Closing the Loop between Short-term Operational Volatilities and long-term Investment Risks in Microgrids Center for Advanced Infrastructure and Transportation Rutgers University, New Jersey
[email protected]
Farnaz Farzan, Ph.D. DNV GL Energy Advisory Chalfont, Pennsylvania
[email protected] Farbod Farzan Department of Civil & Environmental Engineering & Center for Advanced Infrastructure and Transportation Rutgers University, New Jersey
[email protected] Kaveh Gharieh Department of Civil & Environmental Engineering & Abstract— In this article, we demonstrate that how closing the loop between operational dynamics and investment decisions for microgrids allows us to explicitly incorporate short-term operational volatility and long-term financing and market variations into investment decisions. Here, microgrid cost savings function describing the short-term benefit growth of the micro-grid under short-term (operational) uncertainties is fed into a stochastic longterm investment model. It turns out that cost saving function can be expressed as a regression function on a number of indices defined by design and operational characteristics of microgrids. Two regression models are constructed. Model (I) is a pure linear model and model II includes linear terms and an interaction term. Two sets of experiments (I and II) and results are demonstrated. Experiment (I) focuses on how volatility measures impact investment decisions. In experiment (II) the impact of operational interactions of generation assets in investment decisions is demonstrated. Index Terms—Microgrid, Operational volatility.
I.
Operation
and
Investment,
INTRODUCTION
A vision shared by many experts is that the future communities will be self-sufficient on energy production and will adopt microgrids as in [1]. With power generation capacity of 10 – 50 MW, microgrids are usually intended for local production of power with islanding capabilities and capacity to sell back to macrogrids. A typical microgrid
Mohsen A. Jafari, Ph.D. Department of Industrial & Systems Engineering & Center for Advanced Infrastructure and Transportation Rutgers University, New Jersey
[email protected] Ralph Masiello, Ph.D. DNV GL Energy Advisory Chalfont, Pennsylvania
[email protected] portfolio of resources include Photo Voltaic (PV), wind, gas fired generation, storage, combined heat and power (CHP) and connectivity to the grid. In this article we tackle the problem of closing the loop between operational dynamics and investment decisions for microgrids. In particular, we demonstrate how this approach allows us to explicitly incorporate short-term operational volatility and long-term financing and market variations into investment decisions. We will assume that decisions are made with the objective of maximizing the cash flow due to investment in the micro-grid at the end of planning horizon. This includes cash flows due to investments and operational savings prior to the end of horizon, end-of-horizon and beyond-horizon projected investment cash flows. The value of microgrid portfolio depends on return on the investment and its growth on operational savings. For financial assets portfolio, the investment payoff depends on assets’ prices which embed in them sufficient aggregate information on operation and financial health of their respective company and/or industry. Historical data on prices and insight into company and/or industry futures usually drive investment in financial assets. For the micro-grid, the investment payoff is directly linked to the operation of the physical assets, and return on investment depends on how these operations are optimized in short-term. The long-term value of the micro-grid depends on when (in terms of market conditions) investments were made and also on the amount and investment financing costs. Price of technology (e.g., price of PV, WT or storage) and parameters such as finance charge rate, finance term, and relative relationship between finance rate and discount factor could result in different optimal investment decisions.
1 978-1-4799-3653-3/14/$31.00 ©2014 IEEE
Typical investment models on infrastructure assets work on the assumption of short-term average performance of these asset(s) and that the underlying system operates optimally (computed on the basis of some average function). Operational dynamics driven by endogenous factors (i.e., asset reliability and degradation, demand prioritization, resource allocation and risk management) and exogenous factors (i.e., weather forecasts, prices of natural gas, external demand) are usually ignored or captured only on the basis of discrete choices or simple variance analysis. Therefore, for investment purposes, two microgrids with statistically similar average behavior measured on the basis of a small sample of criteria will yield the same short term cost savings Operational volatilities and risks will be totally ignored. At the same time, modularized approach to long-term investment, where assets are acquired and generation capacity is increased in stages, would impact short-term operational dynamics. Short-term returns from the microgrid will in turn influence long-term decisions on when and what to invest on. In this article, we intent to demonstrate that short-term risks and volatilities matter significantly and must be integrated with the long term volatilities that are usually attributed to market and financing factors. II.
term and long-term volatilities and risks. This design yields a series of statistical functional forms defined on simple microgrid design capacity indices. We will assume that these functional forms can be estimated by regression models defined on design capacity indices of the generation assets, namely IGF,t , IPV,t , IWT,t and IST,t . IGF,t is the ratio of design generation capacity of gas fired assets to expected daily demand of the microgrid; the other indices are calculated similarly. Two types of models are examined here, namely Model I and Model II, as shown in Table I. Model I is a pure linear model and is computed by adding constant term to the sum of the products of independent factors and coefficients. Model II includes pure linear terms and an interaction term. β’s are model parameters to be estimated from daily operational data. The estimation of β’s capture operational volatility, including variance of natural gas price and electricity spot price variation, and correlation between solar intensity, wind speed, spot prices and electricity demand. We use determinant of the correlation matrix of the above factors in our calculations. As we will see later, β’s themselves are estimated from volatility measures. TABLE I.
Constant term
INTEGRATION OF MICROGRID OPERATION AND INVESTEMNT
We will use the recent operation and investment model as in [2]. Here, microgrid cost savings function is calculated from a model, which optimizes day-ahead planning and the same day control of the microgrid under a host of stochastic variables. It turns out that cost saving function for a microgrid can be expressed as a statistical regression function on a number of simple indices defined by design and operational characteristics of microgrids. This function describes the short-term benefit growth of the micro-grid under short-term (operational) uncertainties, e.g., stochasticity of electricity demand, electricity spot price, solar intensity and wind speed. This functional form is fed into a stochastic long-term investment model, which decides when to invest on microgrid components and expansions. The investment model is formulated as a stochastic mixed integer programming (SMIP) problem, and it captures long-term market and financing volatilities, such as investment cost of PV and storage, natural gas prices, availability of investment funds, and correlation between electricity peak prices and natural gas prices.. A Monte Carlo simulation approach is taken where several sample path realizations over the course of planning horizon are generated, and a deterministic model for investment optimization for each sample path is solved. At the end, probabilistic characteristics of investment decisions along with optimal cash flow are obtained over all sample paths. Both operational and investment models were validated using numerical experiments. A. Microgrid Short-Term Cost Saving Functional Form We use the above planning/control/investment framework and run a design of experiment, which captures both short-
EXPECTED COST SAVING OF MICROGRID
Model I: coefficients Model II: coefficients
Independent variables
IPV,t β2,t
IWT,t β3,t
IST,t β4,t
IPV,t . IST,t
β0,t
IGF,t β1,t
β0,t
β1,t
β2,t
β3,t
β4,t
β5,t
n/a
β0,t can be interpreted as the cost of electricity supplied by the grid. The other terms in the table refer to micro-grid’s cost saving or revenue resulting from on-site resources. B. Investment model The analysis is on the basis of cash flow reflecting the actual outflows and inflows of monetary values. It requires proper identification of costs and benefits resulting from the investment, including any marginal values introduced by the investment to the system. Here, we include sunk cost incurred by a new investment and opportunity cost, which is the benefit forgone if the investment is undertaken. An opportunity cost is also incurred if the asset or resource can be used in some alternative way with some positive return. We do not include taxation and depreciation of assets. The present value of the future cash flow is computed using discount factor (DF), which is calculated on the basis of project financing cost. In private sector, funding resources include both borrowed funds and equity capital. While the rate charged due to the borrowed fund is determined externally, the financing cost of equity funds can be considered as the return that average investor in the firm expects to receive. Here we will compute DF as a weighted average of debt and equity financing. The present value is netted out by subtracting first cost from the present value. The investment model is a mixed integer quadratic programming with the objective of maximizing the end of 2
horizon cash flow plus the horizon time value of any cash flows beyond the horizon. Input variables are categorized in three groups: “On-site Resources”, “Financial Parameters” and “Resource Investment Constraints”. We use horizon model based as in [3]. Therefore, cash flow at the end of horizon plus the value of beyond-horizon cash flows at the end of horizon is the investment criterion to be maximized within the optimization model. We look at incremental investment decisions to form a microgrid over a specific horizon. The decisions are made on what capacity of each resource (i.e., GF, PV, WT and electricity storage), if any, should be purchased at each time period (i.e., one year). Within each period, the active micro-grid yields a payoff in the form of cost savings and possible revenue. There would be initial cash available in the first period and it is assumed that in the beginning of each period any available cash can be either used to purchase assets or to spend in other investment opportunities. We also assume that cash inflow resulting from micro-grid’s revenue will be added to the available cash in each period. III.
DESIGN OF EXPERIMENT TO ESTIMATE E(COSTMG,T)
We assume that microgrid can have up to 4 assets, each asset with its own average design capacity index. With three values of low, medium and high assigned to each index, a 34 factorial design of experiment is built. This design of experiment yields a regression model defined on Ix,t’s with estimated β’s for coefficients. Fixing the configuration indices for microgrid and by varying the volatility factors (i.e., natural gas price, spot price variation, correlation matrix determinant) a 33 factorial design is designed. From this design each β can be regressed on gas price at time t, spot price variation at time t, and determinant of the correlation matrix at time t. Table II gives low, medium and high values for natural gas, spot price variation and determinant of the correlation matrix. We note that these numbers do not necessarily reflect actual values in practice, and are solely used for experimental purposes. TABLE II.
VALUES USED FOR VOLATILITY FACTORS FOR REGRESSING COEFFICIENTS
Natural gas price ($/mmBtu) Spot price variation Determinant of correlation matrix
Low 3.34 0.01 0.0037
Medium 5.42 1.00 0.31
High 7.50 2.00 0.98
The combined factorial designs yield Model I with model coefficients estimated as shown in Table III. TABLE III. Constant term
β0,t β1,t
7493 9550
REGRESSION MODELS FOR COEFFICIENTS
Coefficient of Gas price 8134 - 2177
Coefficient of Spot price variation - 10636 - 8983
Coefficient of Correlation matrix determinant 15431 - 5094
3907 - 32291 14417
β2,t β3,t β4,t
- 9713 – 8216 – 3163
- 7768 1565 - 14262
-1970 - 5447 - 4095
Given gas prices, variations in spot prices, and correlation matrix we compute β’s, which in turn are used to calculate E(CostMG,t) for a wide range of design capacity indices. Illustrative examples are shown in the next section. IV.
ILLUSTRATIVE EXAMPLE AND DISCUSSION
Two sets of experiments (I and II) and results are demonstrated here. Experiment I focuses on how volatility measures are taken into account in investment decisions and how they impact these decisions. These experiments will use linear regression Model I of Table 1. In Experiment (II) we use Model II with the objective of determining the impact of operational interactions of generation assets in investment decisions. A. Experiment I Two scenarios are constructed with all input data the same except for volatility measures which are shown in Table IV. TABLE IV.
VOLATILITY DATA FOR TWO ILLUSTRATIVE SCENARIOS
Initial natural gas price ($/mmBtu) Natural gas price volatility Natural gas price drift Spot price variation Correlation matrix determinant
Scenario I 7.00 0.02 0.045 0.01 0.50
Scenario II 8.00 0.04 0.09 2.00 0.30
We will assume that natural gas prices follow a Geometric Brownian motion (GBM). There is no specific stochastic process for PV and electricity storage investment cost. Since there is no sufficient historical data to estimate a stochastic process for PV and electricity storage investment cost over time, we assume a decreasing trend and assign a binomial probability mass function to the rate by which the investment cost decreases in each year. Table V gives the natural gas estimates for 4 years and Table VI provides estimates for technology capital costs for microgrid assets over 4 years. TABLE V.
Scenario I Scenario II
TABLE VI.
NATURAL GAS PRICES OVER 4 YEARS PERIOD
Year 1
Year 2
Year 3
Year 4
($/mmBtu)
($/mmBtu)
($/mmBtu)
($/mmBtu)
7.17 8.44
7.21 9.04
7.07 9.97
7.21 11.65
PV AND STORAGE AVERAGE CAPITAL COSTS OVER 4 YEAR PERIOD
PV Storage
Year 1 ($) 3485714 4593333
Year 2 ($) 2788571 4057444
Year 3 ($) 2230857 3584076
Year 4 ($) 1784686 3165934
Wind turbine
1285714
1235714
1185714
1135714
3
Gas fired
240000
252000
264000
276000
Using Table III and the above volatility data we obtain β’s over 4 years as shown in Table VII and Table VIII for scenarios I and II. TABLE VII. Year 1
β0,t β1,t β2,t β3,t β4,t
Year 2
Year 3
Year 4
26805666
26921004
26507261
26927032
-3175697
-3206566
-3095831
-3208179
-24388753
-24526481
-24032420
-24533679
-23715877
-23832378
-23414463
-23838466
-3817368
-3862218
-3701330
-3864562
TABLE VIII.
β0,t β1,t β2,t β3,t β4,t
COST FUNCTION COEFFICIENTS FOR SCENARIO I
COST FUNCTION COEFFICIENTS FOR SCENARIO II
Year 1
Year 2
Year 3
21736597
23521310
26272762
31262888
-10502674
-10971390
-11893602
-12264244
-35125365
-37216608
-41331192
-42984867
-26605024
-28373958
-31854389
-33253193
-15348643
-16042649
-17112583
-19053051
Figure 1 Region one incremental capacity investment decisions
Year 4
β1,t is the effect of gas fired generation on cost savings of microgrid for period t, β2,t is the effect of PV generation on the cost savings of microgrid at period t, and so on. We normalize these effects by the capital costs of the corresponding assets to find value measures for the assets. This gives us more fair comparison of these assets as we run the investment model. Fig. 1 and Fig. 2 illustrate investment results over two dimensions: the value ratios for PV and WT decrease left to right (X-axis) and the value ratio for GF increases top to bottom (Y-axis). While there are some similar investment patterns between the two scenarios, the details are significantly different. It can be seen that in both scenarios, by moving from left to right (increasing capital cost of PV), investment on PV loses its attraction. In addition, according to low capital cost of wind turbine in comparison to other assets, it exists in most investment decisions. Also by moving downwards in both figures (decreasing gas fired capital cost) investment on gas-fired generators becomes more attractive. But, this pattern is more evident and occurs earlier for Scenario II. To further demonstrate the impact of volatility measures on investment decisions, we compare the results from the proposed methodology to a traditional approach where investments are made according to average data without taking into account any volatility measures. The results are shown in Table IX,X for two cases; the two methodologies yield different investment patterns, and the proposed integrated approach leads to higher cash flow at the end of the planning periods.
Figure 2 Region two incremental capacity investment decisions
B. Experiment II Our hypothesis is that the investment results may be misleading if interactions between assets exist in the actual microgrid but operation and investment models ignore them. For illustrative purposes, let us assume that PV and storage have interaction effects on cost saving of microgrid; this is described by Model II of Table XI. Depending on the value that it generates the interaction between PV and storage may make investment in these assets more or less attractive. The incremental investment decisions in various resources are shown in Fig. 3. Model II yields higher investment in storage by several folds. The interaction between PV and ST forces the investment to allocate more capacity to these assets in year 4 in comparison with same case w/o interaction. PV dominates the investment because of the higher contributions to the saving. By allowing interactions between the two assets, it can be the case that storage is not only used for arbitrage but also coupled with PV production. Therefore, at 4
some point in time (year 4) storage value exceeds its costs and becomes more attractive for investment. This observation tends to verify our hypothesis and it necessitates the use of appropriate model in cases that such interactions exist.
TABLE XI.
TABLE IX.
PROPOSED METHODOLOGY AND AVERAGE BASED OPERATIONAL SAVING RESULTS (SCENARIO I)
Year1 0 0 5 0
GF PV WT ST Cash flow ($)
4.00E+06
Scenario 1 Proposed methodology Investment decisions (MW) Year2 Year3 0 0 4.46 6.74 0 0 0 0 1.50E+07
2.90E+07
Year4 0 2.71 0.85 0.14
4.00E+06
1.50E+07
2.60E+07
3.20E+07
TABLE X.
PROPOSED METHODOLOGY AND AVERAGE BASED OPERATIONAL SAVING RESULTS (SCENARIO II)
GF PV WT ST Cash flow ($)
GF PV WT ST Cash flow ($)
Year1 9.25 0 2.32 0
Scenario 2 Proposed methodology Investment decisions (MW) Year2 Year3 0 0 4.46 6.74 0 0 0 0
Year4 0 0 3.39 0.67
4.00E+06 1.70E+07 3.20E+07 4.80E+07 Average based operational saving Investment decisions (MW) Year1 Year2 Year3 Year4 9.25 0 0 0 0 0 6.74 6.97 2.32 5.26 0 0 0 0 0 0 4.00E+06
1.60E+07
2.80E+07
GF PV WT ST
Year1 9.255 0 4.895 0
GF PV WT ST
Year1 9.255 0 4.895 0
Experiment I Investment decisions (MW) Year2 Year3 0 0 1.769 15.731 4.359 0 0 0 Experiment II Investment decisions (MW) Year2 Year3 0 0 1.769 15.731 4.359 0 0 0
Year4 0 9.039 0 0.076
Year4 0 9.891 0 0.262
4.60E+07
Average based operational saving Investment decisions (MW) Year1 Year2 Year3 Year4 2.58 0 0 0 0 0 6.74 6.97 3.99 5.26 0 0 0 0 0 0
GF PV WT ST Cash flow ($)
INCREMENTAL INVESTMENT DECISIONS WITH ANS WITHOUT INTERACTION TERM
V.
CONCLUSION
Experiments results clearly show how considering the microgrid’s short-term operational volatility affects the investment decisions. Comparing results of the proposed methodology to the traditional approaches which do not take into account volatility measures demonstrates that the proposed integrated approach leads to higher cash flow at the end of the planning periods. In addition, it was observed that applying proposed model which can capture the operational interactions of generation assets yield to different investment decisions. It can be concluded that short-term risks and volatilities matter significantly and must be taken into account in investment decisions along with the long term volatilities that are usually attributed to market and financing factors.
REFERENCES [1] [2] [3
Sim, F, “Using Moore’s Law to Make Energy Personal”, Intel Open Energy Initiative, Intel Corporation, 2010. Farzan, F,”Towards Uncertainty in Micro-grids: Planning, Control and Investment,” Ph.D. dissertation, Dept.Industrial & Systems Engineering, Univ. Rutgers, Piscataway, NJ 08854, 2013. Weingartner H. M.,”Mathematical programming and the analysis of capital budgeting problems”, Princeton-Hall, Englewood Cliffs, NJ, 1963.
3.40E+07
5
