partly 

Table 5 – Pair-wise Correlations Between Balancing-Energy Prices

and Generation by Fuel Type
17

driven by the average wind generation profile in ERCOT because wind generation is typically greater at 

night when balancing-energy prices tend to be lower. Hence, wind generation tends to be above its 

average level when balancing-energy prices are below their average level. 

Modeling Electricity Prices

The pair-wise correlation coefficients in Table 5 present an incomplete picture of the relationship between 

wind generation and hourly prices for balancing energy. Other factors play a role, such as the time of 

day, weather, and system conditions. Furthermore, hourly electricity prices are characterized by 

seasonality, price spikes and mean reversion, all of which must be accounted for.

25 ‘Seasonality’ means 

that the balancing-energy prices change in a predictable way with the seasons, weeks, or the time of day. 

ERCOT’s balancing-energy market prices are also subject to price spikes – the average hourly price can 

triple from one hour to the next. Typically, balancing-energy prices return to their previous levels after a 

price spike within a few hours (usually within one or two hours), which means that the balancing-energy 

price series exhibits mean reversion. 

The goal of this section is to estimate an econometric model of the zonal price of balancing energy and 

estimate how wind generation affects it. The ordinary least-squares regression model is inappropriate for 

this task because it assumes that the errors in one time period are independent of the errors in previous 

periods. Autoregressive Moving Average (ARMA) models permit serial dependence in the errors and 

are often used to model electricity prices.26

Estimation Strategy

 The ARMAX model is an ARMA model with exogenous 

variables. Appendix B provides a more detailed description of ARMA and ARMAX models. 

We estimated an ARMAX model with the hourly zonal balancing-energy market price as the dependent 

variable and wind generation, weather, natural gas generation, and previous values of the balancingenergy price and error terms as the dependent variable.27

 

25 Rafał Weron, Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach, (John Wiley & 

Sons, Ltd, January 2007).

 The first step in fitting an ARMA or ARMAX 

model is to make the underlying time series stationary. This is usually accomplished by first differencing, 

26 Javier Contreras, Rosario Espínola, Francisco Nogales, and Antonio Conego, “ARIMA Models to Predict NextDay Electricity Prices,” IEEE Transactions on Power Systems, Vol. 18, No. 3, (August 2003), 

http://www.est.uc3m.es/fjnm/esp/papers/ARIMAprices.pdf; M. Zhou, Z. Yan, Y.X. Ni, G. Li, and Y. Nie, 

“Electricity Price Forecasting With Confidence-Interval Estimation Through an Extended ARIMA Approach,” IEEE 

Proceedings – Generation, Transmission and Distribution, Vol. 153, Issue 2, (Stevenage: IET, March 2006), 187-

195, http://ieeexplore.ieee.org/servlet/opac?punumber=2195. 27 See Appendix B for a detailed description of the ARMAX model.
18

which means analyzing the period-to-period change in the time-series variable (the balancing-energy 

price in this case) rather than the level of that variable in each period. However, the price pattern in 

ERCOT is complex and first differencing (or first and 24th differencing) does not achieve a stationary 

price series. Since the balancing-energy price data have a persistent daily and weekly pattern, we 

removed the pattern to separate the daily and weekly trend in the balancing-energy price series from the 

shocks. This weekly trend was removed by subtracting the median hourly weekly pattern from the hourly 

balancing-energy prices in each year and zone.

28 What remains is a transformed price series called the 

“adjusted price” for each zone that represents deviations from the average weekly price pattern. 

We posit that the level of wind generation is an exogenous variable. Indeed, ERCOT can curtail wind, 

but the amount of wind produced at any given time depends on installed wind capacity, wind speeds, and 

transmission constraints, all of which are exogenous in the short run. Wind is essentially treated as an 

exogenous shock to the ERCOT system. We attempted to include transmission constraints in the model 

to help explain the balancing-energy price spikes, but the constraint variables were insignificant.29 We 

also included the quantity of natural gas generation in some specifications because natural gas is 

frequently the marginal fuel in ERCOT.30 Levels of natural gas generation are expected to have a 

positive influence on price because the greater the level of natural gas generation, the higher the market 

clearing price given that ERCOT is moving along the natural gas marginal-cost curve as it dispatches 

more natural gas generation. Finally, we include hourly temperature to capture the effect of load. Zonal 

temperatures were calculated broadly because we needed to create a single-temperature variable for each 

zone. The following city temperatures were used to represent each zone: North: Dallas; Houston: 

Houston; West: Odessa; South: San Antonio. 

Table 6 contains eight of the ARMAX model specifications we estimated separately for each year and 

zone (i.e., 3 years x 4 zones = 12 estimations for each model specification, and 8 x 12 = 96 estimations 

were produced in total).31

Table 5

 Separate models were estimated for each year given the annual differences 

observed in . The “adjusted price” is the dependent variable in each ARMAX model. Wind 

generation varies significantly throughout the day and we allow wind generation to have a different effect 

 

28 The first step in calculating the adjusted balancing energy price is to calculate the median price for each of the 168 

hours of the week by zone and year. The second step is to subtract this median price from the original price series. 

The median is preferable to the mean because the median is less responsive to price spikes than the mean. 

29 We used a sample of three months of daily constraint data from ERCOT’s Daily Grid Operating Report, which 

contains information on system alerts and constraints, and tested whether the information in the reports “explained” 

the price spikes. We found that the coefficients of the grid operating report variables were statistically insignificant. 30 Ideally, we would use the daily natural gas price at the Houston ship channel, but we do not have access to this 

price series.

31 The results of other ARMAX estimations are excluded in the interest of brevity. 
19

at night than it does during the day by including “night-wind” and “day-wind” variables. Night-wind is 

defined as wind that is generated before 8:00 am and after 7:00 pm. Day-wind is defined as wind that is 

dispatched after 8:00 am and before 7:00 pm. The number of Autoregressive (AR) and Moving Average 

(MA) terms in each model are included in the last two columns of Table 6. See Appendix B for 

definitions of the AR and MA terms. 

Table 6 - ARMAX Model Specifications

Dependent 

Variable

Independent variables AR 

terms

MA 

terms

Model 1 adjusted price night-wind, day-wind, temperature, constant 1-2 1-4 

Model 2 adjusted price night-wind, day-wind, temperature, natural-gas, constant 1-2 1-3 

Model 3 adjusted price night-wind, day-wind, temperature, natural-gas, constant 1 1-3 

Model 4 adjusted price night-wind, day-wind, temperature, natural-gas, constant 1 1-3 

Model 5 adjusted price night-wind, day-wind temperature, natural-gas, constant 1-2 1-5 

Model 6 adjusted price wind-generation, temperature, natural-gas, constant 1-2 1-4 

Model 7 D.adjusted price D.night-wind, D.day-wind, D.natural-gas 1 1-3 

Model 8 adjusted price night-wind, day-wind, natural-gas, temperature, constant 1, 24 1-2 

Notes: A “-“ indicates that all intermediate AR/MA terms were included while a ,”” indicates that no intermediate AR/MA terms were 

included. The prefix “D.” refers to the first difference. Since Model 7 uses first differences, it is referred to as an ARIMAX model.

Estimation Results

The estimation results of the ARMAX models in Table 6 are presented in Table 7.

32 All of the results are 

statistically significant, the AR terms suggest stationarity, and the ARMAX errors are free of serial 

dependence.33 The models were selected by examining the Akaike and Bayesian information criteria, a 

typical selection process.34 Five of the 12 zone-year models produce inconclusive results because the 

ARMAX errors were not stationary. 

2007 2008 2009

Model Day

($)

Night

($)

Model Day

($)

Night

($) 

Model Day

($)

Night

($)

Houston 1 -0.0071* -.0069*

North 2 -0.00067* -.0040* 7 -0.0042* -0.0029* 1 -0.0035* -0.0021*

South 2 -0.0057* -.0034*

West 2 -0.0118* -.0094* 3 -0.0164* -0.0150*

The coefficients represent an estimate of how the balancing-energy price in ($/MWh) zone changes when wind generation increases by 1 MWh.

*Coefficient is statistically different to zero at the 5% level.

 

32 Contact the authors for the full set of ARMAX estimation results. 33 We performed Portmanteau and Bartlett tests on the ARMAX errors and Wald tests on the AR terms. 34 Rafał Weron, Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach, (John Wiley & 

Sons, Ltd, January 2007).

Table 7 - ARMAX Model Coefficients on Wind Generation
20

Focusing on the conclusive results, the ARMAX results show that wind does have a statistically significant 

impact on the balancing-energy market price in ERCOT. The coefficients on day-wind and night-wind 

represent how the zonal balancing-energy price changes when an additional MWh of wind is dispatched in a 

given hour. Consider, the 2007 day-wind coefficient for the Houston Zone, which is -0.0071. This 

coefficient estimate suggests that if wind generation in ERCOT is increased by 1 MWh between 7:00 pm 

and 8:00 am, the price in the Houston zone would decrease by $0.0071/MWh, or 0.71¢/MWh. Provided

system conditions don’t change drastically, a 10 MW increase in wind generation will decrease the price in 

the Houston zone by 7.1¢/MWh, on average. We caution the reader against extrapolating these results 

beyond a marginal increase in wind generation, as the model results would be invalid. 

A consistent pattern exists between the day-wind and night-wind variables in each zone and year because 

the coefficients on wind generation during the day (day-wind) are “more negative” than the coefficients of 

wind generation at night (night-wind). Wind generation has a stronger (i.e., more negative) effect on the 

balancing-energy price during the day than it does at night. The night-day differential is consistent with 

EWEA’s literature review of the merit order effect in Europe.35 This result is largely because the slope of 

the marginal cost curve, which the QSE balancing-energy market offer curve should mimic, is steeper 

during the day than it is at night. However, the magnitudes of this study are much lower because the studies 

reviewed by EWEA estimated the entire merit order effect (i.e., the total price effect of all of the wind 

dispatched in a given hour), while this research only estimates a marginal effect of one additional MWh of 

wind. The majority of the studies that the EWEA report reviewed also were based on production cost 

simulations, not econometrics, so they estimated the full merit-order effect rather than the marginal effect. 

As shown in Table 7, wind generation has the greatest effect on balancing-energy prices in the West zone, 

where the majority of the wind capacity is located. The coefficients on night-wind and day-wind are also 

higher in 2008 compared to 2007, which is likely due to increased installed wind capacity. The estimates 

in Table 7 are incomplete because it is difficult to remove the daily and weekly pattern from balancingenergy prices and make them stationary without significantly transforming the price series. The ARMAX 

model isn’t valid unless the dependent variable is stationary. It is possible to filter and/or transform the 

balancing-energy prices to make them stationary through methods such as the Fourier or wavelet 

transforms, but interpreting the wind coefficient becomes more difficult and the results may vary 

depending upon the transformation used. 

 

35 Pöyry, “Wind Energy and Electricity Prices: Exploring the ‘Merit Order Effect’,” Literature Review for the 

European Wind Energy Association, (April 2010), 

http://www.ewea.org/fileadmin/ewea_documents/documents/publications/reports/MeritOrder.pdf. 
21

Frequently, researchers overcome this problem by analyzing the price of a specific hour each day

(e.g., the price in hour 10 for each day in 2007), as this series is often easier to make stationary. Given 

the missing ARMAX estimations in Table 7, we also employed this hour-by-hour method, analyzing the 

price data separately for each hour in the day. This second group of estimates can also serve as a check 

of the reasonableness and magnitude of the estimates in Table 7. 

We developed a second set of hour-by-hour ARMAX models that examine the zonal balancing-energy 

prices in each hour separately (i.e., one estimation examines only hour 10, another only hour 11, etc). 

The hour-by-hour strategy produces 288 separate estimates of the wind coefficient (24 hours x 4 zones x 

3 years = 288 estimates). Multiple ARMAX specifications were estimated on the hour-by-hour 

balancing-energy price series and the most successful is presented here. The zonal balancing-energy 

price (unadjusted) was estimated to be a function of wind generation, natural gas generation, and three 

autoregressive terms (AR1, AR2, and AR3). The hour-by-hour ARMAX estimates for the North and 

South zones are presented in Table B1 of Appendix B and all of the estimates shown have errors free of 

serial dependence (i.e., white noise errors). The hour-by-hour coefficients have a similar magnitude to 

the ARMAX models on the full time series in Table 7. 

Very few of the hour-by-hour estimates on wind generation in the North and South zones are statistically 

significant, particularly in 2008. This does not mean that wind did not have an effect on price. Rather, it 

means that this particular specification, which only views each hour in isolation and ignores the effect of 

the price in nearby hours, does not estimate one. The hour-by-hour models also provide a check of the 

reasonableness of the full time series mode estimates in Table 7. 

Table B2 in Appendix B contains the hour-by-hour estimates for the Houston and West zones. Wind 

generation generally has a statistically significant impact on balancing-energy prices in the West zone. 

That effect also tends to be stronger during the day than at night. Additionally, the coefficients on wind 

generation tend to be higher in 2008 compared to 2007 and 2009, which is consistent with the estimates in

Table 7. Like the North and South zones, the marginal effect of wind is largely statistically insignificant 

in the hour-by-hour ARMAX models of the Houston zone balancing-energy price. 
22

Conclusion

Our econometric analysis suggests that wind generation has a small but measurable impact on balancingenergy prices in ERCOT. We also found that the marginal effect of an additional MWh of wind 

generation is greater during the day because the slope of the supply curve is steeper during the day than it 

is at night. The results presented in this paper differ from estimates of the merit order effect in Europe 

because those studies used production cost simulation models to estimate the entire merit-order effect, 

while this study only estimates the marginal merit-order effect. However, these results contain interesting 

information about the relationship between wind generation and the balancing-energy market price in

ERCOT, and how it varies across the time of day and ERCOT’s four zones. 
A1 

Appendix A – Additional Figures and Graphs

Figure A1 - ERCOT Zones

Source: FERC, “Electric Power Markets: Texas (ERCOT),” Texas (ERCOT) Electric Regions, 

http://www.ferc.gov/market-oversight/mkt- electric/texas.asp

Figure A2 - 2007 ERCOT Balancing-Energy Market Price Percentiles by Zone

-50

0

50

100

150

200

$/MWh

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

10th pctile 25th pctile 50th pctile 75th pctile 90th pctile

North Zone Price Percentiles - 2007

-50

0

50

100

150

200

$/MWh

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

10th pctile 25th pctile 50th pctile 75th pctile 90th pctile

South Zone Price Percentiles - 2007

-50

0

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100

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200

$/MWh

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

10th pctile 25th pctile 50th pctile 75th pctile 90th pctile

Houston Zone Price Percentiles - 2007

-50

0

50

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150

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$/MWh

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

10th pctile 25th pctile 50th pctile 75th pctile 90th pctile

West Zone Price Percentiles - 2007
A2 

Figure A3 - 2008 ERCOT Balancing-Energy Market Price Percentiles by Zone

-50

0

50

100

150

200

$/MWh

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

10th pctile 25th pctile 50th pctile 75th pctile 90th pctile

North Zone Price Percentiles - 2008

-50

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200

$/MWh

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

10th pctile 25th pctile 50th pctile 75th pctile 90th pctile

South Zone Price Percentiles - 2008

-50

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$/MWh

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

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Houston Zone Price Percentiles - 2008

-50

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$/MWh

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

10th pctile 25th pctile 50th pctile 75th pctile 90th pctile

West Zone Price Percentiles - 2008
A3 

Figure A4 - 2009 ERCOT Balancing-Energy Market Price Percentiles by Zone

-50

0

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100

150

200

$/MWh

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

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North Zone Price Percentiles - 2009

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$/MWh

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

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South Zone Price Percentiles - 2009

-50

0

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100

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$/MWh

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

10th pctile 25th pctile 50th pctile 75th pctile 90th pctile

Houston Zone Price Percentiles - 2009

-50

0

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$/MWh

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

10th pctile 25th pctile 50th pctile 75th pctile 90th pctile

West Zone Price Percentiles - 2009
B1 

Appendix B – The ARIMA Model 

When examining time-series data, such as the hourly zonal balancing-energy prices in ERCOT, it is 

reasonable to expect that a given observation at time t is related to and/or affected by observations of that 

variable in previous time periods (e.g., time period t-1). Ordinary least-squares regressions are 

inappropriate in such cases because they assume that the errors are independent over time. Researchers 

frequently use the ARIMA model to model time-series data with serial dependence in the errors. The 

ARIMA model is a blend of the moving average and autoregressive models so it allows for a very general 

form of serial dependence. 

Moving average model

The moving average model posits that the dependent variable is a function of lagged values of the error 

term, known as “MA” terms. With a simple moving average model MA, one term is defined as follows: 

ݕ௧ ൌ ߤ ൅ ߳ݐ െ ߠଵ߳௧ିଵ where ߠଵ is the first moving average or MA (1) term. Higher order MA terms are 

the coefficients on the higher order lags of ߳௧. 

Autoregressive model

The autoregressive model assumes that the dependent variable yt depends on previous, or “lagged,” values 

of yt itself, and the effect is captured by “AR” terms. A first-order autoregressive model is as follows: 

ݕ௧ ൌߤ൅ߩଵݕ௧ିଵ ൅ ߳௧ where ߩଵ is the first order autoregressive, or AR(1), term. Higher order AR terms 

are the coefficients on the higher order lags of yt. 

ARMA and ARMAX models

The ARMA model incorporates both AR and MA terms. In the ARMA(p,q) model, the dependent 

variable yt is a function of p autoregressive terms and q moving average terms.36 ARMA(p,q) models 

have the following general specification: 

 ݕ௧ ൌߤ൅ߩଵݕ௧ିଵ ൅ ߩଶݕ௧ିଶ ൅ڮ൅ߩ௣ݕ௧ି௣ ൅ ߳௧ െ ߠଵ߳௧ିଵ െڮെߠ௤߳௧ି௤

The ARMAX model is an ARMA model that includes exogenous variables. ARMA and ARMAX 

models that also apply differences to the dependent variable are referred to as Autoregressive Integrated 

Moving Average (“ARIMA”) and ARIMAX models, respectively. After selecting the ARMAX 

specifications in this study, both the Bartlett and Portmanteau tests were performed on the errors to 

confirm that the ARMAX errors had the properties of white noise. Once an ARMAX specification with 

 

36 William Greene, Econometric Analysis, 4th ed. (Upper Saddle River, NJ: Prentice-Hall, Inc., 2000). 
B2 

“white noise” errors was found, we performed a Wald test to ensure that the AR coefficients were 

consistent with those of a stationary time series. The last step was to run sensitivities on the ARMAX

specification and select a final model. The Akaike and Bayesian information criteria were used to select 

between competing ARMAX models that had white noise errors.

37 

North South

Hour 2007 2008 2009 2007 2008 2009

0 0.0008 0.0019

1

2

3

4 -0.0064* -0.0063*

5 -0.0061* -0.0012 -0.0006 -0.0064* 0.0001 -0.0009

6 -0.0019 0.0041 -0.0018 0.0052 -0.0001

7 -0.0004 0.0018

8 -0.0030* 0.0017 -0.0025* 0.0039

9 -0.0026 -0.0024 -0.0027 0.0015 -0.0026

10 -0.0040* -0.0046 -0.0035* -0.0036*

11 -0.0035* 0.0000 -0.0027* -0.0027 0.0035 -0.0024

12 -0.0045 -0.0027 -0.0033

13 -0.0060 -0.0011 -0.0036 0.0033

14 -0.0038 -0.0009 0.0050 -0.0025

15 0.0016 -0.0020 0.0026 0.0181 0.0015

16 -0.0069 0.0041 -0.0017 -0.0065

17 -0.0105 -0.0013 -0.0035 -0.0079 0.0119 0.0004

18 -0.0101 -0.0031 -0.0039* 0.0048 -0.0053

19 -0.0097

20 -0.0029† -0.0034 -0.0004

21 -0.0014 -0.0020* 0.0007 -0.0023*

22 -0.0030 -0.0006 -0.0002 -0.0013 -0.0006

23 -0.0020 -0.0031* -0.0020

* Statistically significant at 5%

†Statistically significant at 10%

 Blank – inclusive estimate

 

37 Rafał Weron, Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach, (John Wiley & 

Sons, Ltd, January 2007).

Table B1 - Hour-by-Hour ARMAX Models Coefficient

on Wind Generation
B3 

Houston West

Hour 2007 2008 2009 2007 2008 2009

0 0.0110 0.0010 -0.0089* -0.0171* -0.0107

1 -0.0073* -0.0174* -0.0056*

2 -0.0083* -0.0049*

3 -0.0121* -0.0052*

4 -0.0062* -0.0105* -0.0154* -0.0056*

5 0.0005 -0.0008 -0.0149 -0.0158*

6 -0.0018 0.0038 -0.0051 -0.0127*

7 0.0005 -0.0079*

8 -0.0022* 0.0035 -0.0039*

9 -0.0017 -0.0025† -0.0048*

10 -0.0036* -0.0054* -0.0243* -0.0062*

11 -0.0022 -0.0100* -0.0171* -0.0055*

12 -0.0028 -0.0025 -0.0142* -0.0175* -0.0049*

13 -0.0023 0.0055 -0.0109 -0.0045*

14 0.0040 -0.0027 -0.0115 -0.0230 -0.0037*

15 0.0027 0.0091 -0.0070 -0.0193*

16 0.0147 -0.0007 -0.0142 -0.0195 -0.0046

17 -0.0074 0.0095 -0.0023 -0.0135 -0.0183 -0.0069

18 -0.0081 -0.0046* -0.0199* -0.0192* -0.0074*

19 -0.0059 -0.0195* -0.0132

20 -0.0011 -0.0086

21 0.0003 -0.0021* -0.0090* -0.0155* -0.0062*

22 -0.0005 -0.0004 -0.0066* -0.0167* -0.0066*

23 -0.0011 -0.0034* -0.0017 -0.0060* -0.0252* -0.0081*

* Statistically significant at 5%

†Statistically significant at 10%

 Blank – inclusive estimate

Table B2 - ARMAX Model by Hour – Coefficient 

on Wind Generation
F1146-E(10/2008)

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Subcontract Report

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4. TITLE AND SUBTITLE

The Relationship between Wind Generation and Balancing-Energy 

Market Prices in ERCOT: 2007-2009

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DE-AC36-08-GO28308

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E. Nicholson, J. Rogers, and K. Porter

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NREL/SR-5500-49415

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WE10.4221

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This paper attempts to measure the average marginal effects of wind generation on the balancing-energy market 

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Grid; integration; Texas; generation; capacity; markets; electricity; congestion; 

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