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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

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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

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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.

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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.

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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

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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).

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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.

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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

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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.

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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),

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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:

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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

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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.

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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

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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:

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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