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1
Long-term Investment Planning for the Electricity Sector in Small Island Developing
States: Case Study for Jamaica
Travis Atkinson1
Paul V. Preckel2
Douglas Gotham3
October 23, 2019
See latest version here
1 PhD Candidate, Department of Agricultural Economics, Purdue University 2 Professor, Department of Agricultural Economics, Purdue University 3 Director, State Utility Forecast Group, Purdue University
2
Abstract
Small Island Developing States (SIDS) tend to prioritize generation expansion planning
(GEP), giving transmission investments only second-order priority. This may result in resource
misallocation. In this paper, we evaluate the implications of prioritizing GEP by utilizing a
dynamic mathematical programming model to examine two empirical questions: 1) Does
simultaneously planning for generation and transmission investments improve planning
efficiency? 2) What is the impact of loop flow (a phenomenon intrinsic to electricity networks) on
long-term investment planning? The island of Jamaica is used as a case study. We find that
simultaneous planning of generation and transmission investments results in lower total cost when
compared to a sequential planning framework and becomes more important when we account for
fuel price uncertainty. Though this benefit is smaller than anticipated, the modest additional
computational requirements make the simultaneous model more efficient and worthwhile. Our
study also indicates that loop flow does not affect least-cost investment decisions in in this context.
This is likely due to an abundance of transmission capacity and alack of complexity in the
network’s design. To broaden the scope for future empirical research on SIDS, we develop our
open source program in the General Algebraic Modeling System (GAMS), in an effort to reduce
the barriers to electricity infrastructure research in developing countries. The model is of a flexible
design such that it can incorporate bottom-up policy analysis relevant to the electricity sector.
Key words: energy modelling, generation and transmission expansion planning, infrastructure
investments, Small Island Developing States, electricity
JEL Codes: Q4, L94
Acknowledgments
Special thanks to the Jim and Neta Hicks Graduate Student Small Grant Program which
provided funding support for data collection. Thanks as well to the Office of Utilities Regulation
for providing data used in this study.
3
1. Introduction
Growing electricity demand, the replacement of older generation units, and the increasing
penetration of renewable energy resources make long-term infrastructure investment planning
crucial to electricity sectors the world over. This is particularly true for Small Island Developing
States (SIDS), which, relative to the world average, have been recording a faster increase in
electricity consumption and access (Figure 1 and Figure 2). To begin, however, it is important to
define some technical concepts. First, loop flow is a phenomenon intrinsic to electrical networks
that causes electricity to flow along all paths connecting two nodes, not just along the shortest
distance (Chao and Peck, 1996). This is governed by laws of physics known as Kirchhoff’s voltage
laws. Second, generation expansion planning (GEP) models optimize generation capacity to satisfy
future expected demand, ignoring transmission constraints. Generation and transmission
expansion planning (GTEP) models, however, include transmission constraints in the optimization
process. While there is an extensive literature on long-term infrastructure investment planning, we
have two concerns.
First, the literature is dominated either by theoretical IEEE network designs or on larger,
more developed territories (e.g. USA, Europe) which lack the economic (e.g. high debt and limited
fiscal flexibility) and geographic (e.g. small size, diseconomies of scale and isolated electricity
networks) features of SIDS, sometimes limiting the applicability of these studies to the SIDS
context. Second, given the higher cost of generation infrastructure relative to transmission
infrastructure, SIDS tend to focus heavily GEP, neglecting (or only subsequently accounting for)
investments in transmission infrastructure. This may call into question the efficiency of these long-
term plans as well as the impact of loop flow. This is because GEP, ignoring transmission
constraints, risks producing a long-term investment plan that may require extra investment in
transmission infrastructure, thereby increasing total investment cost.
In this paper, we explore these issues, extending the extant literature with a focus on the
economic and geographic limitations faced by SIDS. Specifically, we ask the following questions:
(1) Does simultaneously planning for generation and transmission investments improve planning
efficiency? (2) What is the impact of loop flow on long-term investment planning? We examine
these results using the island of Jamaica as a case study.
4
Figure 1: Per capita electricity consumption (kWh). (World Bank, 2019)
Figure 2: Electricity access in percent. (World Bank, 2019)
Optimization models are a staple of decision analysis and long-term planning within the
electricity sector. Utilities use optimization models to inform decisions about electricity generation
and transmission investments while government agencies use optimization models to assess policy
options. Wu, Zheng and Wen (2006) and Hemmati et. al. (2013) and present a good overview of
the development of generation and transmission expansion planning over the years, spanning both
the economics and engineering literature. Traditional expansion planning focuses on a vertically
5
integrated, regulated monopoly in generation, transmission and distribution. Typically, the planner
chooses the least cost generation expansion, and then carries out transmission expansion. This
sequential form of analysis is done largely because the cost of generation infrastructure
significantly exceeds the cost of transmission, and planning sequentially is less computationally
challenging. Additionally, in most connected networks (i.e. no island within the network), any
generation expansion plan could be made feasible by sufficient transmission expansion.
Figure 3: Traditional transmission expansion planning procedure. (Wu et al., 2006)
There have been several variants of GEP models. Botterud, Ilic and Wangensteen (2005)
present a model for optimal generation capacity investment decisions in a de-centralized setting.
Antunes, Martins and Brito (2004) present a mixed integer linear programming model for GEP,
seeking to minimize total expansion costs, the environmental impact attributable to installed
capacity and the environmental impact driven by output. To account for multiple independent
power producers (IPPs) in a de-regulated environment, Budi and Hadi (2019) attempt a complete,
perfect, non-cooperative game-theoretic framework in for GEP. Recent extensions of this segment
of the literature aim to account for increasing penetration of renewable generation resources
(Gitizadeh et al., 2013). While there has been much focus on utility-scale generation resources,
research has also ventured into distributed generation expansion planning (Barati et al., 2019).
However, given the small size of SIDS, significant levels of distributed electricity resources may
lead to negative externalities. In Jamaica’s case, for instance, there is concern that if large
customers leave the grid in favor of distributed generation, customers remaining on the grid would
face higher prices due to lost economies of scale (Jones, 2017).
6
One weakness of GEP-only models is that they may fail to account for loop flow, which
has important implications for electricity markets in terms of competition and the exercise of
market power (Cardell et al., 1997; Chao and Peck, 1996; Chao et al., 2000). This phenomenon
can also misalign private and social costs and can potentially misallocate resources leading to
inefficiencies within the sector (Chao and Peck, 1996). These externalities are magnified by the
complexity and scale of the network (ibid). So, are SIDS large enough and do their network
topologies have features that make loop flow a significant economic consideration, or does loop
flow have only minor impacts on decision making?
Another weakness of GEP-only models is that they ignore the role of new transmission
infrastructure. Depending on the starting configuration, it may be more economical to build new
transmission lines instead of new power plants. There are two primary reasons for this. First, to
some degree, generation and transmission can be considered substitutes in that demand for
electricity can be met either with local generation or by transmission from remote generation
(Krishnan et al., 2016). Second, the existing transmission network influences the placement of
generation infrastructure (ibid). Consequently, transmission decisions will impact future
generation investments and vice versa. Our second research question therefore concerns modelling
approaches used for generation and transmission expansion planning (GTEP). Unlike GEP, GTEP
co-optimizes both generation and transmission investments. However, in cases where both
generation and transmission investments are considered, SIDS typically optimize these two
investment decisions sequentially. That is, generation investments are first optimized, and once
decisions are made about where and when to build new power plants, transmission line investments
are optimized to accommodate the added generation capacity. However, this approach can
potentially lead to unnecessary costs by failing to account for the substitutability of local
generation and remote generation plus transmission.
Recent advancements have allowed for simultaneous optimization of generation and
transmission investments (Figure 4). This strand of literature suggests that simultaneously
optimizing generation and transmission investments, yields better solutions (Hemmati et al., 2013;
Krishnan et al., 2016; Zhang et al., 2015). Others (Roh et al., 2007; Sauma and Oren, 2006) have
also advanced this field for the electricity market, while researchers like Nunes et al. (2018)
explore integrating natural gas networks within a GTEP framework.
7
Figure 4: Transmission expansion planning procedure in a deregulated environment. (Wu et al.,
2006)
Much of the literature utilizes hypothetical IEEE network topologies, and where empirical
studies based on more realistic networks can be found, they often focus on larger geographic
territories such as the United States and Europe. Such networks typically include transmission
lines with significantly higher voltage levels when compared to SIDS and cover a significantly
longer distance. Such territories may also comprise power pools or network topologies that differ
from the network designs in SIDS, characterized by isolated electricity generation and relatively
sparse internode connectivity. SIDS are also under-represented because research over the past few
decades focuses on de-regulated environments. Yet, the electricity sectors in SIDS remain largely
vertically integrated, regulated monopolies or state-owned entities. We therefore seek to extend
the existing literature on long-term infrastructure investment planning for the electricity sector by
focusing on the economic and geographic idiosyncrasies of Small Island Developing States.
2. Jamaica as a case study
Roughly one-third of the World’s SIDS are found in the Caribbean.4 Jamaica, with 10,990
km2 land area and host to a population of 2.7 million people, is the largest English-speaking island
in this region. Jamaica is an excellent case study given its size, market structure and ongoing
developments within the sector.
4 https://sustainabledevelopment.un.org/topics/sids/list
8
The Jamaica Public Service Company (JPSCo) is a vertically integrated, regulated utility
with monopoly rights to transmission and distribution. Since 1996, four independent power
producers (IPPs) have been allowed to enter the market and have signed bi-lateral, long-term
power purchase agreements with JPSCo. The government of Jamaica (GoJ) retains a 20% stake in
JPSCo. Unlike many larger countries, Jamaica does not have competition in the market. Instead,
Jamaica has competition for the market, i.e. competition for generation capacity. Following an
official request from the government, interested firms submit bids to build and operate a power
plant. The government evaluates each proposal and chooses the winner. The marginal cost of
electricity heavily influences this determination. The winning firm then builds the power plant.
JPSCo retains monopoly rights to transmission and distribution and is therefore the only
“wholesale” buyer of electricity. Based on reported costs and transmission constraints, JPSCO
determines economic dispatch under the supervision of the regulator. The Office of Utilities
Regulation is the regulating body that oversees the sector and sets downstream prices for
consumers.
In terms of existing capacity and output, JPSCo owns 75% of total generation capacity and
contributes 56% of net generation.5 Total installed capacity is 952 MW, 70% of which utilizes
heavy fuel oil (HFO) or automotive diesel oil (ADO). However, liquefied natural gas (LNG) is
fundamentally changing the energy landscape since its introduction in 2016. It now accounts for
120 MW of total installed capacity, but with plans already in motion to replace three of the nation’s
four largest power plants by the end of 2019, LNG will likely be the primary fuel source within a
few years. The remaining capacity includes run-of-river hydro and wind resources and a 20 MW
solar plant. These developments make this study particularly timely and relevant.
From a public policy perspective, Jamaica’s National Energy Policy (2009) articulates the
government’s vision for modernizing and diversifying the electricity sector, making the choices of
technology, timing and location of great interest. These developments are not unique to Jamaica,
but have been observed across several SIDS (Timilsina and Shah, 2016). Improving the planning
framework for these countries will therefore make planning more efficient and potentially reduce
costs. Understandably, long-term planning will need to be complemented by operational studies
with shorter time-scales, particularly as countries integrate more renewable resources into their
5 Calculated based on 2017 data for Jamaica.
9
networks. However, long-term investment planning has strategic relevance towards shaping the
energy future for SIDS in the coming century.
To this end, Jamaica’s Office of Utilities Regulation (OUR) is currently developing an
integrated resource plan (IRP) that should simultaneously co-optimize generation and transmission
infrastructure investments. However, pending its completion, the most recent, publicly accessible
expansion plan we have found is a GEP completed in 2010. We however found that: (1) despite
Jamaica’s renewable energy target, the 2010 GEP did not evaluate renewable energy options; and
(2) despite acknowledging that transmission expansion planning should accompany generation
expansion planning, the GEP focused only on generation. It therefore does not explicitly account
for expanding the transmission network.
OUR officials, however, affirm that while the 2010 GEP report did not include
transmission planning, they do routinely evaluate transmission plans and consider the impact of
loop flow when doing their analyses (Fagan and Stephens, 2018). The OUR references software
packages such as Plexos, PSSC and Dixellent, planning tools utilized by the regulator, as tools
designed for such purposes. We therefore interpret the lack of additional transmission planning
details in the 2010 GEP as a consequence of the proprietary nature of these planning tools and the
need to balance the right to public information while maintaining sufficient privacy in the energy
sector for national security, legal and economic reasons. Nevertheless, noting the proprietary
nature these planning tools and given that the ongoing IRP is yet to be published, this paper could
provide an open-source tool for academic purposes that may be useful for confirming results from
these proprietary models and broadening the scope for other researchers to do further energy
related research in SIDS.
3. Methodology
We use a dynamic optimization framework based on the Direct Current Optimal Power
Flow (DCOPF) model described in Krishnan et al. (2016) with modifications inspired by the Long-
term Investment Planning model designed by Purdue University’s Power Pool Development
Group for selected contiguous African nations. Figure 5 visually illustrates the model: we input
supply, demand and price parameters into a cost minimization framework subject to economic and
engineering constraints, and subsequent results include costs (investment and operating),
10
investment decisions (location and timing of new assets), generation by technology and
transmission flows.
Figure 5: Graphical description of model
We solve this model as a Mixed Integer Linear Program (MILP) in the General Algebraic
Modeling System (GAMS), using the IBM/CPLEX solver. While an Alternating Current Optimal
Power Flow (ACOPF) model more accurately captures the operational details of an electrical
system, the non-convexity of the problem, including nonlinear constraints, combined with
indivisibilities, makes the ACOPF a difficult model to solve and may leave one in doubt about the
global optimality of solutions. It is therefore common practice in both academia and industry to
use a linear approximation of the ACOPF for planning purposes. This is the DCOPF framework,
which balances the tradeoff between model fidelity and computational tractability. We present the
primary equations for this model below:
11
Notation
Sets
l Transmission lines (directed by definition)
g Generation plants
n,z Nodes in network
h Hour types
t, 𝜏 Year or time-period index
Subsets
𝑒 Existing generator (subset of 𝑔)
𝑐 Candidate generator (subset of 𝑔)
𝑗 Existing transmission line (subset of 𝑙) 𝑘 Candidate transmission line (subset of 𝑙)
Parameters
Parameters Units Definition
𝐵𝑙 Siemens Susceptance of transmission line 𝑙 𝑟 Fraction Discount rate ∈ (0,1)
𝑦𝑒,𝑡 Indicator 0 if existing generator is retired in period 𝑡, 1 otherwise
𝐼𝑒,𝑡 $ Millions Annualized investment cost of candidate generation plant
𝐼𝑘,𝑡 $ Millions Annualized investment cost of candidate transmission lines
𝐹𝑔 $ per year Fixed operating and maintenance (O&M) cost of generator g
𝑉𝑔 $ per MWh Variable operating and maintenance (O&M) cost of generator g
𝜙ℎ Hours Number of hours of hour type ℎ
𝑃𝑔𝑀𝐴𝑋 MW Maximum generation capacity of generator g
𝜆𝑔 Fraction Forced outage rate of generator g ∈ [0,1]
𝜓𝑔,ℎ Fraction Unforced outage rate of generator g for hour type h ∈ (0,1)
𝑆𝑙𝑀𝐴𝑋 MW Maximum power flow across line 𝑙
𝐷𝑛,ℎ,𝑡 MW Demand at node n for hour type h in year 𝑡
𝛫𝑡 $ Millions Infrastructure investment budget in USD millions in year t
𝑞𝑔,ℎ Fraction Availability factor of generator 𝑔 in hour type ℎ ∈ (0,1]
𝑞𝑔,ℎ𝑝𝑒𝑎𝑘 Fraction Availability factor of generator during peak hours ∈ (0,1]
𝛼𝑡 MW Peak demand in year 𝑡
𝑅 Fraction Reserve margin ∈ (0,1), i.e. share of installed capacity that
must be available above peak demand
Binary Variables
𝑥𝑐,𝑡 1 if candidate generator is built
𝑤𝑘,𝑡 1 if candidate transmission line is built
12
Variables
Variables Units Definition
𝑃𝑔,ℎ,𝑡 MW Real power produced by generator 𝑔 for hour type ℎ in
year 𝑡
𝑆𝑙,𝑛,𝑧,ℎ,𝑡 MW Power flow across line 𝑙 from node 𝑛 to node 𝑧, for hour
type ℎ in year 𝑡. (This will be negative if flows is from 𝑧
to 𝑛).
𝜃𝑙,𝑛,ℎ,𝑡 Radians Bus voltage angle for line 𝑙 at node 𝑛 for hour type ℎ in
year 𝑡 𝑈𝑡,𝑙𝑐 Slack variable for use with big “M” method
The objective is to minimize the net present value (NPV) of the total investment and
operation costs of the electricity system and is given by
min ∑ {[𝑇𝑂𝐶𝑡 + ∑ (𝐼𝑐,𝑡 × ∑ 𝑥𝑐,𝜏
𝜏≤𝑡
)
𝑐
+ ∑ (𝐼𝑘,𝑡 × ∑ 𝑤𝑘,𝜏
𝜏≤𝑡
)
𝑘
]}
𝑇
𝑡
÷ (1 + 𝑟)𝑡
(1)
where 𝑇𝑂𝐶𝑡 denotes the total operating and maintenance (O&M) cost of power plants in year t as
defined by
𝑇𝑂𝐶𝑡 = [∑(𝐹𝑒 × 𝑦𝑒,𝑡)
𝑒
+ ∑ (𝐹𝑐 × ∑ 𝑥𝑐,𝜏
𝜏≤𝑡
)
𝑐
+ ∑ (𝑉𝑔 × 𝑃𝑔,ℎ,𝑡 × 𝜙ℎ)
𝑔,𝑛,ℎ
]
÷ 1,000,000
(2)
𝐹𝑒 and 𝐹𝑐 denote the fixed O&M cost for existing and candidate generators respectively, measured
in $ per year. 𝑦𝑒,𝑡 is a binary parameter that captures whether or not an existing generator is
available (=1) or has been retired (=0). This is an exogenous representation of plans already
committed and approved by Jamaican market participants. 𝑥𝑐,𝑡 is a binary variable taking a value
of 1 if a candidate generator 𝑐 is built in year t. Hence, ∑ 𝑥𝑐,𝜏𝜏≤𝑡 accounts for whether or not a
candidate power plant was built during or prior to year t. 𝑉𝑔 is the variable O&M cost of a generator
g, measured in $/MWh. 𝑃𝑔,ℎ,𝑡 denotes real power generation by generator g for hour type h in year
t, measured in MW. 𝜙ℎ is the number of hours of type h. We then convert total O&M costs to
millions of dollars to make the units of measurement consistent with the units for capital
investments.
13
Continuing with the objective function, 𝐼𝑐,𝑡 and 𝐼𝑘,𝑡 are the investment costs corresponding
with prospective power plants and transmission lines, measured in millions of dollars. 𝑤𝑘,𝑡 is a
binary variable taking a value of 1 if a candidate transmission line is built in year t. Hence,
∑ 𝑤𝑘,𝜏𝜏≤𝑡 has a value of unity if the candidate transmission line is available in year t. Finally, 𝑟
denotes the discount rate for calculating the NPV.
The model is constrained such that candidate generators 𝑐 can be built no more than once
((3)-(4)).
𝑥𝑐,𝑡 ∈ {0,1} ∀ 𝑐, 𝑡 (3)
∑ 𝑥𝑐,𝑡 ≤ 1 ∀ 𝑐, 𝑡
𝑡
(4)
Similarly, the model will not allow a candidate transmission line to be built more than once ((5)-
(6)).
𝑤𝑘,𝑡 ∈ {0,1} ∀ 𝑘, t (5)
∑ 𝑤𝑘,𝑡 ≤ 1 ∀ 𝑘, 𝑡
𝑡
(6)
These restrictions represent constraints on the physical land available for the development of
electricity infrastructure.
In (7), power generated by a power plant 𝑃𝑔,ℎ,𝑡 cannot exceed the generator’s capacity 𝑃𝑔𝑀𝐴𝑋
adjusted by the generator’s forced and unforced outage rates 𝜆𝑔 and 𝜓𝑔,ℎ and by the generator’s
availability factor 𝑞𝑔,ℎ
0 ≤ 𝑃𝑔,ℎ,𝑡 ≤ 𝑃𝑔𝑀𝐴𝑋 × (1 − 𝜆𝑔) × (1 − 𝜓𝑔,ℎ) × 𝑞𝑔,ℎ × 𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦𝑔,𝑡 ∀ 𝑔, ℎ, 𝑡 (7)
where 𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦𝑔,𝑡 = 𝑦𝑒,𝑡 for existing plants or ∑ 𝑥𝑐,𝜏𝜏≤𝑡 for candidate generators.
Equation (8) is the reserve margin constraint. The reserve margin is a metric used in long-
term planning models to ensure resource adequacy, and is defined as some capacity level above
expected peak demand. Here, 𝑞𝑔,ℎ𝑝𝑒𝑎𝑘
is the availability factor of generator 𝑔 during peak hours and
is bounded by 0 and 1. 𝛼𝑡 is the peak demand for year 𝑡 and 𝑅 is the reserve requirement. For
14
Jamaica, this reserve requirement is 25%, more than double the reserve margin for the USA,
leading to comparatively higher capacity costs. This is another example of the impact of the small
size of SIDS on the operations of the electricity sector.
∑ 𝑃𝑔𝑀𝐴𝑋
𝑔
× 𝑞𝑔,ℎ𝑝𝑒𝑎𝑘 × 𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦𝑔,𝑡 ≥ 𝛼𝑡 × (1 + 𝑅) ∀ 𝑔, 𝑡
(8)
Equations (9)-(15) represent transmission line constraints and our implementation of
Kirchhoff’s voltage laws (KVL) that govern the flow of electricity and lead to loop flow. Power
flow across existing lines at all points in time 𝑆𝑗,𝑛,𝑧,ℎ,𝑡 is limited by the capacity of that line 𝑆𝑗𝑀𝐴𝑋.
−𝑆𝑗𝑀𝐴𝑋 ≤ 𝑆𝑗,𝑛,𝑧,ℎ,𝑡 ≤ 𝑆𝑗
𝑀𝐴𝑋 ∀ 𝑗, 𝑛, 𝑧, ℎ, 𝑡 (9)
Power flow across candidate lines at any point in time 𝑆𝑘,𝑛,𝑧,ℎ,𝑡 is also constrained by that line’s capacity
𝑆𝑘𝑀𝐴𝑋 once that line has been constructed ∑ 𝑤𝑘,𝜏𝜏≤𝑡 .
− ∑ 𝑤𝑘,𝜏 × 𝑆𝑘𝑀𝐴𝑋
𝜏≤𝑡
≤ 𝑆𝑘,𝑛,𝑧,ℎ,𝑡 ≤ ∑ 𝑤𝑘,𝜏 × 𝑆𝑘𝑀𝐴𝑋
𝜏≤𝑡
∀ 𝑘, 𝑛, 𝑧, ℎ, 𝑡 (10)
Because bus voltage angles 𝜃𝑙,𝑛,ℎ,𝑡 are measured in radians, they are restricted to be within
the [−𝜋, 𝜋] interval
−𝜋 ≤ 𝜃𝑙,𝑛,ℎ,𝑡 ≤ 𝜋 ∀ 𝑙, 𝑛, ℎ, 𝑡 (11)
Power flow from node 𝑛 to node 𝑧 at all points in time 𝑆𝑙,𝑛,𝑧,ℎ,𝑡 is the product of suseptance
𝐵𝑙 and the difference between the bus voltage angle at the sending node 𝜃𝑙,𝑛,ℎ,𝑡 and the bus voltage
angle of the receiving node 𝜃𝑙,𝑧,ℎ,𝑡. For existing transmission lines:
𝑆𝑗,𝑛,𝑧,ℎ,𝑡 = 𝐵𝑗 × (𝜃𝑗,𝑛,ℎ,𝑡 − 𝜃𝑗,𝑧,ℎ,𝑡) ∀ 𝑗, 𝑛, 𝑧, ℎ, 𝑡 (12)
For candidate transmission lines, we would need to multiply an analogue of the right-hand side of
(12) by the build variable ∑ 𝑤𝑗,𝜏𝜏≤𝑡 to account for whether or not that transmission line is available.
However, this would result in a non-linear problem. Since we are using a linear approximation of
the ACOPF model, we employ the big “M” method to constrain power flow across candidate lines
as used in (Krishnan et al., 2016). That is:
15
𝑆𝑘,𝑛,𝑧,ℎ,𝑡 = 𝐵𝑘 × (𝜃𝑘,𝑛,ℎ,𝑡 − 𝜃𝑘,𝑧,ℎ,𝑡) + (∑ 𝑤𝑘,𝜏
𝜏≤𝑡
− 1) 𝑀 + 𝑈𝑡,𝑙𝑐
… ∀ 𝑘, 𝑡 𝑛, 𝑧
(13)
where 𝑀 is a large constant and 𝑈𝑡,𝑙𝑐 is a slack variable. This slack variable is non-negative (14)
and constrained by (15) below.
𝑈𝑡,𝑘 ≥ 0 ∀ 𝑡, 𝑘 (14)
𝑈𝑡,𝑘 ≤ 2 × (1 − ∑ 𝑤𝑘,𝜏
𝜏≤𝑡
) × 𝑀 ∀ 𝑡, 𝑘 (15)
Hence, if a candidate line has not been built by year 𝑡 (i.e. ∑ 𝑤𝑘,𝜏𝜏≤𝑡 = 0), then (13) is non-binding.
Alternatively, if the candidate line has been built by year t (i.e. ∑ 𝑤𝑘,𝜏𝜏≤𝑡 = 1), then 𝑈𝑡,𝑘 = 0, and
(13) is binding, analogous to (12). In our model, we do not account for line losses.
For our power balance equation, demand is limited by supply. Hence, in (16), for each
time period, total generation ∑ 𝑃𝑔,ℎ,𝑡𝑔6 and net inflows ∑ (𝑆𝑙,𝑛,𝑧,ℎ,𝑡 − 𝑆𝑙,𝑧,𝑛,ℎ,𝑡)𝑛 is equal to demand
𝐷𝑛,ℎ,𝑡.
∑ 𝑃𝑔,ℎ,𝑡
𝑔
+ ∑(𝑆𝑙,𝑛,𝑧,ℎ,𝑡 − 𝑆𝑙,𝑧,𝑛,ℎ,𝑡)
𝑛
= 𝐷𝑛,ℎ,𝑡 ∀ 𝑛, ℎ, 𝑡 (16)
In this study, we adopt the perspective of a social planner, reflective of the market structure
that typifies SIDS and represent the budget constraint by (17), which limits investments in new
generation capacity and transmission infrastructure to an annual maximum budget. In our base
model, we consider first a non-binding budget constraint to allow for maximum investment in
order to guarantee that supply limits demand, and merely demonstrate the flexibility of our model
to incorporate this feature. Our results indicate that an annual average of US$ 52 million is required
from 2019-2021, falling over time to US$ 18 million as most investments are front-loaded over
the planning horizon.
∑ 𝐼𝑐,𝑡 × 𝑥𝑐,𝑡
𝑐
+ ∑ 𝐼𝑘,𝑡 × 𝑤𝑘,𝑡
𝑘
≤ 𝛫𝑡 ∀ 𝑡 (17)
6 There is a direct mapping of each generator to each node already embedded.
16
Equations (1)-(17) capture the primary physical, economic and operational features of the
electricity network in mathematical formulations.
4. Data
In this section, we discuss the data used in this study as well as our approach to addressing
some data gaps we encountered. Table 1 summarizes our data. Most of the data were collected in
person from the Office of Utilities Regulation in June-July of 2018.
4.1. Generating Capacity, Demand and Costs
Data on the supply side of the energy system includes a technical inventory of Jamaica’s
generation and transmission infrastructure. For generators, this includes: a complete list of
generators, their locations, heat rates, capacity factors, name-plate capacities, capacity factors for
renewable energy plants, etc. We model candidate hydro resources using a list of potential sources
on the website of the Petroleum Corporation of Jamaica (PCJ).7 We assume constant availability
factors for candidate run-of-river hydro resources consistent with capacity factors provided by the
OUR. In the absence of wind output data, we use wind speed data from the Meteorological Office
of Jamaica to develop availability factors for wind resources throughout an average 24-hour
period. We obtain hourly output data for each day of the year 2018 from the parent company of
the only solar plant in Jamaica. Since Jamaica is 18° north (close to the equator), there is little
seasonal variation in average solar radiation. Using average hourly output as a fraction of the
maximum of average hourly output, we create hourly availability factors and adjust downward
until the model is calibrated to actual capacity factors provided by the OUR. We then apply these
availability factors to all candidate solar generators.
Technical features of candidate generators are obtained from the U.S. Energy Information
Agency (EIA) including estimates of costs (EIA, 2016). For transmission infrastructure, technical
details include length and type of wires, susceptance, reactance, and node-to-node connections.
While candidate sites to build hydroelectric generators were determined based on PCJ information,
7 https://www.pcj.com/developing-jamaicas-renewable-energy-potential/
17
other renewable energy generators were subjectively assigned absent actual data on possible
locations for future solar power and wind plants.
Demand-side data focuses on temporal, sectoral and regional load diversity. For this study,
we use forecasted demand growth rates for each rate class based on OUR data. OUR demand
forecasts (produced in 2015) under-estimated actual demand in 2017. For this reason, we utilize
the forecasted growth rates starting at the actual 2017 values. An alternative would be to generate
our own forecasts. However, using the OUR methodology to generate demand forecasts would
require at least 12 different estimations; a set of 6 estimations for the number of customers for each
rate class and another set of 6 estimation for the average consumption for each rate class. This
could result in separate papers entirely. The primary objective of this paper is to answer two
focused, empirical questions about energy modelling in SIDS: (1) Does simultaneously planning
for generation and transmission investments improve planning efficiency? (2) What is the impact
of loop flow (a phenomenon intrinsic to electricity networks) on long-term investment planning?
Finally, while we obtained temporally distributed demand for Jamaica in 2017 as well as a
demand forecast for different sectors of the Jamaican economy, the data lacks regional distribution.
To overcome this challenge, we multiply hourly demand for 2017 by the known share of total
demand by rate class. This gives us a distribution of demand across rate classes for each hour. To
obtain regional distribution of demand, we multiply hourly demand for each rate class by the share
of population (for streetlights, residential and small commercial customers) or the share of hotel
rooms per parish8 (for large commercial, industrial and “other”9 customers). We do this because
of the heterogenous growth rates of each rate class and the fact that the concentration of economic
activities differ across parishes. We use these variables (number of hotel rooms and population)
because the OUR 2017 report identifies them as explanatory variables for electricity demand.
Other predictor variables such as gross domestic product (GDP) are not available in a spatially
disaggregated format and therefore could not be used. We project forward using demand growth
rates (OUR, 2017).
For financial parameters, we use fixed and variable O&M costs for each generator from
the OUR. We obtain investment costs for candidate generators from the EIA estimates of costs
8 A parish is a geographic sub-division of the island. 9 “others” refers to two institutions given a special designation by the utility given their consumption of electricity.
18
(EIA, 2016) and adjust to 2017 dollars. To convert to discrete capacity choices, we adjust
investment cost by generator capacity relative to the capacity sizes listed in the EIA tables. We use
annual fuel costs in real 2017 dollars based on the EIA projection tables (February 2018).
19
Table 1: Summary and status of required data
Required Data Status Source Gaps in data
Supply side Inventory of generators in
Jamaica
Obtained OUR, JPS Availability factors and unforced outage
rates not temporally disaggregated
Technical features of
candidate generators
Obtained EIA (2016)
Location of candidate
generators
Partially obtained PCJ Locations subjectively assigned (except
for hydro generators)
Technical features of
transmission lines in
Jamaica
Obtained OUR,
JPSCo
Demand side
Historical annual demand Obtained only at
aggregate level
(2009-2016)
OUR
(2017)
Disaggregated by customer type but not
location
Annual demand forecast Obtained only at
aggregate level
(2016-2040)
OUR
(2017)
Disaggregated by customer type but not
location
Annual peak demand Obtained only at
aggregate level
(2001-2016)
OUR
(2017)
Not disaggregated by customer type or
location
Annual peak demand
forecast
Obtained only at
aggregate level
(2016-2040)
OUR
(2017)
Disaggregated by customer type but not
location
Historical hourly demand
and peak demand
Obtained only at
national level (Jan. 1,
2017 – Dec. 31, 2017
in half-hour
intervals)
OUR
(2017)
Not disaggregated by customer type or
location
Hourly demand forecast Computed Computed using hourly demand for
2017, demand shares per rate class and
regional distribution of rate classes.
Costs
Fixed and variable
operating and maintenance
(O&M) costs
Obtained OUR
Investment costs Obtained EIA (2016)
Fuel price projections Obtained EIA (2018)
20
5. Results
In this section, we discuss the findings of our study. We compare investment decisions,
costs and the generation portfolio across model specifications. We discuss our calibration of the
model in the appendix. After calibration, three model specifications are used. First, generation
and transmission decisions are simultaneously co-optimized. This is our reference case. The
second specification sequentially optimizes generation and then transmission decisions, given the
generation plan optimized in the first stage. Both models account for loop flow. The difference
between the models captures the impact of a simultaneous vs sequential framework. The third
model simultaneously optimizes generation and transmission decisions but does not account for
loop flow. The difference between this model and the first model captures the impact of loop
flow. We examine the impact of loop flow and assess the difference between a sequential and
simultaneous planning framework. We also perform sensitivity analysis on fuel prices which is
one of the most significant sources of uncertainty. We first present the results of the baseline
scenario and the discuss the differences
5.1. Reference case
In our reference case, the NPV cost of investment and operations over the 2017-2040 time
horizon to US $2.727 billion (Table 2). This follows the construction of 8 power plants totaling
934 MW in capacity. As shown in Figure 6, these plants are primarily located in the south-eastern
region (with the largest population density as well as the manufacturing center of Jamaica) as well
as in the north west region of Montego Bay (the second city and tourism capital of Jamaica). These
investments represent the replacement of 11 power plants (631 MW) within the planning horizon,
but also suggests that our approach to generating a regional distribution of demand is consistent
with what one would expect given the distribution of economic activity across the island.
Interestingly, no transmission corridor is expanded in our reference case. This is because 68%
(631/934 MW) of the new capacity is replacing decommissioned plants. Given investments in
transmission infrastructure by JPSCo since 2012, there is adequate transmission capacity to
accommodate the new power plants in our reference scenario.
Also of note, the only renewable energy plant constructed is an exogenously imposed 37
MW solar plant that was already scheduled to be constructed in Jamaica. This suggests that under
a least cost, business as usual scenario, Jamaica’s renewable energy potential is less competitive
than natural gas. As illustrated in Figure 7, the use of heavy fuel oil (HFO) falls precipitously by
21
2019, and in 2026, as major power plants are decommissioned. Similarly, wind generation ceases
after 2036 as existing wind plants are scheduled to be decommissioned at this time. Natural gas
(NG) dominates new capacity investments.
Figure 6: Map of Jamaica with optimal capacity investments (reference case) Source: JPSCo (modified) – Black shapes represent new generation investments; year of investment in call-out boxes
Figure 7: Generation portfolio (reference case)10
10 NG = Natural Gas, HFO = Heavy fuel oil, ADO = Automotive Diesel Oil
0
1000
2000
3000
4000
5000
6000
7000
20
17
20
18
20
19
20
20
20
21
20
22
20
23
20
24
20
25
20
26
20
27
20
28
20
29
20
30
20
31
20
32
20
33
20
34
20
35
20
36
20
37
20
38
20
39
20
40
GW
h
Years
Generation Portfolio: Reference Case
wind
solar
NG
hydro
HFO
ADO
22
Table 2: Cost comparison of model specification
Units Simultaneous Model
with Loop Flow
Sequential
Model with
Loop Flow
Simultaneous
Model without
Loop Flow
Total Cost
(US$mil)
US$ million 2,727 2,731 2,727
Difference* US$ million
3 0.0
Difference* %
0.12% 0.0%
* Relative to simultaneous model with loop flow
5.2. Sequential Model
As expected, the sequential model resulted in higher NPV cost than our reference case.
This is driven by the treatment of transmission constraints. Recall that in the first stage of the
sequential model, transmission constraints are ignored and the power balance equation needs only
satisfy aggregate demand. This results in a similar capacity investment pattern as our reference
case. However, instead of constructing a 237 MW natural gas advanced combustion turbine
(NGACT) facility in St. Andrew in 2026, a similar facility is built in Old Harbour in year 2026
(Figure 8). In the second stage of the model, regional demand, not aggregate demand needs to be
satisfied. This necessitates the expansion of 3 transmission corridors to satisfy demand at each
node in the network. This demonstrates the utility of the simultaneous model. GEP, while
satisfying aggregate demand, may fail to satisfy local demand, requiring additional investments in
transmission capacity to ensure demand at each location is satisfied. Finally, while total cost is
higher in the sequential model (US$ 3 million), this magnitude is less than anticipated. We
conjecture that these results are driven by the fact that transmission capacity is not a scarce resource
in Jamaica. However, when one considers exchange rate vulnerabilities and the fact that SIDS
governments (the typical owners of utilities) are fiscally constrained, the cost differential of these
models is likely biased downward.
23
Figure 8: Optimal capacity investments (sequential model) Source: JPSCo (modified) – Black shapes represent new generation investments; year of investment in call-out boxes; red call-out
box indicates departure from reference case.
Figure 9: Map of Jamaica with optimal transmission investments (sequential model) Source: JPSCo (modified) - Black lines represent new transmission line investments; year of investment in call-out boxes
24
5.3. Model with no loop flow
Contrary to our expectation, we find no evidence that loop flow affects long-term
investment planning in Jamaica. There is no difference in total system cost between models with
and without loop flow constraints (Table 2). This implies that Jamaica’s network topology lacks
the complexity, size and scarcity of transmission capacity to make loop flow a significant
economic consideration, at least from a long-term planning perspective. Results may differ in an
operational plan that considers much smaller time-scales (e.g. 5 minutes) and greater transmission
detail.
6. Sensitivity Analysis
Operating costs are primarily driven by fuel prices, which we take as exogenous in our
model. However, fuel price is a significant source of uncertainty. We therefore re-evaluate our
models using high and low fuel price projections (EIA, February 2018). As Table 3 indicates, total
costs are higher under a scenario with higher fuel prices and lower when the converse is true.
Nevertheless, across model specifications, results are consistent; the simultaneous model is more
efficient than the sequential model, and loop flow does not have a significant impact. In fact, we
observe that the difference between the models increase under fuel price uncertainty. This indicates
that the simultaneous model has greater utility, particularly when one considers uncertainty in fuel
prices.
As one would expect, higher fuel prices make renewable resources more attractive,
resulting in greater investment in these resources and a reduction in natural gas investments (Table
4 and Figure 10). Unlike the baseline scenario, higher fuel prices results in investments in
transmission capacity (Figure 11) to accommodate additional generation resources. However, the
distribution of power plants remain consistent with economic activities and population distribution
in Jamaica.
25
Table 3: NPV Total cost given fuel price scenarios
Model Type Baseline Fuel
Price Scenario
High Fuel
Price
Scenario
Low Fuel
Price
Scenario
Simultaneous
model with Loop
Flow
Total Cost
(US$mil)
2,727 2,785 2,484
Difference** 58 - 243
Difference (%)** 2.1% -8.7%
Sequential model
with Loop Flow
Total Cost
(US$mil)
2,731 2,800 2,496
Difference
(US$mil)*
3 15 12
Difference (%)* 0.12% 0.52% 0.47%
Difference
(US$mil)**
72.59 - 231.45
Difference (%)** 2.7% -8.3%
Model excluding
loop flow
constraints
Total Cost
(US$mil)
2,727 2,785 2,484
Difference
(US$mil)*
0 0 0
Difference (%)* 0% 0% 0%
Difference
(US$mil)**
58.02 - 243.11
Difference (%)** 2.1% -8.9%
* Relative to simultaneous model of the same fuel price scenario
** Relative to the simultaneous model of the baseline fuel price scenario
26
Figure 10: Map of Jamaica with optimal generation capacity investments (simultaneous model;
high fuel prices scenario) Source: JPSCo (modified) – Black shapes represent new generation investments; year of investment in call-out boxes; hydro plant
capacities are more diverse and are therefore indicated in call outboxes
Figure 11: Map of Jamaica with optimal transmission investments (simultaneous model; high fuel
prices scenario) Source: JPSCo (modified) - Black lines represent new transmission line investments; year of investment in call-out boxes
27
Table 4: Total new capacity investment by technology and model specification
Baseline Fuel Prices High Fuel Prices Low Fuel Prices
(1) (2) (3) (1) (2) (3) (1) (2) (3)
wind 0 0 0 150 150 150 150 150 150
solar 37 37 37 37 37 37 37 37 37
Nat.
gas 897 897 897 830 830 830 797 797 797
hydro 0 0 0 56.1 56.1 56.1 47.3 30.9 47.3
Total 934 934 934 1073.1 1073.1 1073.1 1031.3 1014.9 1031.3
(1) Simultaneous model with loop flow
(2) Sequential model with loop flow
(3) Model excluding loop flow constraints
Interestingly, there are even less investments in thermal plants under low fuel prices
scenario. Though appearing counter-intuitive at first, further investigation of our results indicate
that this is driven by the relative prices of ADO, HFO and natural gas. While we only allow for
new thermal plants to be natural gas plants (consistent with commitments by the government and
the utility), the lower cost of ADO and HFO increases the utilization of these existing thermal
plants, minimizing the need to build new natural gas plants and satisfying smaller excess demand
with renewable energy resources. Unlike our baseline fuel price scenario, two transmission
corridors are built under low fuel price scenario to connect new hydro resources to the network.
Irrespective of fuel price scenario, natural gas dominates new generation capacity
investments. The primary difference relative to our reference case is slightly higher renewable
energy generation, particulalrly from wind, close to the end of the planning horizon (Figure 14
and Figure 15).
28
Figure 12: Map of Jamaica with optimal generation capacity investments (simultaneous model;
low fuel prices scenario) Source: JPSCo (modified) – Black shapes represent new generation investments; year of investment in call-out boxes; hydro plant
capacities are more diverse and are therefore indicated in call outboxes
Figure 13: Map of Jamaica optimal transmission investments (simultaneous model; low fuel
prices scenario) Source: JPSCo (modified) - Black lines represent new transmission line investments; year of investment in call-out boxes
29
Figure 14: Generation portfolio (high fuel prices scenario)
Figure 15: Generation portfolio (low fuel prices scenario)
7. Conclusion
In this paper, we extend the literature on long-term infrastructure investment planning in
the electricity sector by focusing on the economic and geographic idiosyncrasies of SIDS and the
role they play in long-term planning. We demonstrate this using Jamaica as a case study. We find
that co-optimizing generation and transmission investment decisions is less costly than the
0
1000
2000
3000
4000
5000
6000
7000
2017 2019 2021 2023 2025 2027 2029 2031 2033 2035 2037 2039
GW
h
Years
Generation Portfolio (High Fuel Prices)
wind
solar
NG
hydro
HFO
0
1000
2000
3000
4000
5000
6000
7000
2017 2019 2021 2023 2025 2027 2029 2031 2033 2035 2037 2039
GW
h
Years
Generation Portfolio - Low fuel Prices
wind
solar
NG
hydro
HFO
ADO
30
traditional sequential approach to long-term planning historically practiced in SIDS. The benefit
of simultaneous planning increases when one considers fuel price uncertainty. The cost differential
is less than anticipated, but is likely a lower bound having not examined the impact of exchange
rate volatility (another potential source of uncertainty). For these reasons, we determine that the
modest additional computational requirements of simultaneous planning is justified in long-term
infrastructure investment planning in SIDS.
We do not find evidence that loop flow impacts least cost investment decisions. We
therefore reject our initial hypothesis that failing to account for loop flow would under-estimate
costs and misallocate resources as indicated by Chao and Peck (1996). Our results are attributable
to the small size, the near radial topology of the Jamaican electricity network, and an abundance
of existing transmission capacity in the island. We conclude that a lack of complexity, size and
scarcity of transmission capacity may result in similar outcomes for other SIDS, particularly those
in the Caribbean region which share similar features. Loop flow would likely be of greater import
to short-term operational plans.
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Appendix – Model Calibration
In calibrating the model, we compare results with information provided by the OUR as
well as data found in JPSCo’s 2017 annual report. This was necessary because the two data sources
provided two sets of information and neither was all-encompassing. For instance, while we have
reported net output from different renewable resources from the OUR, there was no information
on the net output from non-renewable resources. This information is however available in the
JPSCo’s 2017 annual report. Nominal magnitudes also differ somewhat depending on the data
source. We therefore examine both nominal figures as well as figures in terms of share of total
output.
Table 5 compares our simulation with data available in JPSCo’s 2017 annual report. We
conclude that our model is well calibrated given the information that we have. In terms of operating
cost, our simulation yielded US$344 million compared to JPSCo’s US$549 million. Given that we
included only the direct costs associated with generation (which is 61% of total JPSCo costs),
excluding administrative costs, we believe the simulated operating costs is within expected
bounds. Since our net generation data was obtained from the OUR and not from JPSCo (which
differ in nominal values for output), we observe differences in net output from slow speed diesel
(SnSSD), hydro plants owned by JPSCo, gas turbine plants (GGT) and combined cycle plants
(CCT) when compared to the JPSCo report. This is similarly true for the net output of JPSCo and
33
IPPs in nominal terms. However, when one compares the share of total output by each set of plants
(the final two columns), we find the differences to be within tolerable limits.
In Table 6, we find encouraging results when our simulation is compared with the actual
source data from the OUR. The first column represents anonymized plants. Columns 3 and 4
represent the output in GWh from our simulation versus the reported output from the OUR. The
final two columns compare our simulated capacity factors with reported OUR capacity factors.
The maximum error is 0.01.
Table 5: Comparing simulation with data from JPSCO's annual reports
Variable Units Simulated Reported Nominal Difference
Difference (%)
Simulated Share (%)
Reported Share (%)
Operating Cost USD Mil. 344 549 -205 -37
SnSSD Net. Gen GWh 1120 1467 -347 -24 25 34
JPSCo Hydro GWh 172 157 15 10 4 4
JPSCo GGT GWh 0 92 -92 -100 0 2
JPSCo CCT GWh 937 820 116 14 21 19
JPSCo Net Output GWh 2234 2536 -302 -12 50 58
IPPs Net Output GWh 2274 1827 447 24 50 42
Operating Cost USD Mil. 344 549 -205 -37
Table 6: Comparing simulation with OUR data Output Capacity Factor
Plant Technology Simulated (GWh) Reported (GWh) Simulated Reported
h1 hydro 39.9 40.0 0.76 0.76
h2 hydro 17.1 17.0 0.78 0.78
h3 hydro 28.2 28.0 0.67 0.67
h4 hydro 23.7 23.6 0.75 0.75
h5 hydro 6.0 6.0 0.62 0.62
h6 hydro 2.5 2.5 0.36 0.36
h7 hydro 29.1 29.0 0.81 0.81
h8 hydro 25.8 26.0 0.46 0.46
W0 wind 5.2 5.3 0.20 0.19
W1_2 wind 95.1 96.5 0.29 0.28
W3 wind 96.8 99.7 0.33 0.32
W4 wind 62.1 63.1 0.30 0.29
S1 solar 40.7 40.9 0.19 0.20