mat wind thermal 2010

8/3/2019 Mat Wind Thermal 2010

1/160

20% Wind Generation and the

Energy Markets

A Model and Simulation of the Effect of Wind on the

Optimal Energy Portfolio

Jessica Zhou

Advisor: Professor Warren B. Powell

April 12, 2010

Submitted in partial fulfillment

Of the requirements for the degree of

Bachelor of Science in Engineering

Department of Operations Research and Financial Engineering

Princeton University


2/160

ii

I hereby declare that I am the sole author of this thesis.

I authorize Princeton University to lend this thesis to other institutions or individuals for

the purpose of scholarly research.

Jessica Zhou

I further authorize Princeton University to reproduce this thesis by photocopying or by

other means, in total or in part, at the request of other institutions or individuals for the

purpose of scholarly research.

Jessica Zhou


3/160

iii

Abstract

This thesis studies the effect of increasing wind power output to 20% of energy

generation on the PJM Day-ahead and Real-time Energy Markets. Currently, wind power

only has 0.5% market share in the PJM power grids; this will drastically change with the

20% wind target by 2030 from the Department of Energy. Due to the amplified volatility

from additional wind generation, the optimal portfolio of generation assets that minimizes

total system cost and volatility must evolve by 2030. Day-ahead scheduling around wind

forecasts and Real-time portfolio rebalancing to accommodate wind deviations will also

heavily impact total system costs. To study the effect of 20% wind penetration, the thesis

first models the unit commitment optimization problem for the Day-ahead Market. Then,

it simulates the Real-time Market portfolio rebalancing using actual PJM data for

generator parameters, hourly demand, and hourly wind. Model and simulation results

show that additional wind reduces costs with 70% efficiency due to wasted wind and

need for peaker rebalancing, though 100% efficiency can be achieved by using an hour-

ahead wind forecast. However, energy storage capacity must increase 1000% to achieve

above results. Additional results show 26% lower coal generation in the optimal portfolio

resulting in potentially 10% lower carbon emissions, increased optimal energy reserve

requirements from 1% to 3-4% to minimize additional risk from wind, and electricity

prices potentially reduced by 67% during peak hours.


4/160

iv

Acknowledgement

I would first like to express my gratitude for Prof. Warren Powell, who took me

as his advisee, gave me numerous suggestions on potential energy and finance related

topics, and gave very insightful comments on the various drafts the thesis has gone

through. His advice and guidance contributed greatly to this thesis from start to finish.

I would also like thank Prof. Hugo Simao, who gave me tremendous help in the

formulation of the integer linear program involved in solving the unit commitment

model. He helped me with both AMPL and MATLAB formulations despite not knowing

either programming language. Prof. Simao also established a way for MATLAB to call

CPLEX, without which solving an integer program would have been impossible.

Next, I would like to thank Ilya Ryzhov, who has always been a wonderful T.A.

and made ORFE so much more enjoyable. But most importantly, Ilya was the one who

approached me about working with Prof. Powell, and started this whole experience for

me. He even spent an entire night helping me debug a part of my model.

I must also thank James Yan, Selene Kim, Cincin Fang, Iris Zhou, Emi

Nakamura, Vivian Wang, Chau Nguyen, Sarah Tang, and Laura Bai for helping me with

proofreading this thesis. They are just amazing people. I would also like to thank all my

friends, the Colonial Club, and Triple 8 Dance Company for making my four years at

Princeton an unforgettable experience. Finally, I thank my parents, who are the most

amazing people in the world. Thank you Mom and Dad.


5/160

v

To Mom and Dad. I dedicate everything to you.


6/160

vi

Contents

Abstract iiiAcknowledgement ............................................................................................................. ivContents viList of Figures ......................................................................................................................xList of Tables .................................................................................................................... xiiChapter 1. Introduction ........................................................................................................1

1.1 PJM Power Market Auction in the Day-ahead Market .........................................41.2 The Real-time Energy Market Rebalancing ..........................................................61.3 DOEs 20% Wind by 2030....................................................................................8 1.4 Overview of the Thesis .......................................................................................11

Chapter 2. Unit Commitment Literature Review ...............................................................122.1 The UC Model .....................................................................................................122.2 Additional Complexities .....................................................................................16

2.2.1 Adjustment to Day-ahead schedules in the Real-time Market .....................18Chapter 3. Day-ahead Market Model .................................................................................20

3.1 Model Assumptions.............................................................................................213.2 List of Variables ..................................................................................................243.3 Day-ahead Model ................................................................................................26

3.3.1 Decision Variables .......................................................................................26


7/160

vii

3.3.2 Objective Function .......................................................................................273.3.3 Constraints ...................................................................................................273.3.4 Tunable Parameters ......................................................................................31

3.4 Data Parameters...................................................................................................32 Chapter 4. Real-time Market Simulation ...........................................................................34

4.1 Simulation Assumptions .....................................................................................354.2 Simulation Variables ...........................................................................................374.3 Simulation Model ................................................................................................39

4.3.1

State Variables: ............................................................................................39

4.3.2 Exogenous Variables ...................................................................................404.3.3 Decision Variables: ......................................................................................414.3.4 Transition Functions ....................................................................................444.3.5 Objective Function .......................................................................................474.3.6 Simulation Change with 20% Wind ............................................................48

4.4 Finding the Optimal Policy .................................................................................484.4.1 How to Optimize Tunable Parameters .........................................................494.4.2 Optimizing and ......................................................................................50

Chapter 5. Simulation Data ................................................................................................545.1 Demand Data .......................................................................................................55

5.1.1 Actual PJM Demand ....................................................................................565.1.2 Day-Ahead Demand Bid ..............................................................................57

5.2 Wind Data ...........................................................................................................60Chapter 6. Model and Simulation Results .........................................................................65


8/160

viii

6.1 Output Legend .....................................................................................................666.2 Day-ahead Model Results ...................................................................................686.3 Day-ahead Model Results with 20% Wind .........................................................746.4 Real-time Simulation Results ..............................................................................77

6.4.1 System Costs ................................................................................................816.4.2 Optimal Portfolio of Generation Sources ....................................................826.4.3 Strength of the Simulation ...........................................................................85

6.5 Real-time Simulation Results with 20% Wind ...................................................86

6.5.1

Total System Costs with 20% Wind ............................................................90

6.5.2 Optimal Portfolio with 20% Wind ...............................................................926.6 Potential Improvements for 20% Wind ...............................................................96

6.6.1 With More Storage .......................................................................................976.6.2 With Better Wind Forecasts .......................................................................100

Chapter 7. Discussion and Conclusions ...........................................................................1067.1 Accuracy and Sources of Error .........................................................................1067.2 Cost Reduction with 20% Wind ........................................................................1087.3 New Optimal Generation Mix ...........................................................................1117.4 New Reserve Policies ........................................................................................1137.5 Electricity Prices ...............................................................................................1137.6 Conclusions and Areas for Further Research ....................................................114

Appendix 1 Model Parameters......................................................................................117Appendix 1.1 Generator Input Parameters ................................................................117Appendix 1.2 Order for Generator Ramp Up ............................................................118


9/160

ix

Appendix 1.3 Order for Generator Ramp Down .......................................................119Appendix 2 MATLAB Codes .......................................................................................120

Appendix 2.1 MATLAB Codes for Day-ahead Model .............................................120 Appendix 2.2 MATLAB Codes for Real-time Simulation .......................................133

Sources of Data ................................................................................................................142References 144


10/160

x

List of Figures

Figure 1-1: Comparison between hourly Day-ahead and continuous Real-time demand .. 6Figure 1-2: Real-time demand fluctuations against average demand ................................. 7Figure 5-1: 2009 monthly average hourly demands ......................................................... 56Figure 5-2: 90 days of winter and summer hourly demands ............................................ 57Figure 5-3: Winter and summer hourly actual demands and Day-ahead demand bids .... 58Figure 5-4: Winter and summer differences between actual demand and demand bids .. 58Figure 5-5: Jan 2 hourly actual demand and hourly demand bids .................................... 59 Figure 5-6: 2009 hourly wind data .................................................................................... 60Figure 5-7: 90 days of winter and summer hourly wind ................................................... 61Figure 5-8: 2009 daily wind data for each hour of the day ............................................... 62Figure 5-9: 2009 actual predicted 12:00 A.M. wind, using past 7 days wind data ......... 62 Figure 5-10: 2009 actual and predicted hourly winds, using past 7 days wind data ....... 63Figure 5-11: 2009 actual and predicted hourly winds, using past 7 hours wind data ..... 63 Figure 6-1: Feb 4 results from the Day-ahead model ....................................................... 68Figure 6-2: Close up of peak hours for Feb 4 Day-ahead model output........................... 70Figure 6-3: Aug 10 Day-ahead model output ................................................................... 71 Figure 6-4: Close up of peak hours for Aug 10 Day-ahead model output ........................ 73Figure 6-5: Extreme close up of peak hours for Aug 10 Day-ahead model output .......... 74Figure 6-6: Feb 4 Day-ahead model output with 20% wind generation ........................... 75


11/160

xi

Figure 6-7: Aug 10 Day-ahead model output with 20% wind generation ........................ 76Figure 6-8: Feb 15-19 Day-ahead commitments and Real-time

adjusted generator outputs ..............................................................................77Figure 6-9: Feb 18 Day-ahead commitments and Real-time adjusted generator outputs . 79Figure 6-10: Aug 21-25 Day-ahead commitments and Real-time

adjusted generator outputs ..............................................................................80Figure 6-11: Winter simulation pie charts for generation and costs for both markets .. 83Figure 6-12: Summer simulation pie charts for generation and costs for both markets 84

Figure 6-13: Jan 8- 12 Day-ahead and Real-time adjusted outputs with 20% wind ......... 87

Figure 6-14: Aug 3-7 Day-ahead and Real-time adjusted outputs with 20% wind .......... 89Figure 6-15: Winter, 20% wind pie charts for generation and costs for both markets .. 93Figure 6-16: Summer, 20% wind pie charts for generation and costs for both markets 94Figure 6-17: Jan 8-12 Day-ahead and Real-time outputs 20% wind, 4000% storage ... 99Figure 6-18: Winter, 20% wind, better forecasts pie charts for generation and costs . 102Figure 6-19: Summer, 20% wind, better forecasts pie charts for generation and costs103


12/160

xii

List of Tables

Table 2-1: Variables and descriptions for Unit Commitment Literature Review ............. 13Table 3-1: PJMs breakdown of generator number and capacity by type ........................ 22Table 3-2: Variables and definitions for the Day-ahead unit commitment model ........... 25 Table 4-1: Variables and definitions for Real-time sequential decision simulation ......... 38Table 4-2: Optimizing policy parameters: Iteration 1....................................................... 51Table 4-3: Optimizing policy parameters: Iteration 2....................................................... 51Table 4-4: Optimizing policy parameters: Iteration 3....................................................... 51Table 4-5: Optimizing policy parameters: Iteration 4....................................................... 51Table 4-6: Optimizing policy parameters: Iteration 5....................................................... 52Table 4-7: Optimal policy parameters for different cases ................................................ 52Table 6-1: Generator color legend .................................................................................... 67Table 6-2: Feb 4 Day-ahead model output for optimal , for all hours and all units .... 69Table 6-3: Aug 10 Day-ahead model output for optimal , for

each hour and each generator ...........................................................................72Table 6-4: Total system costs after 90 days of winter and summer simulation ................ 81Table 6-5: Winter simulation percentage of total generation and

of total costs in both markets ...........................................................................83Table 6-6: Summer simulation percentage of total generation and

of total costs in both markets ...........................................................................84


13/160

xiii

Table 6-7: Generation by fuel type Simulation output vs. PJM actual .......................... 85Table 6-8: Total system costs after winter and summer simulation

Normal and 20% wind ..................................................................................90Table 6-9: Winter, 20% wind percentage of total generation and

of total costs in both markets ...........................................................................93Table 6-10: Summer, 20% wind percentage of total generation

and of total costs in both markets ....................................................................94Table 6-11: Real-time adjusted output comparison between normal

wind and 20% wind .........................................................................................95

Table 6-12: Total system costs, winter and summer 1000% vs. 4000% storage ........... 97Table 6-13: Total system costs, winter and summer 1000% vs. 40,000% storage ........ 98Table 6-14: Total system costs, winter and summer Normal vs.

20% wind with better forecasts ......................................................................100Table 6-15: Winter, 20% wind, better forecast percentage of total

generation and costs for both markets ...........................................................102Table 6-16: Summer, 20% wind, better forecast percentage of

total generation and costs for both markets ...................................................103Table 6-17: Real-time adjusted output comparison between 7-day

forecast and 7-hour forecast ...........................................................................104


14/160

1

Chapter 1.Introduction

Energy plays a major role in the U.S. economy, where energy consumption totals

100 quadrillion BTU (30 billion MWh) a year, and energy expenditures are at nearly 9%

of annual GDP (U.S. Energy Information Administration, 2008). Due to the high costs

and environmental detriments of fossil fuels, renewable energy is a major area of research

and development in the twenty-first century. The Department of Energy has announced a

target of 20% power generation from wind technologies by the year 2030 (U.S.

Department of Energy, 2008). While wind energy is practically free with no marginal


15/160

2

costs, the costs rise out of trying to schedule plants around the highly volatile wind. There

is now a need for an optimal portfolio of generation assets that will minimize the risk

from both noisy energy demand and wind outputs. This portfolio also requires

rebalancing in real time to respond to wind volatility, and this has implications on the

total system costs. The role of storage and wind forecast on the optimal power portfolio

and total operating costs must also be examined to prepare for wind generation by 2030.

The effects of wind on the Energy Markets could result in numerous changes in policy,

market design, electricity price, and the environment in the coming decades.

One party that will be greatly affected by increased wind market penetration is the

power grid operator. The Pennsylvania-New Jersey-Maryland Interconnection, or PJM, is

the largest power grid operator in the United States. It is a regional transmission

organization (RTO) that oversees the network of electric power in the northeast part of

the country. PJM provides a wholesale Energy Market where buyers and sellers can trade

electricity. It works much like a stock exchange, with market participants establishing a

price for electricity by matching generation supply and energy demand (PJM, 2006a).

This wholesale Energy Market is separated into the Day-ahead Energy Market, a forward

market for each hour of the next day, and the Real-time Energy Market that adjusts for

excesses and shortages from the Day-ahead commitments.

However, the problem is not as simple as just matching energy buyers and sellers.

Different generation technologies behave differently and have their own system

constraints. While cheaper coal plants may require time to ramp up, and once on must

remain on for the next eight hours, a gas turbine plant can fire up and down in minutes

but at the cost of a high fuel price. Wind and solar energy are intermittent energy sources


16/160

3

whose output levels are difficult to forecast; exogenous weather conditions control their

generation. With different power generation technologies, each supplying power at

different prices within different time frames, PJM essentially faces a portfolio problem of

selecting the optimal set of utility assets that can provide power to best fit a forecasted

demand curve while minimizing total system costs. To do this, PJM solves a unit

commitment optimization problem that plans the generation for each hour of the next

day. However, energy demand is volatile in real time, and the portfolio must be

rebalanced at five minute intervals in the Real-time Energy Market. Selecting a risk-

minimizing portfolio a day ahead, and rebalancing the portfolio to respond to demand

spikes is at the core of PJM operations.

The problem becomes far more complex when the Department of Energy (DOE)

introduces a new wind requirement. Increasing wind generation to 20% would be a forty-

fold increase from the current 0.5% wind penetration in the PJM interconnection region

(PJM, 2007). Wind is a highly noisy random process, and scheduling generations around

it in the Day-ahead Market and frequent rebalancing to accommodate wind deviations in

the Real-time Markets could have drastic portfolio and cost consequences.

The goal of this thesis is to examine the impact of wind energy on the Energy

Market by first modeling PJMs Day-ahead Energy Market using unit commitment

optimization, and next simulating the Real-time Energy Market when actual demands and

wind generation deviate from the forecasted values. The thesis examines the current PJM

generation levels as well as the scenario with 20% wind penetration into the market. By

comparing the two cases, it provides insight on how the Energy Market might look like

after the year 2030.


17/160

4

Before examining the different problems and their computational complexities,

this chapter further elucidates the PJM Day-ahead Energy Market in section 1.1, the

Real-time Market in section 1.2, and how these systems may be impacted by a minimum

wind energy contribution constraint in section 1.3. Finally, section 1.4 outlines the

structure of this thesis.

1.1PJM Power Market Auction in the Day-ahead MarketIn the move to deregulate the power industry, PJM has adopted an unregulated,

market-based bidding structure (Mansur, 2001). The system divides the next operating

day into 24 hourly blocks. PJM uses a simultaneous optimal auction, where both energy

suppliers and buyers submit their offers and bids for each hour of operating day by noon

on the previous day (Yan & Stern, 2002). Load Serving Entities (LSEs) and other energy

retailers issue demand bids that consist of the forecasted demand needs for that hour in

megawatts (MW) and their maximum buying prices for each hour; the combined demand

bids creates an aggregate hourly demand schedule curve that the market requires for the

next day (Conejo, Contreras, Espinola, & Plazas, 2005). Meanwhile, power producers

submit supply offers, generator data (such as min/max capacity, ramping time, etc.) and

minimum selling prices, for each forward hour; these offers can be step functions of

prices during the hour, or an increasing function if the plant is firing up during that

hour (Conejo, Contreras, Espinola, & Plazas, 2005). The grid operator then selects

generation assets, matching the bids and offers to find market clearing prices. PJM

attempts to minimize costs subject to transmission and reliability constraints to solve a

unit commitment(UC) problem (Tong, 2004).


18/160

5

Hobbs et al. discusses the unit commitment problem in relation to RTOs in great

detail (2001), but at its core, the UC model attempts to schedule generators to fit power

supply to power demand subject to different generator and system constraints. The

problem of selecting assets arises from the nature of different energy sources, namely

their marginal costs, their ramping speed, and their minimum on and off requirements.

Nuclear assets, for example, have low marginal costs per MW (Cordaro, 2008). However,

adjusting the power output of a nuclear facility will cause severe stress on the system.

Once on, nuclear plants need numerous days before they are fully stable and can be

turned off again. Once off, they need many days again to cool off before they can turn

back on. Nuclear power is much better suited to handling a constant minimum power

level that must be available, or the baseload, in the demand schedule. Other baseload

suppliers include coal, geothermal, and hydro power plants (Cordaro, 2008). On the other

hand,peakerassets handle the generation during peak demand and while baseload plants

are ramping. Gas turbine units can be fired up quickly to meet energy demand spikes,

they do not have extensive minimum on or off times, and can be turned off in the next

hour if they are no longer needed (Bowring, 2005). However, they have high marginal

costs from fossil fuels and are only economical to turn on when demand is high and

marginal energy prices are high. Generators thus not only bid their energy price curves

but also start-up cost curves, minimum and maximum generation levels, and physical

ramping rates (Yan & Stern, 2002).

After solving the UC problem, all the generators are scheduled for the next day,

midnight to midnight, the Day-ahead Locational Marginal Prices (LMP) are solved for

each node on the transmission grid. These are the buying and selling prices for each MW


19/160

6

of power that is agreed upon in the Day-ahead forward market (Ott, 2003).The Day-

ahead Market offer and bid period closes at noon, and generator schedule and Day-ahead

LMPs are posted at 4 P.M. From 4 P.M. to 6 P.M, additional or modified offers may be

made by uncommitted generators on PJMs Balancing Market (PJM, 2010a). PJM solves

a second unit commitment problem to re-schedule the generators once more information

on the next days demand and generator statuses become known. Additional knowledge

of demand, wind, and generator status becomes available towards the end of the day, and

PJM continues to make additional UC runs to optimize the next days generation

schedule (PJM, 2010a).

1.2 The Real-time Energy Market RebalancingThe Real-time Energy Market accounts for demand that deviates from Day-ahead

bids, and LSEs can buy additional power from generators at Real-time LMPs. Even with

an optimal selection of generators committed for the next days market operations,

uncertainties arise in real time as demand and intermittent energy outputs fluctuate.

Figure 1-1: Comparison between hourly Day-ahead and continuous Real-time demand


20/160

7

Figure 1-1 shows how actual demand levels may differ from the hourly forecasted

demand levels (Petersen, 2008). The step-like purple line shows the Day-ahead demand

schedule, while the blue line reveals the actual demand for the day.

Figure 1-2: Real-time demand fluctuations against average demand

Figure 1-2 shows the minute-by-minute demand (Kirby, 2004); the red line below

magnifies the variation in the top green curve, and shows that demand can vary up to

sixty MW from the mean level. PJM uses a method of frequency regulation, where it

stores extra power supplied into batteries, flywheels, and pumped hydro, and dispatches

quick-firing generators (often energy in storage) as needed on a sub-hourly basis

(Petersen, 2008). Currently, PJM makes dispatch decisions every five minutes (Botterud,

Wang, Monteiro, & Miranda, 2009). Generators are fired based on their fuel costs, with

the cheapest fuel type firing first to meet demand. Each generator, however, have

different ramp up rates. Cheaper fuel sources may only ramp up a small amount in the

short time frame, and a more expensive fuel must be used to fill additional load.


21/160

8

Real-time demand, generator types fired, and system traffic congestion all

contribute to determining Real-time LMPs. Generators fired and LSEs that request

additional power in the Real-time Market receive and pay Real-time LMPs for the trade

(Ott, 2003).

With intermittent energy like wind power, there is additional uncertainty that PJM

will need to address throughout operating day. Currently the level of wind energy

contribution in the PJM network is projected to only be around 0.5% by 2010 (PJM,

2007). Therefore, wind fluctuations have minimal impact on a system that already has

noise from demand. Wind power is accepted into the system as it comes, and PJM does

not currently charge penalties for wind over or under commitment; all imbalances are

settled in the Real-time Energy Market (National Grid, 2006).Wind uncertainty becomes

a far bigger issue when its total contribution in the system increases.

1.3DOEs 20% Wind by 2030In 2008, the Department of Energy published a report that details the feasibility of

having 20% of all energy consumption coming from wind power generation by the year

2030 (U.S. Department of Energy, 2008). The main findings of the report include:

1. Annual new turbine installations need to increase more than threefold.2. Costs of integrating additional wind power into the grid are modest.3. Achieving 20% wind is not limited by the availability of raw materials.4. Challenges for the placement and costs for new transmission to access

wind energy need to be addressed. (U.S. Department of Energy, 2008)


22/160

9

Still, even with the challenges to meeting the goal, the report concludes that the

U.S. can affordably and feasibly far surpass the 20% scenario. Due to the economic and

environmental benefits of wind energy, the DOE is making a great push to achieve the

20% wind generation target through cash grants and tax credits.

The main challenge of adding wind energy into the system is not its economic

costs but rather the volatile nature of wind. In Lamonts overview of wind energy, he

contends that wind generators cannot consistently deliver a committed level of power

since wind speeds are hard to forecast hourly and especially hard to predict 24 hours in

advance (2004). A meteorological method with weather and atmospheric variables is

used for longer term (several hours ahead) forecasts, while time series modeling is used

in short term (minute-ahead) predictions (Botterud, Wang, Monteiro, & Miranda, 2009).

With wind power being a huge part of generation in Europe, there has been great progress

in wind power prediction technology in the last decade. However, a point forecast for the

Day-ahead Market is still unreliable.

The grid operator, in our case PJM, must manage wind volatility with its own

reserves and issue orders for other assets to dispatch during low wind periods. Since

turning generators up and down results in accruing generator start-up and shut-down

costs, there is transaction cost associated with the frequent regulation of power sources in

real time. With wind energy currently making up a small fraction of energy generation,

wind volatility is not a major concern since energy demand is also noisy and PJM must

already take demand volatility into consideration. However, at above 15% of total power

generation, the costs from under and over commitment become substantial (Watson,


23/160

10

Landberg, & Halliday, 1994). Though PJM continues to emphasize the importance of

wind forecasting for their grid operations, forecasts can never eliminate uncertainty.

However, pumped hydroelectric storage may be paired with wind generation to

smooth out the volatility from intermittent energy. The Electricity Storage Association

(2009) provides an overview of pumped hydro generation detailed here. The basic

concept of pumped hydro is simple. Two water reservoirs are separated by a vertical

elevation. When there is excess energy supply, the surplus energy is used to pump water

from the lower reservoir to the upper one. When there is a supply deficit, upper reservoir

water is released back down to the lower reservoir, while generating energy just like

conventional hydroelectricity. The lower reservoir accumulates water, ready to be

pumped again. Some conventional hydro plants have extra capacity to function as

pumped storage, but there are also other technologies such as using underground mines

and the sea as lower reservoirs. Pumped storage represents the largest capacity of grid

energy storage currently available. They serve to greatly reduce the volatility from wind

generation, since they can be adjusted very quickly to respond to wind fluctuations. Their

major disadvantages, however, are their long construction time and high capital

expenditure. PJMs predicted pumped hydro storage capacity for 2010 is about 5000 MW

(PJM, 2007). When wind penetration reaches 20%, the amount of storage necessary to

accommodate the extra volatility will be a subject of discussion in this thesis.

Numerous other areas of research arise in preparation for increased wind

penetration. A few areas are outlined in a paper by Botterud, Wang, Monteiro, and

Miranda (2009). First, optimal operating reserves may change. With more wind, and thus

more variability introduced, the required operating reserve is expected to rise. The unit


24/160

11

commitment problem, usually formulated as a deterministic optimization problem, may

need reformulation to incorporate the uncertainty of wind forecasts. The problem of how

to integrate wind power predictions into RTO dispatch procedures is another area of

focus; transmission security and congestion constraints need to dictate when wind output

must be turned down so as to not overload the system.

One method to find the impact of increased wind generation for an RTO is by

simulation. Modeling the UC problem and simulating the real time economic dispatch

with PJMs regional data and a 20% wind generation level will reveal how generator

asset management may change with increased wind technology.

1.4 Overview of the ThesisThe thesis will first go through the existing literature on how an optimal mix of

generators can be selected using a unit commitment model in chapter 2. Chapter 3 will

then propose a mixed integer linear program to solve the UC problem for a single-day

with actual PJM system and generator data. The single-day model will be called upon in a

simulation, discussed in chapter 4, that emulates the Real-time Market using volatile

demand and wind data overviewed in chapter 5. The analysis of the model and simulation

outputs, especially the case with 20% wind generation, is covered in chapter 6. Finally,

chapter 7 discusses the findings and presents further areas of research on the topic.


25/160

12

Chapter 2.Unit CommitmentLiterature Review

The following chapter examines the portfolio selection problem from the RTOs

perspective. PJM aims to select the optimal set of assets to dispatch each hour. However,

generators have dispatch constraints such as ramp-up and ramp-down time, as well as

minimum on time (generators must be on for a certain number of hours before it can be

turned off) and minimum off time (generators must be off for a certain number of hours

before it can be turned on) (Padhy, 2004). To do this, PJM faces a unit commitment

problem that optimally selects the units to dispatch each hour of the next day. This

chapter will first present a literature review of the UC problem and a few well known

methods to solve it.

2.1 The UC ModelIn their book, The Next Generation of Electric Power Unit Commitment Models,

Hobbs, Rothkopf, ONeil, and Chao define the unit commitment problem as the

scheduling of production for electric power generating units over a daily to weekly time

horizon in order to accomplish some objective (2001). The objective function is to

minimize total operating costs, and the constraints involve both generator and system


26/160

13

constraints. Generator constraints involve their ramping time and minimum on and off

time, while system constraints include demand satisfaction and transmission constraints.

The UC problem is fairly complex as a large scale nonlinear mixed integer program, but

there are several methods and algorithms to find a near-optimal solution.

One formulation of the UC problem is as follows (Yan & Stern, 2002), (Padhy,

2004), (Guan, Luh, Yah, & Amalfi, 1992). Table 2-1 lists the model variables, where represents each hour of the next day, 124, and 1 , where is the numberof generators in the RTO jurisdiction.

Table 2-1: Variables and descriptions for Unit Commitment Literature Review

Variables Definitions

Decision variable

1, 1, , Generator on/off status Committed generation (MW) for generator at time Accumulated number of hours generator i has been on or off at time tGenerator parameters

Fuel cost for generator at time Startup cost for generator at time Minimum capacity for generator at time Maximum capacity for generator at time Minimum on time for generator Minimum off time for generator Ramp rate for generator System parameters Total demand bids for time Total spinning reserve requirement for time Spinning reserve generation of unit at time . A function of


27/160

14

Objective function:

The objective of unit commitment is to minimize total system costs which include

fuel costs and start up costs, for all generators and for all hours of the day.

: ,

The objective is usually nonlinear: the fuel cost is often modeled as a quadratic

function of , and the startup cost is usually a negative exponential function of thenumber of hours a generator has been off (Padhy, 2004). In fact, start up costs tend to be

different depending on whether a generator is in its cold, warm, or hot state (PJM,

2006b). In certain formulations, the shutdown cost and maintenance cost are also

modeled. A more complete objective function can also include transaction costs, bid

costs, and fixed costs of generation in the total system cost (McCalley, 2007).

Constraints:

Problem constraints include both generator constraints (constraint 1 through 4)

and system constraints (constraint 5 and 6).

1. Transition constraint

, , 0 , 0The transition constraint keeps track of the number of hours a generator has been

on or off. , accumulates until a shutdown or startup occurs, at which time the numberof hours on or off is 1 again (|,| 1.


28/160

15

2. Generator capacity constraints

,

0 0, 0

This ensures that the generator operates within its allotted capacity when it is on,

and does not generate power when it is off.

3. Generator minimum on and off time constraint

1, 1

1, 1

This constraint forces the unit to stay on if it has not met the minimum on time

requirement, and forces it to stay off if it has not met the minimum off time requirement.

4. Generator ramp time constraint

, , , 1 , 1Where is the ramping rate of generator per hour multiplied by 1 hour. Thisconstraint ensures that output from each unit is within ramping ranges.

5. Demand constraint

Total system generation satisfies forecasted demand for each hour.


29/160

16

6. Reserve requirement constraint

System generation satisfies reserve requirements. is the spinning reservegeneration of unit at , and is the spinning reserve requirement (usually a percent of) at .

Beside the above constraints, there are also line flow constraints, used to model

security and transmission (McCalley, 2007) Certain areas and zones also have their own

spinning reserves and operating reserves in addition to the system-wide constraints

(McCalley, 2007). Individual generators can have must-on or must-off requirements for

certain periods if, for example, they are under maintenance.

2.2 Additional ComplexitiesThe UC problem is a mixed integer nonlinear program. Solutions to the UC

problem have been researched for decades because of the system cost saving potential

involved (Yan & Stern, 2002). Padhy (2004) lists fifteen different methods for solving

the unit commitment problem. Some common methods are listed below:

1. Priority listing generators are sorted based on lowest operational cost andthen filled into the demand curve

2. Mathematical programming integer linear programming and dynamicprogramming

3. Lagrangian relaxation the most widely used method, which relaxesconstraints with Lagrangian multipliers


30/160

17

Over the last few years, the Lagrangian relaxation technique has been used widely

to achieve near optimal solutions. However, with the current technology of integer

program solvers, there has been a trend to formulate the UC problem as an integer linear

program (Chang, Tsai, Lai, & Chung, 2004).

But research continues in the recently deregulated market environment. For

example, Yan and Stern (2002) propose a different formulation of the UC problem for

deregulated simultaneous optimal auctions with a different objective function than the

traditional UC formulation. Rather than minimizing the total sum of fuel price and start

up price, Yan and Stern (2002) suggest minimizing market clearing price and start up

price:

: ,

Where: is the market clearing price at t.

,, ,, , , max

, . . 0

The market clearing price, however, does not have the separability property

necessary to utilize the Lagrangian relaxation method (Yan and Stern 2002).

With a large system operator like PJM, additional constraints for transmission,

security, and voltage are needed for each node and link in the transmission grid (Yamin

& Shahidehpour, 2003). These control the flow out of each node and through each branch

in the network while satisfying congestion and power limits through the transmission

lines.

It is also important to note that there exist specific complexities for different

utilities. For example a hydro asset faces unique reservoir water flow balance constraints


31/160

18

(Li, Hsu, Svoboda, Tseng, & Johnson, 1997). Individual plants also have different fuel

costs and ramp times depending on whether it is in its cold, warm, or hot state.

Depending on which state the generator is in, it will have different response delays to

PJM's initial notification for turning on and off as well (PJM, 2006b). Finding the optimal

model with fast and accurate computational techniques remains a challenge in the field.

PJM, when considering the UC problem, also accounts for bid and offer prices to

ensure market clearing (PJM, 2010b). PJMs vast repertoire of technologies for

scheduling operations includes not only its Unit Dispatch System (UDS), but also an

Enhanced Energy Scheduler (EES), the PJM eSchedules, Load Forecasting Algorithms,

the eMKT and Market Database System, a Hydro Calculator, the Two-Settlement

Technical Software, the PJM Synchronized Reserve and Regulation Scheduling Software

(SPREGO), and a Transmission Outage Data System (PJM, 2010b). Together, these

technologies help schedule all the generators in the RTO to satisfy the demand across

thirteen states.

2.2.1Adjustment to Day-ahead schedules in the Real-time MarketWhen uncertainties arise on operation day, adjustments must be made to the

schedules created the day prior. The main idea is to simply fill any excess demand above

current generation levels with the cheapest available units that can ramp up. When real

time demand levels are below total system power output, then the most expensive units

that can ramp down should do so to save costs. The PJM manual on Balancing

Operations describes how this is done with PJM tools (PJM, 2009a). However, additional

complexities are abundant. Some additional considerations include, for example, different


32/160

19

requirements from different areas in its control, the time error of PJMs notifications to

its generators, maintaining reserve requirements, transmission and voltage constraints,

and starting generation after a black-out (PJM, 2009a). A simulation for the adjustments

made to Day-ahead commitments in the Real-time Market is detailed in chapter 4.


33/160

20

Chapter 3.Day-ahead Market Model

This chapter develops a model that solves the UC problem for a single 24-hour

period in the Day-ahead Market. Much of the model comes from the formulation detailed

in the previous chapter, but many constraints are modified and linearized to assure fast

computation and feasibility. The model employed in this chapter is a mixed integer linear

program (MILP) for a 24-hour period. It takes as inputs the various generator parameters,

the status of generators at the end of each day, and the next days total demand bid and

wind forecast to schedule the next days generator outputs. The Real-time Market


34/160

21

simulation of the next chapter rebalances for any shortages and overages as they arise

during operation day, and it calls upon this model once a day to solve the next days

generation schedule. The model is formulated in MATLAB and calls on CPLEX, an

integer program solver package, to solve the MILP. See appendix 2.1 for program codes.

In this chapter, section 3.1 lists the model's assumptions that simplify it from the

actual PJM model. Section 3.2 introduces the variables used in the model detailed in

section 3.3. Finally, the parameters used as inputs in the model are listed in section 3.4.

3.1Model Assumptions

To fully model the PJM's Day-ahead Market with thousands of generators on a

network spanning thirteen states would be outside the scope of this thesis. Instead, certain

aspects of the model must be simplified to lower the run time of the model and to

compensate for the limited parameter data available as inputs.

The first simplification to the problem is to eliminate supply side offers from the

equation. "Market Behavior", which contains bidding information such as minimum sell

price, is among PJM's most closely guarded information (Spinner, 2005). Without a

public record of past offer history, it is impossible to even make an educated guess at

offer prices. Therefore, the model makes the assumption that PJM can freely select which

generator it wishes to turn on and off at each hour, as long as they are available,

regardless of their offer sell price and demand side buy price.

Second, the nodal transmission and security dimensions of the problem are

eliminated. This assumption is necessary due to a lack of data for transmission

parameters and also to keep the problem size manageable.


35/160

22

The third simplification is to reduce the number of generators in the problem from

PJM's projected 1305 generators in 2010 (PJM, 2007) to 45 non-wind generators, and

what should be five wind generators. This scale down maintains the ratio of each type of

generator, and their MW of generation, to the total number of generators and total PJM

MW generation. PJM has numerous small wind farms scattered across its region, and five

wind farms to a total of 50 generators would preserve the ratio approximately. Total

demand requirement and total wind generation per hour will also be correctly adjusted by

a factor of for the decreased number of generators. Table 3-1 summarizes the

breakdown of generators in PJM (PJM, 2007). Refer to appendix 1.1 for the generators

and associated capacities used in the model.

Table 3-1: PJMs breakdown of generator number and capacity by type

Coal Oil/Gas Nuclear Hydro Wind Diesel Pumped Jet/Gas Total

Units:

257 94 32 96 128 42 24 632 1305

Percent : 19.69% 7.20% 2.45% 7.36% 9.81% 3.22% 1.84% 48.43%

MWs: 69480 10056 30994 2338 874 411 5225 49468 168846

Percent: 41.15% 5.96% 18.36% 1.38% 0.52% 0.24% 3.09% 29.30%

However, there is insufficient data on each individual wind farms power output;

PJM only makes available data for aggregate grid wind output. Thus, it is necessary to

make a fourth assumption that the five wind farms work as one unit. So the actual

number of generators in the model is 46, 45 non-wind units, and 1 wind farm. A better

model would incorporate the correlation between wind outputs at different locales.

However, this model assumes PJM has one wind farm that produces at the total wind

output level of the PJM region.


36/160

23

A fifth assumption relates to how wind forecasts are made for the model.

Normally, wind forecasts use time series data together with meteorological factors such

as weather and atmospheric conditions (Botterud, Wang, Monteiro, & Miranda, 2009).

However, due to a lack of data on the meteorology of each day, the wind forecasts for the

model are made with only historical wind data, taking a quantile of the previous seven

days wind generation at the corresponding hour.

In addition, for all the renewable energy in this model, the marginal cost per MW

is assumed to be zero. This sixth assumption is mainly due to lack of data for individual

hydro and wind generators marginal costs. Since renewable energies mostly depend on

natural phenomenon such as rainfall, river flow, and atmospheric conditions, the per-MW

costs for these units are not easily calculated. However, this assumption has some

validity, since renewable energies do not have a cost input for each MW of power

production (such as costs for a BTU of fossil fuel). They are essentially free without their

fixed costs, which are generally not considered for unit commitment.

Another assumption due to lack of data is the elimination of startup costs from the

objective function. Normally, the total cost that the problem optimizes involves fuel cost

and startup cost. The startup costs are decreasing exponential functions that depend on

the number of hours a unit has been off. It takes the form (Padhy, 2004):

, 1, Here, m, counts the number of hours the generator has been off since it was last turnedoff. The parameters include , the boiler cool down coefficient, , the boiler cool downvariable cost, and , the fixed start up cost. A linear approximation of the startup costis discussed in literature, but specific values for these parameters are not available for


37/160

24

each generator type. Even so, startup costs are small relative to variable costs, and thus

are set to zero in the model. Shutdown costs, generally less than start up costs, are seldom

mentioned in UC formulations; they are also assumed to be zero. In finance terms, this is

similar to assuming no transaction costs when buying and selling assets.

An eighth assumption eliminates cold/warm/hot status distinction, and thermal

and non-thermal unit differences. In practice, an asset in its hot state ramps up quicker

than one in a cold state (PJM, 2006b). The model also assumes that all thermal units

behave similarly, and that other generator types behave like thermal units. Hydro plants

are modeled without rainfall or water drainage effects, but are modeled as thermal units

with quick ramp rates and no minimum on/off requirements.

A final simplification must be made about when to run the model. PJM solves its

next-day UC problem at noon each day. The results are announced at 4 P.M., but there is

a Balancing Market that operates from 4 P.M. to 6 P.M., where market participants may

submit revised offers. From 6 P.M. onwards, PJM performs additional UC runs to include

updated generator status. It then sends out individual modifications to specific generator

owners (PJM, 2010a). Since our model is not run multiple times each day, and does not

re-adjust as more information becomes known, it is more convenient to run the model

once at the end of each day (11 P.M.). This assumption avoids sudden jumps in generator

behavior from the end of one day to the beginning of the next.

3.2List of VariablesBefore examining the details of the model, Table 3-2 summarizes all the variables

used in the Day-ahead unit commitment model that are discussed in detail in section 3.3.


38/160

25

Table 3-2: Variables and definitions for the Day-ahead unit commitment model

Variable Definition

Decision variable

, Generator on/off status. Is 1 if generator is on at time , Turn-on marker. Is 1 if generator is turned on at time , Turn-off marker. Is 1 if generator is turned off at time , Committed generation (MW) for generator at time Generator parameters

Fuel cost for generator Minimum capacity for generator Maximum capacity for generator Minimum on time for generator Minimum off time for generator Ramp up rate for generator Ramp down rate for generator System parameters

, Total demand bids for time , Wind commitment for time (a function of the quantile)Tunable parameters Reserve requirement Quantile of wind commitmentEnd of Day parameters

, Generator s on/off status at , the end of the day today, Number of hours generator has been on at , the end of the day today, Number of hours generator has been off at , the end of the day today, Whether generator satisfies the minimum on-time at , Whether generator satisfies the minimum off-time at , Generator s generation (MW) at , the end of the day today


39/160

26

As Table 3-2 shows, the time subscript for the Day-ahead model is complex. Note

that this model is for a lagged information process. Thus all variables will be denoted

with the following indexes:

, : Information/decision about generator , known/executed at, actionable at .

For this model, is the end of the current day (11 P.M.), when the simulator callsthe model, and are hours of the nextday, from midnight to midnight. Thus, refers tosimulation time, while is model time used in the single-day model. For this model, is11 P.M. of each day, and it would be synonymous to define from 1 to 24.

The model runs over 1 and , where = 24 hours, and is the set of46 units under PJMs jurisdiction, 45 non-wind assets and one wind farm.

3.3Day-ahead ModelThe details of the model for a set of generators and time periods are presented

below.

3.3.1Decision VariablesThere are four decision variables for each generator at each hour. They function

together to decide when and how much power each generator will supply.

, 1, 0, , , 1 , 1, 0, , , 1


40/160

27

, 1, 0, , , 1 , 0 is the MW generated by generator at time .

3.3.2 Objective FunctionThe objective of unit commitment is to minimize the total system costs.

: , is the variable fuel cost from generator to produce 1 MW of power.

3.3.3 ConstraintsIndividual generator constraints, constraints 1 through 7, and system constraints,

constraints 8 through 10, make up the ten constraints for the problem.

1. Generator capacity constraint:, , , , 1 , , , , 1 and are the minimum and maximum capacities of generator . The

constraints ensure that assets produce within their capacity limits when the units are on.

2. Generator on/off constraints:, , 11 , , 1

1 Constraint formulation taken directly from Chang, Tsai, Lai, & Chung (2004).


41/160

28

, ,, , ,2 , , 2These constraints ensure that a unit cannot turn on and turn off in the same hour.

3. Generator on/off constraints carried over from the previous day:,, , ,, ,, , ,This constraint is the previous constraint but for 1, when 1 , since

is 11 P.M. today. , is an input parameter in the model. It is the current ( 11 P.M.)on/off status of generator . The model factors in whether a generator is on or off at theend of the current day when modeling for the next day.

4. Minimum on and off time constraints:, , 1, , 13 , , 1 1

,

.

1,

1,

4

, , 1 1

Here, is the minimum number of hours a unit must be on before it can beturned off, and is the minimum number of hours a unit must be off before it can beturned on. These two constraints ensure that if the unit is just turned on or off, it cannot

be turned off or on again until after the minimum on or off period.

5. Minimum on and off hours carried over from previous day:, , 1,, , 2 Constraint formulation taken directly from Chang, Tsai, Lai, & Chung (2004).3 Constraint formulation taken from Chang, Tsai, Lai, & Chung (2004), with modifications.4 Constraint formulation taken from Chang, Tsai, Lai, & Chung (2004), with modifications.


42/160

29

, , 1,, , These constraints are the same as the previous set, but they factor in how many

hours a generator has been on and off at , or at 11 P.M. today. , is the number of hoursa generator has been on ifit is still on at 11 P.M. today, and , is the number of hours agenerator has been offifit is still off at . , and , are outputs after the simulation forone day. They are extracted from the current days simulation and used as inputs into the

next days Day-ahead model. See section 4.2.1 for details on , and , , including howthey are calculated.

, and , are also parameters into the model. , 1 if generator has notbeen on for more than the minimum on time, and is 0 otherwise. , 1 if generator has not yet satisfied the minimum off time, and is 0 otherwise.

6. Ramping constraints:, ,, , , 2, ,, , , 2Above, 0 and 0 are the ramp up and down rates (MW/hr) for each

generator.

7. Ramping constraints carried over from previous day:,, , , ,, , ,


43/160

30

These constraints are for 1, and , is an input parameter that comes fromthe current (11 P.M.) capacity.

8. Demand requirement constraint: , , , 1, denotes the total demand bid for . Total generation must satisfy demand at

each hour of the next day.

9. Frequency regulation constraint: , , max, , 1This constraint specifies that the generators that are on cannot all be operating at

maximum capacity, but rather they must aggregately have a certain reserve capacity

should they be needed. max, is this reserve requirement, and 0 1 is atunable parameter. PJM, following North American Electric Reliability Corporation

(NERC) standards, uses 1% of peak demand forecasts (or max, ) as their reserverequirement (Botterud, Wang, Monteiro, & Miranda, 2009).

10.Wind generation quantile constraint:, , , 1,In this constraint, , is the th quantile of the distribution of the past

seven days actual wind generation for the same hour. , is a function of andpast wind data. This statistic is calculated by taking the matching hours wind generation

from the past seven days, and finding a quantile. The decision for which quantile to use is


44/160

31

a policy, and is a tunable parameter. This constraint only applies to the single windasset in the model.

3.3.4 Tunable ParametersThough the mixed integer linear program as it is formulated above is readily

solvable in an integer solver package like CPLEX, nuances still remain. For instance,

how much frequency reserve requirement is optimal to minimize risk as actual wind and

demand deviate from forecasted values in real time? What is the optimal quantile of wind

to commit in the Day-ahead Market to minimize costs for Real-time economic dispatch?

There are two tunable parameters that are used in the Day-ahead model that will play a

crucial role in optimizing costs the Real-time Market simulation:

: the percentage of peak demand that determines the reserve capacity for all thegenerators that are on at each hour.

: the quantile of the hours wind generation for the past seven days, committed

in the Day-ahead UC problem.

These two parameters will be revisited again in section 4.4, when the parameters

will be tuned to optimize the stochastic decision model for the Real-time Energy Market.

This makes up the core integer linear program that is formulated as a program in

MATLAB. See appendix 2.1 for the MATLAB coding of the MILP.


45/160

32

3.4Data ParametersThe parameters used in the model are listed in this section. For actual numerical

values used in the model, refer to appendix 1.1. The sources for these numerical

parameters are found in the Sources of Data section at the end of this work.

Generator parameters:

1. Minimum and maximum capacity (, ) the maximum capacity wasobtained from PJMs data on generator capacity, and minimum capacity is

assumed to be 20%-30% of max capacity.

2. Minimum on and off times (, ) these are taken from PJMs survey ofits generators.

3. Ramp up and ramp down rates (, ) ramp up rates are taken fromPJMs survey of its generators, and ramp down rates are assumed to be the

negative of ramp up rates.

4. Variable cost of production () the variable fuel costs of production aretaken from Shaalans handbook of electric generation (Shaalan, 2001). The

costs are approximate averages including both fuel and variable maintenance

cost for each MW of generation. True fuel costs are typically nonlinear.

System parameters:

1. Demand bids (,) PJM supplies data for hourly demand bids (submittedby 12:00 P.M. the previous day) for each day since 2000. These values are

used for the Day-ahead model. The simulation runs with 2009 values, with


46/160

33

both summertime and wintertime cases. The wintertime runs from January 2 st

to April 1st, with January 1st as an initializing day. January 1st's model

assumes that no generator is on at 11 P.M. of December 31st, 2008, and it is

therefore inaccurate. It is only there to provide realistic end-of-day generator

status parameters for January 2nd. Summer time runs from July 2st to

September 29st, with July 1st as an initializing day. All bid totals are scaled

down by a factor of (or 26.1), since PJM has 1305 generators, while this

model assumes only 50 generators for simplification. Though not used for the

Day-ahead model, the actual hourly data is available on the PJM website for

each day of the past decade. This will be used in the simulator of the Real-

time Markets. These values are also scaled down by a factor of 26.1.

2. Wind data , PJM also provides actual historical hourly windgenerations for the past six years. However, they do not have data on

forecasted wind. Indeed, wind forecasts are less significant with the current

low level of wind penetration. Forecasts for the model, , , aremade using the PJM historical wind data by taking the distribution of the past

weeks wind output for the corresponding hour, and applying the appropriate

quantile. For the model and simulation, the 2009 winter (Jan 1st to Apr 1st) and

summer (Jul 1st to Sep 29th) wind values are used. Wind generation is also

scaled down by a factor of 26.1.


47/160

34

Chapter 4.Real-time Market Simulation

In the Day-ahead model, all forward agreements are made for each hour of the

next day. When the next day arrives, however, actual demand and intermittent energy are

exogenous and will deviate from their forecasted values. PJM rebalances its energy

portfolio by applying frequency regulation at five minute intervals in the Real-time

Market. The dispatch and shutdown decisions compensate for supply shortages or store

excess energy. This chapter details the simulation of PJMs Real-time Market rebalance

decisions.


48/160


49/160

36

remains constant until the beginning of the next hour, when new exogenous demand

requires portfolio rebalancing again within five minutes.

The next two assumptions relate to which generators are fired first when there is a

supply shortage, and which generators are turned down first when there is a supply

surplus. PJM considers a number of variables such as fuel costs, startup and shutdown

costs, and generation offer amounts (PJM, 2010a). Working with only fuel costs, the

obvious answer is that the cheapest generators should be turned up first and the most

expensive generators should be turned down first. However, generator minimum on and

off times should also be considered. Generally, units with low minimum on and off time

requirements should be favored over those with a high requirement.

When firing up generators in the simulation, all plants with minimum on time > 5

cannot turn on if they are off. These generators are also the low cost coal and nuclear

plants; it is not economical to turn them on for a temporary demand spike that is likely to

last less than 5 hours. Although they cannot turn on if currently off, they are among first

to ramp up if currently on. On the other hand, the generators whose minimum on time 5 are ranked by the product of their minimum on time and fuel price, with the smallest

product fired first. With the exception of hydro (whose marginal cost is zero), these units

ramp up after the coal and nuclear units due to their higher fuel costs, but are the only

units that can turn on if they are currently off.

For turning down generators, the most expensive generators naturally have the

smallest minimum on and off times, so simply ranking the generators by their fuel costs

(highest to lowest) automatically insures that the lowest minimum off time units are the

first to ramp down. However, it is still necessary to specify that all plants with minimum


50/160

37

off time > 4 cannot turn off. These are again coal and nuclear plants that should not be

turned off to accommodate a brief demand drop. See appendix 1.2 and 1.3 for ordered

lists of generator ramp up and ramp down priorities.

Finally, with the addition of pumped storage available to pair with wind in real

time, some assumptions about pumped storage are in order. The storage spaces for these

assets are assumed to be large tanks rather than a natural reservoir, i.e. the capacity in

storage can go down to zero and there is no rainfall, evaporation, or river-flow. This

simplifies the model for hydro storage but maintains the general concept of a stored

energy. The total efficiency of converting wind energy to pumped water and then back to

energy again is 80% for the simulation.

4.2 Simulation VariablesAs with the Day-ahead model, the Real-time simulator also contains a large set of

variables. Some variables used in this chapter are also used in the Day-ahead model in

chapter 3. Specifically, the individual generator parameters are the same. However, this

chapter does introduce many new variables such as the state variables and simulation

decision variables. Refer to Table 4-1 for a list of variables that are discussed in more

detail in section 4.2.


51/160

38

Table 4-1: Variables and definitions for Real-time sequential decision simulation

Variable Definition

State variables

, Generator on/off status. Is 1 if generator is on at time , Number of hours generator has been on since it was last turned on, Number of hours generator has been off since it was last turned off, Power generation (MW) for generator at time Amount of power stored in pumped hydroelectric storage at time Variables used to calculate state variables

, Vector of, , used together with , to calculate , , Vector of,, used together with , to calculate , Decision variables

Amount of power pumped into storage at time Amount of power pumped out of storage at time , Power fired up by generator at time when there is supply shortage, Power turned down by generator at time when there is oversupplyVariables used to calculate decision variables Amount by which demand exceeds total generation at time Amount by which total generation exceeds demand at time Total system power generation at time Exogenous variables

Demand at time , Wind generation at time Parameters Efficiency coefficient of converting wind energy to pumped storage The maximum capacity of pumped hydroelectric storage


52/160

39

4.3 Simulation ModelThe simulation steps forward in time, making decisions at each hour to respond to

new information as they arrive. The sequential decision problem can be modeled with

state variables, exogenous variables, decision variables, transition functions, and an

objective function.

4.3.1 State Variables:The state variable is the minimum necessary information to make decisions,

formulate the model, and compute the objective function. For the Real-time dispatch

problem, the state variable includes the following variables:1. , 1, 0, , the assets on/off status2. , 0: number of hours a unit has been on until ,

(only if it is currently on at

)

3. , 0: number of hours a unit has been off until ,(only if it is currently off at )

4. , : the MW generated by unit at time .Note that , is deterministic for all non-wind generators. The wind generation

, is exogenous (more on exogenous variables in section 4.3.2). In fact, ,, ,,, , , are all only relevant when discussing non-wind units. Specifically, they onlyapply to thermal units, but there is an assumption that hydro units not involved in pump

storage behave like thermal units (see section 3.1). Therefore the above four state

variables apply to all \.


53/160

40

Also note that , is calculated from , and , , for . Tofind , , one needs to first determine whether the generator is currently on (, 1),and then find when it was last turned on, though only searching as far back as

hours

before the current hour. This is because if the unit was turned on more than ago, thenit automatically satisfies the minimum on time constraint. Thus the vector

, is necessary to compute , . The same applies for , , which iscalculated from , and , .

5.0 : The amount of energy in storage.These variables together describe the current state of all generators.

4.3.2Exogenous VariablesThere are only two factors of uncertainty in the model: the volatile demand and

wind. All exogenous information will be marked by a ^ symbol above the variable.

Define the following:

1. = the exogenous demand. arrives at the beginning of time so it isknown at and after .

2. , = the exogenous wind power output of the wind farms. , arrivesat the beginning of time so it is known at and after .

At any point in time , and , are known if and are unknown if .The data for these two exogenous variables come for PJMs data sets for hourly

demand and hourly wind generation for the region.


54/160

41

4.3.3Decision Variables:The decision variables are those that control the decisions at each time step. The

decisions in this simulation include how to manage wind by storing to / pumping from

hydroelectric storage and how much to fire up / turn down output when demand deviates

from supply. Thus, there are four decision variables to maintain at each hour. All Real-

time decisions are denoted with different superscripts on the variable .1. the amount of wind energy that exceeds the Day-ahead committed

amount, which is also the amount put into storage.

i. min , 0, , ,,, where,, is the MW of generation that was allocated by the Day-aheadmodel (a quantile of the historical wind) at time (end of previousday). is the coefficient of efficiency for converting MW of wind power toMW in hydroelectric storage. is estimated to be around 70%-85%(Electricity Storage Association, 2009). For our simulation, is set at 80%.

2. the amount pumped from storage when there is a shortage of windgeneration from its committed value.

i. min, 0,,, ,. Note that the decision is also exactly equal to ,, the state variable for the capacityprovided by pumped storage at time

. (See the transition functions in 4.3.4

for their relationship).


55/160

42

3. , the additional MW that generator dispatches at hour , when there is ashortage of supply. For ,, the rule for when to fire is no simple equation, butrather an algorithm described below.

i. First, ,depends on the exogenous power shortage that is present at thehour. Define as the MW of supply shortage.

ii. max , 0 , where is the total MW of generation inthe system, i.e. the total generation of non-wind generators, plus the

exogenous wind, and adjusting for storage and pumping:

,\ , iii. If 0, go through a list of generators sequentially. Generators

are ranked by both their cost and minimum on time required. See section

4.1 on how they are ordered.

iv. For the generator, first check if the generator is already on (, 1

.

v. If , 1, then , min , , , . The firstterm is the remaining capacity of generator , the second term is how mucha generator can ramp up in five minutes.

vi. If , 0, then check two conditions: , and 5. If

,

, then the generator cannot turn on. If

5, the generator is a

coal plant or nuclear plant whose minimum on time is too long to make it

economical to turn on for a temporary shortage. If, or 5,move on to the next generator and return to step iv.


56/160

43

vii. If all three conditions , 0, , and 5 are met, then, min , , , , . The extramax function in this equation is to ensure that when the generator is turned

on, it is outputting at least its minimum capacity.

viii. Update : ,ix. Go to the next generator on the list and return to step iv until 0.

4. , the output (MW) that asset must turn down at hour , when there is anexcess of supply. A similar algorithm as above is used to find ,.i. First, ,depends on the exogenous power surplus present at the hour.

Define as the MW of over-supply.ii. max , 0

iii. If 0, go through a list of generators sequentially. Units areranked by both their fuel cost and their minimum off time required. See

section 4.1 for how they are ordered.

iv. For the generator, first check if the generator is currently off. If , 0,then go to the next generator and repeat step iv.

v. If, 1, check two conditions: , and 4 . If these twoconditions are satisfied, it means that the generator has met its minimum on

time constraint and is not a coal/nuclear plant (whose minimum off time is

too long to make it economical to shut off for a temporary overage).

Therefore, the plant can not only turn down but also turn off.


57/160

44

vi. If, 1, , and 4, then the generator can turn off. Thus, min , , , . The second term is negativebecause since 0.

vii. If, 1 , but , or 4, this means that the generator canonly turn down but cannot turn off. Therefore:

, min , , , , viii. Update : ,

ix. Go to the next generator on the list and return to step iv until 0.

4.3.4 Transition FunctionsThe transition functions are the central elements to how the next time step is

determined. They detail the evolution of the state variables over time. Normally, the

transition functions are the equations that take all the elements of the state variable to. However, this problem requires two different types of transition functions. Thereare intra-hour transitions and inter-hour transitions.

Intra-hour transition functions:

Intra-hour transitions come from the fact that PJM makes its reserve adjustment

every five minutes. However, since there is no data for sub-hourly demand and wind, the

simulation approximates this by assuming demand is hourly, but generation must

rebalance to match the level of demand or wind within five minutes. Therefore, at the

beginning of each hour, information arrives for the actual demand and wind output for


58/160

45

that hour. All shortage and overage are adjusted within the initial five minutes of the

hour. Excess wind is also put to storage within the five minute time frame. After the first

five minutes, the state for rest of the 55 minutes is assumed to be constant. Thus, the

transition goes from to , where denotes the five minutes out of the hour. Butsince one hour is the smallest unit of time considered, intra-hour transitions are not

modeled. Rather, the new state replaces the old for the hour. Below, willbe denoted by . But in the MATLAB program, replaces as a new at eachtime step.

The transition functions are as follows:

1. , , , ,2. , ,

(Alternatively: , , , with , 0 for all )3.

, 1, , 00, , 0

, and , are functions of, and , respectively. , and , are both updated to replace , and , in each of the two vectors, which updates, and , respectively. , and , are updated as follows:

4. , 1, , 0 , 0

,

,

5. , 1, , 0 , 0,,


59/160

46

Inter-hour transition functions:

These are the transitions between hours, where a decision in one hour may affect

the state of the system in the next hour. Due to the nature of unit commitment, all

generators that are assigned outputs by the Day-ahead model are committed to their

generation amount and cannot deviate unless it is ordered to or approved by PJM (PJM,

2010a). If these generators are asked to fire up at , the additional output wouldrealistically only be for a 5 minute interval, after which theyd have time to re-adjust back

to their committed Day-ahead scheduled generation by the next hour. Thus, their output

at 1 is still what was decided for them the previous day. In the inter-hour period, thegenerators that are affected by the decisions from the previous period are those not

committed in the Day-ahead Market but newly turned on. If they are newly fired, they do

not turn down until a turn down decision is made in a future hour. Additionally, the

amount of power in hydroelectric storage is also modeled inter-hourly.

The transition functions are as follows:

1. , , , ,, ,, 0,, 0 means generator is not committed at time according to the decision

from the single-day model made at time (where is 11 P.M. of the previous day).2.

The seven functions above demonstrate how the simulation walks forward in time

updating each time period. They are the central components of the program that make the

adjustments for the Real-time Market.


60/160

47

4.3.5 Objective FunctionThe objective function is the ultimate goal of the simulation. The goal of PJMs

Real-time Market economic dispatch is the same as that of the Day-ahead unit

commitment problem: to minimize the total system costs, which depend on the current

state of the system and decisions to rebalance the portfolio.

To find the objective function, first define the contribution function,, , as the total fuel cost of the system. The contribution function is thesame as the objective function in the Dayahead model:

, , However, because the model is not deterministic but stochastic, different

sample paths for exogenous demand and wind will result in different totalcontribution. Thus an expectation is taken around the total contribution function.

,

The expected total contribution function will differ depending on the policy

used to make decisions. Denote the set of all policies available to choose from as and the individual policies as . The objective is to minimize the expected totalcontribution function using the best . Let be the decision made underpolicy . Thus, the final objective function becomes:

min: , In this simulation, the two policy parameters are and see section 3.3.

Thus the particular objective function of the simulation is:


61/160

48

min:, , ,

4.3.6 Simulation Change with 20% WindWith wind penetration hitting 20%, wind energy will make a substantial impact

on the energy market. The simulation, however, remains intact. The only change to the

simulation lies in the values of , and . Current wind penetration in PJM isroughly 0.5% of total generation. Therefore, when running the case with 20% wind,

, is inflated forty-fold to get wind penetration to 20%. However, it is unclearwhether pumped storage will also develop as fast as wind power will. It is unlikely that

pumped storage reservoir space will also increase to 4000% its current capacity by 2030.

Thus, the simulation assumes will only increase tenfold. This is a base value that isemployed in most simulations runs. Section 6.4.1 explores simulation results assuming

different levels of storage to see whether more storage will impact costs.

4.4Finding the Optimal PolicyIn order to obtain outputs from the simulation, and ultimately compare the results

from current wind output to 20% wind output, it is necessary to first tune the policy

parameters. Finding the optimal policy involves testing different parameters and

comparing the objective


62/160

49

4.4.1How to Optimize Tunable ParametersThere are two policies used in order to optimize the objective function. The first

policy determines how much total reserve capacity should be maintained in the system.

Recall from section 3.2 that the frequency reserve constraint is:

, , max, , 1 is the tunable parameter for the reserve requirement. PJM currently follows

NERC standards by setting as 1%.The second tunable parameter is for the wind commitment. Wind commitment in

this simulation is set as a quantile of the distribution of wind data from the past seven

days at the corresponding hour. Recall from section 3.2 that the wind generation quantile

constraint is:

, , , 1,Where , is the th quantile of the distribution of the past seven days

actual wind generation for the same hour. Thus is another tunable parameter.Usually, optimizing over a single tunable parameter involves varying theparameter over a range and comparing the objective value from different policies to see if

one policy results in a better objective (lower total cos

mat wind thermal 2010

Documents