2016 IEEE PES Power Africa Conference
PV-array Sizing in Hybrid Diesel/PV/Battery Microgrids under Uncertainty Nathaniel J. Williams and Paulina Jaramillo
Jay Taneja
Department of Engineering and Public Policy Carnegie Mellon University Pittsburgh, PA USA
IBM Research – Africa Nairobi, Kenya
Abstract—Levels of electricity access in sub-Saharan Africa are low with large populations living far from existing electricity infrastructure. This has led to interest in decentralized electrification solutions like microgrids, which can reach remote communities more quickly. To address a lack of capital to deploy these projects, governments have sought private investment in the sector. Studies have found that hybrid microgrids using both conventional and renewable generators provide electricity at lower cost than diesel powered systems. These studies focus on metrics such as levelized cost of electricity (LCOE) and life cycle cost (LCC) and do not account explicitly for investment risk. This paper employs a stochastic technoeconomic model to examine the impact of PV array sizing in microgrids on debt and equity investment metrics like debt service coverage ratio (DSCR) and net present value (NPV) using a risk based approach. Results indicate that high levels of PV penetration mitigate fuel price risks when low-cost capital is available.
and battery storage offers significant cost advantages. In addition, hybridization has the potential to mitigate the risks related to uncertainty about future diesel fuel prices. Most previous work to evaluate the economic viability of rural microgrids relies on a cost-minimization framework using point value inputs. It this excludes considerations of the additional risk mitigating benefit of hybridization, which could lead to different microgrid design decisions. Furthermore, the financial metrics used in other studies, such as levelized cost of energy (LCOE) [5] and life cycle cost (LCC) [6], [7], are often of limited interest to potential debt and equity investors. Equity investors are more often interested in the short- to medium-term net present value (NPV) or internal rate of return, while debt financiers want to know whether the project generates sufficient revenues to repay debt on schedule, often measured by a debt service coverage ratio (DSCR).
Keywords—Finance; Hybrid power systems; Microgrids; Photovoltaic systems; Power generation economics
This paper examines PV array and battery bank sizing decisions for hybrid microgrids while explicitly accounting for risk, particularly to enhance the perspective of investors.
I.
INTRODUCTION
The International Energy Agency (IEA) Africa Energy Outlook 2014 estimates there are 620 million Africans without access to electricity [1]. The IEA also projects that achieving universal access to modern energy sources by 2030 would require an average annual investment of $48 billion. This is a more than five-fold increase from 2009 levels. A large majority of unconnected people in Africa, 80%, lives in rural areas, often far from existing grid infrastructure. As a result, the IEA’s Energy for All scenario projects that 40% of new investment in energy access will go to micro/mini-grid electrification projects [2]. A significant portion of this capital will need to be sourced from the private sector. However, significant barriers to attracting private investment in microgrid-based electricity access exist. The perceived risk associated with deploying infrastructure to serve the rural poor ranks high on this list. It is therefore necessary to explore how these risks can be mitigated with different business models, policies, and technologies [3]. There is extensive literature on techno-economic models of hybrid microgrids [4]. Many conclude that hybridizing diesel powered microgrids with photovoltaic (PV) generators
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II.
METHOD
The analysis in this paper uses a Stochastic TechnoEconomic Microgrid Model (STEMM), currently under development at Carnegie Mellon University [8]. As with other techno-economic models, STEMM simulates microgrid performance using an hourly dispatch model. The technical model then generates outputs like fuel consumption, satisfied electricity demand, and component lifetimes. However, rather than solely relying on LCOE as its metric, STEMM assumes a project finance structure and also calculates financial metrics like equity NPV and DSCR. This provides an investor’s perspective on microgrid financial performance. Furthermore, STEMM allows users to model uncertain inputs as probability distributions and uses Monte Carlo simulation to propagate these uncertainties through the model. The resulting financial metrics are therefore represented as probability distributions, providing a more complete picture of investment risk. This section describes the methods that STEMM employs.
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A. Technical Model The technical model relies on a simplified hourly dispatch model. Several sub-models, described below, generate inputs and process outputs from the dispatch model as described in figure 1. The PV array is dispatched to supply load first. Battery charging follows a cycle charging algorithm whereby it switches between charging and discharging states when reaching minimum and maximum set point states of charge (SOC), respectively [9]. While in a charging state, excess PV power and available diesel generator capacity on dispatched generators is fed into the battery bank. While in a discharging state, batteries are dispatched after the PV array and before the diesel generators. Excess PV generation is still used to charge the battery bank even in a discharging state, so long as batteries remain below 100% SOC. Diesel generators are dispatched last. The smallest generator that can satisfy remaining load is dispatched. If remaining load is larger than the largest generator, the largest generator is dispatched and the algorithm repeats until demand is met. If all available generating capacity cannot meet the full demand, STEMM incorporates two strategies. If the microgrid is equipped to manage load on a customer level, the model assumes each customer demand is approximately equal and load is shed in increments of the total load divided by the number of customers. Where such capabilities are not available, the entire load is shed and the microgrid shuts down until available supply can meet total demand. The case studies in this paper assume that the operator exerts no control on demand and must therefore shed the entire load. The impact of demand management will be the subject of future work.
is assumed to be normally distributed based on a user defined time step variability parameter. Demand variability and uncertainties are quantified as relative standard deviations [8]. B. Financial Model The STEMM financial model simulates monthly cash flows using technical model outputs such as fuel consumption, electricity demand, and component run times; as well as cost, tax, and financing inputs. Cash flows are real valued. There is a general assumption that costs are fixed in real terms with the exception of fuel prices. STEMM models fuel prices using a Geometric Brownian Motion (GBM) model based on long term price drift and volatility inputs [17]. The model also assumes that a mix of debt and equity finances projects and that debt is repaid through equal monthly payments. Finally, corporate taxes are calculated assuming straight-line depreciation and indefinite carry over of losses. C. Outputs Primary model outputs are equity NPV, minimum DSCR, and LCOE. Equity NPV is the NPV of equity cash flows using a target real equity return as the discount rate. Positive NPVs indicate that a project reaches the target return. DSCR is the ratio of cash flow available to service debt to the debt payment due in a period, in this case one month. Minimum DSCR is the minimum DSCR across all months within the model horizon. A DSCR lower than one indicates that the project is unable to make its debt payment from cash flows generated by the project. LCOE is a commonly used indicator of the lifecycle cost per kWh of electricity generated. STEMM calculates LCOE for each model year and converts it into average LCOE by averaging LCOEs for each year weighted by annual delivered electricity. III.
Figure 1. Overview of technical model [8].
STEMM calculates the availability of PV power using a fill-factor based model relying on hourly solar irradiation and temperature data [8], [10], [11]. The model derives hourly temperature profiles based on daily maximum and minimum temperature data from the NASA SSE database [12] using an algorithm from the Meteonorm 7 theory handbook [13]. Finally, STEMM models PV cell operating temperature with a Normal Operating Cell Temperature (NOCT) model [14] used to adjust PV array output based on a linear correction factor. The battery performance model in STEMM relies on the Kinetic Battery Model (KiBAM) [15]. Battery and generator lifetimes depend on total Ah throughput [16] and operating hours [9], respectively. STEMM also accounts for technical and non-technical losses as a percentage of total demand. Expected load profiles are entered by the user with uncertainty on relative hourly demand modeled as independent normal distributions at each hour of the day. Mean total daily demand is as well modeled as a normal distribution with load profiles normalized to this value. Variation from this mean load profile
CASE STUDIES
The case studies in this paper are based on a typical rural Rwandan load center of 500 households. The load profile, shown in figure 2, comes from planning documentation from Rwanda’s electricity utility, the Rwanda Energy Group (REG) [18]. Two primary drivers of uncertainty in financial outputs are fuel price and total electricity demand. Total demand on the microgrid is modeled as uncertain using a normal distribution. The relative standard deviation of this distribution is treated parametrically to account for different levels of demand uncertainty. Volatility in the GBM fuel price model is also treated parametrically to examine the effect of different levels of fuel price volatility on financial risk. The base case volatility assumption is taken as 20% based on long term oil price data [19]. The model horizon and debt tenor used is 10 years.
Figure 2. Load profile for 500 household rural community used in the case studies [18].
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Table I summarizes uncertain model inputs and their distributions. Table II describes the cost assumptions for these case studies. The microgrid relies solely on revenues from energy consumption with a tariff of US$1/kWh, fixed in real terms over the model horizon. These case studies rely on fixed tariffs as a simplifying assumption because if tariffs could vary with, for example, fuel prices, consumer behavior may change in response. Price elasticity of demand for electricity in these settings is currently poorly understood and therefore difficult to model. To understand how PV array and battery sizing decisions affect risk and financial performance, PV array and battery bank size are treated parametrically as described in Table II. The technical configuration assumes three diesel generators of capacities 25kW, 50kW, and 100kW and power inverters of capacity 225kW. Diesel generator sizings were determined by running HOMER [20] in a diesel based scenario. The inverter capacity is oversized in the model to simplify the analysis and prevent clipping in any scenario. Solar resource data is taken from the HelioClim-3 database [21] for the coordinates 2°S, 30°E. Temperature data is drawn from the NASA SSE database for the same coordinates [12]. TABLE I. Input Solar resource rel. bias Solar resource rel. st. dev.
PROBABILISTIC MODEL INPUTS
Distribution Normal
μ: 5.9%, σ: 2.6% [8], [22]-[25]
Lognormal
μ: 20%, σ: 5.0% [8], [22]-[25]
Max. daily temp.
Normal
Min. daily temp.
Normal
Lifetime battery throughput Generator operating life Non-technical losses PV system losses PV annual degradation Fuel price Daily electricity demand (DED) Hourly load profile (HLP) Demand time step variability
Parameters
Triangular Triangular Triangular Beta Triangular GBM Model
μ: NASA SSE Data, σ: 3.1°C [12], [26] μ: NASA SSE Data, σ: 2.5°C [12], [26] min: 2.2MAh, mode: 2.7MAh, max: 3.3MAh [16] min: 20,000 hrs, mode: 25,000 hrs, max: 30,000 hrs min: 0%, mode: 2%, max: 4% [27] α: 12.8, β: 96.7 [28] min: 0.2%, mode: 0.5%, max: 0.8% [29] drift: 0%, volatility: parametric [19]
Normal
μ: EARP Data, σ: parametric [18]
Trunc. Normal Trunc. Normal
μ: EARP Profile, σ: 10% × μ scaled to DED, truncated at zero μ: HLP σ: 8% × μ truncated at zero
IV.
RESULTS
Figure 3 presents results of Monte Carlo simulations for both equity NPV and the 90% exceedance value (P90) of the minimum DSCR as a function of PV capacity installed in the microgrid. The blue and orange bands represent small (91kWh) and large (1.8MWh) storage cases, respectively. For equity NPV, dashed lines represent the median values and the lower and upper bands plot the 10th and 90th percentile values, tracing out an 80% confidence interval. The upper panel shows results when the microgrid is levered 75% with concessional debt (0% real cost of debt); the center panel represents a commercial debt case with a 10% real cost of debt
and 50% leverage; and the lower panel gives the unlevered (100% equity) case. In all cases, the real cost of equity is 15%. Concessional lending rates lower the cost of borrowing, thereby increasing the amount of debt that the project can carry while meeting DSCR targets. The columns represent cases with different levels of demand uncertainty and annual fuel price volatility. Examining the DSCR plots in Figure 3, it is clear that demand certainty is important in establishing bankability for these projects. The only bankable cases, those having at least a minimum DSCR greater than one, are those with large storage capacity, high PV penetration, and low demand uncertainty. Low PV penetration levels do not generate the fuel consumption savings necessary to mitigate downside fuel price risk in the P90 case. At high PV penetrations, the small storage scenario again limits reductions in fuel consumption and the associated risk mitigation benefit. Because these scenarios are based on an energy tariff-based revenue model, demand uncertainty equates to revenue uncertainty. High levels of PV penetration are capital-intensive and therefore more sensitive to demand uncertainty than low penetration scenarios that rely more heavily on diesel, as can be seen in the divergence of DSCR curves in the low- and high-demand uncertainty cases. In low-capital, diesel-heavy scenarios, demand uncertainty is mitigated by the fact that operating costs are highly correlated with revenues. In terms of equity NPV, low PV penetrations and small battery banks provide better median returns. However, none of the small storage/low PV cases are bankable, meaning these projects would need to be financed entirely or nearly entirely by equity. The median NPV in the unlevered case falls just short of the target return and favors small storage/low PV cases. The only scenarios that could meet lending requirements are those with low demand uncertainty, large energy storage, and relatively high PV penetration. Of these, only the concessional debt case achieves positive median equity NPVs. Focusing on this case, one observes that median equity NPV peaks around 150kWp while the P90 NPV peaks closer to 200kWp PV penetration. At 150kWp, median NPV is $173,000 and the P90 NPV is $38,000. A larger array of 200kWp produces a slightly lower median NPV of $165,000 but a higher P90 NPV of $71,000. This presents a trade off for microgrid developers. Higher median returns can be achieved with a small PV array However, for a $8,000 reduction in median NPV, the downside risk can be reduced by about $33,000 in the P90 case. All of this is to say that larger penetrations of PV generation into hybrid microgrids can serve to mitigate downside risk, driven by exposure to volatile fuel prices, by sacrificing some expected returns. V.
DISCUSSION
From a policy perspective, these results suggest that offering concessional debt facilities to microgrid developers can have a two-fold benefit of promoting the use of clean technologies like PV and helping to mitigate fuel price risks faced by microgrid equity investors. From the perspective of investors, this scenario offers reduced risk exposure at the cost of a small reduction in median returns. Because risk is a major barrier to investment in microgrid projects, this may be a trade off that investors are willing to make. 191
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TABLE II. Cost/Revenue Inputs [8] Value Operating Costs $,2700/kWp Initial fuel cost $500/kW Generator O&M $250/kWh PV/battery O&M $4,400 + $475/kW Fixed costs $40/customer $580/customer Revenue $92/customer Tariff
400 200 0 - 200 - 400
0
50
100
150
200
250
400 200 0 - 200 - 400
300
0
50
PV Capacity (kW)
100
150
200
250
0.5 0.0
50
100
150
200
200 0 - 200 0
50
250
150
200
250
300
250
300
250
300
250
300
250
300
1.5
1.0 0.5 0.0 - 0.5
300
100
PV Capacity (kW)
P90 Min. DSCR
1.0
0
400
- 400
300
1.5 P90 Min. DSCR
P90 Min. DSCR
25% Demand Uncertainty 10% Fuel Price Volatility
PV Capacity (kW)
1.5
- 0.5
$1.00/kWh
25% Demand Uncertainty 20% Fuel Price Volatility 75% Leverage with 0% Real Cost of Debt NPV (thousands $)
NPV (thousands $)
10% Demand Uncertainty 20% Fuel Price Volatility
$1.41/liter $0.15/hour $8/kWp/month $300/month
Parametric Inputs Levels 10%, 25% 10%, 20% 0%, 5%, 10% 0%, 25%, 50%, 75%, 100% 5%, 10%, 15% 1, 20, 40 0, 50, 100, 150, 200, 250, 300
Input Demand uncertainty Fuel price volatility Cost of debt Leverage Cost of equity Battery strings PV Array Size (kW)
NPV (thousands $)
Capital Costs PV system Power electronics Batteries Diesel generators Meters LV distribution Connection cost
PROBABILISTIC MODEL INPUTS
0
50
PV Capacity (kW)
100
150
200
250
1.0 0.5 0.0 - 0.5
300
0
50
PV Capacity (kW)
100
150
200
PV Capacity (kW)
200 0 - 200 - 400
0
50
100
150
200
250
400 200 0 - 200 - 400
300
NPV (thousands $)
NPV (thousands $)
NPV (thousands $)
50% Leverage with 10% Real Cost of Debt 400
0
50
PV Capacity (kW)
200
250
0.5 0.0
50
100
150
200
0
50
250
150
200
1.5
1.0 0.5 0.0 - 0.5
300
100
PV Capacity (kW)
P90 Min. DSCR
1.0
0
0 - 200 - 400
300
1.5 P90 Min. DSCR
P90 Min. DSCR
150
200
PV Capacity (kW)
1.5
- 0.5
100
400
0
50
PV Capacity (kW)
100
150
200
250
1.0 0.5 0.0 - 0.5
300
0
50
PV Capacity (kW)
100
150
200
PV Capacity (kW)
200 0 - 200 - 400
0
50
100
150
200
PV Capacity (kW)
250
300
400
NPV (thousands $)
NPV (thousands $)
NPV (thousands $)
Unlevered 400
200 0 - 200 - 400
0
50
100
150
200
PV Capacity (kW)
250
300
400 200 0 - 200 - 400
0
50
100
150
200
PV Capacity (kW)
Figure 3. 80% confidence intervals of equity NPV and P90 min. DSCR. Blue ( ) represents the small (91kWh) storage scenario and orange ( ) represents the large storage scenario (1.8MWh). In all cases, the real cost of equity is 15%.
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As with any investment decision, potential investors in microgrid utilities in developing countries will base their decisions both on expected returns and risk. The findings in this paper suggest that technical design and generator sizing decisions have a significant effect not only on expected returns but also on financial risk. Microgrid developers and system designers should therefore also carefully examine how PV array and storage sizing decisions may affect the risk exposure of the microgrid business and its ability to secure both debt and equity finance. Furthermore, it has been seen that uncertainty around electricity demand strongly affects the bankability of microgrid projects that rely on business models based on energy tariffs. It should therefore be important to lenders that microgrid businesses demonstrate a high level of revenue security. Because consumer behavior in newlyelectrified communities is poorly understood, further research should focus on better characterizing the electricity consumption patterns of these new users to reduce demand uncertainty. ACKNOWLEDGMENT The authors gratefully acknowledge the contributions the Rwanda Energy Group for providing documents and data that form the basis of several case study inputs and the Scott Institute for Energy Innovation for funding work on the ground in Rwanda.
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