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by
Tong Zhang
2013
The Thesis Committee for Tong Zhang
Certifies that this is the approved version of the following thesis:
Generation Capacity Expansion Planning using
Screening Curves Method
APPROVED BY
SUPERVISING COMMITTEE:
Ross Baldick
Surya Santoso
Supervisor:
Generation Capacity Expansion Planning using
Screening Curves Method
by
Tong Zhang , B.E.
THESIS
Presented to the Faculty of the Graduate School of
The University of Texas at Austin
in Partial Fulfillment
of the Requirements
for the Degree of
MASTER OF SCIENCE IN ENGINEERING
THE UNIVERSITY OF TEXAS AT AUSTIN
May 2013
Dedicated to my parents and girlfriend.
Acknowledgments
I would like to thank many people who helped me during my research.
First of all, I would like to thank my advisor, Dr. Ross Baldick, for his
support and guidance. He is super wise and experienced in power engineering,
and he is always able to patiently point out my faults in research and to
generously makes my way to finish this thesis easier. I would also thank Dr.
Surya Santoso for serving as my second reader, his advice is precious.
Secondly, I would like to thank my friends. Joo Hyun Jin has been a
crucial source of advice, giving me instruction about dealing with generation
data and AURORAxmp simulation. Ye Zhao helped me a lot in thesis writing,
his experience in Latex is of great importance.
Finally, I would like to thank my parents. Without them I won’t be
able to come to this world. Also I want to thank my girlfriend for her trust
and support. Family is always my power in doing anything.
v
Generation Capacity Expansion Planning using
Screening Curves Method
Tong Zhang , M.S.E.
The University of Texas at Austin, 2013
Supervisor: Ross Baldick
Generation capacity expansion planning has been evolving in rencen-
t decades. First, the long-term planning procedure is taking more detailed
considerations of short-term operation impacts. Second, as more renewable
resources being integrated into the grid, a new strategy of dealing with the
non-dispatchable renewable energy should be developed, with more ancillary
services needing to be procured from thermal units. These trends are expected
to continue.
This thesis describes a methodology in generation capacity expansion
planning. The screening curves method can be used to estimate optimal gener-
ation mix for a target year. This thesis first introduces three screening curves
methods, which are classified based on their ability to deal with detailed short-
term operational issues. It then includes ancillary service and wind integration
impacts. Finally, it presents a case study of a projected ERCOT 2030 system.
vi
Table of Contents
Acknowledgments v
Abstract vi
List of Tables ix
List of Figures x
Chapter 1. Introduction 1
Chapter 2. Screening Curves Methods and Models 4
2.1 Conventional Screening Curves Method . . . . . . . . . . . . . 4
2.1.1 Standard conventional screening curves method . . . . . 4
2.1.2 Concise version . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Basic screening curves method . . . . . . . . . . . . . . . . . . 11
2.3 Enhanced screening curves method . . . . . . . . . . . . . . . 13
2.3.1 Definitions in enhanced screening curves method . . . . 14
2.3.2 Preliminary calculations . . . . . . . . . . . . . . . . . . 17
2.3.2.1 Step 1: identify restart points . . . . . . . . . . 17
2.3.2.2 Step 2: exclude long off-line duration restarts . 17
2.3.2.3 Step 3: eliminate inflexible restarts . . . . . . . 19
2.3.2.4 step 4 : update values of tm . . . . . . . . . . . 21
2.3.3 Enhanced screening curves module . . . . . . . . . . . . 22
Chapter 3. Ancillary Service Impact 25
3.1 Introduction to ancillary service . . . . . . . . . . . . . . . . . 25
3.1.1 Spinning reserve . . . . . . . . . . . . . . . . . . . . . . 25
3.1.2 Non-spinning reserve . . . . . . . . . . . . . . . . . . . . 27
3.2 Energy producing and spinning reserve capacity co-optimization 28
vii
3.3 Separated spinning reserve capacity optimization . . . . . . . . 29
3.3.1 Step 1: determine available SR time period . . . . . . . 31
3.3.2 Step 2: calculate system SR operation cost . . . . . . . 32
3.3.3 Step 3: select least cost technology for SR . . . . . . . . 34
3.4 Non-spinning reserve capacity planning . . . . . . . . . . . . . 36
Chapter 4. Data Assumptions 37
4.1 Capital cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2 FOM cost and VOM cost . . . . . . . . . . . . . . . . . . . . . 39
4.3 Variable fuel cost . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3.1 Fuel prices . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3.2 Heat rate and efficiency . . . . . . . . . . . . . . . . . . 41
4.3.3 Variable fuel cost . . . . . . . . . . . . . . . . . . . . . . 43
4.4 Start-up cost and tm . . . . . . . . . . . . . . . . . . . . . . . 44
4.4.1 Start-up cost . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4.2 tm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.5 Data assumptions summary . . . . . . . . . . . . . . . . . . . 46
Chapter 5. Case Study 47
5.1 Case study with screening curves methods . . . . . . . . . . . 47
5.1.1 Case study based on conventional SCM . . . . . . . . . 47
5.1.2 Case study based on basic SCM . . . . . . . . . . . . . 50
5.1.3 Case study based on enhanced SCM . . . . . . . . . . . 51
5.1.4 Case study discussion . . . . . . . . . . . . . . . . . . . 52
5.2 Case study considering ancillary services . . . . . . . . . . . . 55
5.3 Current ERCOT generation mix . . . . . . . . . . . . . . . . . 55
5.4 Case study using AURORAxmp . . . . . . . . . . . . . . . . . 57
5.5 Results summary and analysis . . . . . . . . . . . . . . . . . . 58
Chapter 6. Conclusion 60
Bibliography 62
viii
List of Tables
3.1 Calculations of spinning reserves [15] . . . . . . . . . . . 26
3.2 Terms for non-spinning reserves . . . . . . . . . . . . . . 28
3.3 Capital cost and variable O&M cost . . . . . . . . . . . . 34
3.4 Cost calculation for spinning reserve . . . . . . . . . . . 35
4.1 Capital costs by year [9] . . . . . . . . . . . . . . . . . . . 38
4.2 Annualized capital costs . . . . . . . . . . . . . . . . . . . 39
4.3 Fixed operation and maintenance cost [9] . . . . . . . . . 40
4.4 Variable operation and maintenance cost [9] . . . . . . . 40
4.5 Coal and NG price by year [5] . . . . . . . . . . . . . . . . 41
4.6 Heat rate by year [9] . . . . . . . . . . . . . . . . . . . . . . 42
4.7 Variable operation and maintenance cost [9] . . . . . . . 44
4.8 Hot start-up cost [3] [9] . . . . . . . . . . . . . . . . . . . . 45
4.9 tm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.10 Thermal units cost data summary . . . . . . . . . . . . . 46
5.1 Data for conventional screening curves method . . . . . 48
5.2 Generation mix based on conventional SCM . . . . . . 49
5.3 Data for basic SCM . . . . . . . . . . . . . . . . . . . . . . 50
5.4 Generation mix based on basic SCM . . . . . . . . . . . 50
5.5 Data for enhanced SCM . . . . . . . . . . . . . . . . . . . 52
5.6 Generation mix based on enhanced SCM . . . . . . . . 53
5.7 Generation mix considering ancillary services . . . . . . 55
5.8 Installed thermal capacity in ERCOT 2012 . . . . . . . 56
5.9 AURORAxmp simulation result . . . . . . . . . . . . . . 58
5.10 Capital costs by year . . . . . . . . . . . . . . . . . . . . . 59
ix
List of Figures
2.1 Annual generation cost curve . . . . . . . . . . . . . . . . 6
2.2 Annual load-duration and net load-duration curve . . . 7
2.3 Conventional screening curves method . . . . . . . . . . 8
2.4 Concise conventional screening curves method . . . . . 10
2.5 Chronological load and net load curve . . . . . . . . . . 11
2.6 Identify restart points . . . . . . . . . . . . . . . . . . . . . 13
2.7 Basic screening curves method . . . . . . . . . . . . . . . 14
2.8 Step 1: identify restart points . . . . . . . . . . . . . . . . 18
2.9 Step 2: Exclude long off-line restarts . . . . . . . . . . . 18
2.10 Step 3: Eliminate not flexible restarts . . . . . . . . . . 20
2.11 Enhanced screening curves method . . . . . . . . . . . . 23
3.1 Optimized generation mix . . . . . . . . . . . . . . . . . . 30
3.2 Optimized generation mix . . . . . . . . . . . . . . . . . . 31
3.3 Spinning reserve operating cost . . . . . . . . . . . . . . . 33
4.1 Heat rate of a 400 MW combined-cycle gas turbine [3] 42
5.1 Conventional SCM . . . . . . . . . . . . . . . . . . . . . . . 49
5.2 Basic SCM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.3 enhanced SCM . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.4 Installed capacity in ERCOT 2012 [4] . . . . . . . . . . . 56
5.5 AURORAxmp simulation result [10] . . . . . . . . . . . . 57
x
Chapter 1
Introduction
Generation capacity expansion has always been an important part of
power system planning. With more detailed parameters considered and with
renewable energy integrated into power grid, many new methods and improve-
ments have been proposed. Besides, commercially available software is able
to deal with generation mix optimization. However, the huge amount of data
input and long running time are big drawbacks. Thus, we are still interested
in building up a simpler and faster model that can provide us with reliable
results. Further, such a model gives us a way to conveniently analyze different
impacts on generation planning.
This paper describes three models based on screening method. The
screening curves method is a simple way using annual load shape information
and costs of competing power plant technologies, such as annualized capital
costs, variable fuel costs, and operation and maintenance costs, to find a least-
cost generation mix solution. The three models are: conventional screening
curves model, basic screening curves model, and enhanced screening curves
model. Each model has its own advantages and drawbacks regarding running
time, accuracy, assumption limitation and other aspects.
1
Conventional screening model was first proposed in [14] in 1969. In
conventional screening approach, total yearly costs of planning alternatives are
computed against load duration curves (or capacity factor curves), providing a
least-cost generation mix solution. In 2008, with more as more wind generation
being integrated into power grid, renewable integration impact is considered
in this model in [11] and [12] as must-run generation. In this improvement, the
load-duration curve is replaced by net load-duration curve, where net load is
defined to be the load curve values minus wind production values. Note that
the only parameters needed in this model are capital cost, fuel cost and net
load-duration data.
However, with increasing penetration of wind energy, start-up costs
are no longer negligible for thermal generators. Basic screening curves model
was developed in [13] in 2011, a long-term analysis of evaluating start-up cost
was implemented. Moreover, the increased intermittent renewables requires
more ancillary services. The impact of considering ancillary services is fully
discussed in [2] in 2011. Besides, we develop a new method of determining
generation technology mix including ancillary services. A chronological net
load curve may be included as a parameter for calculating annual start-up
cost.
The enhanced screening model was developed in [3] in 2012 and is im-
proved by us. This model provides a detailed representation of short-term
scheduling impacts, such as unit commitment (UC), operational and mainte-
nance (O&M) costs. Detailed fixed O&M costs, variable O&M costs, mini-
2
mum stable running capacity of thermal generators should be provided. The
chronological net load curve is very important in this model.
The thesis is structured as follows: Chapter 2 describes three screening
curves methods; Chapter 3 focuses on ancillary service impacts; Chapter 4
provides data assumptions; Chapter 5 explores the ERCOT 2030 case study
using screening curve method and AURORAxmp software; and Chapter 6
draws a conclusion.
3
Chapter 2
Screening Curves Methods and Models
In this chapter, three models of generation mix planning will be intro-
duced. They are the so called screening curves methods. We classify them
into three categories based on their ability to deal with detailed short-term op-
eration issues. Each of them has its own desirable properties and drawbacks,
and these will be discussed.
2.1 Conventional Screening Curves Method
2.1.1 Standard conventional screening curves method
Conventional screening curves method (conventional SCM) is the foun-
dation of the other two SCMs, and was first proposed in [14] in 1969. In
conventional SCM approach, yearly total cost is represented as an affine func-
tion of variable fuel cost (VFC), and variable operation and maintenance cost
(VOMC). The annualized capital cost and fixed operation and maintenance
cost (FOMC) are fixed. Thus, for one megawatt (MW) generation capacity,
the annual generation cost is a function of its annual firing time duration:
TotalCost(T ) = CapC + FOMC + (V FC + V OMC) · T (2.1)
Where CapC is the annualized capital cost per MW; FOMC is the
4
fixed operation and maintenance cost per MW per year; V FC is variable fuel
cost per MWh; V OMC is variable operation and maintenance cost per MWh;
T is the total year firing hours of that given MW.
On generation side, note that capital cost, fixed O&M cost and fuel
cost vary for different types of power plant. So the total costs of different
power plants are different for a given operating time duration T . Therefore,
our goal is to choose the mix of power plant to minimize the total cost over
all technologies. Figure 2.1 is annual generation cost curve, showing the
total generation cost curve per MW for three competing technologies, baseload
(nuclear and coal), combined-cycle gas turbine (CC), simple-cycle combustion
turbine (CT). The minimum cost is the lowest piece-wise linear function of
firing hours. The points of the intersections on the horizontal axis separate
different technologies, and the intervals of these points determine the annual
firing duration of those technologies.
Also, on load demand side, a cumulative distribution function (CDF) of
load level can be built up, which is called annual load-duration curve. At
any particular demand level, annual load-duration curve evaluates the number
of hours that demand exceeds that level, see Figure 2.2. However, as more
as more wind generation being integrated into power grid, renewable integra-
tion impact should be considered, this issue was modeled in [11] and [12] as
must-run generation. Generally, in long-term planning, it can be modeled as
negative load. So we define net load to be real load minus the wind generation,
and the corresponding curve is the net load-duration curve. Load-duration
5
0 2000 4000 6000 80000
100
200
300
400
500
600
Gen
erat
ion
Cos
ts(k
$)
Firing Hours (hour)
Coal CC CT
8760
Figure 2.1: Annual generation cost curve
curve and net load-duration curve, shown in Figure 2.2, both provide a one
to one relationship between a load or net load level and its annual demand
duration. For example, in Figure 2.2, the 68 GW net load level has to be
satisfied for 1214 hours during a year. Since only net load demand can affect
thermal utility investment, we will only focus on the net load in the following
chapters.
The firing hour of annual net load-duration and generation must match
each other, so the load level is equivalent to generation capacity (or genera-
tion level). As discussed above, generation cost curve determines the optimal
operating duration for each technology, and net load-duration curve gives a
one-to-one relationship between firing duration and generation capacity. Thus,
6
0 2000 4000 6000 80000
10
20
30
40
50
60
70
80
90
100
110
Load
Lev
el (G
W)
Firing Hours (hour)
68 GW1214 h
Load
Net LoadWind
Figure 2.2: Annual load-duration and net load-duration curve
the method of combining the two curves gives us a picture of the optimal gen-
eration capacity in a given year, and the analysis using these two curves is the
so-called screening curves method. The resulting screening curve is as shown
in Figure 2.3. In this graph, coal power plant and nuclear power plant are
modeled as baseload generation, and we will keep this approximation for the
following models.
2.1.2 Concise version
The net-load duration curve works only as a look-up table. A concise
version is, by eliminating the firing hour parameter, to express generation cost
as a function of load level or load point (lp). One way to see this is, as in
Figure 2.3, to rotate load level axis in lower graph 90 degree counterclockwise
7
0 2000 4000 6000 80000
20
40
60
80
100 Net load-duration curve
Load
Lev
el (
GW
)
Firing Hours (hour)
CT28 GW
8760
CC28 GW
Baseload39 GW
0
200
400
600 Baseload CC CT
Gen
erat
ion
Cos
t (k$
)
Figure 2.3: Conventional screening curves method
8
onto horizontal axis in upper graph. Load level axis becomes new horizontal
axis of the upper graph. Since the original look-up table load-duration curve is
non-linear, after rotation, the new concise cost function is not affine, as shown
in Figure 2.4. Another way to see this is to express firing hour as a function
of load point (lp), and Equation (2.1) becomes:
TotalCost(lp) = CapC + FOMC + (V FC + V OMC) · T (lp) (2.2)
Where lp is load point; CapC is the annualized capital cost per MW;
FOMC is the fixed operation and maintenance cost per MW per year; V FC
is variable fuel cost per MWh; V OMC is variable operation and maintenance
cost per MWh; T is the total year operating hours of each lp. Note that now
total cost is a function of lp in Equation (2.2), instead of a function of T in
Equation (2.1).
Again, the least-cost generation mix is given by the lower envelope
curve. The points of the intersections on horizontal axis separate differen-
t technologies, and the intervals of these thresholds directly determine the
optimal capacity for each technology, see Figure 2.4. Three technologies are
considered here, coal, combined cycle gas turbine (CC) and combustion tur-
bine (CT). Baseload cost function is represented by coal power plant, since
nuclear generation capacity is usually unchangeable and determined by many
other factors.
Furthermore, we introduce some more notations to better describe this.
9
90 80 70 60 50 40 30 20 10 00
100
200
300
400
500
600
Baseload 39 GW
CC28 GW
Gen
erat
ion
Cos
ts (k
$)
Load Level (GW)
Baseload CC CT
CT28 GW
Figure 2.4: Concise conventional screening curves method
First of all, we define a set K to represent all possible technologies:
K = {Nuclear, Coal, CC, CT}. Also we use k as an index for set K.
Secondly, we define a set LP to represent all possible load points: LP =
{1, 2, 3, ..., lpmax}. Also, lp is used as an index for set LP .
The least-cost generation mix is given by objective function:
MinTotalC(lp) = mink∈K{ TotalC(lp)k }, lp ∈ LP (2.3)
Where total cost of each technology is given by:
TotalC(lp)k = CapCk + FOMCk + (V FCk + V OMCk) · T (lp) (2.4)
The conventional screening method is simple and requires very few
computational efforts. It is a good methodology aimed at building up an
10
initial estimate for an optimal future generation mix. But it fails to account
for start-up costs and short-term unit commitment strategies. These could
affect the optimal mix, especially when the intermittence of significant wind
integration has made the start-up cost of the thermal system non-negligible
as a fraction of overall thermal cost. Thus, more detailed factors should be
provided in order to further study the generation planning.
2.2 Basic screening curves method
0 10 20 30 4030
35
40
45
50
55
60
Load
Lev
el (G
W)
Time (hour)
Load
Net Load
Wind
Figure 2.5: Chronological load and net load curve
Basic screening curves method (Basic SCM) is expanded to deal with
detailed short-term operational impact. It was developed in [13], where only
start-up factor was considered. In fact, this greatly improves the accuracy of
11
the conventional SCM, and still keeps the model simple and easy to implement.
With regard to start-up impact, the start-up costs and total number
of start-ups for each load point are needed. Preliminary calculations are
required before SCM can be applied.
Thus, we add the chronological net load curve for the purpose
of getting information about restarts. Instead of annual duration in annual
load-duration curve, the chronological load curve is a real-time demand curve.
This gives us information about when and at which generation level (=load
level) the start-up happens. A two-day chronological net load curve example is
shown in Figure 2.5. Moreover, with chronological net load curve, identifying
the restart point is easy. For instance, if we want to focus on time period from
10 to 35, start-up points are quite obvious in Figure 2.6, which are represented
by red curves. Then every value of load demand is rounded down to the load
level. For instance, loads between 40 GW to 40.99 GW are rounded down to
40 GW load level. Therefore, the annual start-up times can be calculated for
all the load levels, which is denoted by N(lp).
Plugging the start-up impact into Equation (2.2), we get
TotalC(lp)k = CapCk + FOMCk + (V FCk + V OMCk) · T (lp) + SCk ·N(lp)
(2.5)
Where SC is the start-up cost per start; N(lp) is the number of start-
ups of each lp per year.
The basic SCM is visualized in Figure 2.7. This result is different from
12
Figure 2.6: Identify restart points
conventional SCM, since we take start-up cost into account. We will discuss
the reason in Chapter 5.
In basic screening curves method, the number of start-ups in each load
level (lp) should be calculated prior to implementing SCM. Although this
method given by Equation (2.5) is only a small step forward, the result turned
out to be accurate (this will be discussed in chapter 5) and the total compu-
tation time is not significantly increased.
2.3 Enhanced screening curves method
Enhanced screening curves method (Enhanced SCM) explores a more
detailed analysis in the presence of short-term economic scheduling consider-
13
90 80 70 60 50 40 30 20 10 00
100
200
300
400
500
600
Gen
erat
ion
Cos
ts (k
$)
Load Level (GW)
Baseload CC CT
Baseload 37 W
CC27 GW
CT31 GW
Figure 2.7: Basic screening curves method
ation. This effort was first proposed in [3], and is further developed here.
In unit commitment issues, sometimes it is more profitable to keep a
power plant running at a reduced output than to shut it down and restart
it. This alternative gives us a way to further consider short-term details in
our long term generation planning. However, we do not consider minimum
shut-down time, minimum start-up time and other unit commitment dynamic
constraints.
2.3.1 Definitions in enhanced screening curves method
To begin with, we define some variables:
1. (h, lp) pair
14
(h, lp) pair is a point representing chronological hour h and load level lp in
chronological net load curve (cumulative time duration and chronological
time are denoted by T and h separately). This discretization will help
us assign operation status for each point. For example, we could assign
status to an (h, lp) pair:
Status(h, lp) =
0 shut down1 spinning reserve2 minimum ouput3 full output
(2.6)
2. IG
IG is defined as the capacity of inflexible generation (IG). The output
of IG is assumed to be fixed, and not controllable during the whole year.
Nuclear is a type of inflexible generation.
3. m
m is defined as the ratio of minimum output divided full output, This
value is assumed to be the same for all flexible generation. For
normal thermal generators, this value is usually 30% to 40%.
4. tm
tm is defined as the maximum time duration of a unit running at its
minimum stable output to avoid a restart. Since we ignore start-up
time and other issues, the no-load cost of operating a generator for tm
hours should be equal to start-up cost to be economically viable. tm
15
is calculated by Equation (2.7) if no-load cost and start-up cost are
collected.
tm =SC
NLC(2.7)
Where SC is start-up cost; NLC is the no-load cost.
Before knowing generation mix, there is no information about fuel type
and start-up cost for each load level, so tm for each lp cannot be cal-
culated. Thus, in the model proposed in [3], tm is assume to be the
same for all technologies, and has a fixed value of 8 hours. But still,
in this thesis, we improve this model and consider tm to be different for
each technology, and this will be discussed in next section.
5. Merit order
As shown in Figure 2.4, there is a natural merit order for generators. In
fact, lower load levels have lower fuel costs, and higher load levels have
higher fuel costs. Thus, we never run generators of higher levels unless
those with lower load levels are all running. In other words, it is sensible
to first shut down generators of higher levels, and then those of lower
levels.
Admittedly, load levels of generators could be arranged in an order other
than merit order, but it is easy to prove this alternative will lead to
the same optimal result. Additionally, this change would be hard to
understand and would be confusing to us when we are to model this.
16
2.3.2 Preliminary calculations
Prior to applying actual SCM, four steps of preliminary calculations
should be carried out. The four steps involve unit commitment strategy. We
illustrate this step by step, and a case study is represented as visualization.
The first three steps are first proposed in [3].
Also it is important to mention that there is no information about
generation mix in preliminary calculations, instead, every (h, lp) pair stands
equal in this unit commitment strategy analysis. Thus, all parameters are
assumed to be the same for all technologies.
2.3.2.1 Step 1: identify restart points
Step 1 is the same as we have explored in basic screening curves method.
In the example, we study the time period from 10 to 35, and thus the points
on red curves represent the start-up points in Figure 2.8.
2.3.2.2 Step 2: exclude long off-line duration restarts
If the off-line duration is longer than tm (the maximum time duration of
a unit running at its minimum stable output to avoid restart), the utility owner
would rather shut it down for economic concerns. We specify tm limitation
as green lines, and consequently restart points below them are the selected
restarts (red curves) in this step, as illustrated in Figure 2.9.
17
Figure 2.8: Step 1: identify restart points
Figure 2.9: Step 2: Exclude long off-line restarts
18
2.3.2.3 Step 3: eliminate inflexible restarts
On generation side, if a restart at a generation level of lp is to be
avoided, flexible generators of all load levels below this lp should be able to
operate at their minimum stable output before that restart point. However, if
the IG capacity is so large to a degree that we do not have enough flexibility to
do so and at the same time able to meet the demand (generation greater than
demand), the only way is to shut down some generators. Because of merit order
of the generation levels, we shut down generators from higher level to lower
level. Until we have enough flexibility to run all remaining flexible generators
at or above their minimum stable output.
This step has to be applied to each lp qualified for the first two steps
from high to low levels. In the example, we consider for lp = 45 GW, IG =
35 GW and m = 0.3. Although these values mean too much IG capacity, they
give us a visualization of how this step eliminate inflexible restarts.
In Figure 2.10, black curve represents demand, blue lines represent gen-
eration related levels. Solid blue line is the generation level lp to be analyzed.
Shadowed area is inflexible generation. The dash blue line is the flexibility lim-
itation, and the generators of lp have the output flexibility from this limitation
up to lp. Flexibility limitation is given by:
FlexLim = lp− (1−m) · (lp− IG)
= IG+m · (lp− IG)(2.8)
Where lp is the generation level we want to analysis; m is the ratio
19
Figure 2.10: Step 3: Eliminate not flexible restarts
20
of minimum stable output over full output; IG is the amount of inflexible
generation. In this example, flexibility limitation is 38GW.
The two candidate restart points 1⃝ and 2⃝ are qualified for the first
two steps discussed above. Restart point 1⃝ satisfies flexibility requirement.
Whereas, when we consider 2⃝, before restart point 2⃝ (h = 24 to 29), the
load demand curve dropped out of generation flexibility limitation. The pink
curve represent load levels that are lower than minimum generation output in
Figure 2.10. This result means restart point 2⃝ cannot be avoided, lp = 45 GW
has to be shut down for h = 23 to 30. And thus we have to continue to test
lp = 44 GW, and keep going until the load demand is within generation output
range.
Step 3 is computational expensive. However, in a lot of generation
planning practices, the amount of capacities of IG only takes up a small fraction
of the total generation system. So the generation flexibility limitation will
not be violated, and load demand curve is always above minimum output of
the generation system. For cases like ERCOT generation system, there is no
commitment issue due to lack of flexibility, so step 3 can be skipped.
2.3.2.4 step 4 : update values of tm
tm is updated by Equation (2.7) tm = SCNLC
for technologies with dif-
ferent SC and NLC. Then the updated tm is put back in step 2, until all
possible tms are enumerated.
This step allows us to be more accurate on considering short-term unit
21
commitment strategies. The values of tm for different technologies are not
and should not be regarded as the same. However, the computational effort is
linearly increasing as we keep calculating for different values of tm. Fortunately,
the number of thermal generation types are small. Usually it is desirable
to only account for coal and combined-cycle gas turbine, the reason will be
discussed in chapter 4. Thus, the computational effort is actually doubled
when considering two values of tm. If the step 3 can be skipped, this doubled
computation time is acceptable.
2.3.3 Enhanced screening curves module
In preliminary calculation section, we discussed how to get restart
points considering unit commitment issue. And at the same time, we are
able to determine what status each (h, lp) pair is. Consequently, we can pro-
cure the time duration for a lp when generators are running at their minimum
stable output and that when they are running at their full output. We de-
fine Tm(lp) to be time duration of a lp operating at its minimum output and
Tf(lp) to be time duration at full output. So the total running duration is
T (lp) = Tm(lp) + Tf(lp). In fact, generators may run at an output between
minimum and maximum, but here we simplify the situation to be minimum
output and full output only.
TotalC(lp)k =CapCk + FOMCk + V OMCk · T (lp)
+ V FCk · Tf(lp) +m · V FCk ·Tm(lp)
eff+ SCk ·N(lp)
(2.9)
Where Tm(lp) is the time duration of running at minimum output of
22
lp; Tf(lp) is time duration of running at full output of lp; m is the ratio of
minimum output over that of full output; eff is the efficiency of minimum
generation per unit fuel; SC is start-up cost per start; N(lp) is the number of
start-ups of each lp per year.
The enhanced SCM is shown in Figure 2.11, given the same set of
parameters as for conventional and basic ones. We will discuss details about
result analysis in Chapter 5.
90 80 70 60 50 40 30 20 10 00
100
200
300
400
500
600
Gen
erat
ion
Cos
ts (k
$)
Load Level (GW)
Baseload CC CT
Baseload 38 GW
CC26 GW
CT31 GW
Figure 2.11: Enhanced screening curves method
Enhanced SCM considers start-up cost, unit commitment coordination.
Therefore, the result is more accurate compared with conventional and basic
SCMs. However, the cost of accuracy is the intensive computational efforts. It
is favorable to assume the generation capacity has enough flexibility and skip
23
“eliminate inflexible restarts” step (step 3). The resulting flexibility issues
are left to flexible capacity procurement (FCP), which, in practice, will be
considered anyway.
24
Chapter 3
Ancillary Service Impact
3.1 Introduction to ancillary service
In practice, the generation must provide extra capacity for the ancillary
services. The purpose of ancillary services is to help maintain the security and
the quality of the supply of electricity. In particular, control of the frequency
requires a certain amount of active power be kept in reserve to be able to
re-establish the balance between load and generation at all times. In general,
reserve can thus be defined as the amount of generation capacity that can be
used to produce active power over a given period of time and which has not yet
been committed to the production of energy during this period [15]. Different
types of reserve services are required, here, for our screening curves models,
we only introduce spinning reserves and non-spinning reserves in this chapter.
3.1.1 Spinning reserve
Spinning Reserve (SR) is the on-line reserve capacity that is synchro-
nized to the grid system and ready to meet electric demand within 10 minutes
of a dispatch instruction by the ISO. The purpose of SR is to maintain system
frequency stability during emergency operating conditions and unforeseen load
swings. SR is usually allocated to various units. This allows the automatic
25
generation control system to restore frequency and interchange quickly in the
event of a generating unit outage [1]. The required amount of spinning reserves
is calculated differently in different areas, see Table 3.1.
Table 3.1: Calculations of spinning reserves [15]
Region Calculation of spinning reserves
European No specific recommendationThe recommended maximum is:
√10Lmax + 1502 − 150
Spain Between 3√Lmax and 6
√Lmax
CAISO 50%[max(5%Phydro + 7%Pnon−hydro, Plargest.contingency) +Pnon−firm.import]
PJM 1.1% of peak + probabilistic calculation on typical daysand hours
ERCOT 2800 MW
Where, Lmax is the maximum load of the system during a given period;
Phydro the scheduled hydro generation; Pnon−hydro is the generation from non-
hydro generation; Plargest.contingency is the loss due to most severe contingencies;
Pnon−firm.import is total interruptible imports.
ERCOT uses the term “responsive reserve”to refer both to generation
that can provide spinning reserve and also to demand that can provide a
similar response. However, in this thesis, we will only consider SR provided by
26
generation side. In addition, the most critical requirement for SR is the ability
to increase production subsequent to a failure of a generator. In ERCOT case,
SR is set to be able to back up the failure of two largest nuclear power plants,
which is then set to be fixed as 2800 MW. Moreover, in two decades, no
potential nuclear power plants or large power plants are on the plan to be
built. Hence, no extra capacity for SR is needed in 2030. For simplicity and
conservative consideration, SR is fixed as 3000 MW.
3.1.2 Non-spinning reserve
Non-spinning reserve is off-line generation capacity that can be ramped
to capacity and synchronized to the grid within 10 minutes of a dispatch
instruction by the ISO, and that is capable of maintaining that output for at
least two hours. It is needed to maintain system frequency stability during
emergency conditions. These include quick-start diesel or gas-turbine units as
well as hydro or pumped hydro units [1]. Spinning units can also be used for
non-spinning reserve. This is the reason why sometimes non-spinning reserves
are called quick start reserve. In fact, six domestic electricity markets name
non-spinning reserve as follows [16], see Table 3.2. In this thesis, we call them
all to be non-spinning reserve for simplicity.
27
Table 3.2: Terms for non-spinning reserves
Region Term for non-spinning reserves
PJM Quick start reserve
CAISO Non-spinning reserve
MISO Supplemental reserve
ISO New England 10-minute non-spinning reserve
NYISO 10-minute non-synchronized reserve
ERCOT 10-minute non-spinning reserve
3.2 Energy producing and spinning reserve capacity co-optimization
The conventional SCM does not represent the “excess”online capacity
needed for ancillary services (AS) and other issues. With regard to AS, as
described in [2], besides net load, augmented net load was introduced. It
is defined as the summation of net load plus the extra capacity needed for
ancillary services.
To match the augmented net load demand, each generator is as-
sumed to contribute the same fraction of its online capacity to pro-
ducing energy and to spinning reserve. Derivation of expected total cost
considering reserves can be found in [2]. Here, we simplify it as four parts:
capital cost, fixed O&M cost, energy producing cost, spinning reserve (SR)
28
cost. SR cost is assumed to be the same as no-load cost (NLC):
TotalC(lp)k
= CapCk + FOMCk + [(1− r) · (V FCk +NLCk) + r ·NLCk] · T (lp)aug
= CapCk + FOMCk + [(1− r) · V FCk +NLCk] · T (lp)aug(3.1)
Where r is the percentage of spinning reserves; Taug is the total annual
firing hours of each lp in augmented net load curve. It should be mentioned
that net load is (1−r) ·100% of the augmented net load at any arbitrary time.
3.3 Separated spinning reserve capacity optimization
In section 3.2, one of the assumptions is that “each generator is assumed
to contribute the same fraction of its online capacity to producing energy and
to spinning reserve”. In fact, as will be seen in this section, it is economically
cheaper to provide spinning reserve (SR) with peak technologies. We pro-
pose a new method of determining the spinning reserve capacity, this is called
separated spinning reserve capacity optimization.
Separated spinning reserve capacity optimization is achieved by opti-
mizing generation mix and SR separately. In other words, generation capacity
expansion planning can be done first without concerns about SR. Then, S-
R planning works as a follow-up step to accomplish final generation capacity
expansion. An obvious benefit is that any one of the screening curves meth-
ods discussed in chapter 2, using the accuracy needed, can be implemented
29
without modification.
The separated spinning reserve capacity optimization is conducted in
three consecutive steps. We will show this method together with an example
as illustration.
Suppose the generation mix optimization without SR has already been
solved using any model described in chapter 2. For example, we use an opti-
mized generation mix from section 2.1, the net load-duration curve and gen-
eration mix are repeated as shown in Figure 3.1.
0 2000 4000 6000 80000
10
20
30
40
50
60
70
80
90
100
8760
Load
Lev
el (G
W)
CT
CC
Baseload
Net Load
Figure 3.1: Optimized generation mix
30
0
10
20
0
10
20
0
10
20
30
s 3s 2
CT
Firing Hour (hour)s 1 8760
CC
Bas
eloa
d
Figure 3.2: Optimized generation mix
3.3.1 Step 1: determine available SR time period
The available capacity of each technology is a function of system fir-
ing hour (firing hour can be substituted to capacity factor, but for notation
simplicity we use firing hour), which is the total amount of capacities of each
technology minus the amount of those under commitment. See the thick curves
in Figure 3.2. The dash-dot-dot lines represent SR requirement levels.
If the capacity of a technology is more than SR requirement during a
period of firing hours, the corresponding time period is called available SR
time period of that technology. For instance, if the required SR is 5 GW, the
firing hour intersections are determined as that in Figure 3.2, noted by s1,
s2 and s3. When the system firing hour is longer than s1, CT will have the
31
extra 5 GW capacity to support SR, the available SR time period of CT is
firing hour ∈ [s1, 8760]; When it is longer than s2, CC and CT both will have
the extra 5 GW capacity to support SR, the available SR time period of CC
is firing hour ∈ [s2, 8760]; If it is longer than s3, all units are able to support
SR, the available SR time period of baseload is firing hour = [s3, 8760].
Different amounts of fixed SR requirements may be considered the same
way as was described above. For SR requirement proportional to demand level,
the fixed horizontal dash-dot-dot lines should be replaced by “mini”demand
curves proportional to demand level. Other considerations of SR can also be
implemented just by replacing the dash-dot-dot SR curve.
Back to the example, it can be observed that the system is not able to
satisfy 5 GW SR requirement if the system firing hour is less than s1, which
is during peak hours. This is obvious since SR was not considered in the
generation mix used here. This indicates that extra 5 GW SR should be built.
3.3.2 Step 2: calculate system SR operation cost
Before deciding which types of generation are to be built, it is impor-
tant to analyze the current system SR operation cost. SR operation cost of
a generator is called no-load cost (NLC), which is equal to or less than the
summation of variable operation and maintenance cost (VOMC) and no-load
fuel cost. Note that the no-load fuel cost is included for synchronizing gen-
erators. Also note that if a generator is producing power less than its full
output, it can be used to provide SR without paying extra VOMC. Hence,
32
the actual NLC is usually less than the summation of VOMC and no-load
fuel cost. Suppose the NLCs for all candidate units are the value as listed
in Table 3.3. The resulting system SR operating cost is shown in Figure 3.3.
Dash black lines represent the operation cost for the technologies when they
are able to support SR. Solid red line represents the minimum operation cost
of all available generations. The parameter W is the willingness-to-pay when
all units are not able to support SR.
0 87600
10
20
30
V CC
V BL
V CT
s 3s 2s 1
Firing Hour (hour)
W
Figure 3.3: Spinning reserve operating cost
The total operation cost can be calculated for off-peak hours (firing hour >
s1), this is denoted as SROCpre short for pre spinning reserve operation
cost. This cost is the shadowed area under the red solid line in Figure 3.3
(firing hour > s1).
33
Table 3.3: Capital cost and variable O&M cost
Baseload CC CTCapital cost
(k$/MW· year) 174.72 60.12 38.52NLC
($/MWh) VBL = 4.31 VCC = 3.45 VCC = 3.45
Because curtailment is not allowed and SR is mandated, W is set to be
a large value. Such value is so large that it is desirable to build new capacity
for SR. In next step, what types of technology to be built will be decided.
3.3.3 Step 3: select least cost technology for SR
Building new capacity for SR may lower the subsequent system SR
operation cost. For example, if we were to build 5 GW baseload, during
period of firing hour ∈ [s1, s1], the SR operation cost would drop to VBL
instead of VCT . New capacities building cost and the subsequent operation
cost are calculated:
InvstCT = CapCCT+s1·NLCCT+SROCpre (3.2)
InvstCC = CapCCC +s1 ·NLCCC +SROCpre− (NLCCT −NLCCC) · (s2−s1)
(3.3)
InvstBL = CapCBL+ s1 ·NLCBL+SROCpre− (NLCCT −NLCBL) · (s2− s1)
(3.4)
Where Invstk is the investment of building 5 GW technology k; CapC
is the annualized capital cost; NLC is the no-load cost; SROCpre is the pre
34
spinning reserve operation cost calculated in step 2. CapC and NLC are listed
in Table 3.3; s1, s2 and s3 are 36, 1520 and 7456 respectively. The capital cost
and operation cost parts are listed in Table 3.4.
Table 3.4: Cost calculation for spinning reserve
Part 1 Part 2 Part 3CT (k$) 38.52 0.26 0CC (k$) 60.12 0.12 -5.37
Baseload (k$) 174.72 0.16 -4.10
Where Part 1 is “CapCk”, Part 2 is “s1·NLCk”and Part 3 is “−(NLCk−
NLCCC) · (s2 − s1)”. Except for SROCpre, operation costs are dominated by
capital costs as long as the extra capacity needed for SR is small. In fact,
the weight of SR operation cost is even smaller than that shown in Table 3.4.
During firing hour ∈ [s1, s2] period, there are generators producing power at
their minimum output and consequently are natural reserves. Because such
generators are already on with NLC being paid to producing energy anyway,
there is no extra VOMC to be paid. The actual NLC is lower than NLC, so
part2 and part3 are even smaller. Therefore, the approximate total investment
cost is:
Invst ≃ CapC + SROCpre (3.5)
SROCpre is the same for all investment choices. So it is reasonable
to determine the technology of least investment by choosing the technology
with least capital cost. In this example, the optimal technology is CT. In
35
fact, it is perceivable, and can be proved by the three steps described above,
that in most practical cases, the economically-driven SR technology is the peak
technology with lowest capital cost. Thus, separated spinning reserve capacity
optimization does not need to be explicitly calculated every time studying SR
investment strategy. Instead, it is an argument to show that the best choice
of SR is usually peak technology with cheapest capital cost.
It is important to mention that these three steps can be more strictly
done by adding 1 GW by 1 GW each time till it reaches the SR requirement
amount. And by doing this, it is understandable why assigning 4 GW to CT
and 1 GW to other units is not as profitable compared with assigning them
all to CT.
3.4 Non-spinning reserve capacity planning
ERCOT currently procures sufficient non-spinning reserve and regula-
tion up to ensure their sum is larger than 95 percent of net load forecasting
errors. Because non-spinning reserves are limited by 10-minute requiremen-
t, the capacity required is different from case to case and the costs are low
compared with other costs, so the generation mix for non-spinning reserve is
not optimized based on cost issues in our model. Besides, it is perceivable
that most non-spinning reserves are quick start combustion turbines. Hence,
non-spinning reserve is not included in screening curves method calculation,
but is set as a fixed number depending on the case considered.
36
Chapter 4
Data Assumptions
This chapter discusses data assumptions in the ERCOT case generation
expansion planning study.
In screening curves method (SCM), it is not computational favorable to
consider data from all power plants in different places. Instead, generators of
the same type are generalized and represented by one generation technology.
Four types of technologies are included here: nuclear, coal, combined-cycle gas
turbine (CC), simple-cycle combustion turbine (CT).
We have collected data values from a lot of resources, including EIA,
EPRI, ERCOT, AURORA and papers. Some of the predicted data may vary
a little bit. To be consistent with my future work, most data used in this
thesis are from AURORA database [10].
Furthermore, even if the price for what are accurate, the prices for
existing and potential generators are usually different as new mechanism de-
velops. In this chapter, we assume a unique set of data for each generation
technology.
It is important to be specific to nuclear power plant. The
Fukushima accident froze many of the current and future projects of nuclear
37
units all around the world. In Texas, it is possible that no new nuclear power
plants will be built in the future. So nuclear capacity, 5,133 MW, is assumed
to be fixed in the following analysis. Consequently, all the costs associated
with it are less important when determine generation mix, since constant part
in objective function will not affect optimization solution (minimizer) in our
model. It should be noted that the operation strategy of nuclear power plants,
like shut down during springs, will affect the optimal value (minimum) of the
problem, but this does not change the generation mix. In addition, nuclear is
an inflexible generation unit, so there is no start-up cost, flexibility ratio and
other flexibility related parameters associated with nuclear technology.
4.1 Capital cost
Capital cost is usually referred to as the total overnight cost of building
a power plant. Data in Table 4.1 are taken from [9]. As discussed above, capital
costs in 2030 will be utilized in the model, ignoring the fact that, in 2030, most
of the power plants will be built before this target year with different costs.
Table 4.1: Capital costs by year [9]
Year Coal CC CT(k$/MW) (k$/MW) (k$/MW)
2013 2790 651 9602015 2871 666 9882020 2756 634 9492025 2563 581 8822030 2343 517 806
38
SCM is used to optimize over a year interval. Thus, annualized cap-
ital costs should be calculated. In order to do this, amortization issue is
considered: Mortgage amounts are overnight capital cost in 2030; Mortgage
terms are assumed to be 40 years; Interest rates are 7% for coal, combined
cycle gas turbine and combustion turbine, 5% for nuclear. The annualized
capital costs are listed in Table 4.2
Nuclear capacity is assumed to be constant and not explicitly optimized
here. But if we were to optimize considering nuclear generation capacity,
interest rate of 5% is a reasonable assumption to keep it economically viable
in screening curves method. A rate of 7% would make nuclear too expensive,
and thus not competitive to coal power plant.
Table 4.2: Annualized capital costs
Nuclear Coal CC CTAnnualized capital cost
(k$/MW · year) 224.00 174.72 60.12 38.52
4.2 FOM cost and VOM cost
Fixed operation and maintenance cost (FOMC) is a fixed annual O&M
cost independent of operation time duration. It includes minor periodic wages,
maintenances, property taxes, facility fees, insurances and overheads [3]. Some
resources even divide it into materials and labor parts. Normally, it is hard
to forecast future labor costs, therefore FOMCs in 2010 are employed here,
39
which are shown in Table 4.3 taken from [9].
Table 4.3: Fixed operation and maintenance cost [9]
Nuclear Coal CC CTFOMC
(k$/MW · year) 89.88 30.04 14.58 14.88
While variable operation and maintenance cost (VOMC) is defined as
the variable O&M cost per MWh, the annual VOMC depends on yearly op-
eration time. It usually includes inspection cost and other expenditure. It
is important to mention that VOMC is considered in spinning reserve cost
calculation. VOMC data in 2010 are included in Table 4.4.
Table 4.4: Variable operation and maintenance cost [9]
Nuclear Coal CC CTVOMC
($/MWh) 2.05 4.31 3.45 7.07
4.3 Variable fuel cost
Variable fuel cost (VFC) is defined as the fuel cost per MWh. It is the
product of fuel price and heat rate. Moreover, VFC is the additional fuel cost
to VOMC when a generator is operating. Spinning reserves do not have VFC,
since the no-load operation costs are already embedded in VOMC.
40
4.3.1 Fuel prices
Nuclear fuel price:
The uranium price is assumed to be fixed at 0.62 $/MMBTU [7] in the
planning horizon. Details about uranium price can be found in [6].
Coal fuel price:
Coal fuel price in 2030 is 2.18 $/MMBTU. The forecasted coal prices
by year are listed in Table 4.5.
Natural gas price:
Natural gas price in 2030 is 6.29 $/MMBTU. The forecasted gas prices
by year are given by Henry Hub Price, and are listed in Table 4.5.
Table 4.5: Coal and NG price by year [5]
year 2013 2015 2020 2025 2030Coal price
($/MMBTU) 1.83 1.91 2.03 2.10 2.18NG price
($/MMBTU) 3.31 3.91 4.58 5.63 6.29
4.3.2 Heat rate and efficiency
Heat rate is an expression of the conversion efficiency of power gener-
ating engines or collectively plants. The higher the heat rate a unit has, the
less efficient the unit is. Table 4.6 contains the heat rate forecasts for each
technology.
41
Table 4.6: Heat rate by year [9]
Year Nuclear Coal CC CT(MBTU/MWh) (MBTU/MWh) (MBTU/MWh) (MBTU/MWh)
2013 10448 8800 6340 96582015 10448 8795 6414 94732020 10448 8767 6373 90122025 10448 8740 6333 85502030 10448 8740 6333 8550
Figure 4.1: Heat rate of a 400 MW combined-cycle gas turbine [3]
42
The heat rate data above are forecasted for full output. Actually, heat
rate for a unit is a function of output power, see Figure 4.1. For simplicity,
the heat rate at minimum output is calculated by defining a parameter eff
(eff < 1). It represents the conversion efficiency of operation at minimum
over that at full output. This is given by
Hear rate at minimum =Heat rate at full output
eff(4.1)
4.3.3 Variable fuel cost
Variable fuel cost (VFC) is the product of fuel price and heat rate. This
is can be derived from
V FC = Fuel price ·Heat rate (4.2)
Also, as discuss in enhanced screening curves method, if a generator is
not assigned to operate at its full output, the actual cost would be different
from VFC. Particular for generator operating at its minimum stable output,
the actual fuel cost is given by
V FC at minimum = m · Fuel price ·Heat rate at minimum
= m · V FC
eff
(4.3)
Where m is the ratio of minimum output over full output; V FC is the
variable fuel cost at full output; eff is the heat rate efficiency operating at
minimum.
43
It should be noticed that m should be assumed to be the same for all
flexible generators, since it is used to determine the flexibility in “step 3”of
enhanced SCM preliminary calculation before actual SCM applied. Parameter
eff is set to be the same for all flexible generation units. In this thesis, we
set m to be 0.3 and eff to be 0.85.
The VFC and VFC at minimum output for each unit are shown in
Table 4.7.
Table 4.7: Variable operation and maintenance cost [9]
Nuclear Coal CC CTVFC
($/MWh) 6.50 19.05 39.80 53.78VFC at minimum
($/MWh) N/A 6.72 14.05 1.98
4.4 Start-up cost and tm
4.4.1 Start-up cost
Start-up cost (SC) is defined as the cost for each restart. It is the cost
to bring the boiler, turbine, and generator from shut-down conditions to a
state ready to connect and be synchronized to the system.
Start-up costs vary depending on the type of generator and the amount
of time the generator has been off-line. Usually three types of starts are
considered [3]: hot start, when the unit has been less than 10 hours out of
operation; warm start, when it is more than 10 hours and less than 50 hours;
44
cold start, when it is more than 50 hours.
Data found from different resources vary a lot, and most of them are
not classified into hot start, warm start or cold start. In this thesis, we consider
hot start-up cost data from [3] and [9], which are listed below in Table 4.8.
Table 4.8: Hot start-up cost [3] [9]
Nuclear Coal CC CTHot start-up cost
($/start) N/A 80 40 15
4.4.2 tm
As is discussed in section 2.3.1 and repeated here, tm is defined as the
maximum time duration of a unit running at its minimum stable output to
avoid a restart. The cost of running at minimum output is set to be equal to
start-up cost. tm is calculated by Equation (2.7): tm = SCNLC
. Values of tms
are calculated and rounded to be integer, see Table 4.9.
Table 4.9: tm
Nuclear Coal CC CTtm
(hours) N/A 17 11 2
Notice that the tm associated with single-cycle combustion turbine (CT)
is only less than 2 hour. This is almost the same as tm = 0, which is the case no
45
unit commitment issue considered. This can be calculated in basic screening
curves method, without preliminary calculations. Taking computational effort
into account, tms utilized in this case study are only 11 hours and 17 hours.
4.5 Data assumptions summary
Data discussed above are summarized in Table 4.10. All units are
converted to the level of MW (MW· year or MWh); Costs independent of
operation are of level of k$; Costs depend on operation are of level of $.
Table 4.10: Thermal units cost data summary
Nuclear Coal CC CTAnnualized capital cost
(k$/MW · year) 224.00 174.72 60.12 38.52FOMC
(k$/MW · year) 89.88 30.04 14.58 14.88VOMC
($/MWh) 2.05 4.31 3.45 7.07VFC
($/MWh) 6.50 19.05 39.80 53.78Hot start-up cost
($/start) N/A 80 40 15tm
(hours) N/A 17 11 2eff
(100%) N/A 0.85 0.85 0.85m
(100%) N/A 0.3 0.3 0.3
46
Chapter 5
Case Study
In this section, case study of ERCOT 2030 generation capacity expan-
sion planning is studied. Optimal generation mix results of screening curves
methods with and without ancillary service are presented and analyzed. Al-
so, the simulation result, performed by AURORAxmp software, based on the
same data, is presented. Finally, this chapter summarizes these results and
concludes the future optimal generation capacity expansion trend.
5.1 Case study with screening curves methods
In this section summarizes equations (derived in chapter 2), data as-
sumptions (discussed in chapter 4) and results of screening curves method.
5.1.1 Case study based on conventional SCM
Formula:
TotalCost(lp) = CapC + FOMC + (V FC + V OMC) · T (lp) (5.1)
Where subscript k indicates technology k; lp is the load point; CapC is
capital cost per MW; FOMC is the fixed operation and maintenance cost per
47
MW; V FC is variable fuel cost per MW; V OMC is variable operation and
maintenance cost per MW; T is the total year operating hours on each lp.
Data assumptions:
Table 5.1: Data for conventional screening curves method
Nuclear Coal CC CTAnnualized capital cost
(k$/MW · year) 224.00 174.72 60.12 38.52FOMC
(k$/MW · year) 89.88 30.04 14.58 14.88VOMC
($/MWh) 2.05 4.31 3.45 7.07VFC
($/MWh) 6.50 19.05 39.80 53.78
Result:
The result is shown in Figure 5.1 and listed in Table 5.2. As was de-
scribed in chapter 4, since ERCOT is not planning on building more nuclear
power plants , the nuclear capacity is set to be fixed as 5 GW. So the opti-
mization is in fact over three technologies: coal, CC, CT. As formulated in
Equation (2.3), the minimum total cost on each lp is given by lowest envelope
of the cost curves. The intervals of the intersections determine the capacity of
the generation technology.
48
90 80 70 60 50 40 30 20 10 00
100
200
300
400
500
600
Coal34 GW
CC28 GW
Gen
erat
ion
Cos
ts (k
$)
Load Level (GW)
Coal CC CT
CT28 GW
Nucl.5 GW
Figure 5.1: Conventional SCM
Table 5.2: Generation mix based on conventional SCM
Technology k Nuclear Coal CC CT TotalCapacity based onconventional SCM 5 GW 34 GW 28 GW 28 GW 95 GWPercentage based onconventional SCM 5.26% 35.78% 29.47% 29.47%
49
5.1.2 Case study based on basic SCM
Formula:
TotalC(lp)k = CapCk + FOMCk + (V FCk + V OMCk) · T (lp) + SCk ·N(lp)
(5.2)
Where SC is the start-up cost per start; N(lp) is the number of start-
ups of each lp per year.
Data assumptions:
Hot start-up cost is assumed to be the cost for all restarts, the values
of it vary on different resources. We use data collected by [9], as follows:
Table 5.3: Data for basic SCM
Nuclear Coal CC CTHot start-up cost
($/start) N/A 80 40 15
Result:
Table 5.4: Generation mix based on basic SCM
Technology k Nuclear Coal CC CT TotalCapacity based on
basic SCM 5 GW 32 GW 27 GW 31 GW 95 GWPercentage based on
basic SCM 5.26% 33.68% 28.42% 32.63%
50
90 80 70 60 50 40 30 20 10 00
100
200
300
400
500
600
Gen
erat
ion
Cos
ts (k
$)
Load Level (GW)
Coal CC CT
Coal32 GW
CC27 GW
CT31 GW
Nucl.5 GW
Figure 5.2: Basic SCM
5.1.3 Case study based on enhanced SCM
Formula:
TotalC(lp)k =CapCk + FOMCk + V OMCk · T (lp)
+ V FCk · Tf(lp) +m · V FCk ·Tm(lp)
eff+ SCk ·N(lp)
(5.3)
Wherem is the ratio of minimum stable output over full output; Tm(lp)
is the time duration of generators running at their minimum output on load
level lp; Tf(lp) is time duration of those running at their full output on load
level lp; eff is the efficiency of a generator running at its minimum output.
N(lp) is the number of unavoidable restarts on load level lp, this is different
from that used in basic SCM.
51
Data assumptions:
m and eff are the same for all technologies, while tms are assigned
differently, see Table 5.5.
Table 5.5: Data for enhanced SCM
Nuclear Coal CC CTtm
(hours) N/A 12 3 1eff
(100%) N/A 0.85 0.85 0.85m
(100%) N/A 0.3 0.3 0.3
Result:
In ERCOT 2030 case, the amount of capacities of inflexible generation
(nuclear generation) makes up only a small fraction of the entire generation
system, so the system has enough flexibility for any levels of flexible generators
to run at their minimum stable output. Therefore, if the off-line time duration
is less than tm of that generator, it is able to avoid a restart. Since no flexibility
limitation will be violated, we can skip step 3 in enhanced SCM, and this
accelerates the computation speed a lot. Two tm are considered (3 h and 12 h)
for CC and CT. The result is illustrated in Figure 5.3 and listed in Table 5.6.
5.1.4 Case study discussion
Three methods has been applied to the same case, the differences are
within 3%. Depending on the simulation accuracy and computation time
52
90 80 70 60 50 40 30 20 10 00
100
200
300
400
500
600G
ener
atio
n C
osts
(k$)
Load Level (GW)
Coal CC CT
Coal33 GW
CC26 GW
CT31 GW
Nucl.5 GW
Figure 5.3: enhanced SCM
Table 5.6: Generation mix based on enhanced SCM
Technology k Nuclear Coal CC CT TotalCapacity based onenhanced SCM 5 GW 33 GW 26 GW 31 GW 95 GW
Percentage based onenhanced SCM 5.26% 34.74% 27.37% 32.63%
53
requirements, we may choose the one that fits best.
Conventional SCM does not consider start-up impact issue. Ignoring
start-up cost leads to investing more capacities on coal and CC generation,
which have higher start-up costs. This results in an underestimate of CT.
This can be seen from the fact in ERCOT 2030 case that only 28 GW of CT
conducted by conventional SCM, comparing with 31 GW of CT by basic and
enhanced SCMs.
Basic SCM does not consider short-term operations like unit commit-
ment. It overlooks the ability of a generator running at its minimum stable
output to avert a restart. So this approximation may lead to lower capacity
of coal. The result get from basic SCM is 32 GW of coal generation, and this
is 1 GW less than that derived from enhanced SCM.
Enhanced SCM is the one considers most of factors. The result is more
accurate than those of the previous two methods. But the cost of accuracy
is the intensive computational efforts. The difference between basic and en-
hanced SCM is the short-term operation impact. In fact, this impact will only
reduce investment on technologies with long tm, like coal generation. For sim-
ulation using SCM as a sub-problem and doing a lot of iterations, enhanced
SCM is not the first choice.
54
5.2 Case study considering ancillary services
ERCOT currently has 2800 MW spinning reserve (responsive reserve in
ERCOT) and about 1300 MW non-spinning reserve. As discussed in chapter
3, the least-cost solution of building spinning reserve is CT; The quick start
characteristics of non-spinning reserve requires building up CT. So adding ca-
pacity for ancillary service is equivalent to adding extra 3800 MW combustion
turbines to the generation system. The corresponding new generation mix,
considering ancillary service impacts, is listed in Table 5.7.
Table 5.7: Generation mix considering ancillary services
Technology k Nuclear Coal CC CT TotalCapacity based onconventional SCM 5 GW 34 GW 28 GW 32 GW 99 GWPercentage based onconventional SCM 5.05% 35.78% 28.28% 32.32%Capacity based on
basic SCM 5 GW 32 GW 27 GW 35 GW 99 GWPercentage based on
basic SCM 5.05% 32.32% 27.27% 35.35%Capacity based onenhanced SCM 5 GW 33 GW 26 GW 35 GW 99 GW
Percentage based onenhanced SCM 5.05% 33.33% 26.26% 35.35%
5.3 Current ERCOT generation mix
Installed capacity in ERCOT till 2012 is shown in Figure 5.4 according
to [4]. Among them, the thermal capacity mix is summarized in Table 5.8.
55
Figure 5.4: Installed capacity in ERCOT 2012 [4]
Table 5.8: Installed thermal capacity in ERCOT 2012
Technology k Nuclear Coal Natural Gas TotalERCOT 2012
capacity 5.4 GW 18.4 GW 45.6 GW 69.4 GWERCOT 2012percentage 7.90% 26.48% 65.62%
56
5.4 Case study using AURORAxmp
AURORAxmp simulation based on the same data assumptions is per-
formed in [10]. This simulation covers curtailment, CO2 price and other de-
tailed issues. The result is illustrated in terms of capacity addition and retire-
ment till year 2040, see Figure 5.5. Consequently, the result of total generation
capacity mix in ERCOT 2030 case is summarized in Table 5.9.
Figure 5.5: AURORAxmp simulation result [10]
An observation is captured that the system generation capacity is less
than 99 GW. This is due to considerations of demand curtailment and “spin-
ning reserve” using demand response . Another observation is the retirements
57
Table 5.9: AURORAxmp simulation result
Technology k Nuclear Coal Natural Gas TotalCapacity usingAURORAxmp 1.5 GW 15.0 GW 76.6 GW 93.1 GWPercentage usingAURORAxmp 1.61% 16.11% 82.28%
of nuclear power plants in 2027 and 2028. These are the result of the license
expiration and that there is no interest in extending it. The general trend
forecasted by AURORAxmp is increasing peaking technologies and decreasing
baseload technologies.
5.5 Results summary and analysis
ERCOT currently has capacity of coal and natural gas generation about
18 GW and 36 GW respectively. The growing load demand requires expansion
on power generation.
SCM implies building up 15 GW coal and 15 GW natural gas generators
in period from 2013 to 2030. The increase in natural gas generation is the result
of the load growth and wind growth in ERCOT, which require low capital cost
gas turbines to cope with net load peaks.
However, this result is, yet, conservative on natural gas power genera-
tion expansion. This is due to the increasing price on natural gas. As is shown
in Table 5.10, natural gas price will be doubled in 2030. In contrast, growth
58
in coal price is negligible. Besides, the capital costs are decreasing. These two
factors together contribute to the rise in coal units weight. Actually, based on
SCM simulations on other years, the trend in coal power plant is decreasing
before 2023 and increasing after 2023.
Table 5.10: Capital costs by year
Year Coal CapC CC CapC CT CapC Coal Price NG Price(k$/MW) (k$/MW) (k$/MW) ($/MMBTU) ($/MMBTU)
2013 2790 651 960 1.83 3.312015 2871 666 988 1.91 3.912020 2756 634 949 2.03 4.582025 2563 581 882 2.10 5.632030 2343 517 806 2.18 6.29
While AURORAxmp indicates all 30 GW capacities should be natural
gas generators. This is driven by CO2 price. In fact, CO2 price has huge im-
pacts on accelerating coal units’ retirement. Its implementation makes average
marginal cost of coal units exceed that of gas units. Consequently, it reduces
production and penetration level of coal [10]. Failure to consider this factor in
SCM leads to a conservative evaluation on natural gas unit expansion.
59
Chapter 6
Conclusion
Three screening curves methods are introduced. They are useful tools
for conducting least-cost generation expansion planning for a target year. More
detailed factors, concerning practical short-term operation impacts on long-
term planning, can be considered and implemented in the screening curves
method. We can choose one based on our needs of accuracy and computation
requirement.
Wind integration impacts on power generation expansion are discussed.
The net load curves are developed to deal with the non-dispatchable property
of wind energy. Economically-driven planning strategy on ancillary service is
provided and can be easily applied to any one particular generation system.
These new improvements on screening curves method are proved to be effec-
tive. Study of the ERCOT 2030 real case shows the feasibility of utilizing
screening curves method. Observation of needs in peak technologies for deal-
ing with wind integration is captured. Another trend is illustrated that there
will be increasing coal units due to the growing price of natural gas.
Finally, the result comparison with AURORAxmp simulation sheds
light on the future potential improvement directions. These include consid-
60
erations of carbon price impact, curtailment issues and power plant license
constraints.
The main drawback of screening curves method is its limitation to
dealing with only one target year. On the contrary, since a power plant is a
commodity lasting for a few decades, generation investment in one year will
affect many years after that, and is affected by investments many years before
it. Therefore, generation expansion planning requires a comprehensive study
over a few years around that target year. This can by done by doing a decade-
long dynamic programming study, with screening curves method serving as an
optimal instruction in each year. We will accomplish this in our future work.
61
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