A multi-criteria, long-term energy planning optimisation model with integrated on-grid and off-grid electrification – The case of Uganda
Introduction
The United Nations has defined universal access to electricity as one of its Sustainable Development Goals to be reached by 2030. Approximately 675 million people in sub-Saharan Africa (SSA) live without access to electricity, equating to more than half of all un-electrified people globally [1]. As most research on energy planning optimisation has been conducted in and applied to countries with well-developed power infrastructure, there is an alarming paucity of approaches designed for developing countries with low initial electrification rates. A recent review failed to identify any such long-term energy planning optimisation research applied to a case in SSA [2]. Yet, the objectives and challenges of a multifold national electrification rate increase differ markedly from planning objectives in developed countries.
A suitable formulation of the long-term Generation Expansion Planning (GEP) problem is required to assist decision makers in designing cost-efficient energy system [3]. A solution to the problem yields the optimal type and size, location, as well as construction timing for new generation capacity over a long planning horizon to satisfy an expected energy demand. A planning horizon can be considered to be long-term if it spans 15 years or more [4].
Several review studies have discussed methods and trends for generation expansion as well as transmission expansion planning. Zhu et al. [5] as well as, more recently, Koltsaklis and Dagoumas [6] analyse the GEP literature, Latorre et al. [7] as well as Lumbreras and Ramos [8] review the transmission planning problem, while Hemmati et al. [9] discuss various combined generation and transmission planning approaches. Mathematically, the complete long-term GEP problem is a Mixed Integer Nonlinear Programming (MINLP) problem with multiple decision criteria and uncertainties. MINLP formulations have been used by Yuan et al. [10], as well as by Hemmati et al. [11], with the latter incorporating energy storage and environmental factors into their GEP model. If transmission is addressed, further nonlinearities exist if Kirchoff’s Second Law is explicitly modelled. For instance, Zhang et al. formulated a MINLP planning problem considering transmission infrastructure [12]. Rider et al.’s proposed MINLP approach for generation and transmission planning combined heuristics and interior point approaches to solve their nonlinear sub-problems [13].
However, especially in those cases where the GEP problem has been applied to long-term case studies, avoiding the considerable computational complexity associated with such non-linear methods has led to highly insightful results. Recent advances have focused on considerably broadening the scope and level of analysis of the long-term GEP problem [8], which in turn required different assumptions to simplify the model. The consequential diversification of the GEP literature has integrated such issues as various risk assessments, a variety of new decision criteria beyond pure economic optimality, operational power system aspects, the inclusion of interdependencies with other systems such as water supply, energy storage and security of supply, as well as policy design. Associated simplified solution approaches have included mathematical optimisation techniques such as Linear Programming (LP), various decomposition approaches, Mixed Integer Linear Programming (MILP) as well as meta-heuristic approaches. For instance, in their long-term energy planning study, Thangavelu et al. used an LP formulation to incorporate security of supply concerns with an environmental objective of low emissions [14]. Guo et al. similarly used an LP formulation to study the effect of different operational time scales as part of the Chinese power system under a cap-and-trade carbon scheme [15]. However, due to their potential to model binary investment decisions as well as fixed cost functions, MILP approaches have been a dominant method to expand the GEP problem. Pozo et al. proposed a three-level MILP model which integrates generation and transmission expansion planning [16]. Other scholars have used MILP models to account for reliability measures [17], different types of problem-inherent uncertainties [18] and scheduling decision making [19]. Metaheuristic approaches have frequently been argued to allow for a broad study of long-term energy planning [20]. Metaheuristic methods have been proposed as alternatives to classical optimisation methods. These can arise when studying optimal operational conditions of power plants [21], associated components such as converters [22] or complex electricity demand forecasting [23]. Kaboli et al. provide an informative visual classification overview of such metaheuristics [24]. Proposed algorithms include the hybrid Genetic Algorithms (GA)/dynamic programming approach developed by Park et al. [25], the adaptive Simulated Annealing (SA) algorithm proposed by Yildirim et al. [26], and Particle Swarm Optimisation (PSO) based algorithms [20], which have also been successfully used for transmission planning [27]. Some models were specifically designed to handle uncertainties through approaches such as stochastic programming [28] or interval-parameter linear programming [29].
This paper focuses on the subset of problems which related to national-level expansion planning. While some studies, such as Chen et al.’s work on China [30], do not divide their national power system into distinct cells, a number of recent works have done so to study sub-national implications of their planning models. For example, Guo et al. in their long-term energy planning study of the Chinese power system deployed a linear levelised cost approach for their objective function, dividing the Chinese system into ten geographic cells [15]. Guerra et al. integrated generation and transmission capacity planning in their MILP formulation applied to the Colombian power system, which they divided into five sub-national cells [31]. Georgiou formulated an MILP model to solve the long-term energy planning problem for the Greek national electricity system [32]. Georgiou similarly modelled the system using five different geographic cells and studied optimal transmission requirements between these cells. Sharan and Balasubramanian presented a single-period MILP model which includes power and fuel transportation costs and apply it to the case of Southern India, modelled via 48 demand nodes [33]. These last three works argue for the benefits of simultaneously optimising generation and transmission infrastructure. Furthermore, the GEP problem can be formulated as either driven by a centralised monopoly-utility or by a deregulated market with several market participants [19].
The different types of decision criteria associated with generation and transmission planning imply that multi-objective models are well-suited for energy planning [8], an assertion which has been similarly made in the context of different market designs [34] and for renewable energy integration [35]. To be able to obtain solutions for a long-term national-level planning problem with reasonably high geographic resolution or multiple periods, multi-objective expansion planning using classical optimisation techniques has been dominated by assumptions which allow for linear methods. Ren et al. formulate a Multi-Objective Linear Programming (MO-LP) model for the planning of distributed energy systems and their environmental impact [36], while Luz et al. [37] as well as Zhang et al. [35] use MO-LP formulations to plan systems with high renewable energy penetration. Among the most prominent approaches for this type of problem are Multi-Objective Mixed Integer Linear Programming (MO-MILP) methods [38]. For instance, Muis et al. use a MO-MILP formulation to assess renewable energy integration in the presence of a carbon emission reduction target [39]. Antunes et al. similarly use a MO-MILP formulation for their environmentally informed GEP model instance [40]. In terms of the types of optimisation criteria studied, previous multi-objective approaches have most commonly considered the trade-off between costs and environmental impact. For instance, Koltsaklis et al., in their spatial MO-MILP energy planning model applied to the Greek system, included an environmental constraint in terms of carbon emissions, and solved their problem for different levels of maximum-allowed emission levels, effectively yielding non-dominated solutions in the cost-versus-emissions space [4]. In addition to minimising costs and environmental impact, Meza et al. modelled minimum imported fuel and energy price risks objectives [41], [42], Unsihuay-Vila et al. considered a technical objective of diversifying the generation mix as part of their MO-MILP model [43], Luz et al. maximised generation at peak load [37], while Trotter et al. minimised different political risk factors associated with different network designs in the Southern African Power Pool [44] and a continental African case [45].
Different methods exist for solving multi-objective optimisation problems [46]. In the context of the GEP, popular approaches have included weighted sum methods (see [42], [43]), compromise programming based on minimising the Chebyshev distance between the multi-objective solution and the (infeasible) ideal solution of the single-objective cases (see for instance [36], [38], different variations of the ε-constraint method (see for instance [35], [37]) where all but one of the objectives are introduced as constraints, and Fuzzy Decision Theory [47].
Applying the long-term GEP to developing countries alters the problem in several fundamental ways when compared to its conventional formulation. It is crucial to have robust planning methods in place for sub-Saharan Africa which cover the next two decades in order to efficiently overcome the energy access challenges there [49]. Specifically, three crucial aspects which characterise the long-term energy planning problem in developing countries have not yet been addressed in the mainstream GEP literature. Namely, these are (1) the presence of substantial planned suppressed demand due to insufficient initial power infrastructure as evidenced by electrification rates below 100%, (2) the challenge of dealing with highly unequal access to electricity on a sub-national level, and (3) the importance of integrating on-grid and off-grid electrification options into an expansion planning optimisation model. The following paragraphs explain these three issues and the literature gaps associated with them in turn, while Section 1.3 explains this paper’s novel contributions to the literature by specifically addressing these three gaps.
First, while demand for electricity exists throughout a given developing country, the power infrastructure may only cover small parts of the country. In SSA, the average access rate is below 40%. SSA is home to 18 of the 19 countries worldwide which have reported an electrification rate of below 30% in 2016, the access rate in Uganda is below 25% [1]. Hence, a static constraint to meet all demand in a country which is the way the long-term energy planning problem has commonly been formulated in the literature is not a sensible modelling approach in many developing country contexts. Rather, many African governments have set electrification rate targets below 100% for the next one to two decades. To assist the associated infrastructure expansion decision-making process, a long-term national-level planning model needs to model demand as meeting this electrification rate target throughout the planning horizon, hence allowing for planned suppressed demand.
Second, electricity access is distributed highly unequally throughout SSA [50]. While it is accepted that the implicit socio-political dynamics have often been fundamental to whether or not electrification in developing countries has succeeded or not [2], to the best of our knowledge, they have not yet been explicitly modelled in long-term national-level generation and transmission planning optimisation models. SSA is the only major world region where there is a more than threefold gap between rural and urban electrification (Fig. 1, see also [50]). Similar inequalities exist for different sub-national regions of the same country. As a consequence, electrification has turned into a political good in SSA: Incumbents have frequently promised to provide access to their political supporters during electoral campaigns (see [54] and more recently [45]). Decision makers are thus faced with the challenge of electricity access being a deeply socio-political issue, and energy planning efforts would do well to consider such dimensions.
Third, while the traditional GEP focuses on generation expansion, expanded by some scholars to transmission planning, the low number of connections in many African countries warrants the inclusion of distribution planning. This is necessary to capture where new connections are provided, which in turn yields the actual, non-suppressed demand the network needs to meet. What is more, in addition to the traditional on-grid focus of the GEP, off-grid solutions have been found to be cheap electrification alternatives in many developing countries and thus need to be part of an integrated planning approach [55]. Several planning studies have used geographic information system (GIS) software to determine the cost-optimal mode of electrification in developing countries. Cases include village-level studies [56], country-level assessments in Kenya [57], Burkina Faso [58] and Senegal [59] as well as on a continental African scale for rural [60] and for all households [61]. These GIS-based studies proposed different approximations to calculate the costs of different electrification alternatives for a certain spatial area and then choose the cheapest alternative per spatial area. Mentis et al.’s work is notable for their continental scale, the quality of their GIS data and their usage of small spatial units of 1 km2 [61]. They found a high penetration of standalone technologies as part of the preferred power system, especially for low per capita demand scenarios. Other scholars have used the pre-defined cost-minimisation planning model of the Network Planner software to determine the least-cost choice between grid and off-grid electrification in African cases, namely for Nigeria [62] and Ghana [63]. However, while these approaches allow for choosing a high spatial resolution due to limited computational complexity, all these studies treat grid extension as a black box, attributing an assumed overall cost rather than explicitly modelling electricity flows, the implications for the optimal on-grid generation mix or respective generation plant locations and timing. Interactions between the different spatial areas are limited or non-existent in most of these studies. They were also largely focused on household access to electricity and often not concerned with non-domestic demand which usually makes up around three quarters of overall demand.
This paper is the first to expand the long-term GEP such that it can readily be used for developing country cases with limited initial electricity infrastructure. It contributes to the trends of broadening the GEP problem and the usage of MO-MILP methods evident in the literature review in Section 1.1. Specifically, this paper presents a novel long-term, spatially explicit, multi-period MO-MILP energy planning model, featuring the following three main novel generalisations, each addressing one of the three literature gaps identified in Section 1.2:
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The design and application of a national-level energy planning optimisation tailored towards developing countries with limited initial power infrastructure, imposing the demand-side constraint of meeting a given overall electrification rate target which can be set to any number between 0 and 100% at any time period. Hence, the model is able to choose to meet demand in some sub-national areas, and supress it in others. This constitutes a generalisation of the conventional generation and transmission expansion planning problem where demand has to be met at all nodes and times.
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The model defines sub-national electrification inequalities (both urban versus rural and regional access differences) as a separate optimisation criteria. The model’s multi-objective approach yields the optimal trade-off between minimising system costs and different types of sub-national electrification inequalities expressed in a spatially explicit way, considering a significant number (>100) of sufficiently small discrete geographic cells.
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In addition to integrated generation and transmission expansion planning, the model includes an aggregated formulation of distribution infrastructure to indicate where new connections are planned. Crucially, the model integrates both on-grid and off-grid electrification options to provide energy access, with the latter being projected to play an important part in electrifying developing countries. This integrated model is able to derive implications for the optimal split between off-grid and on-grid electrification of people without access, as well as derive the implicit load implications on the grid.
Furthermore, the model’s application is novel as it constitutes the first energy optimisation study of any kind of the Ugandan network. As all data used is real-life data, the paper is able to compare its solutions with official Ugandan energy expansion policies and offer improvements over current plans.
The remainder of this paper is structured as follows. Section 2 presents the problem statement to describe the overall structure and key assumptions of the model. Section 3 mathematically defines the model, Section 4 provides the solution algorithm. Section 5 briefly introduces the post-optimisation power flow analysis method used for validating the modelling results, while data requirements for the Ugandan case are briefly discussed in Section 6. Section 7 presents the solution of the model and tests the least-cost network via an indicative load flow analysis, Section 8 shows the significant differences between the model results and Uganda’s official national energy expansion plan. Finally, a conclusion is offered in Section 9.
Section snippets
Problem statement
The problem is stated in terms of the following factors and assumptions:
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Overall structure and objectives: The MO-MILP model performs long-term energy planning by dividing the system into a number of distinct geographic cells c over multiple time periods t. It is tailored towards cases with low initial electrification rates, and minimises the discounted system costs, consisting of the investment as well as operation and maintenance cost of generation, transmission and distribution
Mathematical formulation
This section presents the novel MO-MILP model laid out in Section 2. First, the objective functions are discussed in Section 3.1. The subsequent sections address the constraints modelling demand (Section 3.2), energy balances (Section 3.3), generation and environmental impact (Section 3.4), transmission (Section 3.5), distribution (Section 3.6) and network resilience (Section 3.7). The solution approach, based on applying an ε-constraint method to the non-monetary objective functions, is
Solution algorithm
To solve the presented MO-MILP model, an ε-constraint approach is implemented. The idea is to convert both non-cost objective functions f2 and f3 to constraints by requiring them to not exceed a certain finite value ε2 and ε3, respectively. The model is then solved repeatedly for different ε2 and ε3 combinations to yield a Pareto Front of non-dominated solutions of the original MO-MILP problem.
While for some MO-MILP problems, algorithms based on the ε-constraint method can be problematic, such
Validation method: Indicative load flow analysis
To indicate that the proposed energy networks for Uganda are valid, the Power Systems Analysis Toolbox (PSAT) 2.1.10 was used to conduct load flow analyses [65]. The networks of generation, loads and transmission lines obtained from the results of the optimiser were translated into the Matlab model format required for PSAT using a Python script. PSAT was run using Matlab 2016b. The only change was the addition of the slack bus to the model to enable the solver to converge. Load flow analysis
Data: Uganda case study
As no previous optimisation study of Uganda's power system exists, data for geospatial generation potentials, demand and demographics, costs and existing infrastructure had to be pooled from a variety of sources: To populate the model for the case of Uganda presented in this paper, 40 different sources providing data and/or relevant assumptions were used. Table 1, Table 2 list the data sources for all scalars and parameters, respectively. Several parameters were not readily available and had to
Results and discussion
This section first presents the results of a case of 10 districts in Uganda in Section 7.1, thus falling into the 5–10 cell interval used in recent long-term energy problem research [4], [15], [31]. Section 7.2 then discusses the results from the national-level, 112-district instance of Uganda. Section 7.2 also presents the results of the indicative load flow analysis of the least-cost network to suggest the validity of the model results.
Comparison with Uganda’s official generation expansion plan
To compare the official capacity targets from Uganda’s governmental development policy “Vision 2040” [70] with the model results presented in this paper, an additional demand scenario was studied. This demand scenario followed from assuming the Uganda’s official policy target of a 3668 kWh per capita consumption case in 2040.
Fig. 14 compares Uganda’s Vision 2040 capacity targets with the model results using this high-end demand scenario. The higher total installed capacity resulting from the
Conclusion
National power systems in many developing countries are characterised by substantial suppressed electricity demand due to low connection rates, highly unequally distributed energy access, and the relevance of both on-grid and off-grid electrification approaches. This study designed the first integrated, multi-criteria optimisation model for long-term national-level energy planning tailored to developing countries with low initial electricity infrastructure. The model successfully generalised
Acknowledgements
The authors would like to acknowledge excellent comments and suggestions from Peter Twesigye, Hans Pirnay, Yusuf Kiranda, Alex Money, Gunes Erdogan, Kevin Wheeler, Max Walter and Daniel Junglas, as well as from the audiences of the 2018 Energy Systems Conference in London, UK, and the 2018 Practical Challenges of Sustainable Electrification in Africa Conference in Oxford, UK. Dimitris Mentis from KTH Stockholm, Peter Twesigye from UMEME Ltd. Uganda and Martin Kretschmer from GIZ Uganda
References (103)
- et al.
Electricity planning and implementation in sub-Saharan Africa: a systematic review
Renew Sustain Energy Rev
(2017) - et al.
A spatial multi-period long-term energy planning model: a case study of the Greek power system
Appl Energy
(2014) - et al.
State-of-the-art generation expansion planning: a review
Appl Energy
(2018) - et al.
The new challenges to transmission expansion planning. Survey of recent practice and literature review
Electr Power Syst Res
(2016) - et al.
Nonlinear integrated resource strategic planning model and case study in China's power sector planning
Energy
(2014) - et al.
Multistage generation expansion planning incorporating large scale energy storage systems and environmental pollution
Renew Energy
(2016) - et al.
An integrated source-grid-load planning model at the macro level: case study for China's power sector
Energy
(2017) - et al.
Long-term optimal energy mix planning towards high energy security and low GHG emission
Appl Energy
(2015) - et al.
A multi-region load dispatch model for the long-term optimum planning of China’s electricity sector
Appl Energy
(2017) - et al.
An interval-parameter minimax regret programming approach for power management systems planning under uncertainty
Appl Energy
(2011)