Multi-year stochastic planning of off-grid microgrids subject to significant load growth uncertainty: overcoming single-year methodologies

Highlights

• Stochastic optimization of isolated microgrids, considering load growth uncertainties.

• Ageing model for battery, photovoltaic plant, diesel generator, converters and tank.

• Load following operation strategy including the effects of assets degradation.

• Detailed multi-year simulations at hourly time resolution for microgrid sizing.

• Comparison between deterministic and stochastic, single- and multi-year optimization.

Abstract

The optimal design of off-grid microgrids in developing countries is difficult to achieve, as several political and socio-economic risks can hamper investments of private companies. Estimating the energy demand and its growth is a challenging task, subject to high uncertainty that rarely have been accounted for in multi-year simulations at hourly resolution. Besides, from a long-term perspective, the assets degradation can significantly affect the performance of stand-alone hybrid energy systems. In this paper, we address these challenges and propose a novel stochastic dynamic method to size microgrids, simulating with accuracy the system operation and considering the unavoidable uncertainty in load growth and the components ageing. A predefined scenario tree structure allows capturing the load growth uncertainty and obtaining different capacity expansion strategies for each scenario. An illustrative case study for an isolated power system in Kenya using data collected in 23 Kenyan microgrids is shown. The proposed stochastic formulation results in a considerable reduction of the size of components with respect to traditional single-year approaches. Savings in terms of Net Present Cost (NPC) are beyond 16-20% and the effects of assets degradation are about 6%. Results lead to recommend multi-year optimization tools, as single-year methodologies can hardly achieve the same performances.

Introduction

Microgrids are seen as a promising solution for fostering rural electrification in remote areas in developing countries, as they often prevent the construction of expensive grids extensions that would economically supply only some villages [1]. However, electrifying rural communities that have never experienced electricity is very challenging, given the high social, technical and political risks, as well as lack of finance, which can lead to demand grows even beyond 14-15%/y [2], no growth at all or failures of the projects [1], [3]. In order for developers to successfully address these challenge, optimization methodologies considering the long-term behavior of the system should be considered, so to minimize the financial burden of microgrid projects. However, rarely this approach is considered by developers and, moreover, current design methodologies usually approximate the multi-year behavior with a single-year hourly scenario of load and renewable production [1], [4], [5] or representative days [6]; thus causing loss of accuracy due to incomplete forecasts with negative effects on the simulation of the components behavior given the operating strategy in place. Accordingly, the assets degradation both in decreasing capacity and efficiency over time is usually neglected or extremely simplified when modeling, e.g. the expenditures in replacements or retrofits, which affects the infield profitability of the project.

Planning for future upgrades of the system, including uncertainties in the system dynamics and the degradation of components, can allow deferring investment costs and reducing risks, which mitigate both the fiscal burden and the risk profile of microgrid projects. Papers in the literature have rarely discussed the challenges of a significant load growth, which is typical of rural areas in developing countries, together with stochastic multi-year simulations at hourly time resolution, to account for the degradation of the assets [1], [7], [8], [9], [10], as discussed in this study. All above reasons lead to conclude that it is useful and timely to investigate new methodologies for a multi-year approach for the optimal sizing of microgrids.

The optimal sizing of off-grid power systems is usually carried out by means of tools or design methodologies that model the system behavior during the project lifespan and aim at minimizing a given economic indicator [1], [11], often the Net Present Cost; sometimes reliability and/or environmental impact are also accounted for [12]. Traditionally, in order to reduce the mathematical complexity of the optimization, the planning problem is approximated by using the so-called ”single-year” formulation. In this case, the behavior of the system for the entire lifetime of the project, usually lasting several years (e.g. a decade), is approximated by analyzing a single year, as shown in [4], [13]. This approach simplifies the optimization problem but cannot describe important phenomena like the progressive degradation of the performance of components or the long-term growth of energy demand, driven by changes in the social behavior of the community that can be activated by the electrification itself. While in developed countries the load growth is generally limited and reasonably predicable, in the rural communities of developing countries the demand growth can be significant and difficult to forecast [2]. This is the reason why the so-called ”multi-year” approaches, that accurately describe and simulate the entire lifespan of a project, such as the used for illustration in this paper, are of upmost importance in these contexts.

Multi-year planning of large power systems is a long-established topic in developed countries [6], [14], [15]. Most methodologies focus on power generation and network expansion issues, addressing adequacy problems and driving new investments. As the combined optimization of grid and capacity expansion is computationally demanding, authors usually approximate the multi-year behavior of the system by a number of representative days [6] or using monthly [16], [17] or yearly [18] duration curves. In this case, stochastic and robust optimization have been recently proposed to cope with the uncertainties related to the load and the renewable production [17], [19], yet including the above-mentioned approximations to restrain the computational burden of the optimization. In this study we aim at going beyond this limit, simulating the entire multi-year horizon of the project lifespan.

Multi-year optimization taking into account load uncertainties has been proposed also for microgrids to be installed in developed countries, be them interconnected to the main power network [20], [21] or isolated like in the case of many islands [7], [8], [9], [10]. The authors of [20] proposed a stochastic multi-year model to size an interconnected microgrid using a Mixed-Integer Linear Programming (MILP) model; nevertheless, no assets degradation is considered, each year is represented by a single day and the capacity upgrading is not optimized in different scenarios of load growth. While the papers mentioned above are focused on the multi-year upgrading of batteries only, reference [9] proposed the optimization and repowering of the entire off-grid system, including wind turbines and diesel generators, but still using representative days. All these studies highlighted that multi-year approaches can bring interesting benefits; this suggests their possible use also to size microgrids of developing countries.

While the papers mentioned above proposed a full stochastic implementation, also decomposition approaches have been proposed. In [21], the multi-year optimization is decomposed into a number of single-year optimizations, one for each year of the project; however, this method does not take into account uncertainties and it is still based on representative days. Authors in [7] proposed a MILP model with a similar decomposition approach, where in the first stage the system is optimized without considering any upgrade, then in a second stage the previous solution is modified according to a matrix setup; only batteries are considered. Yearly scenarios, represented by 12 days, were used to address uncertainties in load demand, wind and renewable production, although the load growth rate was considered constant (2%). Contrarily to [8], authors in [7] included a simplified model for the battery degradation; however, these results are limited because only a few typical days represent each year. These approaches confirm the computational challenges of stochastic multi-year optimization and provide interesting results despite their approximated formulation. In our study, instead, we propose to address the full stochastic multi-year problem at once, also including the simulation of the realistic system operation.

Recently, the topic of multi-year optimization has been proposed also for isolated microgrids to be installed in developing countries. The study in [22] proposed a multi-year approach for planning a microgrid composed by wind turbines, a photovoltaic plant and a storage system, without the complexity of scheduling fuel-fired generators, and yet with a simplified time horizon and no stochastic perspective. No stochastic aspects nor assets degradation have been considered in [23], [10] and [24], whose authors focused on describing how to estimate the load demand for a community. In particular, the work in [23] proposed a multi-year planning procedure based on the DER-CAM software [25], including a dynamic model of the load growth, driven by social evolution; yet, no assets degradation nor uncertainties in the load have been considered. Conversely to the above-mentioned literature, only the study in [10] attempted to partially account for the actual system operation of the system by developing a custom two-stage planning approach in which every year the optimal size of the assets is assessed independently from the others and then long-term simulations are evaluated to identify the life-cycle cost of the system. However, no load growth uncertainties have been addressed, as instead done in this paper. The only activity on stochastic optimization of off-grid systems, submitted alongside this paper, is the very recent approach in [26] that addresses the issue of multi-year stochastic optimization, including the optimal capacity expansion for a typical microgrid, however no assets degradation has been considered and no actual operating strategy has been simulated, as for the typical MILP approaches. According to the proposed literature review and to the best knowledge of the authors, no paper has so far addressed the stochastic multi-year planning of off-grid microgrids in developing countries, including the effects of asset degradation and simulating in detail the operating strategy of the system, as done in this activity.

In the few works where the ageing of components is considered, the model of the degradation is a simple linear trend proportional to the installation year, which can be acceptable for assets like photovoltaic panels, but is a rather inaccurate approximation for batteries, whose ageing strongly depends on how they are used [7]. Furthermore, most of the approaches addressing asset degradation approximate the time project lifetime by means of representative days. The exception is [10], which however does not implement any stochastic approach, does not apply standard heuristic methods, and only provides a limited comparison with standard methodologies. Other complex formulations developed to model battery degradation rely on rainflow algorithms [27]; however, their use within optimization problems would be too complex in terms of computational requirements, particularly for a multi-year analysis. Since in typical off-grid microgrids the batteries are discharged deeply every day, the maximum throughput model is conversely a good compromise between accuracy and computational complexity [10], [27]. It is worth reminding that, according to this model, the cumulative energy that can be obtained from a battery is limited, and the available capacity decreases proportionally to the already discharged energy. This is the model implemented in this paper for the batteries. Conversely, the ageing phenomena of photovoltaic panels and converters are mainly related to the thermal stress on components, hence they can be represented as a linear degradation with time [28], [29].

The usual way of approximating years with representative days allowed authors to reduce the computational burden, at the cost of reducing the accuracy of the simulations, especially for battery degradation. This is particularly significant for MILP approaches in which the computational burden significantly grows with the problem size, making it difficult to represent both the entire multi-year time-span and components’ degradation within a stochastic formulation [30]. This general acceptance is also supported by the study in [31], whose results show that some tens of representative days can well represent the uncertainties in generation expansion problems; however, the topic of capacity degradation was not addressed in the same study, as instead discussed in our paper. According to the study in [32] that compared different methodologies for optimizing the size of a rural microgrid, the formulation using heuristic algorithms obtained nearly the same solution of the MILP-based model, but with a time reduction from 59% to 98% with respect to the latter. Therefore, we regard heuristic methodologies as a viable option for stochastic multi-year optimization that requires nevertheless further investigation.

Finally, it is worth noticing that in most of the previous methods, with the only partial exception of [10], the optimal dispatching of the microgrid is performed conjointly with its optimal design, therefore assuming that the load and the renewable sources can be effectively forecasted also in the long term. However, in practice this is difficult to achieve due to the unavoidable forecasting errors and the limited hardware capabilities of the microgrid control system. In the study in [32] the authors highlighted that when a MILP model is used to optimize both the design and the operation of the system, but the real microgrid is then operated with a simple load-following approach, OPEX are underestimated and the life-cycle costs can rise even beyond 15% the expected value. This finding strengthens the consistency of simulating a realistic operating strategy for a rural microgrid system, as done in this paper.

Given the proposed literature analysis and to the authors’ best knowledge, no other paper has proposed a dynamic stochastic planning methodology for off-grid microgrids, including a detailed load growth representation, the dynamic system upgrade, and the components degradation, as done in this study. The aim of this paper is to provide a new methodology able to jointly reduce costs and risks for developing microgrid projects. Given its paramount importance for the optimal design of microgrids in developing countries, in this study we focused on the uncertainties of long-term load growth; however the approach described in this activity can be easily extended to include also the uncertainties related to renewable sources.

The main contributions of this paper are summarized as follows.

• A scenario-based stochastic approach to optimize both the initial size of components and their upgrading during the lifetime of the microgrid, including the simulations of the entire multi-year horizon of the project at hourly time resolution, to accurately model the asset degradation and replacement, also considering realistic operating algorithms.

• A detailed comparison between the results of multi-year approaches (both deterministic and stochastic) and of traditional single-year methodologies.

• Analysis of the impact of assets degradation on the design and optimality of the results.

The methodology is illustrated with a case study based on a real off-grid system placed in Kenya.

The rest of the paper is organized as follows. Section II describes the model whose mathematical formulation is detailed in Section III. Then, the case study is described in Section IV and the results are discussed in Section V. Finally, conclusions are drawn.