Mitigating Renewable Variability through Control and Optimization Techniques by Anand ...

127 Pages·2013·1.92 MB·English

Mitigating Renewable Variability through Control and Optimization
Techniques
by
Anand Subramanian
A dissertation submitted in partial satisfaction of the
requirements for the degree of
Doctor of Philosophy
in
Engineering - Mechanical Engineering
and the Designated Emphasis
in
Computational Science and Engineering
in the
Graduate Division
of the
University of California, Berkeley
Committee in charge:
Professor Kameshwar Poolla, Chair
Professor Pravin Varaiya
Professor Andrew Packard
Fall 2013
Mitigating Renewable Variability through Control and Optimization
Techniques
Copyright 2013
by
Anand Subramanian
1
Abstract
Mitigating Renewable Variability through Control and Optimization Techniques
by
Anand Subramanian
Doctor of Philosophy in Engineering - Mechanical Engineering
and the Designated Emphasis
in
Computational Science and Engineering
University of California, Berkeley
Professor Kameshwar Poolla, Chair
Motivated by environmental and energy security concerns, many states and countries have
enacted legislation calling for increased renewable adoption in the electricity sector. Unlike
conventional fossil fuel-based electricity sources, renewable resources such as wind and solar
power are characterized by intermittent, uncertain, and non-dispatchable output. Success-
fully addressing this variability in renewable generation is a prerequisite for deep renewable
penetration. The prevailing paradigm in most power systems, exemplified by programs
such as the Participant Intermittent Renewable Program (PIRP) in California, is one where
the system operator accepts all renewable generation and absorbs the attendant variability
through operating reserves. This approach works today at modest renewable generation lev-
els but will result in untenable increases in reserve requirements tomorrow when renewables
serve a sizeable fraction of total electric load. Hence, meeting ambitious renewable penetra-
tion targets will require the implementation of a number of variability mitigation strategies
across the entire spectrum of power system operations. In this dissertation, we identify and
explore areas in which control and optimization techniques can help provide some of these
solutions.
One such mitigation strategy is the coordinated aggregation of deferrable loads and stor-
age, in which load is tailored to match variable supply. We investigate methods of exploiting
these demand-side capabilities by developing and evaluating algorithms for the real-time
scheduling of these flexible resources. We find that the benefits of coordinated aggregation
can be achieved at modest levels of both deferrable load participation and flexibility. We
also provide an analytical framework for understanding how these resources influence the
costs of meeting load requirements incurred in wholesale electricity markets. Specifically, we
explore the interplay between deferrable load scheduling and cost-minimizing procurements
of bulk power and reserve capacity made in the day-ahead forward market.
2
Anothersolutionweconsider, specifictowindpower, involvescurtailinggeneratoroutput
in certain situations. We explore how a wind power producer – subject to financial penalties
for imbalances from contracted amounts – might leverage power curtailment capability to
mitigate financial risk arising from price and production uncertainty. In particular, we
analytically quantify the economic benefit derived from curtailment as an explicit function
of expected prices, and compute empirical estimates of this curtailment benefit using price
data from the various power system operators.
i
All my life, I came to see the ocean,
Today, I come with a few drops of my own in hand.
This thesis is dedicated to:
my mother, Prabamani Subramanian,
my father, Ayalur Krishnaiyer Subramanian,
my sister, Anagha Subramanian,
and my other half, Priyanka Rajagopalan.
ii
Contents
Contents ii
List of Figures iv
List of Tables vi
1 Introduction 1
1.1 Climate Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Renewable Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 DER Proliferation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 The Scourge of Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Dissertation Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Background: Power Systems Operations 12
2.1 Electricity Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Reserves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Real-time Scheduling of DERs 22
3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Scheduling Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.5 Conclusions & Possible Extensions . . . . . . . . . . . . . . . . . . . . . . . 53
4 Impact of Deferrability on Ex-Ante Operations 54
4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3 Optimal Reserve Dispatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.4 Optimal Procurement Without Deferrability . . . . . . . . . . . . . . . . . . 65
4.5 Optimal Procurement With Deferrability . . . . . . . . . . . . . . . . . . . . 75
4.6 Simulation Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.7 Conclusions & Possible Extensions . . . . . . . . . . . . . . . . . . . . . . . 83
CONTENTS iii
5 The Benefit of Wind Curtailment 86
5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3 Optimal Curtailment Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.4 Optimal Contract Offer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.5 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.6 Conclusions & Possible Extensions . . . . . . . . . . . . . . . . . . . . . . . 105
Bibliography 107
iv
List of Figures
1.1 Figures outlining increases in both mean and variance of global temperature . . 2
1.2 Atmospheric CO concentration measured at Mauna Loa observatory over time.
2
The black line shows monthly averages while the red line shows the monthly
average correction for seasonal CO variation. (Data from NOAA Earth System
2
Research Laboratory: http://www.esrl.noaa.gov/gmd/ccgg/trends/) . . . . 3
1.3 Figures displaying solar and wind intermittency issues. . . . . . . . . . . . . . . 5
1.4 Sankey diagram showing breakdown of U.S. energy consumption by both energy
source and demand sector. 1 quad is the equivalent of 2.93 1010 kWh or 1.055
× ×
1018 J. (Image Source: Lawrence Livermore National Laboratory, 2012) . . . . . 11
2.1 Figure showing relative time-frames on which different types of reserve are de-
ployed. (Version of Figure 3 in [51]) . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1 Available generation profiles gA and gB described in proof of Theorem 3.1 . . . 32
3.2 Power allocations to tasks that show feasibility of profiles gA and gB . . . . . . 33
3.3 Available generation profile gC described in proof of Theorem 3.3 . . . . . . . . 42
3.4 Power allocations to each set of tasks that show feasibility of profile gC . . . . . 42
3.5 Load profiles comparing the impact of load scheduling under EDF, LLF, DPAS,
LPAS, and RHC to no scheduling base case for a typical test case . . . . . . . . 48
3.6 Load profiles comparing the impact of load scheduling under LLF, LPAS, and
RHC to no scheduling base case for a test case involving severe generation deficit.
These profiles highlight characteristics of reserve procurement under LLF and
LPAS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.7 Percentage reductions in up (a) and down (b) reserve costs achieved by RHC-
based scheduling at various levels of deferrable load penetration (α). . . . . . . 50
3.8 Percentage reductions in up (a) and down (b) reserve costs achieved by RHC-
based scheduling at various levels of task deferrability (φ) at α = 0.2. . . . . . . 51
3.9 Cumulative distribution function on the maximum number of on-off switches
under three scheduling algorithms: EDF, LLF, and RHC. . . . . . . . . . . . . 52
4.1 TimelineillustratingdifferentstagesatwhichtheCMprocuresvariousgeneration
components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
LIST OF FIGURES v
4.2 Graphical illustration of the optimal bulk power procurement policy in the cases
of no reserve capacity and symmetric reserve energy costs . . . . . . . . . . . . . 67
4.3 Illustration of the feasible set of DA procurement policies . . . . . . . . . . . 70
X
4.4 Illustration of how deferrable loads reduce optimal ex-ante procurements using
this framework. The blue and black circles correspond to the optimal procure-
ments with and without deferrability respectively. This particular case assumes
deferrable load parameters: L = 40 kWh and m = 80 kW. . . . . . . . . . . . . 80
4.5 Optimalreservecapacityprocurementasafunctionoftotaldeferrableloadenergy
need (L) and servicing rate limit (m). The total load requirement is 500 kWh. 81
4.6 Variation in ex-ante procurements over a typical day with (B C) and without
±
(B∗ C∗) deferrable loads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
±
4.7 Optimal reserve capacity procurement as a function of deferrable load proportion
(α) and servicing rate limit (m). All reserve capacities C∗ are expressed as frac-
tions of the initial reserve capacity requirement C. Results are averaged over 50
days. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.1 Timeline illustrating the two-settlement market model assumed for WPP partic-
ipation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2 Graphical illustration of the optimal contract policy on the partition ( , , )
1 2 3
P P P
of expected imbalance prices (µ ,µ ) . . . . . . . . . . . . . . . . . . . . . . . . 95
q λ
5.3 Empirical means of wind generation (µ ) computed from BPA time series data.
w
Empirical means are calculated for each hour of the day. . . . . . . . . . . . . . 102
5.4 Average surplus penalties (µ+) computed using MISO LMP market data from
λ
January-June 2011. Empirical means are calculated for each hour of the day. . 104
5.5 Average surplus penalties (µ+) computed using NYISO LMP market data from
λ
2008. Empirical means are calculated for each hour of the day. . . . . . . . . . 104
vi
List of Tables
3.1 Comparison of scheduling algorithms showing percentage reductions in 4 reserve
cost metrics (compared to the base case of no coordination) . . . . . . . . . . . 47
3.2 Comparison of scheduling algorithms showing average computation time (s) re-
quired for coordinated scheduling at different levels of deferrable load penetration
(α) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.1 Net load statistics for the synthetic test case . . . . . . . . . . . . . . . . . . . 79
5.1 Annual curtailment benefit for a 50 MW WPP with full curtailment capability
sited at 7 different locations within the MISO balancing area . . . . . . . . . . 103
5.2 Annual curtailment benefit for a 50 MW WPP with full curtailment capability
sited at 4 different locations within the NYISO balancing area . . . . . . . . . . 105