Applied Energy 139 (2015) 68–80

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Applied Energy

journal homepage: www.elsevier .com/ locate/apenergy

Strategic design of cost savings guarantee in energy performancecontracting under uncertainty

http://dx.doi.org/10.1016/j.apenergy.2014.11.0270306-2619/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +1 202 285 4227.E-mail address: limao_zhang@hotmail.com (L. Zhang).

Qianli Deng a, Xianglin Jiang b, Qingbin Cui a, Limao Zhang c,⇑a Department of Civil & Environmental Engineering, University of Maryland, College Park, MD 20742-3021, USAb Institute for Financial Studies, Fudan University, Handan Road 220, Shanghai 200433, PR Chinac School of Civil Engineering & Mechanics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China

h i g h l i g h t s

� A methodology is proposed to assist Energy Service Companies to maintain competitiveness in winning bids.� Uncertainties within the energy cost savings are modeled stochastically using the Monte-Carlo simulation.� A strategic energy savings guarantee design curve is derived, where all points return as appropriate guarantees.� A campus case is presented to demonstrate the applicability for finding appropriate guaranteed savings value.

a r t i c l e i n f o

Article history:Received 21 April 2014Received in revised form 6 November 2014Accepted 13 November 2014

Keywords:Energy performance contractingCost savings guaranteeEnergy Service CompaniesUncertainty modeling

a b s t r a c t

Among the key barriers to profit in Energy Performance Contracting (EPC) are uncertainties about attain-ing the realized energy cost savings and potential disputes over the guaranteed cost savings. In this paper,a methodology has been proposed to assist the Energy Service Company (ESCO): (1) to evaluate the riskthreshold if the guarantee has already been made, and (2) to determine the guarantee design, if the guar-antee has not been made yet, that not only promises the ESCO’s profitability from EPC but also maintainsits competitiveness to win the bid. Uncertainties within the energy cost savings are modeled stochasti-cally using Monte-Carlo simulation, taking both the energy price fluctuation and the facility performancevariability into account. Based on that, a strategic energy savings guarantee design curve is derived, thatall the points on it would return as appropriate guarantees. Finally, a campus case is presented to dem-onstrate the applicability for finding the appropriate guaranteed savings value. This method is also worthpopularizing in similar performance-based projects.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Due to fast-growing energy-efficient technologies, a greatpotential of savings has been explored within the existing facilitiesthat fuel the growth of the current economy. In Europe, the energyefficiency potential is assessed to be 7.5% of the total energy use[1]. Buildings, responsible for 40% of the energy consumption and36% of the carbon emissions worldwide, are targeted as the sectorwith the largest energy efficiency margin [2]. According to the U.S.Energy Information Administration [3], nearly 75% of commercialbuildings in the United States are over 20 years old and are con-strained by aging infrastructure and inadequate operatingresources. Thus, the energy efficiency of buildings plays an impor-tant role in achieving environmental goals. However, a wide gap

exists between the technologies available and those actuallyimplemented [4]. In order to address these situations, Energy Per-formance Contracting (EPC) has been adopted as one of the mostcommon contracting models for existing buildings [5]. In the pasttwo decades, the EPC market has shown a remarkable growthtrend matched with the incremental energy demand and potentialfor energy and other efficiencies. On average, 20% of revenuegrowth has been achieved annually by the Energy Service Compa-nies (ESCOs) [6–8].

EPC is a contracting method between the owner and the ESCOthat emerged in North America after the oil crisis in the 1970s.Basically, EPC uses the operational savings of utility bills to fundrepayment of capital for building improvements and avoids the ini-tial capital expenditures [9]. Two common models for paymentused in EPC are the Guaranteed Savings Model (GSM) and theShared Savings Model (SSM) [10]. Compared with SSM, GSM spec-ifies a certain amount of energy savings guarantees in the contracts

Nomenclature

G0 initial energy cost savings guaranteef(t) adjustment factor at year tG annual energy cost savings guaranteeb the owner’s excess savings shared percentageN the maximum year of contracting periodT contracting periodS(t) energy cost savings at year tPE(t) energy price at year tPE0 initial energy price before project startsaEt energy price drift coefficient at year trEt energy price volatility coefficient at year teP a random variable for energy price uncertainty

eP � N(0, 1)Q(t) realized amount of energy savings at year t

QðtÞ engineer’s estimation of amount of energy savings atyear t

aQt drift coefficients of amount of energy savingsrQt volatility coefficients of amount of energy savingseQ a random variable for amount of energy savings uncer-

tainty eQ � N(0, 1)D(t) differences between the realized energy cost savings

and the guaranteed cost savingsDO(t) profit difference held by the ownerDE(t) profit difference held by the ESCODE_total total discounted profit difference from the ESCO’s

perspectiver expected rate of returnd convergence criteria

Q. Deng et al. / Applied Energy 139 (2015) 68–80 69

in order to meet the payback obligation [11]. According to Gold-man et al., [7], the ESCOs market shifted away from SSM to GSMover the last decade, and 86% of EPCs currently use GSM. The mainreasons for this shift are the greater certainty of savings, the lowerfinancing costs, and the lower transaction costs for GSM contractsfrom the owners’ perspective [11]. Therefore, the underperfor-mance risk is reallocated in the form of a guarantee, which isoffered by the ESCO to the owner regarding the periodical energysavings. In other words, risks of failing to meet the annual guaran-teed energy saving are covered by the ESCOs [12].

Since the ESCO is encouraged to develop more desirable energyefficient solutions, the well-designed savings guarantees go a stepfurther to unite the ESCO and the owner for a shared goal [13]. Inpractice, the forms of the energy savings guarantee might be tai-lored to fit the particular requirements of legislation, regulationsand owner due to the uniqueness of each project [5]. But, in gen-eral, the ESCO reimburses the owner if there is a shortfall in therealized energy savings compared with the guarantee, and sharesthe excess profit at a predefined percentage if over-performed.Thus, the guarantee is the key of a contract funding a capital worksupgrade out of existing cash flow. However, tradeoffs exist in theenergy savings guarantee design due to the risk reallocation. Onthe one hand, conservative guarantees are preferred since mostof the ESCOs are risk averse. Either the unforeseeable energy pricesdrop or the defective energy conservation performances may resultin an undesirable energy savings realization. On the other hand,the ESCO needs high-energy savings guarantees to get favorablefinancing rates, which ensure the benefits that persist over the pro-ject’s economic lifetime and are sufficient for paying the invest-ment [14]. Also, the owner prefers to secure the energy savingsbefore contracting starts in order to avoid the risks induced byuncertainties. Therefore, to balance the potential losses, financingbenefits and bidding competitiveness, the energy savings guaran-tee would go neither too high nor too low, based on the estimation.

Current energy cost savings guarantees are mostly determinedbased on empirical estimations, due to the long-term contractingand the environment complexity. According to Goldman et al.[15], no discernible pattern or formula (e.g., guaranteed savingsare set at 80% of the predicted savings) has been found for theguaranteed savings decision. Among the key barriers to profit inEPC are the uncertainties about attaining the realized energy costsavings and the potential disputes over the guaranteed cost sav-ings. Deviations between the guarantee and the realized energycost savings frequently occur during the implementation of EPC[13]. Shonder and Hughes [16] analyzed the measurement and ver-ification reports from all ongoing projects of the Oak Ridge

National Laboratory database. Statistical results show that the real-ized cost savings was 110% of the total guaranteed cost savings.Cost savings shortfalls were only realized in 7 of 88 projects, andthe average amount of the additional cost saving was 12% of theguaranteed cost savings. Hopper et al. [11] found that 72% experi-enced greater savings than were guaranteed by the ESCO based onthe NAESCO/LBNL database. Nineteen percent encountered savingsshortfalls, of which 63% realized shortfalls greater than 10%. In themeantime, Goldman et al. [15] also examined the differencebetween the predicted and realized energy savings. The resultsshowed that the realized savings exceeded the predicted savingsin 63% of the cases. Hopper et al. [11] also found that 54% of pro-jects had realized energy savings that exceeded predictions, and34% experienced shortfalls relative to the predicted savings.According to Ghosh, et al. [17], the ambiguity regarding realizationof estimated savings was ranked as one of the highest market bar-riers for the adoption of EPC in the private building sector.

Owing to the absence of standard procedures for the energycost savings guarantee designs, a methodology has been proposedin this paper for the ESCO to determine how much the annual costsavings should be guaranteed, and what percentage of the excessprofit should be shared, before contracting starts. If the guaranteehas already been made, the proposed method could help to evalu-ate the profit risk threshold. The remaining paper is structured asfollows: in Section 2, previous studies on the risk valuation andallocation techniques in other performance-based contracting sys-tems are reviewed. Comparably, special characteristics of EPC arealso pointed out. Then, Section 3 presents the method and the gen-eral process for determining the appropriate guarantee design. InSection 4, the proposed method is applied to a campus case. Theexisting guarantee design of the contract is evaluated, and otherpotential guarantee designs are also explored. Conclusions are pre-sented in Section 5.

2. Valuation and allocation of contracting risks

Many industrial sectors involve performance-based contractingin fields, such as commercial shipping, public transport, health ser-vices and energy generation, besides EPC [18]. The performance-based contracting method buys performance through an integratedacquisition and logistics process, delivering improved capability toa range of products and services. Generally, long contracting peri-ods and a large number of uncertainties are the major concerns ofretrofit risks in these projects [19–22]. To deal with the varieduncertainties underlying the preset contracting period, contractualguarantees are commonly adopted in the performance-based pro-

70 Q. Deng et al. / Applied Energy 139 (2015) 68–80

jects. Cheah and Liu [23] analyzed the minimum revenue guaran-tee in the case of the Malaysia–Singapore Second Link, a bridgeshortcut connecting Singapore and Johor, Malaysia. The value ofguaranteeing minimum revenue was proved to be related to thebasic project’s Net Present Value (NPV). Huang and Chou [24] alsonoted that the contractual rights and obligations lead to specula-tive opportunities and created values. The guarantee clauses andsubsidies specified in these contracts provided a direct way toavoid potential risks. According to Brandao and Saraiva [25], theminimum traffic guarantee on the 1000 mile long BR-163 toll roadlinking the Brazilian Midwest to the Amazon River was used toevaluate government outlays in public–private partnerships. Also,the long-term pavement guarantee clause of a highway projectwas valuable for the risk allocation within the contracting period[26].

In order to quantify the uncertainties and make appropriateguarantee decisions, valuation techniques for risk assets providepowerful tools for stochastic modeling and risk estimation[27,28], especially in economic analysis [29]. Modern risk valuationtechniques mainly include the NPV-at-risk method, the real optionmethod, and the simulation method. These techniques mostlyfocus on the future execution flexibility, where the changing mar-ket situations are regarded as evolving stochastically over time[30]. Compared with the traditional NPV method, the NPV-at-riskmethod is formed by the combination of the weighted average costof capital and dual risk-return methods, and requires the probabil-ity distributions of variables, which are hard to evaluate in reality.Therefore, the NPV-at-risk method is useful in assisting relativelysimple decision-making in the valuation of investment strategiesfor privately financed infrastructure projects [31].

In finance, an option is a derivative financial instrument thatestablishes a contract between two parties concerning buying orselling of an asset at a reference price [32]. To the project perfor-mance valuation, the real options theory is regarded as a modernapproach that focuses on the managerial flexibility valuation forresponding to a changing scenario characterized by uncertainty[33]. Generally, a real option could be defined as the opportunityto take a beneficial action within a bounded time frame when afavorable condition occurs [34]. For instance, Ford et al. [35] pre-sented a real options approach for proactively using strategic flex-ibility to recognize and capture project values hidden in dynamicuncertainties. Garvin and Cheah [36] also selected a toll road pro-ject to demonstrate that an option-pricing model can be used toidentify strategic considerations. In this way, the real option theoryuses stochastic dynamic programming to obtain optimal decisionsin the face of uncertainties. As an increasingly employed tool in theperformance-based projects, the real option is illustrated as apromising approach for determining the fair value of the varietyof executions.

The simulation technique also provides a powerful tool for sto-chastic modeling and risk valuation in uncertain environments[37,38]. In the past ten years, the simulation techniques haveextended from computer science to decision-making and optimi-zation in engineering fields [39–41]. Ben and Aloui [42] used aMonte Carlo simulation approach to mitigate the risk of nuclearpower plant construction costs through government support inthe project financing. Shen and Wu [43] also proposed a numericalsimulation approach for the contracting period determination of aBuild-Operate-Transfer (BOT) project, with the stimulated valuesof risk factors, such as capital investment, toll price, and expectedrate of return. Applications can be replicated and tailored based onspecific cases. In infrastructure development, governments world-wide often preset the contracting period to a fixed time length andthen invite the private sector to bid on other aspects of the project.Simulation-based methods are adopted to determine the optimum

contracting period with the uncertain parameters, such as the cost,the operation revenue, and the income taken into account [44–46].

Besides risk valuation, risk allocation is another critical issue tobe addressed when dealing with the tradeoffs of contracting con-flict and cooperation between rational decision-makers. As a usefultool for solving the risk allocation dilemma, game theory is a pro-cess of modeling the strategic interactions between two or moreplayers in a situation containing rules and outcomes. A game set-ting is usually developed under conditions of uncertainty and riskfor a general class of problems [47]. According to Medda [48], theprocess of risk allocation between public and private sectors intransport infrastructure agreements is a bargaining process. Whenguarantees have a higher value than financial loss, strategic behav-ior and potential moral hazard problems are likely to occur. Similarresearch has also been done by Ke et al. [49]. Other applications ofrisk allocation involve a broad variety of industrial sectors, such asmanufacturer–retailer supply chain [50,51], water resource sys-tems [52], finance [53], and social behavior [54].

As identified in the previous section, a standard procedure forthe energy cost savings guarantee designing is absent. ThoughEPC shares the basic features of general performance-based con-tracting, such as long contracting period and performance uncer-tainties, the cost savings guarantee of EPC has its specialty on therisk valuation and allocation structure. For instance, one of the spe-cialties in EPC is the future cost savings estimation, which involvesthe uncertainties both from the energy price and the amount ofenergy savings. Also, the profit-sharing beliefs between the ownerand the ESCO are different from general performance-based con-tracting, especially when there is exceedance beyond the guaran-tee. Referred to the current applications of risk valuation andallocation techniques as well as the specific context of EPC, furtheranalysis stays open to be conducted in order to complete the guar-antee design.

3. Methodological approach

3.1. Realized cost savings estimation

This section establishes a model to estimate the realized energycost savings performance under uncertainties. In general, the uncer-tainties of energy savings stem from multiple factors. Some factorscould be assessed and corrected to acceptable levels through themeasurement and verification process, such as the outdoor temper-ature, the occupancy, and the production levels. But, some factors,such as the energy price and the energy conservation performance,are still open to address [55]. Thus, the energy price and the amountof energy savings are selected as two major factors to establish themodel for the energy savings performance estimation.

In probability theory, a stochastic process is often used to rep-resent the evolution of random value or system over time[56,57]. Though the initial condition is known, both the energyprice and the amount of energy savings might evolve over the con-tracting period randomly. As a result, two stochastic processes areadopted to model the energy price and the amount of savings, tak-ing both the general trend and the potential fluctuation intoaccount. According to the ESCOs’ measurement and verificationpractice, the energy savings within the contracting period areeither realized on a yearly basis or calculated as an annual average[15]. Here, we use N to denote the total length of the ESCO’s con-tracting period with T denoting a time index set whereT = {0, 1, 2, . . ., N}. Then, the evolution of the annual energy costsavings could be deemed as a discrete-time stochastic process{S(t):t 2 T}. For a specific year t, t 2 T, the energy cost savings S(t)equals the energy market price, PE(t), multiplied by the amountof energy saved, Q(t) as shown in Eq. (1). As a result, the process

Q. Deng et al. / Applied Energy 139 (2015) 68–80 71

of {S(t):t 2 T} could be derived from the evolution process of theenergy price, {PE(t):t 2 T}, and the amount of energy savings,{Q(t):t 2 T}.

SðtÞ ¼ PEðtÞQðtÞ; 8t 2 T; ð1Þ

3.1.1. Energy priceThe commodity prices have long been modeled by the diffusion

processes in the futures and options markets, which share the sim-ilar statistical nature of randomness as the particle motions [58,59].As one of the stochastic diffusion processes, Geometric BrownianMotion (GBM) is commonly used on the commodity derivativespricing [60]. For instance, in industrial practice, Cortazar and Sch-wartz [61] proposed an early oil pricing model that was based onGBM as a component of an exercise to price a natural resourceinvestment. Sezgen et al. [62] also used the modified GBM todescribe the electricity pricing process. Considering the stochasticnature of energy prices with the general trend and the temporalfluctuation, the study has also adopted GBM to describe the energyprice evolution process within the contracting period.

Eq. (2) represents the energy market price {PE(t):t 2 T} that var-ies evolutionarily as the risk-neutral process, and Eq. (3) is derivedfrom Eq. (2). dPE(t) is the incremental change in the energy pricewithin a short period of dt. dWP(t) denotes the Wiener process,dWPðtÞ ¼ eP

ffiffiffiffiffidtp

, where eP � N(0, 1). For a specific year t, aE(t) isthe drift coefficient and rE(t) is the volatility coefficient for energyprice. Both {aE(t):t 2 T} and {rE(t):t 2 T} might also evolve throughtime.

dPEðtÞ ¼ aEðtÞPEðtÞdt þ rEðtÞPEðtÞdWPðtÞ; ð2Þ

d ln PEðtÞ ¼ aEðtÞ �r2

EðtÞ2

� �dt þ rEðtÞdWPðtÞ; ð3Þ

PEðtÞ ¼ PE0 exp aEðtÞ �r2

EðtÞ2

� �t þ rEðtÞeP

ffiffitp� �

; 8t 2 T ð4Þ

Due to the characteristics of GBM, Eq. (4) has been derived fromEqs. (2) and (3), which are used to simulate the sample path of theenergy price {PE(t):t 2 T}. Inputs in Eq. (4) are set as the initialenergy price level at t = 0, PE0, the annual price drift effect{aE(t):t 2 T}, and the annual price volatility effect {rE(t):t 2 T}. PE0

stands for the current energy market price. Both aE(t) and rE(t)could be derived statistically based upon the historical record ofpast energy prices. However, according to the different dataresources and estimation precision requirements, the statisticalmodels could vary.

3.1.2. Amount of energy savingsBefore signing the contract, the engineers evaluate the energy

efficiency conditions for the selected buildings and decide whatconservation measures could be conducted accordingly. Then, theowner and the ESCO reach an agreement of a measurement andverification plan that specifies how the amount of energy savingsis determined. The agreement defines a relatively accurate estima-tion scope. As a result, though the divergent energy efficiency solu-tions are offered for different projects, the annual amount ofenergy savings could always be reasonably forecasted based onthe system engineers’ calculation and experience. Accuracy of theestimated energy savings is dependent upon historical data, vari-ances of natural conditions, and empirical estimation. Differencesfrequently occur between the estimated and the realized savingsamount according to the facilities’ nature.

Two assumptions have been made in the amount of energy sav-ings modeling: (1) the estimate of the annual energy savings isbased on the system engineers’ best knowledge, including the

predictable trend for the energy conservation performance, and(2) the volatility effect for the amount of savings {rQ(t):t 2 T} isannually independent. In order to reflect the general energy sav-ings performance trend and the uncertain random fluctuations,the risk-neutral process of GBM is also adopted to describe theamount of energy savings {Q(t):t 2 T} as shown in Eq. (5). Eqs. (6)and (7) are directly derived from Eq. (5).

dQðtÞ ¼ aQ ðtÞQðtÞdt þ rQ ðtÞQðtÞdWQ ðtÞ; ð5Þ

QðtÞ ¼ Q 0 exp aQ ðtÞ �r2

Q ðtÞ2

!t þ rQ ðtÞeQ

ffiffitp

" #; ð6Þ

QðtÞ ¼ EðQðtÞÞ ¼ Q 0 exp½aQ ðtÞt�; ð7Þ

QðtÞ ¼ QðtÞ exp �r2

Q ðtÞ2

t þ rQ ðtÞeQ

ffiffitp

" #; 8t 2 T ð8Þ

where dQ(t) is an incremental change in the total energy savingsquantity during a short period dt. dWQ(t) denotes the Wiener pro-cess that dWQ ðtÞ ¼ eQ

ffiffiffiffiffidtp

, where eQ � N(0, 1). For the amountof energy savings, {aQ(t):t 2 T} are the drift coefficients and{rQ(t):t 2 T} are the volatility coefficient. Derived from Eqs. (5)–(7),(8) is used to simulate the sample path of the amount of energysavings {Q(t):t 2 T}. The inputs in Eq. (8) are set as the engineers’empirical estimation of the amount of energy savings fQðtÞ : t 2 Tgand the annual savings amount volatility {rQ(t):t 2 T}. The drifttrend has been involved in the engineers’ estimation fQðtÞ : t 2 Tg:

3.2. Profit sharing structure

This section addresses the different profit-sharing structureswhen the realized savings have over-performed or under-per-formed based on the guaranteed savings. A new variable, profit dif-ference, is defined to track the profitability for both the owner andthe ESCO from EPC. Then, a profit-sharing model is established fol-lowing the same logic as the cost savings guarantee specified.

3.2.1. Definition of profit differenceOne assumption here is that there are no additional investment

activities during the contracting period, and only a one-timeexpenditure is made at the beginning of the contracting period.As a result, the project cost stays fixed, no matter how much therealized energy savings goes below or beyond the guarantee. Then,the realized project profit equals the realized cost savings minusthe one-time project cost as Eq. (9) shows.

Realized profit ¼ Realized cost savings� Project cost ð9Þ

Different from the actual energy savings realization, the originalexpected project profit equals the guaranteed cost savings minusthe one-time project cost as Eq. (10) shows.

Expected profit ¼ Guaranteed cost savings� Project cost ð10Þ

Since the project cost is the same as Eqs. (9) and (10) indicate,the difference between the realized profit and the expected profitequals the difference between the realized cost savings and theguaranteed cost savings, which is defined as the new variable,profit difference, shown in Eq. (11). Uncertainties within the real-ized cost savings are thus directly tied to the achievement of theowner and the ESCO’s expected profit.

Profit difference ¼ Realized profit � Expected profit

¼ Realized cost sav ings

� Guaranteed cost sav ings ð11Þ

72 Q. Deng et al. / Applied Energy 139 (2015) 68–80

If the realized energy savings over-perform beyond the guaran-tee, Realized cost savings > Guaranteed cost savings, then the Profitdifference would be positive, and the owner and the ESCO sharethe exceeding part with a certain percentage. To be more specific,the owner’s profit difference is shown in Eq. (12) and the ESCO’sprofit difference is shown in Eq. (13).

Owner’s profit difference ¼ Profit difference

� Owner’s sharing proportion

¼ ðRealized cost sav ings

� Guaranteed cost sav ingsÞ� Owner’s sharing proportion ð12Þ

ESCO’s profit difference ¼ Profit difference

� ESCO’s sharing proportion

¼ ðRealized cost savings

� Guaranteed cost sav ingsÞ� ESCO’s sharing proportion ð13Þ

If the realized energy savings does not reach the guarantee, Real-ized cost savings < Guaranteed cost savings, then the Profit differenceis negative, and the ESCO reimburses the owner for the deficientpart. To be more specific, the owner’s profit difference is shown inEq. (14) and the ESCO’s profit difference is shown in Eq. (15).

Owner’s profit difference ¼ 0 ð14Þ

ESCO’s profit difference ¼ Profit difference

¼ Realized cost sav ings

� Guaranteed cost sav ings ð15Þ

For a better understanding, Fig. 1 shows the inner relationsamong savings and profits from a graphical perspective. The profitdifference could be either positive or negative. When the realizedenergy cost savings is over-performed beyond the guarantee, boththe owner and the ESCO’s profit difference would be positive,which means they get more profit beyond the expected profit.When the realized energy cost savings do not reach the guarantee,the owner’s profit difference would be zero and the ESCO’s profitdifference would be negative. In this situation, the owner getsthe exact expected profit while the ESCO does not get less thanthe expected profit.

3.2.2. Profit sharing modelThe energy cost savings guarantee is mainly composed of two

parts: (1) the guaranteed annual energy cost savings, and (2) theshared percentage if returns are greater than the guarantee. For

Savings g

Project

Owners expe

ESCOs expe

Under-performed

ESCOs realized profit

profESCOs profit difference

( - )

Fig. 1. Profit differences between the realized energy co

part (1), in order to match the predictable energy cost savings vari-ations affected by an external environment, such as economicinflation, the baseline of energy savings guarantee needs to beadjusted [55]. As shown below, Eq. (16) represents the guaranteedannual energy cost savings {G(t):t 2 T}.

GðtÞ ¼ G0ð1þ f ðtÞÞt 8t 2 T ð16Þ

where G0 stands for the energy cost savings guarantee at t = 0; f(t)stands for the adjustment factor for year t. For part (2), the owner’sshared percentage is denoted by b and the ESCO’s shared percent-age is denoted by 1 � b.

Here, S(t) denotes the realized energy cost savings at year t, andD(t) denotes the profit difference at year t. Eqs. (17) and (18) areused to show the algorithms behind the energy savings guaranteefor both the owner’s profit differences {DO(t):t 2 T} and the ESCO’sprofit differences {DE(t):t 2 T}, which are a more condensed way ofexpressing the same logic of Eqs. (12)–(15).DOðtÞ ¼ maxð0; bðSðtÞ � GðtÞÞÞ; 8t 2 T ð17Þ

DEðtÞ ¼ SðtÞ � GðtÞ �maxð0;bðSðtÞ � GðtÞÞÞ; 8t 2 T ð18Þ

Profit risks are thus reallocated between the owner and theESCO due to the guarantee design. For a visual demonstration,Fig. 2 illustrates the relationships between the guarantee and theprofit differences for both the owner and the ESCO.

3.3. Guarantee design selection

This section discusses the guarantee design selection criteria forbalancing the potential losses, financing benefits and bidding com-petitiveness. Though the proposed guarantee design method is pri-marily from the ESCO’s standpoint, the owner could also take it as areference for bidding selection or financial reliability checking.

The cost savings guarantee G(t) has already been decided beforecontracting starts, while the realized energy savings S(t) evolveswith drift and volatility. A general indicator is needed to showthe total profit difference during the contracting period. As a result,the ESCO’s profit differences through the contracting period{DE(t):t 2 T} are discounted to the present value using the expectedrate of return r. DE_total(G(t), b) denotes the total profit difference ofthe savings guarantee as Eq. (19) indicates from the ESCO’s stand-point. Here, N denotes the total length of the ESCO’s contractingperiod and T denotes a time index set that T = {0, 1, 2, . . ., N}.

DE totalðGðtÞ;bÞ¼XN

t¼1

DEðtÞð1þ rÞt

¼XN

t¼1

SðtÞ�GðtÞ�maxð0;bðSðtÞ�GðtÞÞÞð1þ rÞt

8t2 T ð19Þ

uarantee

cost

cted profit

cted profit

Over-performed

ESCOs realized profit

ESCOs it difference

( + )

Owner profit difference

( + )

st savings and the guaranteed energy cost savings.

0

Guaranteed energy savings

G(t)

Below the guaranteeS(t) < G(t)

Above the guaranteeS(t) > G(t)

Realized energy savings S(t)

DE($)0

Below the guaranteeS(t) < G(t)

Above the guaranteeS(t) > G(t)

Guaranteed energy savings

G(t)DO($)

Realized energy savings S(t)

For Owner For ESCO

(a) (b)Fig. 2. Structure of profit differences in EPC: (a) for the owner, and (b) for the ESCO.

Q. Deng et al. / Applied Energy 139 (2015) 68–80 73

In general, finding appropriate G0 and b to let DE_total(G(t), b) ? 0would be the equilibrium situation. DE_total(G(t), b) < 0 is not ideal,because the ESCO could not get the expected profit through EPC.The ESCO needs to suffer a reduction or even a loss in return whenthe savings guarantee has been offered in the contract. However,DE_total(G(t), b) > 0 is not ideal either. The owner prefers to selectthe ESCO’s contract offering the highest savings guarantee. Positiveprofit difference indicates that there is still escalation spaceremaining for raising higher guarantee and the contract is not com-petitive enough. Therefore, DE_total(G(t), b) = 0 could be deemed asan optimum balance. The ESCO could receive the expected projectprofit, at the same time without sacrificing any contractual com-petitiveness when offering the savings guarantee. The mathemati-cal expression for DE_total(G(t), b) ? 0 would use the enumeration

STEP I Collect related project informat

STEP II Build stochastic models for est

STEP III Allocate profit sharing risks

STEP IV Determine the guarantee desig

Inputs:

- Historical energy price

- Engineers subjective estimation of the ener

- Forecast the future energy price

- Estimate the future amount of energy savin

- Estimate the annual energy cost savings

- Calculate profit difference

- Discount annual profit differences

Outputs:

- Guaranteed annual cost savings G0

- Shared percentage of excess profit and

{ ( ) :EP t t ∈

{S

β

_ (E totalD

( ) ( )ED t S t G= −

0{ , ( ), ( ) :E E EP t t tα σ

Fig. 3. Guarantee design framework fo

method to find the matched pair of G0 and b, that letjDE totalðGðtÞ; bÞj 6 d, where d is a small positive number as the con-vergence criteria, d > 0. The adjustment factor f(t), the expectedrate of return r, and the realized cost savings S(t) are known asinputs.

3.4. Process of guarantee design

Based on the above analysis, framework for the energy savingsguarantee that the design in EPC is structured in Fig. 3 with fourmajor steps.

Step I: Collect project background information

ion

imating realized energy savings

n

gy savings amount

gs

{ }ˆ ( ), ( ) :QQ t t t Tσ ∈

}T

{ }( ) :Q t t T∈

}( ) ( ) ( ) :Et P t Q t t T= ∈

1 β−

1

( )( ), )(1 )

NE

tt

D tG tr

β=

=+∑

( ) max(0, ( ( ) ( )))t S t G tβ− −

}T∈

r energy performance contracting.

Table 1Summary of the EPC university case.

Parameters Symbol Values

Contracting period T 13 yearsAnnual cost savings guarantee adjustment f(t) 0Initial energy price PE0 $26.03/MMBTUEnergy price drift coefficient aE 0.052Energy price volatility coefficient rE 0.085Engineers’ estimation of annual savings amount QðtÞ [73,78,82,83.5,83,82.5,82,81,80,78,74,70,65] Billion Btu

Engineers’ estimation of savings amount deviation rQ 1%, 10%, 25%Expected rate of return r 10%Convergence criteria d 0.01

Note: MMBTU is a unit of energy standing for one million Btu.

Fig. 4. Sample paths of the energy cost savings evolution process: (a) energy cost savings, (b) energy price, and (c) amount of energy savings.

74 Q. Deng et al. / Applied Energy 139 (2015) 68–80

Historical energy price records could be found through officialgovernment or research agencies’ databases. For the energy pricemodeling {PE(t):t 2 T}, the price drift {aE(t):t 2 T} and volatility{rE(t):t 2 T} could then be derived based on the designed modelas the inputs. For the amount of energy savings modeling, the engi-neers’ estimation fQðtÞ : t 2 Tg is based on the energy conservationmeasurements plan. The volatility effect {rQ(t):t 2 T} has also beenset as input, due to the variance between the estimated and therealized amount of energy savings.

Step II: Build the stochastic models for estimating realizedenergy savings

When the inputs are set, the future energy price {PE(t):t 2 T} andthe future amount of energy savings {Q(t):t 2 T} would be simu-lated respectively with randomness added in. Then, sample pathsof the annual energy cost savings {S(t):t 2 T} would be derivedaccordingly.

Step III: Allocate profit sharing risks

The ESCO’s profit difference {DE(t):t 2 T} is reached based on therealized cost savings S(t), the guarantee G(t) and the owner’sshared percentage b if there is excess. Then, the annual profit dif-ference {DE(t):t 2 T} is discounted to the present value using the

Fig. 5. Histograms of the profit differences of the 13th year for both the owner and the ESCO with the $1.9 million savings guarantee: (a) rQ = 1%; (b) rQ = 10%; and(c) rQ = 25%.

Q. Deng et al. / Applied Energy 139 (2015) 68–80 75

76 Q. Deng et al. / Applied Energy 139 (2015) 68–80

expected rate of return r, and the ESCO’s total profit differenceDE_total(G(t), b) is reached.

Step IV: Determine the appropriate guarantee design

The ideal guarantee parameters combination of G0 and b thatmake DE_total(G(t), b) ? 0 are found through the enumerationmethod. Final guarantee designs include the guaranteed annualcost savings G0 and the owner’s shared percentage b, ifoverachieved.

Fig. 6. Relations between guarantee and profit difference given owner’s 100% shareof excess profit.

4. Case study and results

According to Satchwell et al. [8], the ‘‘MUSH’’ markets–munici-pal and state governments, universities and colleges, K-12 schools,and hospitals – have historically hosted the largest share of EPCs.For instance, the MUSH market’s share of total ESCO revenues in2008 accounted for about 69% of the ESCO’s industry revenues.University systems are thus one of the major entities using EPCto obtain needed facility improvements. Since 1993, the State ofMaryland has qualified a group of ESCOs to make performance con-tracts available to state agencies, including universities. The Uni-versity of Maryland campus case is chosen to show theapplicability of the proposed method for finding the appropriateguaranteed savings value. Since this is a real case with a startedcontracting period, there is an existing guarantee design that isused in practice. Based on the case information, we did threethings: (1) used the proposed approach to test the profit differencethreshold of existing guarantee design; (2) used the proposedapproach to derive other guarantee design possibilities, assumingthe contracting period had not started yet; and (3) compared theguarantee designs with comments and suggestions.

Fig. 7. Relations between owner’s share and profit difference given the $1.90 mil-lion guarantee.

Table 2CPU time for different simulation realizations.

rQ = 1% rQ = 10% rQ = 25%

Realizations CPU (s) Realizations CPU (s) Realizations CPU (s)

1 2.8406 1 2.8202 1 2.843810 5.2146 10 5.3874 10 5.3628

100 27.265 100 27.201 100 27.3361000 240.306 1000 239.727 1000 240.284

4.1. Project profile

In order to develop a resource-efficient and carbon–neutralcampus environment, the University of Maryland College Park,entered into a 13-year EPC with the ESCO, Johnson Controls, Inc.,in 2009. Multiple energy conservation measures have been con-ducted, such as lighting upgrades, water conservation measures,building envelope improvements, chiller plant upgrades, buildingautomation control enhancements, HVAC system improvements,steam trap replacement, and window replacement. Detailed caseinformation is displayed in Table 1. The existing guarantee hasbeen decided as the guaranteed annual energy cost savings $1.90million (G0 = $1.90 million) and the owner’s revenue sharing ifexcess 100% (b = 100%).

Besides the guarantee design G0 and b, T and f(t) are also deter-mined before the contracting period starts. Here, the adjustmentf(t) in this case has been set as negligible. Thus, the annual guaran-teed savings stay constant in that G = G0 = G1=, . . ., =G13. ParametersPE0, aE, rE are derived based on the historical energy price recordfrom 1970 to 2009 of the U.S. Energy Information Administrationdatabases [3]. Since the measurement and verification is annual-based, seasonal effect on the energy price could be offset. Anassumption is also made that the price drift aE and the volatilityrE stay constant throughout. Variables associated with the amountof energy savings include the engineers’ estimation QðtÞ and thedeviation rQ. The trend of QðtÞ shows an increase at the beginningdue to the gradually complete installation and a following decreasedue to equipment deterioration. Mature energy efficiency tech-niques demonstrate a lower deviation rQ compared with the inno-vative techniques. To this specific case, three scenarios rQ = 1%, 10%,25%, have been chosen based on the engineers’ estimate for analy-sis. r is the expected rate of return from the ESCO’s perspective.

4.2. Uncertainties of realized cost savings

Monte-Carlo simulation has been performed to yield thenumerical solution of the discrete-time model, using a personallaptop with the processor of Intel(R) Core(TM) i7-3630QM CPU@2.40 GHz, 8.00 GB RAM, and 64-bit Operating System. Samplepaths of the energy cost savings evolution process have been visu-alized in Fig. 4(a), a yearly-based combination of the energy priceevolution in Fig. 4(b), and the amount of energy savings evolutionin Fig. 4(c). Fluctuations are shown on these sample paths due tothe uncertainties.

In order to show the possible variances of profit difference, sim-ulations have been conducted one million times. Both the owner’sand the ESCO’s profit differences DO(G, b) and DE(G, b) vary due tothe energy savings fluctuation. Taking the 13th year as an example,

Fig. 8. Comparing the convergence of different guarantee design: (a) when rQ = 1%; (b) when rQ = 10%; and (c) when rQ = 25%.

1.9 2.4 3.0

Fig. 9. Relations between guarantee and owner’s share of excess profit given zeroprofit difference.

Q. Deng et al. / Applied Energy 139 (2015) 68–80 77

Fig. 5 demonstrates the frequency distributions of the profit differ-ences for both the owner and the ESCO with the savings guaranteeG = $1.90 million. Since the owner holds all the excess profit, ifthere, b = 100%, and the ESCO’s profit differences stay at zero inmost cases. The higher uncertainties underlying the energy conser-vation performance might result in higher potential loss probabil-ities from the ESCO’s perspective.

4.3. Cost savings guarantee design

4.3.1. Profit difference threshold of existing guaranteeIn this section, relationships among the guaranteed annual

energy cost savings G, the owner’s excess profit shared percentageb, and the ESCO’s profit difference DE_total(G, b) are also discussedbased on one million times simulations. Fig. 6 presents the rela-tionships between the guaranteed savings G and the ESCO’s profitdifference DE_total(G, b) when the owner’s excess profit shared per-centage b is given. The graphs indicate that G and DE_total(G, b); arenegatively correlated when b = 100%. The more energy savings thatare guaranteed, the more profit loss that would be compared withthe expectation of whether the owner holds all the excess profitbeyond the energy saving guarantee. But, the correlation is not lin-ear. DE_total(G, b) stays close to zero when G is at a low level. Anincrease of G barely leads to any profit loss within the low-levelrange of the guarantee. Out of the range, increasing G wouldbecome more risky and would lead to a great profit loss if G isdesigned at a high level. Therefore, the ESCO needs to be cautiousabout the annual guaranteed energy savings that should staywithin a certain level, no matter how reliable the installed energyefficient facilities are.

When the guaranteed annual savings stays at $1.90 million, asFig. 7 indicates, the existing guarantee b = 100% meets the zeroprofit difference requirements DE_total(G, b) ? 0. This also provesthe reasonableness of the existing guarantee in the contract. WhenG is given, the owner’s share of excess profit b and the ESCO’s totalprofit difference DE_total(G, b) are negatively correlated. Different

Fig. 10. Relations among guarantee, owner’s share of excess profit and profit difference: (a) rQ = 1%; (b) rQ = 10%; and (c) rQ = 25%.

78 Q. Deng et al. / Applied Energy 139 (2015) 68–80

from Fig. 6, DE_total(G, b) are all positive, which stands for the addi-tion instead of the loss to the expected savings revenue. The largerthe percentage of the excess profit shared with the owner, the lessrevenue addition will be expected for the ESCO.

4.3.2. Guarantee designs comparisonRelations between the guaranteed cost savings G and the own-

er’s shared percentage of the excess profit b are also identified,when the ESCO’s total profit difference DE_total(G, b) ? 0. In orderto find all the matched pairs of G and b, the enumeration methodis adopted as a simple and effective way. For the guaranteed valueG, searching starts from 0 to 5 million with a 5000 interval, and, forthe owner’s shared percentage of the excess profit b, searchingstarts from 0 to 1 with a 0.001 interval. In each of the search,1000-time simulations have been performed to return an averagevalue of DE_total(G, b). Both the computation time and the conver-gence concerns have been taken into consideration. The CPU timefor different simulation realizations is displayed in Table 2, and therelations between the number of realizations and the CPU time arenot linear.

Taking three selected guarantee values (G = $1.9, $2.4 and $3.0million) for example, the convergence diagrams of different simu-lation realizations are shown in Fig. 8. b values are thenfound accordingly under different rQ scenarios in order to matchDE_total(G, b) ? 0. High fluctuations are displayed when the simula-tion realizations are small, and gradually decrease as the realiza-tions increase, especially for G = $3.0 million.

Then, the final simulation findings are shown in Fig. 9. Eachpoint on the curve stands for a close-to-zero profit difference ofthe guarantee design with corresponding G and b, which expandsthe design options from the ESCO’s point of view. When the guar-anteed value G stays within a certain range of low level, b wouldstay constantly close to 100%. When the guaranteed value Greaches a high level such as $3.0 million, a significant drop of bwould occur with high sensitivity. These curves could be a usefultool to help the ESCO deliver quality work with minimal retrofitrisks. As we can see, the existing guarantee (G = $1.90 million,b = 100%) is on the curve, which proves the zero profit differencerequirement is satisfied and the ESCO’s profitability is promised.However, there would not be any significant drop on b if G isslightly increased. Moving the guarantee savings from $1.90 to$2.40 million would not lead to a significant change in the owner’sshared percentage, just dropping from 100% to 93.8% when rQ = 1%,96.9% when rQ = 10%, and 98% when rQ = 25%. Assuming theowner would always expect to see a higher savings guarantee, thenthe guarantee (G = $2.40 million, b = 93.8% when rQ = 1%, 96.9%when rQ = 10%, and 98% when rQ = 25%) could be a good choice,which not only satisfies the zero profit difference requirement,but also looks more appealing to the owner in the biddingcompetition.

4.3.3. Further discussionAccording to the simulation results and the previous analysis,

brief comments on the current energy savings guarantee arederived as follows: (1) the profit difference threshold of existing

Q. Deng et al. / Applied Energy 139 (2015) 68–80 79

guarantee design satisfies the close-to-zero requirement; (2) otherguarantee designs (e.g., G = $2.40 million, b = 93.8% when rQ = 1%,96.9% when rQ = 10%, and 98% when rQ = 25%) are also availablesatisfying DE_total(G, b) ? 0, which provides the ESCO a more com-petitive guarantee design to win the bidding.

Former analysis of guarantee design mainly focuses on theparameters’ relationships in EPC. In fact, any two of the three vari-ables, the guaranteed energy saving G, the owner’s shared percent-age of excess profit b, and the ESCO’s total profit differenceDE_total(G, b), are linked to each other. From a broader perspective,the relationship among these three variables would be displayedin a three dimensional space as Fig. 10 shows below. Then, Fig. 6becomes one of the sections from Fig. 10 given b = 100%. Fig. 7becomes the section given G = $1.90 million, and Fig. 8 becomesthe section given DE_total(G, b) ? 0. In real practice, optimum situa-tions might vary and DE_total(G, b) might fit for other values. Inthose situations, the space structure of the curved surface wouldremain unchanged as seen in Fig. 10, but the section would switchto other favorable sets of the guaranteed energy savings G and theshared percentage of excess profit b.

5. Conclusions

This paper has presented a simulation-based approach to derivethe appropriate cost savings guarantee from the ESCO’s perspectivein EPC. Through the method, the ESCO could determine how muchthe cost savings should be guaranteed annually, and what percent-age of the excess profit should be shared, before contracting starts.The derived guarantee could not only preserve the ESCO for itsprofitability from EPC, but could also maintain its competitivenessto win the bid. For the ESCO, the method could be passed on as astandard procedure for energy cost savings guarantee design, com-pared with the past empirical estimation approaches. For theowner, the method could be taken as a reference for bidding selec-tion or a financial reliability check.

The general guarantee design process is listed. First of all, theuncertainties within the energy cost savings are modeled stochas-tically using Monte-Carlo simulation, with both the energy pricefluctuation and the facility performance variability taken intoaccount. Then, based on the criteria for balancing the owner andthe ESCO’s profit, an appropriate energy savings guarantee designis derived, which reallocates the risks from uncertainties through-out the contracting period. Finally, a campus case is presented toshow the simulation details and demonstrate its applicability forfinding the guaranteed savings value and the associated profitsharing percentage. The results show that the existing annual guar-antee, $1.90 million with 100% share to the owner if exceeded,could ensure the ESCO’s profitability. But, a better choice, $2.40million annual guarantee with 93.8% or above share to the ownerif exceeded, would be available to increase the competitivenessfor the ESCO, if the bidding winner had not been selected. Thismethod is also worth popularizing in similar performance-basedprojects.

Future work can still be done to improve the proposed method-ology. In the current model, the price elasticity effect on theamount of energy savings is ignored for simplification. Forinstance, the potential correlation has not been consideredwhereby if the energy price rises, the owner might be aware andconduct measures to control the amount of energy usage. Thus,the energy cost savings might be less than the current estimation.Another assumption made is that there are no additional invest-ment activities during the contracting period, which are not com-mon cases. Guarantee designs under dynamic investmentdecisions are left open for analysis. Besides, though the equilibriumthinking of game theory has been applied to decide why the close-to-zero profit difference thinking is needed, detailed game theory

modeling between the owner and the ESCO are still open forcompletion.

Acknowledgment

The authors would like to thank the Capital Projects Depart-ment of the University of Maryland for their support and sharingof the project information. All results and conclusions presentedare that of the authors alone.

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