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

Advanced Unit Commitment 

Strategies in the United States 

Eastern Interconnection

Peter Meibom and Helge V. Larsen

RISØ DTU – Technical University of Denmark

Roskilde, Denmark

Rüdiger Barth and Heike Brand

University of Stuttgart

Stuttgart, Germany

Aidan Tuohy

ECAR

Dublin, Ireland

Erik Ela

National Renewable Energy Laboratory

Golden, Colorado

Subcontract Report

NREL/SR-5500-49988

August 2011
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

Advanced Unit Commitment 

Strategies in the United States 

Eastern Interconnection

Peter Meibom and Helge V. Larsen

RISØ DTU – Technical University of Denmark

Roskilde, Denmark

Rüdiger Barth and Heike Brand

University of Stuttgart

Stuttgart, Germany

Aidan Tuohy

ECAR

Dublin, Ireland

Erik Ela

National Renewable Energy Laboratory

Golden, Colorado

NREL Technical Monitor: Erik Ela

Prepared under Subcontract No. AFW-0-99426-01

Subcontract Report

NREL/SR-5500-49988

August 2011
This publication received minimal editorial review at NREL.

NOTICE

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iii

Acknowledgements

The team gives great thanks to Charlton Clark and Stan Calvert of the Department of Energy for their 

support of this work. This work was supported under the Wind and Water Power Technologies Program 

under the DOE Office of Energy Efficiency and Renewable Energy. For their careful review of this 

document, technical review of the study, data validation, and general support, the authors wish to thank 

the following people: Michael Milligan, Bri-Mathias Hodge, Greg Brinkman, and Dave Corbus of NREL; 

Lynn Hecker and Brandon Heath of the Midwest ISO; Matt Schuerger of Energy Systems Consulting 

Services; Charlie Smith of UWIG; Bob Zavadil of Enernex; Jack King of RePPAE; Gary Moland and 

Richard Hunt of Ventyx; Alan Mullane of ECAR; and Mark O’Malley of University College Dublin. The 

team also would like to thank Bruce Green for his editorial support.
iv

Table of Contents

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

1.1. Background................................................................................................................................... 1

1.2. Methodology Overview.............................................................................................................. 3

1.2.1. The Scenario Tree Tool.................................................................................................. 4

1.2.2. The Scheduling Model ................................................................................................... 6

1.3. Data and Data Preparation.......................................................................................................... 9

1.3.1. Measured Wind Feed in and Load Data....................................................................... 9

1.3.2. Forecast Data for Wind Speed and Load ................................................................... 10

1.3.3. Generation and Interconnection .................................................................................. 12

1.3.4. Reserve Requirements.................................................................................................. 12

2. Scenario Tree Tool Results and Analysis ....................................................................................... 14

2.1. Wind Power Forecasts .............................................................................................................. 14

2.1.1. Regional Differences.................................................................................................... 14

2.1.2. Comparison of Different Years................................................................................... 16

2.1.3. Comparison of onshore and offshore ......................................................................... 19

2.2. Load Forecasts........................................................................................................................... 19

2.2.1. Regional Differences.................................................................................................... 20

2.2.2. Comparison of different years..................................................................................... 22

2.3. Forecasts of Net Load ............................................................................................................... 24

2.3.1. Regional Differences.................................................................................................... 25

2.3.2. Inter-annual comparison............................................................................................... 26

2.4. Replacement Reserves.............................................................................................................. 29

2.5. Conclusions................................................................................................................................ 30

3. Scheduling Model Results................................................................................................................. 31

3.1. Costs ......................................................................................................................................... 31

3.2. Production................................................................................................................................... 35

3.3. Reserve........................................................................................................................................ 40

3.4. Wind Curtailment ...................................................................................................................... 49

3.5. Prices ......................................................................................................................................... 51

3.6. Interchange ................................................................................................................................. 52

3.7. Conclusions from Scheduling Model Results........................................................................ 54

4. Coal as a Must-Run Sensitivity ........................................................................................................ 55

5. Conclusions......................................................................................................................................... 58

5.1. Key Findings and Issues........................................................................................................... 58

5.2. Further Work and Improvements............................................................................................ 60

6. References ......................................................................................................................................... 62
v

List of Figures

FIGURE 1: STUDY FOOTPRINT...........................................................................................................................3

FIGURE 2: OVERVIEW OF WILMAR PLANNING TOOL..........................................................................................4

FIGURE 3: CONSIDERED WIND POWER CURVES. ................................................................................................5

FIGURE 4: ILLUSTRATION OF THE ROLLING PLANNING AND THE DECISION STRUCTURE IN EACH PLANNING PERIOD..8

FIGURE 5: STANDARD DEVIATION OF WIND SPEED FORECAST ERROR DEPENDANT ON FORECAST HORIZON GIVEN IN 

M/S. ......................................................................................................................................................10

FIGURE 6: STANDARD DEVIATION OF LOAD FORECAST ERROR DEPENDANT ON FORECAST HORIZON GIVEN IN MW.

............................................................................................................................................................11

FIGURE 7: STANDARD DEVIATION OF THE LOAD FORECAST ERROR IN RELATION TO THE PEAK LOAD DEPENDANT ON 

FORECAST HORIZON. .............................................................................................................................12

FIGURE 8: EXEMPLARY DAY-AHEAD FORECAST SCENARIO TREE OF THE WIND POWER FORECAST FOR THE PJM

REGION GIVEN IN MW. ...........................................................................................................................14

FIGURE 9: RELATIVE FREQUENCY OF THE RELATIVE FORECAST ERROR OF WIND POWER PRODUCTION BASED ON 

THE INPUT DATA FOR THE YEAR 2004 IN ALL MARKET REGIONS.................................................................15

FIGURE 10: RELATIVE FREQUENCY OF THE RELATIVE FORECAST ERROR OF WIND POWER PRODUCTION BASED ON 

THE INPUT DATA FOR THE YEAR 2004 IN SELECTED MARKET REGIONS.......................................................16

FIGURE 11: RELATIVE FREQUENCY OF THE RELATIVE FORECAST ERROR OF WIND POWER PRODUCTION FOR THE

DIFFERENT BASE YEARS IN THE NY_ISO REGION. ...................................................................................17

FIGURE 12: RELATIVE FREQUENCY OF THE RELATIVE FORECAST ERROR OF WIND POWER PRODUCTION FOR THE

DIFFERENT BASE YEARS IN THE PJM REGION. .........................................................................................17

FIGURE 13: RELATIVE FREQUENCY OF THE RELATIVE FORECAST ERROR OF WIND POWER PRODUCTION FOR THE

DIFFERENT BASE YEARS IN THE SPP_CENTRAL REGION. .........................................................................18

FIGURE 14: RELATIVE FREQUENCY OF THE RELATIVE FORECAST ERROR OF WIND POWER PRODUCTION FOR THE 

DIFFERENT BASE YEARS IN THE TVA REGION...........................................................................................18

FIGURE 15: EXEMPLARY DAY-AHEAD FORECAST SCENARIO TREE OF THE LOAD FORECAST FOR THE PJM REGION 

GIVEN IN MW. .......................................................................................................................................19

FIGURE 16: RELATIVE FREQUENCY OF THE RELATIVE FORECAST ERROR OF LOAD BASED ON THE INPUT DATA OF 

THE YEAR 2004 IN ALL MARKET REGIONS. ...............................................................................................20

FIGURE 17: RELATIVE FREQUENCY OF THE RELATIVE FORECAST ERROR OF LOAD BASED ON THE INPUT DATA OF 

THE YEAR 2004 IN SELECTED MARKET REGIONS. .....................................................................................21

FIGURE 18: THE FREQUENCY DISTRIBUTION OF THE RELATIVE FORECAST ERROR FOR MAPP REGION................22

FIGURE 19: THE FREQUENCY DISTRIBUTION OF THE RELATIVE FORECAST ERROR FOR TVA REGION...................23

FIGURE 20: THE FREQUENCY DISTRIBUTION OF THE RELATIVE FORECAST ERROR FOR PJM REGION...................23

FIGURE 21: THE FREQUENCY DISTRIBUTION OF THE RELATIVE FORECAST ERROR FOR MISO_CENTRAL REGION.

............................................................................................................................................................24

FIGURE 22: EXEMPLARY DAY-AHEAD FORECAST SCENARIO TREE OF NET LOAD FOR THE PJM MARKET REGION..25

FIGURE 23: RELATIVE FREQUENCY OF THE RELATIVE FORECAST ERROR OF NET LOAD BASED ON THE INPUT DATA 

OF THE YEAR 2004 IN ALL MARKET REGIONS............................................................................................26

FIGURE 24: RELATIVE FREQUENCY OF THE RELATIVE FORECAST ERROR OF THE NET LOAD FOR THE DIFFERENT 

BASE YEARS IN THE PJM REGION. ..........................................................................................................27

FIGURE 25: RELATIVE FREQUENCY OF THE RELATIVE FORECAST ERROR OF THE NET LOAD FOR THE DIFFERENT 

BASE YEARS IN THE TVA REGION............................................................................................................27

FIGURE 26: RELATIVE FREQUENCY OF THE RELATIVE FORECAST ERROR OF THE NET LOAD FOR THE DIFFERENT 

BASE YEARS IN THE SPP_CENTRAL REGION. ..........................................................................................28

FIGURE 27: RELATIVE FREQUENCY OF THE RELATIVE FORECAST ERROR OF THE NET LOAD FOR THE DIFFERENT 

BASE YEARS IN THE MAPP REGION. .......................................................................................................28

FIGURE 28: AVERAGE DEMAND FOR REPLACEMENT RESERVES DEPENDANT ON THE FORECAST HORIZON FOR THE

INDIVIDUAL MARKET REGIONS FOR THE YEAR 2004 GIVEN IN MW. ............................................................30

FIGURE 29: PRODUCTION COSTS FOR EACH YEAR. ..........................................................................................31

FIGURE 30: PRODUCTION COSTS BY UNIT COMMITMENT STRATEGY BASED ON 2006 INPUT DATA........................32

FIGURE 31: PERCENT COST INCREASE OVER PERFECT FORECASTS BY UNIT COMMITMENT STRATEGY BASED ON 

2006 INPUT DATA. .................................................................................................................................33

FIGURE 32: PRODUCTION COSTS BY REGION, 2006.........................................................................................34

FIGURE 33: PRODUCTION BY GAS AND COAL FOR ALL YEARS............................................................................37
vi

FIGURE 34: CONTINGENCY RESERVE CARRIED ONLINE BY REGION, 2006 DATA. ................................................41

FIGURE 35: ONLINE CONTINGENCY RESERVE BY UNIT TYPE, 2006 DATA. ..........................................................42

FIGURE 36: CONTINGENCY RESERVE CARRIED BY OFFLINE UNITS, 2006 DATA, BY REGION. ...............................43

FIGURE 37: CONTINGENCY RESERVE CARRIED OFFLINE, BY UNIT TYPE. ............................................................44

FIGURE 38: FREQUENCY REGULATION RESERVE BY REGION, 2006 DATA..........................................................45

FIGURE 39: FREQUENCY REGULATION RESERVE BY UNIT TYPE, 2006 DATA. .....................................................46

FIGURE 40: REPLACEMENT RESERVE FROM ONLINE UNITS...............................................................................47

FIGURE 41: ONLINE REPLACEMENT RESERVE PROVISION BY UNIT TYPE, 2006 DATA. ........................................48

FIGURE 42: OFFLINE REPLACEMENT RESERVE PROVISION BY REGION, 2006 DATA. ...........................................48

FIGURE 43: REPLACEMENT RESERVE CARRIED BY OFFLINE UNITS, BY UNIT TYPE, 2006 DATA. ...........................49

FIGURE 44: CURTAILMENT BY YEAR................................................................................................................50

FIGURE 45: CURTAILMENT BY REGION, 2006 DATA..........................................................................................50

FIGURE 46: INTRA-DAY PRICES, 2006 DATA. ...................................................................................................51

FIGURE 47: EXPORTS FOR REGION, 2006 DATA. .............................................................................................52

FIGURE 48: IMPORTS BY REGION, 2006 DATA..................................................................................................53

FIGURE 49: NET IMPORTS BY REGION, 2006 DATA...........................................................................................54

FIGURE 50: PRODUCTION COSTS FOR DIFFERENT METHODS, COAL NOT MUST-RUN AND MUST-RUN RESULTS, 2006

DATA.....................................................................................................................................................55

FIGURE 51: PRODUCTION FROM UNIT TYPE FOR COAL MUST-RUN (MR) AND NOT-MUST-RUN (NMR)..................56

FIGURE 52: CURTAILMENT OF WIND ENERGY WITH AND WITHOUT COAL AS MUST-RUN........................................57

FIGURE 53: ILLUSTRATION OF NEW LOOPING STRUCTURE ALLOWING FOR INCLUSION OF UNCERTAINTY IN THE FIRST 

OPERATION HOURS IN EACH PLANNING LOOP. THE ILLUSTRATION SHOWS ROLLING PLANNING STEPPING 

FORWARD IN TIME IN 6-HOUR STEPS. ......................................................................................................60

List of Tables

TABLE I: WIND CAPACITY AND ENERGY BY REGION.............................................................................................3

TABLE II: COSTS BY YEAR AND UNIT COMMITMENT METHOD..............................................................................32

TABLE III: CHANGE IN PRODUCTION COSTS AS A PERCENTAGE OF PFC COSTS..................................................32

TABLE IV: PRODUCTION COSTS BY REGION, 2006 DATA...................................................................................35

TABLE V: TOTAL PRODUCTION BY FUEL TYPE, IN TWH. ....................................................................................36

TABLE VI: PRODUCTION BY FUEL TYPE, 2006 DATA, BY REGION, IN TWH..........................................................38

TABLE VII: PRODUCTION BY FUEL TYPE, TWH, 2006 DATA, BY REGION (CTD) ...................................................39

TABLE VIII: DATA FOR COST DIFFERENCES IN COAL MUST-RUN AND COAL NOT-MUST-RUN, 2006 DATA...............56
1

1.

1.1.BACKGROUND

INTRODUCTION

During recent years, there has been tremendous growth in the amount of wind power generation in 

numerous countries. This growth is likely to continue. Wind power offers a non-polluting source of 

energy with non-volatile fuel costs. However, because of its dependence on the wind resource, it can 

create difficulties for utilities and system operators when managing the balance between generation and 

load. Wind power cannot be predicted with great accuracy and therefore system operators must plan their 

system with consideration of this uncertainty. This has always been true in power systems since 

generating resources and transmission components can fail at any time unexpectedly, and the system 

demand cannot be predicted with perfect accuracy. System operators will perform a unit commitment, 

which will determine the least cost solution of what generators need to be online to meet the expected 

demand. These are usually performed in advance of the operating day, and in today’s systems are 

generally performed one day prior to the operating day. The unit commitment performed in today’s 

systems is also usually deterministic in nature, and will represent uncertain (or stochastic) variables with 

their expected value. Operating reserve is also scheduled by the unit commitment programs to ensure the 

system can respond to events such as generator or transmission line outages, or demand or variablegeneration forecast errors. This is carried by particular units which are withholding a portion of their 

capacity from providing energy (or are ramped down from their maximum output) so the system can 

balance supply and demand in the event of a generator or network failure or prediction error. 

Advanced unit commitment methods and strategies with high penetrations of wind power have been an 

ongoing research topic in recent years [1] - [5]. With the uncertainty present in wind power and wind 

power forecasts, it is important to plan the system to be robust and efficient towards meeting multiple 

uncertain potential outcomes. It is also important to make best use of wind power forecasts, realizing they 

generally improve in accuracy as time horizons become nearer and often before ultimate decisions have to 

be made. This project sought to evaluate the impacts of high wind penetrations on the U.S. Eastern 

Interconnection and analyze how different unit commitment strategies may affect these impacts.

In January 2010, the Eastern Wind Integration and Transmission Study (EWITS) was published [6]. The 

study evaluated the operating impacts for 20% and 30% wind power on the majority of the Eastern 

Interconnection. It also evaluated different scenarios of where the wind was located as well as different 

transmission plans. This follow-up study was intended to further the analysis performed in EWITS by 

focusing on the impacts of advanced unit commitment strategies used at high penetrations of wind power. 

It will point to both the effect that various assumptions about modeling unit commitment will have on 

integration studies, as well as the effect that the strategies will have on actual system operation with high 

wind power. Specifically, it evaluated the use of a stochastic unit commitment and the use of rolling 

planning for the Eastern Interconnection. The study used consistent data with EWITS where possible. 

Wind power and load forecasts were built using the scenario tree tool (STT) that calculated about one 

thousand scenarios of the wind and load outcomes for different time horizons ahead and for each planning 

loop. This was reduced using sophisticated scenario reduction techniques to have a reasonable number of 

probabilistic forecasts with different probabilities that could be run in the stochastic scheduling model 

(SM). The stochastic scheduling model would minimize the expected cost of energy, but ensure that all of 

the reduced set of scenarios could be met reliably. The forecasts were developed to represent a new 
2

update every few hours, all looking ahead up to the end of the day or end of the next day. The start-up 

times and other commitment constraints of units must be respected so that unit commitment must only be 

a binding decision if there is no more time to make an updated decision. In theory, the use of stochastic 

planning and frequent rolling updates to the planning and unit commitment could give great value over 

the traditional deterministic once-per-day unit commitment commonly performed today in the United 

States. By making the unit commitment to meet multiple scenarios of possible outcomes, it will more 

economically meet the demand on average in real-time. It ensures that costly corrections can be prevented 

when system conditions are far from the expected because the stochastic unit commitment also ensured 

those unlikely scenarios could be met reliably. Rolling planning also ensures that the unit startup is only 

required when the startup time, minimum run times, and minimum down times are binding and therefore, 

when not binding, their decision to turn on can wait until more accurate forecasts are available. This also 

increases the efficiency since the system startups would be based on better forecast information than if the 

unit commitment was restricted to day-ahead decisions only.

The objective was to use the WILMAR (Wind Power Integration in Liberalised Electricity Markets, 

http://www.wilmar.risoe.dk/) planning tool to evaluate each of these methods. Four model runs were used 

to reach this objective with the terms used in the rest of this paper in parentheses.

• Stochastic planning using scenario trees with six branches (six forecasts), unit commitment 

updated every 3 hours (STO).

• Stochastic planning, unit commitment for units with start times greater than 1 hour, updated once 

per day in the day-ahead market (UCDay)

• Deterministic planning with forecast error, and unit commitment updated every three hours 

(OTS). Only one wind power production and load forecast taken into account in each rolling 

planning period being equal to the expected wind power production and load in the scenario tree 

used in the stochastic model runs.

• Deterministic planning with perfect foresight (PFC) i.e. wind power and load forecasts 

corresponds to realized wind power and load.

The comparison of these four model runs, in terms of different operational results and costs, would give 

more insight into the consequences of using these unit commitment strategies with 20% wind for some or 

all of the eastern United States. By comparing STO with UCDay, impacts and benefits could be analyzed 

of rolling planning compared to keeping the unit commitment fixed in the day-ahead market. Comparing 

STO with OTS, the impacts and benefits could be analyzed of running the unit commitment model 

considering stochastic variables of wind and load with a deterministic unit commitment. The following 

results in this paper are derived using the EWITS scenario 2 wind placements and 2004, 2005, and 2006 

wind and load time series data. Figure 1 shows the study footprint and Table I gives wind feed-in energy 

by region. Note that the annual energy will differ slightly from year to year due to the inter-annual 

variability of capacity factors.
3

Figure 1: Study footprint.

Table I: Wind capacity and energy by region

Region Onshore (MW) Offshore (MW) Total (MW) Annual Energy 

(TWh)

ISO-NE 8,837 5,000 13,837 46

MISO+MAPP 69,444 0 69,444 288

NYISO 13,887 2,620 16,507 48

PJM 28,192 5,000 33,192 97

SERC 1,009 4,000 5,009 16

SPP 86,666 0 86,666 245

TVA 1,247 0 1,247 4

Total 209,282 16,620 225,902 745

1.2. METHODOLOGY OVERVIEW

The WILMAR Planning Tool is used to analyze the consequences of wind power on the Eastern 

Interconnection. The WILMAR Planning tool consists of a number of sub-models and databases as shown 

in Figure 2. The green cylinders are databases, the red parallelograms indicate exchange of information 

between sub models or databases, the blue squares are models. The user shell controlling the execution of 
4

the WILMAR Planning tool is shown in black. The main functionality of the WILMAR Planning tool is 

embedded in the Scenario Tree Tool (STT) and the Scheduling Model (SM).

Figure 2: Overview of WILMAR Planning tool. 

1.2.1. THE SCENARIO TREE TOOL

The STT generates stochastic scenario trees containing three input parameters to the SM: wind power 

production forecasts, load forecasts, and demand for replacement reserves. Replacement reserves are

positive reserves with activation times longer than 10 minutes and for forecast horizons from 1 hour to 36 

hours ahead. The main input data for the STT is wind speed and/or wind power production data, historical 

electricity demand data, assumptions about wind production and load forecast accuracies for different 

forecast horizons and regions. 

The STT consists of three modules. The first module generates a significant number of scenarios for wind 

power and load forecasts using the Monte-Carlo Method. Since the Scheduling Model can only handle a 

limited number of scenarios, a second module reduces the number of scenarios by applying a scenario 

reduction algorithm. The scenario reduction process will by construction remove extreme events from the 

reduced scenario trees. Therefore, the calculation of the replacement reserve demand by the third module 

enables the Scenario Tree Tool to quantify the effect that partly predictable wind power and load including 

the more rare extreme events has on the replacement reserve requirements for different forecast horizons. 
5

Module 1

Both for load and wind power forecasts errors, Monte-Carlo simulations taking into account the 

individual forecast error characteristics dependant on the forecast horizon are carried out. The generation 

of forecast scenarios for wind power is based on a simulation of wind speed forecast errors. The 

simulation has to account for the error distribution which varies with increasing forecast horizons. These 

Monte-Carlo simulations are based on Auto Regressive Moving Average (1, 1) (ARMA (1, 1) time-series 

models [9]. With this approach, it is possible to account for a) autocovariances of forecast errors and b) 

the increase of forecast errors depending on the forecast horizon. It is assumed that the distribution of 

wind speed errors follows a Gaussian distribution [10]. Further, spatial correlations of wind speed forecast 

errors as observed in the Eastern Interconnection are explicitly taken into account [11]. To generate wind 

power production and load scenarios, the sample paths of wind power and load forecasts errors are added 

to historical time-series data of respectively wind power production and load time-series data.

The simulation of wind power forecast errors is based on wind speed time series. If only wind power 

time- series data are available as metered data, these power series have to be initially transformed to speed 

series by the use of an appropriate power curve to simulate wind speed forecast errors. In a subsequent 

step, the generated wind speed forecast scenarios are converted to wind power forecast scenarios. 

Figure 3 shows different power curves available for this study. The figure shows a Class II wind site 

power curve for three different area densities. More information on the use of power curves and the 

general methodologies of the wind speed and power data creation can be found in Brower 2010 [12]. 

Figure 3: Considered wind power curves.

Many sample paths of the ARMA series, that are drawn randomly, represent many different possible 

outcomes of forecasting. So, for example, i sample paths (or scenarios) of wind and load forecast are 

derived. The scenarios of wind forecasts are aggregated with the load scenarios. It is not necessary to 

combine every wind scenario with every load scenario and to apply the scenario reduction module to i

2

scenarios in this example. It is sufficient to allocate one load scenario for each wind scenario in a random 

way and to apply the scenario reduction module to a large number of scenarios (e.g. i = 1000). 

Statistically, this leads to the same result.

0

0.3

0.6

0.9

0 5 10 15 20 25 30 35

Wind speed (m/s)

Percentage of Wind power capacity

class II - 1.1

class II - 1.16

class II - 1.18
6

Module 2

For each planning period, one thousand scenarios of forecasts are generated. Yet such a large number of 

forecast scenarios cannot be treated with the stochastic Scheduling Model due to computational 

limitations. Hence, the number of forecast scenarios is reduced by first determining the Euclidean 

distances between the individual forecast scenarios. One scenario of the scenario pair with the smallest 

Euclidean distance is deleted, and the sum of the probabilities of both scenarios is allocated to the 

remaining scenario. This procedure is repeated until a predefined number of scenarios is achieved. 

Afterwards, based on the remaining scenarios that still form a one-stage tree, a multi-stage scenario tree is 

constructed by deleting inner forecasts and creating branching within the scenario tree. A detailed 

discussion of the scenario tree reduction algorithm can be found in [13].

Module 3

The calculation of the replacement reserve demand by the Scenario Tree Tool enables the WILMAR

Planning tool to quantify the effect that partly predictable load and wind power production has on the 

replacement reserve requirements for different forecast horizons. The demand for replacement reserve 

corresponds to the 90th percentile of the total forecast error of load and wind power production for all 

unreduced scenarios being bundled into a reduced scenario tree. It is determined by summing up the 

forecast error of load and wind power production among the unreduced scenarios depending on the 

forecasted hour and generated scenario and comparing it with the expected (average over the forecasts)

load and wind in the forecasted hour. The individual demand for replacement reserves of one branch of 

the resulting tree thereby considers the forecast errors of all wind power and load scenarios that have been 

reduced to this branch. 

1.2.2. THE SCHEDULING MODEL

The Scheduling Model is a stochastic, optimization model with the demand for replacement reserves, 

wind power production forecasts, and load forecasts as the stochastic input parameters. The model 

evaluates optimal unit commitment and economic dispatch at hourly time-resolution. The model 

minimizes the expected value of the system production costs consisting of fuel costs, start-up costs, and 

variable operation and maintenance costs. The expectation of the system production costs is taken over all 

given scenarios of the stochastic input parameters. Thereby it has to optimize the operation of the whole 

power system without the knowledge of which one of the scenarios will be closest to the realization of the 

stochastic input parameter, for example the actual wind power generation. Hence, some of the decisions, 

notably start-ups of power plants, have to be made before the wind power production and load (and the 

associated demand for replacement reserve) is known with certainty. The methodology ensures that these 

unit commitment and dispatch decisions are robust towards different wind power prediction errors and 

load prediction errors as represented by the scenario tree for wind power production and load forecasts. 

The demand for positive reserves (both spinning reserves with activation times below 10 minutes and 

replacement reserves) determines, together with the expected values of load forecasts and wind power 
7

forecasts and the technical restrictions of power plants, the day-ahead unit commitment and day-ahead 

power exchange between regions planned for the next 36 hours. The realized load and wind power 

production, together with the technical restrictions of power plants, determine the actual dispatch of the 

power plants and the actual power exchange in the operating hour in question. Technical restrictions of 

power plants are minimum and maximum stable generation levels, minimum number of operation hours 

and off-line hours, start-up times, piece-wise linear fuel heat rate curves and ramp-up and ramp-down 

rates. For the consideration of large power systems comprising a large number of power plants, it is 

possible to introduce into the Scheduling Model a linear approximation of the unit commitment and to 

aggregate similar power plants (depending on type, used fuel, and vintage) to avoid the usage of integer 

variables thereby saving calculation time. Because of the large number of generating units in the Eastern 

Interconnection (over 7,000 units in all), this approach has been used in this study. This will have the 

effect of not being able to examine every unit individually, and therefore, some of the benefits which may 

be seen in stochastic unit commitment may not be as apparent here as if a full mixed integer approach was 

taken. As units will be aggregated, it may not be possible to show in as fine a detail how stochastic 

methods will produce a better commitment of certain units.

System reserve schedules are also given as an output of the Scheduling Model. Hence, the allocation of 

individual types of reserves over different power plants represents one of the optimization results. The 

model handles contingency reserves, positive and negative frequency regulation reserves (operating on 

automatic generation control), and replacement reserves. The main division between categories of 

positive reserves is between spinning reserves that can only be provided by synchronized (i.e., on-line) 

units due to the short activation times of these reserves, and reserves which can be provided by both 

synchronized and off-line units with short start-up times (e.g., combustion turbines). In this study, half of 

the contingency reserve and all of the frequency regulation reserve must be spinning. For each spinning 

reserve category the reserve capability of a unit is restricted by a maximum reserve capability computed 

by 10-minute ramp-rates and the online capacity minus the generation, whichever is less. Pumped hydro 

storage facilities can also provide contingency reserve when in the pumping mode, because it was decided 

that it can respond very quickly to system needs by discontinuing pumping and therefore, decreasing the 

load that it had been imposing on the system.

The transmission network is represented by splitting the geographical area modelled into a number of 

model regions, with each model region containing a number of production and storage units and having 

scenario trees of load forecasts, wind power production forecasts, and demand for replacement reserves. 

The model regions are connected by transmission lines described by a transmission capacity and an 

average loss. Exchanges between regions are modelled based on a simplified transmission flow model 

(i.e. pipeline flow) with maximum flow between regions determined by offline studies. The grid within 

each modelled region is only taken into account as an average transmission and distribution loss, which in 

this study is part of the electricity load time-series data.

As it is not possible and realistic to cover the whole simulated time period with only a single scenario 

tree, the model is formulated by introducing a multi-stage recursion using rolling planning. Therewith, the 

unit commitment and dispatch decisions and the planned power exchanges are re-optimized taking into 

account that more precise wind power production and load forecasts become available as the actual 

operation hour gets closer in time, and taking into account the temporal technical restrictions (e.g., startup times, minimum up and down times) of different types of power plants. The resulting production of 
8

each power plant and the changes in the production and power exchange relative to the day-ahead 

production and power exchange plan are calculated for each hour. 

In general, new information arrives on a continuous basis and provides updated information about wind 

power production and forecasts, the operational status of other production and storage units, and about the 

load. Thus, an hourly basis for updating information would be most adequate. However, stochastic 

optimization models quickly become intractable with increased time periods, thus, it is necessary to 

simplify the information arrival and decision structure in the Scheduling Model. In this study, a two-stage 

model is implemented. The model is able to step forward in time using rolling planning with a 3-hour 

step, so a one-day cycle consists of eight planning loops each modelling at hourly resolution (see Figure 

4). For each time step, new simulated forecasts (i.e., a new scenario tree) that consider the change in 

forecast horizons are applied. This decision structure is illustrated in Figure 4, showing the scenario tree 

for two planning periods. For each planning period, a two-stage, stochastic optimization problem is 

solved having a deterministic first stage covering 3 hours, and a stochastic second stage with six scenarios 

covering a variable number of hours according to the rolling planning period in question. Hence, the 

scenario tree represents a decision structure where the system operator performs unit commitment and 

dispatch assuming perfect knowledge about the realized wind and load in the first three hours, and 

uncertain knowledge about wind and load in subsequent hours. Every three hours, there is the possibility 

to change the planned unit commitment and dispatch and power exchange for future hours within the 

limits provided by start-up times, minimum run times, and minimum down times as a response to 

receiving updated information about the status of the power system as the operation hours in question get 

closer in time. The perfect foresight assumption for the first three hours is necessary for the model, but to 

get a realistic unit commitment, the wind and load forecast errors within the first three hours contribute to 

the demand for replacement reserves in these hours.

Figure 4: Illustration of the rolling planning and the decision structure in each planning period.

12 15 18 21 00 03 00

Rolling Planning Period 1: 

Day- ahead scheduling

Rolling Planning Period 2

Stage 1 Stage 2

Stage 2 Stage 1
9

The rolling planning proceeds as follows; Planning loop 1 starts at 12 noon on day one and covers the 36 

hours until the end of day two. The forecast horizons involved are up to 36 hours ahead. The day-ahead 

scheduling and power exchange is determined in Planning Period 1, as well as the realized unit 

commitment and dispatch, and power exchange for the first three hours in the planning loop, which 

happens after realization of the stochastic parameters. Furthermore, unit commitment, and dispatch, and 

power exchange plans are made which can cover each scenario for the individual outcome of wind power, 

load, and demand for replacement reserve while respecting unit commitment decisions. The probability of 

each scenario occurring is taken into account when considering commitment decisions.

In planning loops 2 through 8, the optimization period always ends at the end of day two, i.e., the forecast 

horizon of the optimization period is reduced with 3 hours in each planning loop (see Figure 4). Planning 

loops 5 to 8 will also start with day two, and therefore only optimize the schedules of the second day. 

Planning loops 2 to 8 take as a starting point the day-ahead dispatch schedules determined in planning 

loop 1 when rescheduling the unit commitment, dispatch, and power exchange decisions due to updated 

forecasts. The realized unit commitment, dispatch, and power exchange for the first three hours in each 

planning loop is calculated. Rescheduling plans are made for the total forecast horizon and covering each 

scenario of the individual outcome of the load minus wind. In planning loop 9, a new day-cycle starts now 

covering from 12 noon (day two) to the end of day 3. 

Further detailed information about the WILMAR Planning Tool can be found in [5], [8], [14]-[16].

1.3. DATA AND DATA PREPARATION

To keep results consistent, the same data was used for this study as in the EWITS project wherever 

possible. However, there are key differences in the data that are important to mention. The differences are 

necessary because the model used is different than the simulation model used for EWITS.

1.3.1. MEASURED WIND FEED IN AND LOAD DATA

The wind data was taken from the hourly time-series data developed by AWS-Truewind for the years 

2004 to 2006 [12]. Because the Scenario Tree Tool develops about one thousand scenarios for multiple 

forecasts of every hour of the entire year and each wind plant, it required some aggregation so that some 

plants were combined into larger plants. This did not negate any of the geographic diversity impacts in the 

data since the time series data were still added together from the modeled data. The forecast errors used as 

input in the STT considered the geographic diversity of the aggregated wind plants as well. The total 

number of “wind areas” was about 3 – 10 areas per each load region. These were separated mostly by 

geographic location in the region and by whether they were onshore or offshore. Once computed, this data 

was used as the realization of wind power in the scheduling model.

The hourly load data was gathered for use in EWITS and was also used in this study. There were 11 

market regions used (Figure 1): ISO New England, NY ISO, PJM, TVA, SERC, SPP North, SPP Central, 

MAPP, MISO East, MISO Central, and MISO West. Each had one load time-series dataset for the three 

years associated with it that was used as the realization of load demand in the Scheduling Model. 
10

1.3.2. FORECAST DATA FOR WIND SPEED AND LOAD

The forecast data was the key difference in input between this study and EWITS. Because probabilistic 

forecasts were used in the stochastic modeling, the deterministic forecasts from EWITS could not be used 

explicitly. Instead, the deterministic forecasts used in EWITS were analyzed so that the mean error and 

standard deviation were developed as a function of forecast time horizon. For wind speed, three 

deterministic forecasts were used in order to develop an accurate error function. These were a day-ahead 

forecast, a 4-hour-ahead forecast, and a 6-hour-ahead forecast. Interpolation was used to create the error 

calculations for all time horizons up to 36 hours ahead. The resulting standard deviation of wind speed 

forecast errors dependant on the forecast horizon for the individual wind areas are shown in Figure 5. 

Figure 5: Standard deviation of wind speed forecast error dependant on forecast horizon given in 

m/s.

For load, the day-ahead load forecast was used and representations of shorter time horizon errors were 

assumed based on short-term load forecast data available from various ISO websites. However, because 

the data for day-ahead load forecasts are produced at the same time every day, it was noticed that there 

was a higher dependence on the errors with the actual hour of day rather than the forecast time horizon. 

For instance, day-ahead load forecast statistics may show much larger errors at 20 hours ahead (forecast 

developed at noon day prior for 8 AM), then the errors at 36 hours ahead (forecast developed at noon day 

prior for midnight next day). This has much more to do with the fact that the load is more variable at 

8AM then at midnight and very little to do with the forecast time horizons. For the modeling using the 

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Forecast hour [h] 32 34 36

Wind speed [m/s]

MISO WEST 1 MISO WEST 2 MISO WEST 3 MISO WEST 4 MISO WEST 5

MAPP 1 MAPP 2 MAPP 3 ISO NE 1 ISO NE 2

ISO NE 3 ISO NE 4 ISO NE 7 NY ISO 1 NY ISO 2

NY ISO 3 NY ISO 4 PJM 1 PJM 2 PJM 3

PJM 4 PJM 5 SERC 1 SERC 2 SPP Central 1

SPP Central 2 SPP Central 4 SPP Central 5 TVA 1 TVA 2

MISO Central 2 MISO Central 3 MISO Central 4 MISO East 3 MISO East 4

SPP North 1 SPP North 2 SPP North 3
11

WILMAR tool, forecasts are updated every 3 hours as opposed to once per day, and so further analysis of 

the errors was needed for a better representation of the relationship between errors and forecast time 

horizon. Generally, errors should increase as forecast time horizons become greater. To alleviate this 

issue, the errors were smoothed out and manipulated so that the true error characteristics were still intact,

but more realistic values were integrated. The resulting standard deviation of absolute load forecast errors 

dependant on the forecast horizon for the individual market regions are shown in Figure 6.

Figure 6: Standard deviation of load forecast error dependant on forecast horizon given in MW.

Figure 7 shows the standard deviation divided by the peak load of each market region. Whereas the 

absolute forecast error in the region MAPP is the lowest, the forecast error in relation to the peak load is 

the largest in this region. The lowest relative load forecast errors are observed in the market regions of 

TVA and ISO-NE.

0

1000

2000

3000

4000

5000

6000

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 Forecast hour [h] 30 32 34 36

Standard deviation absolute load [MW]

MISO Central

MISO East

MISO West

MAPP 

ISO-NE 

NYISO 

PJM ISO 

SERC 

SPP Central

SPP North

TVA 
12

Figure 7: Standard deviation of the load forecast error in relation to the peak load dependant on 

forecast horizon. 

1.3.3. GENERATION AND INTERCONNECTION

Generation data was also taken from the same inputs as EWITS. Hydropower resources excluding 

pumped hydro storage were given schedules that were outputs of the EWITS analysis of the 

corresponding scenario and year.

Transmission between regions was represented as a transportation model and no intra-regional 

transmission was considered inside the eleven load zones. Monthly interface limits were given as a result 

of the analysis performed in EWITS. Canadian regions and the Entergy region were originally not part of 

the scope for this study, but for more realistic results, hourly tie-line schedules between these regions and 

the modeled regions from EWITS results were set constant in the scheduling model runs.

1.3.4. RESERVE REQUIREMENTS

Reserve requirements were also kept consistent with EWITS. Contingency reserves were consistent 

between each region with the three MISO regions and MAPP able to share with one another as one 

requirement as well as the two SPP regions. These contingency reserves were reserved strictly for 

contingency events. The demand for contingency reserves was 2250 MW per hour for ISO regions. The 

requirement was based on analysis done in EWITS where 2250 MW was decided to be the largest 

contingency in each region based on the transmission overlay and therefore, the losses of supply of large 

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31Forecast hour [h] 33 35 37

Standard deviation relative load [-]

MISO Central

MISO East

MISO West

MAPP 

ISO-NE 

NYISO 

PJM ISO 

SERC 

SPP Central

SPP North

TVA 
13

HVDC interconnections into the region.1

[6]

The forced outage rates of generators were not a part of the 

stochastic input. Frequency regulation reserves for variability and within-hour uncertainty were also used 

with generally the same requirements as EWITS. Frequency regulation reserves are used according to the 

North American Electric Reliability Corporation to reduce area control error and comply with the control 

performance standards. Frequency regulation reserves were fulfilled per region, but with the three MISO 

regions able to share with one another and the same for the two SPP regions. Frequency regulation 

reserve would be used by units with automatic generation control to correct for area control error within 

the dispatch scheduling intervals. These reserve requirements can be seen in detail in . The 

deterministic reserve requirements in EWITS used for hourly uncertainty were ignored in this study. 

Instead, replacement reserves were created as a stochastic input in the STT, and were used only to cover 

wind and load uncertainty issues. Consequently, for the model run with perfect foresight, the demand for 

replacement reserves is zero.

 

1 This requirement was since changed in the final EWITS report due to the idea of the large HVDC 

connections being self-contingent. However, the requirements were kept in this study and are very close to the 

requirements used in the EWITS report.
14

2.

2.1. WIND POWER FORECASTS

SCENARIO TREE TOOL RESULTS AND ANALYSIS

An example of the resulting scenario trees of wind power forecasts is shown in Figure 8. It gives one set 

of day-ahead forecast scenarios of the wind power production for the PJM market region. Each wind 

power scenario has a certain probability of occurrence. Since there is no knowledge of the realized wind 

power and which scenario will be the closest one to the realization during the day-ahead determination of 

the optimal unit commitment and dispatch, the expected values of the wind power forecast shown by the 

blue line are taken into account. It is determined by the sum of all wind power forecast scenarios 

weighted with their individual probability. In subsequent loops, the forecast values are actualized. By the 

use of stochastic programming, the possible distribution of the forecast error is thereby represented by the 

set of these further forecast scenarios. Each of these scenarios has to be considered by the cost optimal 

unit commitment and dispatch. Whereas the deterministic treatment of forecast errors furthermore takes 

only into account the expected value and has no information of the possible distribution of the forecast 

error. Model analyses assuming forecasts with perfect foresight consider only the realized values; in this 

example, represented by the red line.

Figure 8: Exemplary day-ahead forecast scenario tree of the wind power forecast for the PJM

region given in MW.

2.1.1. REGIONAL DIFFERENCES

The forecast errors of wind power production simulated for the different market regions and years are 

analyzed based on the frequency of occurrence of the forecast error relative to the installed wind power 

0

5000

10000

15000

20000

25000

30000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Forecast hour [h] 31 33 35

Wind power production [MW] 

Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5

Scenario 6 Expected Value Realized Value
15

capacity. For the following analysis, only day-ahead scenario trees and the forecast horizon of 12-36 

hours ahead, that is, for the following day, were considered. In addition, no distinction is made between 

different forecast horizons. Figure 9 shows the frequency distribution of the forecast error in all market 

regions based on the wind power data of 2004. This illustration is comparable to a histogram, but with 

interpolation between individual bins of a histogram. The distribution of the relative forecast error varies 

between the different regions. These differences are due to the variation of the wind speed forecast error 

assumed for the different areas (see section 1.3.2), and the installed capacities of the wind power stations 

within these areas. 

Figure 9: Relative frequency of the relative forecast error of wind power production based on the 

input data for the year 2004 in all market regions.

In the PJM market region, the relative wind forecast error is very small compared to regions far from the 

coast, like TVA and SPP_Central. In these regions, wind power forecasting leads to higher relative 

forecast errors. For example, in the TVA region, large relative forecast errors are observed because the 

forecast error standard deviation in the single wind areas ( TVA1 and TVA2) are larger than in the wind 

areas of the PJM region (see section 1.3.2).

For a more detailed analysis, four regions have been selected. PJM was chosen because of its high relative 

frequency of small relative forecast errors of the wind power production. The region TVA was chosen 

because it is the region with the lowest relative frequency of small relative forecast errors. Additionally,

the two NY_ISO and SPP_Central regions were selected with a frequency of small forecast errors larger 

than in TVA, but lower than in PJM. 

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

MISO_Central

MISO_East 

MISO_West 

MAPP 

ISO_NE 

NY_ISO

PJM 

SERC 

SPP_Central 

SPP_North

TVA 
16

Figure 10: Relative frequency of the relative forecast error of wind power production based on the 

input data for the year 2004 in selected market regions.

The lines in Figure 10 show that for all four regions the most frequent values for forecast errors are near

zero. In the NY-ISO, PJM, and SPP_CENTRAL regions, extremely few relative forecast errors are 

higher than 0.4, which means that the forecast error is larger than 40% of the installed capacity during 

only a few hours (< 0.5%) of the year. In the TVA region, more frequently relative forecast errors above 

40% of the installed capacity are observed. This is very likely due to the very small amount of wind in the 

TVA region, with much less advantage due to geographic dispersion as the areas with higher penetrations 

would have.

2.1.2. COMPARISON OF DIFFERENT YEARS

As the basis for the generation of wind power forecast scenarios, historical wind power time-series data 

for the years 2004, 2005, and 2006 were used (see section 1.3.1). The dependency of the wind power 

forecast error on these different wind power time-series data are shown in Figure 11, Figure 12, Figure 

13, and Figure 14 for the NY_ISO, PJM, SPP_CENTRAL, and TVA regions, respectively. For all four 

regions under consideration, the impact of the different base years on the resulting wind power forecast 

errors is small. However, for the NY_ISO, PJM, and SPP_CENTRAL regions, the basis year 2004 led to 

smaller wind power forecast errors than the years 2005 and 2006. For the TVA region, the forecasts based 

on the basis year 2005 lead to smaller forecast errors than for the basis years 2004 and 2006. Considering 

these four market regions, it can be stated that there exists no considerable influence of the different bases 

years on the wind forecast error distribution. The differences in the frequency distribution of the relative 

forecast error of wind power production between the several regions are greater than between the 

different historical years for one region.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

NY_ISO

PJM 

SPP_Central 

TVA 
17

Figure 11: Relative frequency of the relative forecast error of wind power production for the 

different base years in the NY_ISO region.

Figure 12: Relative frequency of the relative forecast error of wind power production for the 

different base years in the PJM region.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

NY_ISO 2004

NY_ISO 2005

NY_ISO 2006

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

PJM 2004

PJM 2005

PJM 2006
18

Figure 13: Relative frequency of the relative forecast error of wind power production for the 

different base years in the SPP_Central region.

Figure 14: Relative frequency of the relative forecast error of wind power production for the 

different base years in the TVA region.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

SPP_Central 2004

SPP_Central 2005

SPP_Central 2006

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

TVA 2004

TVA 2005

TVA 2006
19

2.1.3. COMPARISON OF ONSHORE AND OFFSHORE

In section 1.3, we explain that the forecast error of wind speed in wind areas with offshore wind power 

stations (e.g. ISO-NE 7, NY-ISO 4, PJM 5 and SERC 2) is larger than of onshore wind areas. One might 

think that in regions with offshore wind power stations the total wind power forecast error is larger, yet 

this is not the case. In regions with offshore wind, the wind speed forecast error of onshore areas is 

comparably low (see 1.3.2). As the majority of the wind power capacity is installed in onshore areas, 

these regions have lower total wind power forecast errors than regions in the Midwest. For future 

scenarios with an increasing number of offshore wind parks, it is likely that the total wind power forecast 

error will become larger for these regions.

2.2. LOAD FORECASTS

An example of the resulting day-ahead scenario tree for load in the PJM region is shown in Figure 15. 

The forecast scenarios for load show very small differences compared to the forecast scenarios for wind 

power (see section 2.1). As the relative forecast error for load is very small, the expected value is very 

similar to the realized value. 

Figure 15: Exemplary day-ahead forecast scenario tree of the load forecast for the PJM region 

given in MW.

0

20000

40000

60000

80000

100000

120000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Forecast hour [h] 31 33 35

Load [MW] 

Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5

Scenario 6 Expected Value Realized Value
20

2.2.1. REGIONAL DIFFERENCES

Comparable to wind, the analysis of forecast errors of load in a certain region is based on the frequency of 

occurrence of the forecast errors relative to the peak load in this region. For the analyses, only the values 

of the day-ahead trees were considered with a forecast period of 12-36 hours ahead. Again, no distinction 

is made between different forecast horizons. The frequency distribution of the relative forecast errors of 

load is shown in Figure 16. Due to the assumption of a Gaussian distribution of the load forecast error, 

positive forecast errors occur nearly as often as negative forecast errors. If a region has a lower standard 

deviation of load forecast errors (see section 1.3.2 ), the corresponding frequency distribution shows more 

forecast errors near to zero. In the TVA and ISO_NE regions , the frequency of small forecast errors is 

comparably high whereas the MAPP region has the lowest frequency of small forecast errors. In general, 

large forecast errors occur very infrequently in comparison to wind (see section 2.1.1). 

Figure 16: Relative frequency of the relative forecast error of load based on the input data of the 

year 2004 in all market regions.

Figure 17 shows the frequency distribution of the relative forecast error of load based on the input data of 

the year 2004 in the MAPP, PJM, TVA, and MISO_CENTRAL regions. The MAPP region was selected 

because it has the highest frequency of large forecast errors. TVA was selected because it is the region 

with the best load forecast. Additionally the MISO_Central and PJM regions have been chosen as 

representative of regions where the quality of the load forecast is ranked in between. For all regions the 

relative load forecast error lies during 99.95 % of the hours within the 10% interval.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

MISO_Central

MISO_East

MISO_West

MAPP

ISO_NE

NY_ISO

PJM

SERC

SPP_Central

SPP_North

TVA
21

Figure 17: Relative frequency of the relative forecast error of load based on the input data of the year 2004 in 

selected market regions.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

MAPP

PJM

TVA

MISO_Central
22

2.2.2. COMPARISON OF DIFFERENT YEARS 

Similar to the analyses of the influence of the different base years 2004, 2005, and 2006 on the wind 

power forecast error, the impact of the load time-series data of these years on the load forecast error is 

shown in the following four figures. 

Figure 18: The frequency distribution of the relative forecast error for MAPP region.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

R_MAPP

R_MAPP

R_MAPP
23

Figure 19: The frequency distribution of the relative forecast error for TVA region.

Figure 20: The frequency distribution of the relative forecast error for PJM region.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

TVA 2004

TVA 2005

TVA 2006

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

PJM 2004

PJM 2005

PJM 2006
24

Figure 21: The frequency distribution of the relative forecast error for MISO_CENTRAL region.

Similar to the wind forecast error, the selection of the base year has only a negligible influence on the 

frequency of the load forecast error as shown here for the TVA, PJM and MISO_CENTRAL market 

regions. Significant differences are only depicted for the MAPP region. There, the base year 2005 leads to 

the smallest relative deviations, whereas the base year 2006 displays the largest relative deviations. These 

differences can be traced back to the fact that the peak load, the reference taken for the analyses of the 

load forecast error, varies between the base years. In the MAPP region, the peak load deviates between 

the base years up to 30 % in comparison to the base year 2004. Whereas in the TVA, PJM and 

MISO_Central market regions analyzed here, the differences in peak load are very small.

2.3. FORECASTS OF NET LOAD

An example of scenario trees of net load (load minus wind power feed-in) is shown in Figure 22. It 

considers those scenario trees of wind power and load forecasts in the PJM market region that are shown 

in section 2.1 and 2.2. In this example, primarily during the forecast horizon between 20 and 33 hours 

ahead, the expected values are underestimating the realized net load. In the subsequent planning loops, the 

electricity generation of the conventional power plants has to be adapted so that the finally realized net

load is covered in a minimal cost optimization.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

MISO_Central 2004

MISO_Central 2005

MISO_Central 2006
25

Figure 22: Exemplary day-ahead forecast scenario tree of net load for the PJM market region.

2.3.1. REGIONAL DIFFERENCES

Analyzing the frequency distribution of the forecast error of the net load, the time-series data of the 

realized net load in each region were determined. For the calculation of the frequency of occurrence of the 

forecast error, the difference between the realized net load and the expected forecast of the net load was 

divided by the maximum of the realized net load of the considered year. Figure 23 shows the frequency 

distribution of the error of net load for all considered regions. In the MAPP and SPP_CENTRAL regions, 

more frequently the forecast error is high and reaches more often values above 0.2. For regions like TVA 

and SERC, in more than 90 % of the hours the relative forecast error lies in the interval [-0.2, 0.2]. In 

regions with a low percentage of wind power production compared to its large load, like PJM and SERC,

the frequency distribution of the net load forecast error is similar to the frequency distribution of the 

forecast error of load. In regions with a dominant share of wind power production, like MAPP, 

SPP_CENTRAL and SPP_North, the influence of the forecast error of wind power production on the 

frequency distribution of the net load forecast error is obvious.

0

20000

40000

60000

80000

100000

120000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Forecast hour [h] 31 33 35

Net Load [MW] 

Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5

Scenario 6 Expected Value Realised Value
26

Figure 23: Relative frequency of the relative forecast error of net load based on the input data of 

the year 2004 in all market regions.

2.3.2. INTER-ANNUAL COMPARISON

The choice of the base year has only a negligible influence on the frequency distribution of the forecast error 

of net load in the PJM, TVA and SPP_CENTRAL regions (see Figure 24, Figure 25 and Figure 26). Only in 

the MAPP market region, the difference in the frequency distribution of the forecast error of net load 

between the different base years is larger than in the other regions (see Figure 27). This can be explained 

with the strong varying peak load of these regions between the different base years (see section 2.2.2). 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

MISO_Central

MISO_East

MISO_West

MAPP

ISO_NE

NY_ISO

PJM

SERC

SPP_Central

SPP_North

TVA
27

Figure 24: Relative frequency of the relative forecast error of the net load for the different base 

years in the PJM region.

Figure 25: Relative frequency of the relative forecast error of the net load for the different base 

years in the TVA region.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

PJM 2004

PJM 2005

PJM 2006

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

TVA 2004

TVA 2005 

TVA 2006
28

Figure 26: Relative frequency of the relative forecast error of the net load for the different base 

years in the SPP_Central region.

Figure 27: Relative frequency of the relative forecast error of the net load for the different base 

years in the MAPP region.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

SPP_Central 2004

SPP_Central 2005

SPP_Central 2006

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Relative Forecast Error [-]

Relative Frequency [-]

MAPP 2004

MAPP 2005

MAPP 2006
29

2.4. REPLACEMENT RESERVES

With replacement reserves, a supplementary reserve category for the coverage of forecast errors of wind 

power feed-in and load is introduced (see section 1.3.4). Comparable to the treatment of forecast errors, 

replacement reserves are considered only in the model runs with an imperfect representation of forecasts. 

For stochastic model runs, the scenario trees contain individual demand values in the several scenario 

branches corresponding to the individual load and wind power forecast error described. With 

deterministic model runs, one value of the demand for replacement reserves dependant on the forecast 

horizon according to the expected value of load and wind power forecast is considered. Since no forecast 

error of load and wind power is described by the model runs with perfect foresight, no demand for 

replacement reserves is considered for these model runs.

The resulting average demand for replacement reserves dependant on the forecast horizon for the 

individual market regions is depicted in Figure 28 based on the year 2004. In general, the demand for 

replacement reserves increases with advancing forecast horizon. One can see the influence of the assumed 

increase of the standard deviation of load and wind speed forecast errors on the extent of the demand for 

replacement reserves (see Figure 5 and Figure 6). Furthermore, the level of replacement reserves is 

dependent on the wind power feed-in and the load in the considered market region. Those market regions 

with the largest wind power capacity installed, like SPP_Central, SPP_North, MISO_West, and PJM, 

show the largest demand for replacement reserves. The comparable high demand for replacement reserves 

in the SERC market region can be explained with the high load level and corresponding larger forecast 

errors of load. Consequently, the MAPP and MISO East market regions with low installed wind power 

capacities and low load show the smallest demand for replacement reserves. Because the forecast errors 

for load and wind power production by trend do not show large differences between the historical base 

years considered (see sections 2.1 and 2.2), the choice of the historical base year has no significant 

influence on the demand for replacement reserves.
30

Figure 28: Average demand for replacement reserves dependant on the forecast horizon for the 

individual market regions for the year 2004 given in MW.

2.5. CONCLUSIONS

With the existing methodologies applied by the STT, the stochastic input parameters ( i.e., scenario trees 

of forecast errors of load and wind production as well as the demand for replacement reserves) that are

required by the Scheduling Model have been generated. The data on standard deviation of wind forecast 

errors depending on the forecast horizon could be considered and represented well. Yet data available on 

load forecast errors were more detailed than for previous studies and show a distinct dependency not only 

on the forecast horizon but further on the forecasted hour of the day. For example, the given load forecast 

errors are typically higher during the morning and evening hours than during night. Hence, the algorithm 

to simulate load forecasts has to be extended to consider the dependency on the hour of the day. However, 

the dependence of the standard deviation of the load forecast error on the forecasted hour as assumed for 

this study could be represented well.

0

1000

2000

3000

4000

5000

6000

7000

8000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29Forecast hour [h] 31 33 35

Replacement reserves [MW]

ISO_NE

MAPP

MISO_Central

MISO_East

MISO_West

NY_ISO

PJM

SERC

SPP_Central

SPP_North

TVA
31

3.

Using the data described in the previous sections, the scheduling model was run for 3 different years, 

using EWITS scenario 2 wind placements and 2004, 2005, and 2006 wind and load time-series data. The 

model is implemented in GAMS and solved using the CPLEX solver

SCHEDULING MODEL RESULTS

[17]. A stochastic model run using a 

scenario tree with 6 branches and 3-hourly rolling planning takes approximately 160 hours to run on a 

personal computer with an Intel Core i5 CPU – 650 with 3.2 GHz and 3.9 GB of RAM. A deterministic 

model run takes approximately 35 hours on the same computer. 

The remainder of this section examines the most relevant results seen from the scheduling model for this 

study. For some of the important results, such as costs, all three years are examined so that a comparison of 

different years as well as different scheduling strategies can be seen. For other results, one year is picked as 

an illustrative year, as results for all 3 years are similar. The model reports hourly results, showing 

dispatches, costs, emissions, interchanges etc. for all regions. Here, the totals or averages are given to 

examine the overall impact; however, it should be noted that these results are based on actual expected 

operation, and would include results for high wind/ low load days, low wind/ high load days (i.e., the full 

range of operation that would be seen when operating a system with this amount of wind power).

3.1. COSTS

The first result to examine in this study is the total production costs. As the objective of the model is to 

minimize production costs, this will give a good indication of the differences between unit commitment 

strategies. Production costs here are based on fuel usage, including startup costs. Figure 29 shows

production costs for the four different unit commitment strategies for each of the three years. Table II and 

Table III show the results and the percent increase in costs over the perfect forecast scenario, respectively. 

Figure 29: Production costs for each year.

55000

56000

57000

58000

59000

60000

61000

62000

63000

64000

2004 2005 2006

Production Costs (M$)

OTS

PFC

STO

UCDay
32

Table II: Costs by year and unit commitment method.

Year OTS (M$) PFC (M$) STO (M$) UCDay (M$)

2004 61,526.1 61,253.6 61,537.9 61,795.9

2005 62,422.5 62,075.3 62,437.1 62,715.6

2006 58,688.1 58,055.4 58,564.5 59,259.2

Table III: Change in production costs as a percentage of PFC costs.

Year OTS STO UCDay 

2004 0.44% 0.46% 0.89%

2005 0.56% 0.58% 1.03%

2006 1.09% 0.88% 2.07%

The highest costs occur from keeping unit commitment fixed from the day ahead. The two cases where 

rolling commitment is employed every three hours with imperfect forecasts have very similar costs in all 

years but 2006. In 2006, the case that uses stochastic scheduling produces 0.2% less costs. Figure 30 and

Figure 31 show the production costs and increase in costs compared to the hypothetical perfect forecast

case for each unit commitment strategy for the year 2006.

Figure 30: Production costs by unit commitment strategy based on 2006 input data.

 

57,400

57,600

57,800

58,000

58,200

58,400

58,600

58,800

59,000

59,200

59,400

OTS PFC STO UCDay

Production Costss (M$)
33

Figure 31: Percent cost increase over perfect forecasts by unit commitment strategy based on 

2006 input data. 

For 2006, the most expensive strategy, UCDay, increases costs 2.1% compared to the perfect forecast 

case. The next most expensive, OTS, increases the costs about 1.1%. Finally, the STO case increases the 

costs from the perfect forecast case about 0.9%. This shows that with imperfect forecasts, the lowest 

production costs come from performing unit commitment towards multiple scenarios and updating the 

unit commitment more frequently. The use of rolling planning, updating the unit commitment every three 

hours compared to once a day, gave higher cost savings compared to using stochastic unit commitment. 

With imperfect forecasts, the savings of rolling planning for the Eastern Interconnect amount to about 

$778 million (STO minus UCDay), while the savings from using stochastic unit commitment compared to 

deterministic amount to about $206 million (STO minus OTS). For the other two years, the savings of 

using rolling planning are about half, and a savings from using stochastic unit commitment are not 

apparent. These years may have been over-committing more often with the stochastic case and therefore, 

not gathering the benefits of planning toward multiple scenarios. 2006 also had significantly more wind 

power than the other two years.

By updating unit commitment every three hours, efficient start and stop decisions could be made when 

forecasts are improved. When updating the unit commitment once a day, as is done in most systems 

today, system operators are stuck with the decisions they made while forecasts may have been less 

accurate, even if physically they would be able to change the decision. This could lead to inefficient overcommitment when net demand becomes lower than it was forecast, or under-commitment when net 

demand becomes higher than it was forecast. Under-commitment would lead to the use of more expensive 

fast-start units or use of operating reserves. Stochastic unit commitment strategies prepare the system for 

a series of potential outcomes. In theory, the unit commitment will have more resources online to meet 

the lower net demand scenarios. However, when real-time outcomes end up occurring further from the 

median (deterministic forecast), the stochastic solution will be better prepared to meet the real-time 

outcome more efficiently. 

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

OTS STO UCDay
34

To examine in more detail the differences in costs between unit commitment strategies, each region was 

examined separately for one year. Figure 32 shows these results.

Figure 32: Production costs by region, 2006.

It can be seen that the UCDay case is generally more expensive in most of the regions. PJM and 

MISO_Central had the largest increases in the UCDay case compared to the other cases due to increased 

production in coal generation when it could not be shut down when not needed, and gas generation when 

coal generation could not be turned on when needed. TVA had cheaper costs from the UCDay case 

showing the inefficient use of the transmission system, especially since two of the largest interfaces with 

TVA with this transmission system are PJM and MISO Central. As expected, the PFC case is slightly less 

expensive than the other three cases in most of the regions. Table IV shows these results in more detail.

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

R_ISO_NE

R_MAPP

R_MISO_Central

R_MISO_East

R_MISO_West

R_NY_ISO

R_PJM

R_SERC

R_SPP_Central

R_SPP_North

R_TVA

Production Costs (M$)

UCDay

STO

OTS

PFC
35

Table IV: Production costs by region, 2006 data.

Region OTS (M$) (M$) PFC (M$) (M$) STOC (M$) UCDay (M$)

R_ISO_NE 2,014 1,936 1,988 2,061

R_MAPP 1,343 1,343 1,335 1,311

R_MISO_Central 7,019 7,000 6,997 7,297

R_MISO_East 3,771 3,773 3,763 3,748

R_MISO_West 4,522 4,542 4,518 4,616

R_NY_ISO 2,307 2,179 2,249 2,282

R_PJM 15,077 15,091 15,047 15,304

R_SERC 8,300 8,142 8,242 8,207

R_SPP_Central 3,095 3,012 3,195 3,373

R_SPP_North 3,253 3,043 3,173 3,207

R_TVA 7,987 7,995 7,974 7,853

Total 58,688 58,056 58,481 59,259

3.2. PRODUCTION

The next result examined is the difference in production by fuel type for different unit commitment 

strategies. Table V shows that there is a difference in production from year to year for the different cases;

as wind production increases (highest is 2006; lowest is 2004) due to a higher capacity factor, coal power 

decreases. Nuclear and hydro are mostly coming in as fixed schedules and therefore, do not change much 

between the three years. Wind produces 19% of all energy in 2004, about 19.7% in 2005, and between 

20.5-20.7% in 2006.
36

Table V: Total production by fuel type, in TWh.

One of the most significant impacts on production costs is the difference between natural gas and coal 

production. Figure 33 shows the coal and gas production for each case and each year. For all three years, 

UCDAY has the highest gas production. UCDAY is not able to commit coal during forecast errors that 

require additional supply in real-time. Gas units, however, have fast start times and are mostly used to 

accommodate these forecast errors. The other differences are not as obvious. STO has slightly higher coal 

production in most years. During many days and hours, STO may be committing additional resources for 

uncertainty, and when that uncertainty does not occur, it may have overcommitted the coal, requiring it to 

potentially curtail wind power.

OTS PFC STO UCDAY

2004 2005 2006 2004 2005 2006 2004 2005 2006 2004 2005 2006

Coal 1,698 1,681 1,630 1,697 1,680 1,629 1,699 1,683 1,633 1,698 1,682 1,637

Gas 29 38 36 29 37 34 29 38 35 39 39 37

Uranium 887 886 885 887 886 886 887 886 885 887 886 889

Hydro 143 143 144 143 143 144 143 143 144 143 143 144

Wind 658 680 706 656 678 709 653 676 705 653 676 704

Pumped Hydro 17 19 17 17 19 16 17 19 17 17 19 18

Total 3,432 3,447 3,418 3,429 3,443 3,418 3,428 3,445 3,419 3,437 3,445 3,429
37

Figure 33: Production by gas and coal for all years.

To look further, we observe results of production by fuel type and by region using the year 2006. This is 

shown in Table VI and Table VII.

0

5

10

15

20

25

30

35

40

45

1,580

1,600

1,620

1,640

1,660

1,680

1,700

1,720

OTS PFC STO UCDAY OTS PFC STO UCDAY OTS PFC STO UCDAY

2004 2004 2004 2004 2005 2005 2005 2005 2006 2006 2006 2006

TWH TWH

Coal Gas
38

Table VI: Production by fuel type, 2006 data, by region, in TWh.

Type Fuel R_ISO_NE R_MAPP R_MISO_Central R_MISO_East R_MISO_West

OTS

Coal 17.2 67.3 241.2 120.7 170.2

Electricity 5.2 1.4

Gas 5.0 0.4 0.5 0.0 1.7

Uranium 48.6 43.1 49.5 34.4

Water 21.7 7.4 1.6 0.5 2.7

Wind 46.4 42.2 35.9 18.8 138.0

Total 144.1 117.3 322.3 190.9 347.0

PFC

Coal 16.9 67.3 241.7 120.9 172.0

Electricity 5.3 1.3

Gas 4.6 0.4 0.3 1.7

Uranium 48.6 43.1 49.5 34.4

Water 21.7 7.4 1.6 0.5 2.7

Wind 46.4 42.2 35.9 18.8 138.0

Total 143.5 117.3 322.6 191.0 348.8

STO

Coal 17.2 67.3 241.3 120.6 170.9

Electricity 5.2 1.3

Gas 4.8 0.4 0.4 0.0 1.7

Uranium 48.6 43.1 49.5 34.4

Water 21.7 7.4 1.6 0.5 2.7

Wind 46.4 42.2 35.9 18.8 138.0

Total 144.0 117.3 322.3 190.7 347.6

UCDAY

Coal 19.1 71.4 245.6 119.6 171.5

Electricity 4.7 1.1

Gas 4.6 0.6 1.2 0.0 2.0

Uranium 48.5 3.9 43.1 49.5 34.3

Water 21.7 7.4 1.6 0.5 2.7

Wind 46.4 42.2 35.9 18.8 137.8

Total 145.0 125.5 327.5 189.5 348.4
39

Table VII: Production by fuel type, TWh, 2006 data, by region (ctd).

Type Fuel R_NY_ISO R_PJM R_SERC R_SPP_Central R_SPP_North R_TVA

OTS Coal 389.5 195.2 80.2 66.0 255.5 389.5

Electricity 2.1 1.8 1.4 0.2 0.9 2.1

Gas 2.7 3.2 7.7 8.6 1.3 2.7

Uranium 314.6 227.8 16.5 92.7 314.6

Water 7.3 12.1 5.0 0.5 18.2 7.3

Wind 102.9 15.3 126.4 123.8 4.3 102.9

Total 819.2 456.3 220.7 215.7 372.9 819.2

PFC Coal 26.0 390.5 192.4 79.7 65.6 256.0

Electricity 3.5 2.1 1.8 1.5 0.2 0.8

Gas 4.2 2.7 2.9 7.6 7.8 1.3

Uranium 58.4 314.6 227.8 16.5 92.7

Water 66.6 7.3 12.1 5.0 0.5 18.2

Wind 52.5 102.9 15.3 128.6 124.4 4.3

Total 211.1 820.2 453.2 222.3 215.1 373.3

STO Coal 26.7 389.7 195.8 81.7 66.1 255.5

Electricity 3.5 2.1 2.0 1.5 0.2 0.9

Gas 4.4 2.6 2.8 8.1 8.4 1.3

Uranium 58.4 314.6 227.8 16.5 92.7

Water 66.6 7.3 12.1 5.0 0.5 18.2

Wind 52.5 102.9 15.3 125.5 123.0 4.3

Total 212.2 819.3 456.7 221.7 214.7 372.9

UCDAY Coal 24.8 393.2 192.8 81.6 66.4 250.8

Electricity 3.5 2.6 3.8 1.5 0.2 0.9

Gas 4.8 3.1 2.6 9.0 8.4 1.2

Uranium 58.4 314.6 227.8 16.5 92.7

Water 66.6 7.3 12.1 5.0 0.5 18.2

Wind 52.5 102.9 15.3 126.1 122.2 4.3

Total 210.6 823.7 455.2 223.1 214.3 368.0

Since there is a great deal of trading between regions, and the model is optimizing over the entire system 

and not individually between regions, there does not seem to be one region which best exemplifies what 
40

happens in general. However, certain regions seem to show some interesting results. For example, 

NY_ISO shows a decrease in coal usage for UCDay, and a lower total production overall; as can be seen 

by the increased total costs for UCDay, this would imply that this region makes less than optimal

exchanges to other regions in the UCDay case. Here, inflexible coal may be utilized less to prevent wind 

curtailment either in NY_ISO or elsewhere. 

3.3. RESERVE

This study required multiple types of reserve, some of which are more effected by increased wind power 

than others, as described in 1.3.4. Here, the data for 2006 is taken as an illustrative example of what 

occurs in each year – upon examination, each year shows approximately similar relative results for 

reserve, so only one year is examined.

Figure 34 shows the contingency reserve carried online by region for each method in 2006. The 

requirement for contingency reserve as discussed in section 1.3.4, is 2250 MW for all regions with 50% 

(1125 MW) required to be online (spinning). The spinning requirement can also be seen in Figure 34. The 

sum of MISO East, MISO West, MISO Central and MAPP and the sum of SPP Central and SPP North 

should therefore be greater than the requirement of the contingency reserve region (shown as A_SPP and 

A_MISO in Figure 34). It can be seen that approximately the same amount is carried in most regions. In 

some regions, like in NYISO and SPP, the amount of contingency reserves online is equal to or just 

barely above the requirement, meaning that there are some costs in requiring the contingency reserves 

during some hours. In other regions, like TVA and SERC, the average amount of contingency reserves 

online is substantially higher than the requirement for the STO and OTS cases. This is because some 

solutions allow additional reserve to be carried as units are already online to manage uncertainty. It could 

also be when there are not enough offline reserve and more have to be online to meet the total 

contingency reserve requirement. However, the next section shows this is not the case. This is due to the 

constraint being modeled as an inequality; in certain hours some solutions will already have enough units 

online to more than cover a particular contingency. In these hours the marginal costs of providing 

spinning reserve from online units (contingency reserve and positive frequency regulation reserve) are 

zero, because enough units are kept online irrespective of the demand for spinning reserve. Lastly, it is 

seen that MAPP, with the smallest capacity of all regions that contribute to the MISO contingency 

reserves actually holds the majority of the online contingency reserves. 
41

Figure 34: Contingency reserve carried online by region, 2006 data.

Figure 35 shows the contingency reserve carried by online units, distributed by unit type. Overall it

appears that OTS carries the most contingency reserve online. This is due to the fact that the hydro units 

are not being used to meet other stochastic scenarios and are therefore available online to supply 

contingency reserves. This should be the same for PFC, since it also does not need to meet multiple 

scenarios. We see that for the PFC the pumped hydro provides majority and so these are interchangeably 

used for providing the contingency reserve online.

0

200

400

600

800

1000

1200

1400

1600

A_ISO_NE

A_MAPP

A_MISO_Central

A_MISO_East

A_MISO_West

A_MISO

A_NYISO

A_PJM

A_SERC

A_SPP_Central

A_SPP_North

A_SPP

A_TVA

MW

UCDay

STO

OTS

PFC

Requirement
42

Figure 35: Online contingency reserve by unit type, 2006 data.

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

Coal

Pumped 

hydro

Gas

Oil-L

Water

Total

MW

UCDay

Stoc

OTS

PFC
43

The same year and data is shown for contingency reserve carried by offline units, as shown in Figure 36

and Figure 37. 

Figure 36: Contingency reserve carried by offline units, 2006 data, by region.

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

A_ISO_NE

A_MAPP

A_MISO_Central

A_MISO_East

A_MISO_West

A_MISO

A_NYISO

A_PJM

A_SERC

A_SPP_Central

A_SPP_North

A_SPP

A_TVA

Contingency Reserve Offline (MW)

UCDay

STO

OTS

PFC
44

Figure 37: Contingency reserve carried offline, by unit type.

It can be seen that most regions carry more contingency reserve offline when wind production is known 

perfectly. The demand for replacement reserves is zero when wind and load is known perfectly and hence, 

no offline units are required to provide replacement reserves in this case, making more units available for 

contingency reserves. The operational costs of providing offline reserves are in most cases zero, because 

these gas and oil-fired units would have been kept offline irrespective of the demand for offline reserves, 

due to their high marginal costs. The contingency reserve being carried offline is slightly higher for the 

UCDay case, particularly for gas units as shown in Figure 37. PJM and SERC regions also have over 40,000 

MW and 30,000 MW of combustion turbines in their systems, respectively, and therefore, the sum of offline 

contingency reserve and offline replacement reserve is very close to the total sum of their capacities, since 

their actual production is usually small. Two other important concepts should be mentioned. First, the 

results are for all times of year including spring time, where wind power is very high, load is low, and these 

resources will be offline regardless. Second, the model never simulates the high resolution needs of actual 

contingencies that require the contingency reserve, and therefore, it does not show how these resources 

would actually be used in the simulation, only how they are held ready to be used.

0

20000

40000

60000

80000

100000

120000

140000

Gas

Oil-L

MW

UCDay

Stoc

OTS

PFC
45

The next category of reserve, frequency regulation reserve, is again examined by region and unit type. 

Frequency regulation reserve is required in both the positive and negative directions. Figure 38 shows the 

distribution by region as well as the average requirement.

Figure 38: Frequency regulation Reserve by region, 2006 data.

For frequency regulation reserve, MISO_Central, MISO_East, and MISO_West all contribute to MISO 

regulating reserve, and SPP_Central and SPP_North contribute to SPP regulating reserve. PFC can be seen 

to carry more frequency regulation reserve in most regions. Some of the regions, like NYISO, do not 

schedule more than the requirement. The marginal cost of positive frequency regulation reserve for this 

region was greater than zero every hour and was as high as $200/MWh, and the marginal cost of negative 

frequency regulation reserve was often greater than zero as well. On the other hand, TVA and SERC had 

more than enough frequency regulation reserve for most hours. In practice, regulation reserve has additional 

costs due to additional wear and tear that is caused which would likely keep the amounts closer to the 

requirements. Shown by unit type in Figure 39, you can see that the main changes between unit commitment 

strategies are in the hydro plants. As discussed for the online contingency reserve, the PFC case is like the 

OTS case, and does not model hydro units based on meeting additional scenarios and therefore, there are 

more hydro units with large ramp rates that are able to provide more frequency regulation reserve than 

needed. Hydro units have large ramp rates and for these reserves, are mostly only constrained to provide 

reserves by their maximum capacities. Conventional units are dispatched differently for the different unit 

commitment methods; they would be operating at different levels above their minimum generation level and 

below their maximum generation level giving the difference of amounts.

0

1,000

2,000

3,000

4,000

5,000

6,000

UCDay

STO

OTS

PFC

Requirement
46

Figure 39: Frequency regulation reserve by unit type, 2006 data.

The next category of reserve, replacement reserve, is required to cover for longer term variation from 

wind and load forecast. It is not needed in the PFC case; therefore, only the 3 methods that contain 

uncertainty in the wind and load forecasts are given here (STO, UCDay, and OTS). Figure 40 shows a

clear difference between those different methods of unit commitment and comparison with the 

replacement reserve demand. All of the figures for replacement reserve would show the quantities of 

replacement reserve provision for the first stage, or real time (i.e., first three hours of the planning loop).

0

5,000

10,000

15,000

20,000

25,000

Coal Pumped Hydro Gas Hydro Total

UCDay

Stoc

OTS

PFC
47

Figure 40: Replacement reserve from online units.

It can be seen that UCDay carries more online replacement reserve in general, as it needed to keep more 

units online to deal with the increased uncertainty seen in the unit commitment when it is only carried out 

once a day. STO carries more reserve in general than OTS, as it is modeling the uncertainty explicitly. 

Figure 41 shows online replacement reserve by unit type. Storage is used for replacement reserve only

very rarely since it will be supplying contingency reserve and frequency regulation reserve for most of the 

time. The largest contributor to online replacement reserve is coal units. This is because coal units have 

relatively smaller ramp rates and therefore, may still have additional capacity available, but which is 

ramp-constrained from providing contingency reserve or frequency regulation reserve. Since replacement 

reserve is set aside for potential needs many hours ahead, ramp rates would not be binding.

0

200

400

600

800

1000

1200

1400

1600

A_ISO_NE

A_MAPP

A_MISO_Central

A_MISO_East

A_MISO_West

A_NYISO

A_PJM

A_SERC

A_SPP_Central

A_SPP_North

A_TVA

MW

UCDay

Stoc

OTS
48

Figure 41: Online Replacement reserve provision by unit type, 2006 data.

Figure 42: Offline replacement reserve provision by region, 2006 data.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Coal

Pumped 

Hydro

Gas

Hydro

Total

UCDay

Stoc

OTS

0

2000

4000

6000

8000

10000

12000

14000

16000

A_ISO_NE

A_MAPP

A_MISO_Central

A_MISO_East

A_MISO_West

A_NYISO

A_PJM

A_SERC

A_SPP_Central

A_SPP_North

A_TVA

MW

UCDay

Stoc

OTS
49

Replacement reserve can be carried by offline units more in the STO case. This means that units do not 

need to be online and costing money, but still providing reserve. As seen in Figure 43, this is carried

mostly by gas combustion turbines with some contribution from oil combustion turbines, both quick 

starting units.

Figure 43: Replacement reserve carried by offline units, by unit type, 2006 data.

3.4. WIND CURTAILMENT

Wind curtailment is generally a significant impact when examining integration. Here, the four different 

methods are examined to show how much curtailment is affected by method of operation for each year. 

Figure 44 shows the curtailment for each solution, sorted by method and year. You can see that the least 

amount of curtailment occurs during the perfect forecast case (5-7% reduction in wind curtailment from 

STO to PFC, with higher reduction in 2006 compared to 2004 and 2005). The perfect forecast case will 

schedule as much wind power as possible ahead of time and does not run into the issue of underforecasting. When wind power is under-forecast, it is more likely that transmission congestion or 

minimum generation limits will be reached. Total curtailment is approximately 54 TWh to 70 TWh, 

depending on year and method; this is approximately 8.5% (2004) to greater than 10% (2006) of total 

production from wind, as shown in the production section. You can also see that stochastic cases (STO 

and UCDay) have the most curtailment. Even though stochastic scheduling is better for optimizing over 

all scenarios, there is more likelihood of over-committing than there is in the deterministic cases.

0

10000

20000

30000

40000

50000

60000

Gas

Oil-L

Total

MW

UCDay

Stoc

OTS
50

Figure 44: Curtailment by year.

Figure 45 shows that most of the curtailment happens in the SPP regions, where there is a large amount of 

wind with respect to its amount of interchange. Curtailment is mostly inevitable with all unit 

commitment strategies if insufficient transmission or flexibility is built to accommodate the heavy amount 

of wind in this region. However, the advanced unit commitment strategies provide a modest decrease in 

the amount of curtailment, only slightly higher than the PFC case.

Figure 45: Curtailment by region, 2006 data.

50

55

60

65

70

75

2004 2005 2006

Curtailment (TWh)

OTS

PFC

STO

UCDay

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

R_ISO_NE

R_MAPP

R_MISO_Central

R_MISO_East

R_MISO_West

R_NY_ISO

R_PJM

R_SERC

R_SPP_Central

R_SPP_North

R_TVA

TWh

UCDay STO OTS PFC
51

3.5. PRICES

While WILMAR does not seek to emulate markets, the marginal cost of balancing load and demand in 

each time period gives an indication of what prices may be like. WILMAR produces prices for all time 

periods and planning loops through the marginal cost of the load balance equation for each region, which 

for stochastic periods will be calculated from the expected value of the marginal cost. Day-ahead and 

real-time prices and everything in between can be calculated. The prices between look-ahead periods and 

the real-time should converge to being equal in a market setting and since the study is not emulating 

market behavior, we show only the intra-day prices from the first three hours to explain how the marginal 

cost of energy may differ for the four cases. This is shown in Figure 46.

In general, the differences in prices can come from times when natural gas is the marginal provider and 

when coal is the marginal provider. Intra-Day prices can be seen to be the highest with the OTS case, 

followed by UCDay. OTS is not minimizing the expected cost over multiple potential scenarios, which 

may lead to under-commitment scenarios where combustion turbines may need to be turned on in realtime. UCDay may often commit too little capacity as well since updated forecasts cannot be used to turn 

on slow-start units. In the day ahead, combustion turbines can be planned for differently for each scenario 

and therefore, for the unlikely scenarios the UCDay case is relying on waiting to turn the combustion 

turbines on in real time, where the combustion turbines have high marginal costs. PFC is the lowest price, 

with STO slightly higher. STO has low marginal costs as this mode keeps more units online to manage 

the uncertainty in many potential outcomes, thereby reducing marginal cost as it won’t need to use as 

much of the combustion turbines in real time. For PFC, it is because its unit commitment solution is 

always the most efficient, and combustion turbines will never be needed due to forecast errors.

Figure 46: Intra-day prices, 2006 data.

0

10

20

30

40

50

60

R_ISO_NE

R_MAPP

R_MISO_Central

R_MISO_East

R_MISO_West

R_NY_ISO

R_PJM

R_SERC

R_SPP_Central

R_SPP_North

R_TVA

Intra Day Price ($ /MWh)

UCDay STO OTS PFC
52

3.6. INTERCHANGE

Interchange is scheduled in the model between regions using Net Transfer Capability; therefore, the 

interchanges are scheduled so that those areas with lower costs will export, and higher costs will import 

up to the maximum capability of the interface.

Exports from each region for 2006 are shown in Figure 47: 

Figure 47: Exports for region, 2006 data.

There is very little difference in most cases. The STO and OTS cases seem to have similar exports in most 

regions. However, some regions export more – for example, PJM . MISO East shows a decrease in 

exports, as seen with a decrease in production.

0

20,000,000

40,000,000

60,000,000

80,000,000

100,000,000

120,000,000

Exports (MWh)

UCDay

STO

OTS

PFC
53

Figure 48: Imports by region, 2006 data.

You can see from Figure 48 that most imports occur into the PJM and SERC regions. Again, UCDay sees 

the biggest difference in imports, indicating that exchanges are less optimally scheduled with this method 

compared to others, and thus cause an increase in costs. For example, SERC imports more; this may 

indicate that it needs to import to make up for forecast errors.

Figure 49 shows the net imports for each region for 2006 data. Only one region changes from net imports 

to net exports based on this modeling method, and that is a very slight change in the MISO Central area. 

There are small differences between the intra-day (UCDAY) and day-ahead methods (OTS, PFC and 

STO) however, particularly in SERC, PJM, NYISO, and MISO Central and East. For example, net 

imports are increased in NYISO, and decreased in PJM, both of which are net importers. This would 

imply that operation of the interchanges is one of the reasons for the differences in costs seen for dayahead only commitment. 

0

50,000,000

100,000,000

150,000,000

200,000,000

250,000,000

Imports (MWh)

UCDay

STO

OTS

PFC
54

Figure 49: Net imports by region, 2006 data.

3.7. CONCLUSIONS FROM SCHEDULING MODEL RESULTS

Overall, this section compared two different types of results. Firstly, there was a comparison from year to 

year. This would show how dependent on a particular year certain results were. It could be seen that 

different wind and load time-series data did produce different results, and different years could increase or 

decrease production costs and other results for all methods. 2006 had the most wind power feed-in 

production and the lowest load, leading to it having the lowest production costs. It also had the most 

significant production cost differences between the advanced unit commitment techniques. In 2004 and 

2005, the stochastic scheduling did not seem to have any benefit in terms of production cost over 

deterministic unit commitment. Compared to 2006, stochastic scheduling did not use as little gas as 

deterministic scheduling did. The deterministic scheduling strategy did not have as many times where it 

had to start gas units in 2004 and 2005 due to under-forecasting, as it did in 2006, relative to stochastic 

scheduling, where forecast errors are better modeled in advance. 

Other results included the overall power production, wind curtailment, energy prices, reserve provision, 

and interconnection. The main difference in power production was between the gas, coal, and wind 

power. The way the system scheduled these three fuel types is what determined the overall cost for the 

most part. However, the interchange between regions could affect the results as well. Different regions 

have different costs for each of the fuels and inefficiencies in scheduling could cause sub-optimal 

interchange schedules. The prices found from each of the methods showed higher prices with OTS and 

UCDay for the year shown. These methods had gas on the margin more often setting these prices. The 

wind curtailment was highest for methods applying the stochastic scheduling strategy. This is because 

these methods will often over-commit due to the possibility of under-forecasting, often causing more need 

to curtail the wind power.

-150,000,000

-100,000,000

-50,000,000

0

50,000,000

100,000,000

150,000,000

200,000,000

250,000,000

Net Imports (MWh)

UCDay

STO

OTS

PFC
55

4.

The purpose of this report is to provide more analytical information on the impact that changing methods 

of unit commitment will have on the results for variable generation integration studies, and the 

implications that it could have for system operation. In EWITS, coal was assumed to be ‘must-run,’ and it 

was decided to run a sensitivity analysis in this study with this constraint as well. Therefore, the same 

model was run with one year of data (2006) where the only constraint was that all coal units had to be 

online (unless forced out) and running above their minimum generation limits. The previous results 

examined in this report (section 

COAL AS A MUST-RUN SENSITIVITY

3) were for coal that could be cycled, that is, the system operator can 

commit and de-commit coal with long minimum run and minimum down times, and slow ramp rates to 

reflect coal’s relative lack of flexibility. By operating coal in this mode, its use should be better 

optimized. This section compares the results for the 2006 coal case (i.e. must-run) and that shown in 

section 3 (with coal not-must-run for the year 2006). 

Here, only those results that are significantly affected by the change are examined. Other results did not 

change significantly, and are therefore not shown here. 

There is a significant difference in total production costs, as shown in Figure 50.

Figure 50: Production costs for different methods, coal not must-run and must-run results, 2006 

data.

It can be seen that relaxing the must-run constraint on coal reduces costs, as expected. By removing this 

constraint, coal can be turned off or ramped down if this is the best option for overall system cost. 

Table VIII shows the data so that percentage changes can be examined. You can see that model run STO

is more expensive than OTS, PFC, and UCDay when coal is treated as must-run, that is, the advantage of 

using stochastic rolling planning dissapeares in this case. The cost advantage of allowing coal to 

decommit from time to time is between 3% and 4.5% of system costs corresponding to $1.776 billion to 

56500

57000

57500

58000

58500

59000

59500

60000

60500

61000

61500

OTS (M$) PFC (M$) STO (M$) UCDay (M$)

Production cost (M$)

Coal must run Coal not must run
56

$2.629 billion, a significant amount of money. The cost advantage is biggest for the most advanced UC 

strategy (STO) and lowest for the one without intra-day rescheduling (UCDay).

Table VIII: Data for cost differences in coal must-run and coal not-must-run, 2006 data.

OTS 

(M$)

PFC 

(M$) STO (M$)

UCDay 

(M$)

Coal Must-Run 60803 60457 61111 61035

Coal Not Must-Run 58688 58055 58481 59259

Coal Must-Run - increase vs. STO -0.5% -1.1% 0.0% -0.1%

Coal Not-Must-Run - increase vs. 

STO 0.4% -0.7% 0.0% 1.3%

Increase with coal must-run -3.6% -4.1% -4.5% -3.0%

Another area of interest for the comparison of coal must-run versus not-must-run is production by unit 

type. Figure 51 shows the comparison for those units that produce more than 1 TWh. Firstly, you can see 

that the method does not have a great impact on the changes from must-run to not-must-run. You can see 

that coal is increased, as expected when coal is must-run and production from gas and wind power is 

decreased. The high minimum generation levels of the coal units lead to more curtailment of wind 

generation (between 4 and 8 TWh, depending on the UC strategy) in the coal as must-run case. 

Figure 51: Production from unit type for coal must-run (MR) and not-must-run (NMR).

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

Production (TWh)

STO NMR

STO MR

UCDay NMR

UCDay MR

PFC NMR

PFC MR

OTS NMR

OTS MR
57

The impact on wind curtailment is further shown in Figure 52. Wind curtailment increases between 5% 

(STO) and 12% (PFC) when coal is must-run. The reduction of wind curtailment is a major advantage of 

moving to flexible options to cycle coal on and off. The pattern of wind curtailment depending on UC 

method is the same for coal must-run and not-must-run, with the lowest wind curtailment in PFC and 

highest in UCDay.

Figure 52: Curtailment of wind energy with and without coal as must-run. 

0

10

20

30

40

50

60

70

80

90

OTS PFC STO UCDay

Curtailment (TWh)

Coal must run Coal not must run
58

5.

5.1. KEY FINDINGS AND ISSUES

CONCLUSIONS

This study set out to provide more analysis on the effect of assumptions about unit commitment methods 

on integration studies such as the Eastern Wind Integration and Transmission Study. Taking that study’s 

inputs as a starting point, it modeled the Eastern Interconnection (without transmission overlays, but with 

exchange limits between regions) with 2004, 2005, and 2006 wind and load time-series data using the 

WILMAR planning tool. The purpose of this report is not to run sensitivities on the EWITS report,

because it uses different assumptions about units (they are aggregated here) and transmission (this model 

only examines transfers between regions as opposed to a DC or full AC power flow). Instead, it was to 

examine the different unit commitment methods and how they may impact operation of the system with 

high wind, as well as how the assumptions about unit commitment affect results in these types of 

integration studies. 

The model is divided into two main sections; the STT, which provides scenarios of wind and load using 

forecast data, and the scheduling model, which runs production cost modeling, using the scenarios from 

the STT to optimize the unit commitment stochastically. Three years were examined to gauge the impact 

that particular data pertaining to individual years would have.

From the STT results, the following were the key findings:

• It could be seen that certain regions produced better wind forecasts than others; all regions had 

the vast majority of their forecasts under 40% error. 

• Demand forecasting could be seen to perform better in certain hours and certain look-ahead 

horizons; this is different than other studies where the error was assumed constant, and will need 

to be examined.

• For net load forecasts, certain regions performed better than others in forecasting the demand net 

of wind. The error in net load was consistent throughout the years for the majority of regions. 

• Replacements reserve demand was different for each region and with increasing time horizon.

The scenario trees produced were then used for the scheduling model. The following are the key findings 

from the results of the scheduling model:

• Costs are more significantly affected by the presence of rolling planning (i.e., re-planning the 

system every 3 hours) than by treating stochastic variables stochastically or deterministically; 

planning unit commitment once a day results in an increase in production costs of approximately 

1-2%, whereas deterministic schedules only had higher costs from the stochastic scheduling case 

for one of the three years. However, we note that a comparison between stochastic and 

deterministic scheduling between two methods where unit commitment was once a day may show 

different results and we encourage this analysis in the future. Stochastic UC may produce more 

significant cost savings on a day-ahead only unit commitment.

• Perfect foresight reduced the costs compared to stochastic with rolling planning with 0.5-1%. The 

reduction is caused by the significant reduction in wind curtailment in the perfect foresight case. 
59

• Results across all three years, while varying from year to year (i.e., 2006 data with higher wind 

capacity factors was less costly and showed greater benefits of both rolling planning and 

stochastic scheduling) do not show significant differences in terms of the difference between 

methods, which is the main focus of this study. However, the 2006 data showed much more 

significant benefits of using both stochastic unit commitment and rolling planning. The other 

years may have had more occurrence of over-commitment when planning for more robust 

operation. In other words, there were more occurrences of the system ready for an increase in net 

load, but the net load did not increase as often. Tweaking of the operating reserves and the cost of 

not having enough reserve could potentially bring the results closer to the operator preference (as 

opposed to being too risk averse). 

• Gas units had to be used more in the deterministic and non rolling cases to adjust for forecast 

errors in wind power production and electricity demand, while coal units could be better used in 

the other schedules since the more efficient solution methods chose them due to their lower cost.

• Wind curtailment was 5-7% lower in the perfect foresight case compared to the stochastic scheduling 

with rolling planning due to no over-committing of units taking place in the perfect foresight case. In 

general, wind curtailment was very high, consisting of 8.5% to over 10% of total possible wind power 

production, dependant on year. The high wind curtailment was located in SPP_Central and 

SPP_North, indicating that these regions will need to increase transmission capacities to neighboring 

regions if they are going to accommodate the planned amounts of wind power. 

• Prices derived from marginal unit costs were affected by choice of method; Intra-Day prices was 

seen to be the highest, with the OTS case followed by UCDay. OTS is not minimizing the 

expected cost over multiple potential scenarios, which may lead to under-commitment scenarios 

where combustion turbines may need to be turned on in real time. UCDay may often commit too 

little capacity as well since updated forecasts cannot be used to turn on slow-start units. PFC 

achieves the lowest price, with STO slightly higher. STO has low marginal costs as this mode 

keeps more units online to manage the uncertainty in many potential outcomes, thereby reducing 

marginal cost as it won’t need to use as much of the combustion turbines in real time. For PFC, it 

is due to the fact that its unit commitment solution is always the most efficient and combustion 

turbines will never be needed due to forecast errors.

• Transmission between regions was also affected by the type of unit commitment; the results for 

day-ahead commitment only used the transmission less optimally, resulting in more units being 

online than needed in some regions, with the opposite in other regions. The deterministic 

solutions tended to use transmission more, with higher net imports for net importers and higher 

exports for net exporters.

• If coal was assumed must-run, as in EWITS, there was shown to be an increase in costs of 3% to 

4.5%. Coal could not be shut off at times of high wind; it has to remain online. This means there 

is less room to turn down generation to avoid wind curtailment. The subsequent increase in wind 

curtailment means wind energy, with no fuel cost, is wasted, increasing overall costs. Gas 

production is reduced when coal is must-run; therefore, more flexible gas is being replaced by 

coal, which means balancing of wind and load is only possible with curtailment. This is 

consistent with the view that gas is well suited to balancing wind, due to its greater ramping rates 

and lower minimum generation levels.
60

• When coal is must-run, the cost benefits of moving to stochastic rolling planning are not as clear 

as when it can be committed and de-committed by the model because there is limited flexibility to 

change the unit commitment schedules intra-day due to the coal units being must-run. 

5.2. FURTHER WORK AND IMPROVEMENTS

Future research should focus on introducing uncertainty into the first 3 hours of each planning period. This 

could be done by changing the WILMAR model into alternating between stochastic model runs with 

uncertainty in all future operation hours, calculating the unit commitment of slow units, and deterministic 

model runs using the realised values of wind power production and load to calculate the final dispatch of the 

slow units and the unit commitment and dispatch of the fast units (see Figure 53). In the stochastic model 

runs, the unit commitment of the slow units would need to be restricted to be the same across scenarios 

within the start-up time of the unit. Such model development is already in progress at Risø DTU. 

Figure 53: Illustration of new looping structure allowing for inclusion of uncertainty in the first 

operation hours in each planning loop. The illustration shows rolling planning stepping 

forward in time in 6-hour steps.

The comparison of the different unit commitment strategies took careful attention in modeling and 

contrasting. The scenario of unit commitment fixed in the day-ahead timeframe and modeled 

deterministically however, was never compared with the other cases. This model scenario is the most 

closely related to today’s operation. If this case was compared with others, some of the results may have 

differed. For example, if this case was compared with UCDay, the benefits of stochastic unit commitment 

may have been better seen. We also believe that the continuous linear relaxation of the unit status variable 

had an impact on the results. Smaller test systems and improvements in solution techniques could allow 

12 18 24 06 12 18 24

Stochastic Day-ahead scheduling

Stage 1 (now)

Realised values – only possible to change unit commitment of fast units

Intra-day rescheduling

Realised values

Intra-day rescheduling

Realised values

Intra-day rescheduling

Realised values
61

the use of integer variables. System operators today are using integer programming in their unit 

commitment programs either through lagrangian relaxation or branch-and-bound MIP techniques, and 

therefore, would be implementing any advancement to their unit commitment programs with the same 

usage of integers. We are convinced that the usage of integers would show the benefits of stochastic 

rolling planning more clearly. For example, the All Island Grid Study (Ireland), which used integers due 

to the much smaller system, found benefits of stochastic unit commitment of 0.9% [5]. Other constraints, 

for example, the detailed modeling of combined cycle plants, could also have shown a difference in 

results. The more constraints that the system operator will implement in their unit commitment program, 

the more difficult it becomes to plan deterministically with higher uncertain variable resources, and the 

more difficult it becomes to plan once per day given the use of less accurate forecasts. This theory should 

be tested in future studies. 

Lastly, we would like to discuss the actual implementation of these strategies. Many ISOs in the United 

States have already implemented hour-ahead or shorter unit commitment updates, mostly for the 

commitment of combustion turbines. These models have short optimization horizons (e.g., less than 3 

hours) and less decision variables. Improvements in solution techniques can allow for longer optimization 

horizons as are discussed in this report, and for the start-up of any unit that has ample time to start-up 

according to its start-up times. It should be noted that many of these generating facilities may have 

staffing requirements, and that this type of requirements should be built into their start-up cost and startup time requirements. 

We believe that stochastic unit commitment techniques, though not seen with significant value in this 

study, can improve the cost efficiency and reliability of power system operations. Most ISOs require a 

deadline within which their markets must be closed. Therefore, solution techniques would have to 

improve the computation time required to solve these large problems in sufficient time. More research 

should be performed to determine the optimal scenario set. For example, three scenarios; a low, medium, 

and high, may be the sufficient number that can be solved in a reasonable time.

Finally, the use of probabilistic forecasts has received little attention in most of these studies. In stochastic 

unit commitment studies including this one, a forecast is created based on the statistics of a large set of 

data from the stochastic variable. For example, a year’s worth of data for one wind plant was used to 

create the standard deviation for various forecast horizons, and this was used to make a probabilistic 

forecast based on a normal distribution of wind speed. In reality, these probabilistic forecasts are 

commonly created by organizations that specialize in wind forecasting using a combination of 

meteorological and statistical information. Meteorological inputs may show different probability density 

functions for different times based on the meteorological phenomena. This may impact how the stochastic 

unit commitment programs benefit system reliability. We encourage research on using meteorologicalbased probabilistic forecasts to understand more of these questions. 
62

6.

[1] L. Wu, M. Shahidehpour, T. Li, “Stochastic security-constrained unit commitment,” IEEE 

Transactions on Power Systems, vol. 22, no. 2, pp. 800-811, May 2007.

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