1

Impact of the Uncertainty of Distributed RenewableGeneration on Deregulated Electricity Supply Chain

Hanling Yi, Mohammad H. Hajiesmaili, Ying Zhang,Minghua Chen, Senior Member, IEEE, Xiaojun Lin, Fellow, IEEE

Abstract—Active districts are districts that have a system inplace to coordinate distributed energy generation and externalgrid to meet the local energy demand. They are now widelyrecognized as a clear opportunity towards distributed renewableintegration. Despite apparent benefits of incorporating renewablesources in an active district, uncertainty in renewable generationcan impose unprecedented challenges in efficient operation of theexisting deregulated electricity supply chain, which is designedto operate with no or little uncertainty in both supply anddemand. While most previous studies focused on the impact ofrenewables on the supply side of the supply chain, we investigatethe impact of distributed renewable generation on the demandside. In particular, we study how the uncertainty from distributedrenewable generation in an active district affects the averagebuying cost of utilities and the cost-saving of the active district.Our analysis shows that the renewable uncertainty in an activedistrict can (i) increase the average buying cost of the utilityserving the active district, termed as local impact, and (ii)somewhat surprisingly, reduce the average buying cost of otherutilities participating in the same electricity market, termed asglobal impact. Moreover, the local impact will lead to an increasein the electricity retail price of active district, resulting in acost-saving less than the case without renewable uncertainty.These observations reveal an inherent economic incentive forutilities to improve their load forecasting accuracy, in order toavoid economy loss and even extract economic benefit in theelectricity market. We verify our theoretical results by extensiveexperiments using real-world traces. Our experimental resultsshow that a 9% increase in load forecasting error (modeledby the standard deviation of the mismatch between real-timeactual demand and day-ahead purchased supply) will increasethe average buying cost of the utility by 10%.

Index Terms—Active District, Electricity Market, DistributedRenewable Generation, Electricity Price.

I. INTRODUCTION

Renewable energy sources, including solar PVs and windturbines, are effective means to de-carbonize the power systemand support sustainable economic and social development.In 2014, renewables represented approximately 58.5% of netadditions to global power capacity, enough to supply around7.6% of global electricity if operated at 1/3 of the installationcapacity [20].

The work presented in this paper was supported in part by National BasicResearch Program of China (Project No. 2013CB336700), and the UniversityGrants Committee of the Hong Kong Special Administrative Region, China(Theme-based Research Scheme Project No. T23-407/13-N and CollaborativeResearch Fund No. C7036-15G), and National Science Foundation throughgrants CCF-1442726 and ECCS-1509536.

Hanling Yi, Mohammad H. Hajiesmaili, Ying Zhang, and Minghua Chenare with Department of Information Engineering, the Chinese Universityof Hong Kong. Xiaojun Lin is with School of Electrical and ComputerEngineering, Purdue University.

A popular platform for incorporating renewable energysources is active district. An active district is a local electricpower system typically resided in low-voltage distributionnetwork, consisting of various distributed generation, storagesystems, and responsive load. In an active district, all thedistributed generation resources are owned by the same entity,and it can coordinate local generation and the external grid tomeet the energy demand of a local community, such as a uni-versity campus or a hospital. Active districts can be regardedas microgrids operating in grid-connected mode, which aremore robust and cost-effective than conventional approach ofcentralized grids and represent a promising paradigm of futurepower system [15].

Our study focuses on active districts with non-dispatchable,intermittent, and unpredictable renewables energy, such aswind and solar. The intermittent renewable generation notonly introduces unprecedented challenges to active districtoperation, for example energy generation scheduling [11],[14], [25], but also may lead to nontrivial impact on electricityprocurement of utilities on a regional market, as we showin this paper. In the deregulated electricity supply chainillustrated in Fig. 1, an active district (or a microgrid) obtainselectricity from a local utility to serve its residual demand afterdeducting its actual demand by renewable generation. The lo-cal utility, serving as a retailer, obtains electricity supply fromthe regional electricity market to serve a group of customers.The regional market operator (governed by an independentsystem operator) provides a trading place, determines a marketclearing price based on the supply offers and demand bidsusing a double-sided auction mechanism, and matches thesupply and demand at the price. The market operates in atwo-settlement manner and settles transactions at two differenttimescales and prices, i.e., one day ahead with day-ahead priceand real-time with spot price. In day-ahead market operation,the generation companies (respectively utilities) submit theiroffers (respectively bids) for selling (respectively buying)electricity for the next day, based on generation (respectivelyload) forecasting. Then, the imbalance between day-aheadprocurement and actual load is settled in real-time marketoperation. We refer to Sec. II-B for more details about thetwo-settlement market.

Active district with renewable source can impose challengesin electricity market operations due to the intermittent andunpredictable nature of renewable generation. Our goal is toinvestigate the impact of the renewable uncertainty on theaverage buying cost per unit electricity (ABC) of utilities(formally defined in Sec. II-C). We note that most of the

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previous studies focus on the impact of renewables on thesupply side of the supply chain where the renewables, suchas large wind farms, participate in deregulated markets asgeneration companies [6], [17], [21], [26]. In contrast, ourstudy, along with a few others [8], [12], [16], investigatesthe impact of renewables on the demand side, where thedistributed renewable generation affect the residual demand tobe fulfilled by the supply chain. For instance, McConnell et al.show that distributed solar generation can reduce the electricitydemand and depress the wholesale price, which also knownas the merit-order effect [16]. However, the reduction in localdemand due to renewable generation may force the utilities toraise the retail electricity price in order to recover their capitalcost in transmission and distribution infrastructure [8]. As aresult, retail customers with distributed renewable generationmay observe less cost-saving than expected. In this paper,we investigate the impact of uncertainty from distributedrenewable generation on the electricity supply chain.

In particular, we aim to answer two fundamental questions:• What is the local impact of distributed renewable uncer-

tainty? Namely, how does renewable uncertainty in anactive district affect the ABC of the utility serving theactive district?

• What is the global impact of distributed renewable un-certainty? Namely, how does renewable uncertainty inan active district affect the ABCs of all other utilitiesparticipating in the same regional market?

Answers to the above questions provide a complete under-standing of the impact of distributed renewable generationon the economic operation of all the utilities participating inthe regional market. We carry out a comprehensive study andmake the following contributions.. We show that the utility with larger renewable penetration

will suffer from higher ABC. This answers the first questionon the local impact of distributed renewable uncertainty. Theincrease in ABC will lead to an increase in the electricity retailprice of the active district. As a result, an active district withrenewable generation uncertainty observes less cost-savingthan the case without generation uncertainty.. Somewhat surprisingly, we show that all other utilities

participating in the same regional market will actually observea decrease in their ABCs. This answers the second questionon the global impact of distributed renewable uncertainty. Theobservations reveal an inherent economic incentive for utilitiesto improve their load forecasting accuracy, in order to avoidlosses and even extract economic benefit.. We characterize a set of sufficient conditions for observing

the above-mentioned local and global impacts. These condi-tions, on load forecasting errors and the relationship betweenday-ahead prices and real-time prices, suggest that the above-mentioned local and global impacts can be observed underrather general settings, for example when load forecastingerrors follow arbitrary symmetric distribution with zero mean.. We verify our theoretical results by extensive real-world

trace-driven experiments with different percentages of renew-able penetration. In a set of representative experiments, ourresults demonstrate that a 9% increase in load forecast errorwill increase the ABC of the utility by 10%. Our experiments

Fig. 1. The deregulated electricity supply chain

also validate that the active district with renewable generationuncertainty observes less cost-saving than the case withoutgeneration uncertainty.

The rest of this paper is organized as follows. Sec. II givesa brief introduction on deregulated electricity supply chainand its pricing model. Our theoretical results are presented inSec. III. Experimental results are included in Sec. IV. Sec. Vconcludes the paper.

Due to space limitation, all the proofs are in our technicalreport [24], unless otherwise specified.

II. DEREGULATED ELECTRICITY SUPPLY CHAIN

In what follows we explain the electricity supply chain,the operation of the electricity market, and the market pricingmodel.

A. Electricity Supply Chain

As illustrated in Fig. 1, the deregulated electricity supplychain consists of the following four components [13]:• Retail customers (in particular, active districts or micro-

grids), the end-users that consume electricity.• Utilities, who submit bids to buy electricity supply in the

market in order to serve a group of retail customers.• Generation companies, i.e., power plant owners who

produce electricity and submit offers to sell electricityin the market.

• Electricity market, administered by an independent sys-tem operator (e.g., ISO-NE [1]), that provides a tradingplace, matches supply offers from generation companiesand demand bids from utilities.

Utilities transact electricity with generation companies inthe wholesale electricity market, and the active district andtraditional load (residential or commercial load) procure elec-tricity from the local utility. In addition, distributed renewablegeneration is incorporated by some of the retail customers(active districts or microgrids) to satisfy part of their demandlocally.

B. Electricity Market Model

The electricity market usually operates in a two-settlementmanner and settles transactions at two different timescales andprices, i.e., day ahead with day-ahead price and real-time withspot price.

Day-Ahead Market Operation. In the day-ahead marketoperation, generation companies and utilities submit their

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offers and bids for selling and buying the electricity for eachhour of the next day, based on generation and load forecasting.The market operator then clears the market and determines theday-ahead price through a double-sided auction mechanism.The day-ahead market operation allows generation companiesto schedule their supply one day before actual dispatch, inorder to enhance reliability and improve efficiency of the unitcommitment decision. According to a report from the NYISOmarket, about 90% of the electricity supply is scheduled inthe day-ahead market operation [3].

Real-Time Market Operation. The real-time market isdedicated to balancing the supply and demand in real-timeoperation. The transactions for the utilities and generationcompanies in real-time market operation are settled on a hourlybasis. In Nord Pool [2], for example, the ISO collects offersfrom generation companies and determines the hourly real-time spot price based on the actual supply and demand. Whenthe supply is less (respectively higher) than the demand, themarket is up-regulated (respectively down-regulated) and thereal-time spot price is larger (respectively smaller) than theday-ahead price [10]. Overall, the real-time market opera-tion settles the imbalance between the day-ahead scheduledamounts of electricity and the real-time actual demand.

C. Electricity Pricing Model

In our model, we assume that N utilities, indexed by i,participate in the electricity market. Without loss of generality,we focus on the settlements of electricity supply of a particularhour. We denote the corresponding day-ahead price and thespot price as pd and ps (unit: $/MWh), respectively. In thispaper, we assume that the day-ahead price is given and isnot affected by utility i’s day-ahead purchased amount. Thisassumption is reasonable since the majority of the electricityis traded in the day-ahead market and a single utility does nothave the market power to manipulate the market price. Thespot price is related to both the day-ahead price and aggregatemismatch to be balanced on the real-time market, which willbe discussed more later in this section.

Average Buying Cost per Unit Electricity Of Utility.Define Di (unit: MWh) as the real-time actual demand ofutility i at the particular hour. Further, denote ∆i (unit: MWh)as the mismatch between the real-time actual demand and day-ahead purchased supply for utility i in the real-time marketoperation. Then the day-ahead purchased supply for utilityi in the day-ahead market operation is Di − ∆i. Wheneverthere is an imbalance, i.e., ∆i 6= 0, the utility has to settle thisimbalance in the real-time market operation at the spot priceps, i.e., it either sells the residual electricity back to the marketwhen ∆i < 0, or buys the deficient electricity from the marketwhen ∆i > 0. In this way, the total electricity cost of utilityi in the market, denoted as Ci, is defined as follows (unit: $):

Ci , pd(Di −∆i) + ps∆i. (1)

In other words, for utility i, its actual demand Di is settled intwo timescales: (i) an amount of Di − ∆i is settled in day-ahead operation at price pd, and (ii) the remaining amount ∆i

is settled in real-time operation at the spot price ps. Given

the actual electricity delivery Di, we now define the AverageBuying Cost per unit electricity (ABC) for utility i as

ABCi ,CiDi

=1

Di[pd (Di −∆i) + ps∆i] , (2)

whose unit is $/MWh. If utility i has an accurate predictionfor Di in the day-ahead market operation, i.e., ∆i = 0, thenits ABCi is simply the day-ahead price pd. In practice, it iscommon that ∆i 6= 0 due to load forecasting error, becauseof for example renewable uncertainty. The ABCi in this casedepends on the real-time spot price too.

Real-time Spot Price. The spot price is in general af-fected by the real-time market imbalance, i.e., the day-aheadscheduled supply and the real-time actual demand. Any dis-placement in the market imbalance will cause the spot priceto deviate from the day-ahead price. Specifically, deficientsupply in the market leads to a higher spot price, whileexcessive supply results in a lower spot price. To capture theirrelationship, we first denote the aggregate imbalance from allthe utilities in real-time market operation as ∆ ,

∑Ni=1 ∆i,

and consider first the following model for real-time spotprice [18]1:

ps =

pd, ∆ = 0,

(b1 + a1∆)pd, ∆ > 0,

(b2 + a2∆)pd, ∆ < 0.

(3)

−100 −60 −20 20 60 100

20

25

30

∆ (MWh)

ps ($/MWh)

pd

Fig. 2. The model of real-time spot price ps as a function of day-ahead pricepd and aggregate real-time imbalance ∆.

Remark: (i) The model2 was proposed in [18] by curve-fitting historical data. In particular, [18] suggests that a1 =0.0034, a2 = 0.0005, b1 = 1.2378, and b2 = 0.6638. Thecorresponding function is shown in Fig. 2 with pd = 20.(ii) The spot price function is discontinuous at ∆ = 0,i.e., b1 > 1 > b2. This discontinuity can be interpretedas a premium of readiness that utilities need to pay for thegeneration companies, since they have to generate urgentregulating power upon notice [22]. (iii) In this paper, we

1In practice the spot price also depends on generation imbalance, i.e., in theevent of generator trips or as a result of large-scale renewable generation. Thisgeneration imbalance can increase the variability of the market imbalance.We note that this paper mainly focuses on the demand side of the electricitysupply chain and we do not consider the effect of generation uncertainty onthe market imbalance. This simplification will reduce the variance of marketimbalance.

2In general, a1, a2, b1, b2 should be positive.

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mainly work with the pricing model in (3), to bring out theinsights clearly. However, our insights are not restricted to themodel in (3). In Section III-C, we will show that the localand global impacts hold for a larger class of pricing models,which may be non-linear and/or continuous at ∆ = 0.

III. IMPACT OF UNCERTAINTY OF DISTRIBUTEDRENEWABLE GENERATION ON ABCS

Recall that ∆i is the mismatch between the actual loadserved by utility i during the real-time market operation andthe electricity purchased by utility i from the day-ahead marketoperation. We assume that each ∆i is a Gaussian randomvariable with mean zero and variance σ2

i , i.e.,

∆i ∼ N (0, σ2i ), i = 1, 2, ..., N,

and they are mutually independent. Here, the variance σ2i

reflects the load forecasting accuracy; a large value of σ2i

indicates a (statistically) large forecasting error. As an activedistrict served by utility i incorporates more renewable gen-eration, utility i observes a residual demand of active districtthat is smaller in volume but more difficult to predict accu-rately. More specifically, uncertainty in renewable generationis inherited by the residual demand of active district. It is thusdifficult for utility i to accurately predict its load, resulting ina large load forecasting error and thus a large σ2

i . We remarkthat the Gaussian distribution is commonly adopted to modelload forecasting error [7], [17], [19], [23]. Our analysis extendsto any forecasting errors that follow a symmetric distributionwith zero mean, as discussed in Sec. III-C.

Recall that ∆ =∑Ni=1 ∆i is the total imbalance in the real-

time market operation. For ease of discussion, we define

∆−i , ∆−∆i =

N∑j:j 6=i

∆j , (4)

as the aggregate mismatch of all other utilities except utilityi. It is straightforward to verify that ∆−i is a random variablewith mean zero and variance

σ2−i =

N∑j:j 6=i

σ2j , (5)

where σ2−i represents the aggregate forecasting errors of all

utilities except utility i. Here we assume that the load forecast-ing errors are mutually independent. This assumption allowsus to obtain analytically tractable result and helps us gainvaluable insights. However, in practice the load forecastingerrors may not be independent, as we demonstrated in theexperiment in Sec. IV. We still observe local and global im-pact, as suggested by the analysis, which depicts the robustnessof our main results w.r.t. the correlations in load forecastingerrors.

Next, we will first characterize the expected ABCs ofutilities as a function of load forecasting error, representedby σ2

i and σ2−i. We will then discuss the results and insights.

Theorem 1. Under the model of (3), the expectation of ABCiis given as:

E [ABCi] =E[

1

Di[pd (Di −∆i) + ps∆i]

]=pd +

(a1 + a2)pd2Di

σ2i

+(b1 − b2)pd

2DiE[∆i · erf

(∆i√2σ−i

)], (6)

where erf(x) = 1√π

∫ x−x e

−t2dt is the standard error function,and coefficients a1, a2, b1, and b2 are parameters of the pricingmodel defined in (3).

Remarks: The expected ABCi in (6) depends on threeterms. The first term is simply the day-ahead market clearingprice. The second and the third terms correspond to utilityi’s cost for balancing its mismatch in the real-time marketoperation. Here, the second term is affected by utility i’s loadforecasting accuracy. The third term, interestingly, is affectedby not only the forecasting accuracy of utility i, but also theaggregate forecasting accuracy of all other utilities. Thus, theclose-form expression of E [ABCi] allows us to investigate howthe change in one utility’s forecasting accuracy affects its ownexpected ABC, i.e., local impact, as well as those of all otherutilities participating in the same regional market, i.e., globalimpact.

For ease of discussion on local and global impacts, wepresent the following understanding. Recall that the distribu-tion of ∆i is symmetric. By the Total Expectation Theorem,we have

E [ABCi] =

∫ +∞

0

φ(δi, σ2−i)f∆i

(δi)dδi, (7)

where

φ(δi, σ2−i) , E∆−i

[ABCi|∆i = δi]+E∆−i[ABCi|∆i = −δi] ,

represents the average buying cost per unit electricity for utilityi when its mismatch is |δi| in volume, and f∆i

(·) is the PDFof random variable ∆i. We have the following observation onφ(δi, σ

2−i).

Lemma 1. Given fixed σ2−i, φ(δi, σ

2−i) is increasing w.r.t. δi.

Essentially, Lemma 1 says that the average buying cost ofutility i increases as it has more mismatch (either positive ornegative) to balance.

Lemma 2. Given fixed δi, φ(δi, σ2−i) is decreasing w.r.t. σ2

−i.

Lemma 2 says that the average buying cost of utility i tobalance a fixed amount of mismatch |δi| will decrease if otherutilities in the market have larger load forecasting errors. Thedetails of why E[ABCi] is decreasing w.r.t. σ2

−i can be foundin Appendix C.

The intuitions and insights are included in the proof sketchesof the two lemmas in Appendixes A and B. The observationsin the lemmas are useful in the discussion on the local andglobal impacts in the next two subsections.

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A. Local Impact of Uncertainty of Distributed RenewableGeneration

The local intermittent renewable generation introduces extrauncertainty in the residual demand of the active district. Con-sequently, the utility serving the active district (among its othercustomers) will observe statistically larger load forecastingerror, and the regional market will need to settle (statistically)larger supply-and-demand imbalance in the real-time marketoperation. A careful analysis shows that the utility with largerload forecasting error will suffer from an increase in its ABC.We summarize this observation into the following corollary.

Corollary 1. Consider utility i, given fixed σ2−i, E [ABCi] is

monotonically increasing w.r.t. σ2i . Hence, if the uncertainty of

distributed renewable generation deteriorates the forecastingaccuracy and leads to a larger σ2

i , then utility i will sufferfrom higher expected ABC.

We explain the intuition behind Corollary 1 as follows.Recall that expected ABC of utility i can be expressed in(7), where the integral can be interpreted as weighted sumof φ(δi, σ

2−i) with different δi > 0. When σ2

i increases,∆i ∼ N

(0, σ2

i

)is more likely to take values of large

magnitude, resulting in a larger weight for φ(δi, σ2−i) with

large δi. Now, under the setting of Corollary 1, φ(δi, σ2−i) is

increasing w.r.t. δi from Lemma 1, thus E[ABCi] increases asσ2i increases.

B. Global Impact of Uncertainty of Distributed RenewableGeneration

We now show that the uncertainty of distributed renewablegeneration in active districts not only increases the expectedABC of the utility serving the active districts, but also de-creases the expected ABCs of all other utilities participatingin the same market.

Corollary 2. Consider all utilities except utility i, given fixedσ2j , 1 ≤ j ≤ N and j 6= i, E [ABCj ] is monotonically

decreasing w.r.t. σ2i . The “reverse” direction is also true:

consider utility i, given fixed σ2i , E [ABCi] is monotonically

decreasing w.r.t. σ2−i.

Remark: (i) Corollary 2 implies that a utility servingcustomers with distributed renewable generation will “benefit”other utilities on the same market by reducing their expectedABCs, and conversely a utility serving customers withoutrenewable uncertainty will enjoy a lower expected ABC whencustomers of other utilities install renewable generation. (ii)Corollaries 1 and 2 are significant in that they reveal aninherent economic incentive for utilities to improve their loadforecasting accuracy, in order to avoid economy loss andeven extract economic benefit when the electricity market isoperating under a volatile condition.

We present the intuition for Corollary 2 as follows. It suf-fices to focus on the “reverse” direction, i.e., we fix σ2

i whileincrease σ2

−i to evaluate the changes in E[ABCi]. Accordingto (7), when σ2

i is fixed, the distribution of ∆i, i.e., f∆i(δi), is

fixed. From Lemma 2, we know that φ(δi, σ2−i) is decreasing

w.r.t. σ2−i given fixed δi. Since each term in the integral in (7)

decreases as σ2−i increases, E[ABCi] decreases as well.

C. Sufficient Conditions for Observing the Local and GlobalImpacts

The local and global impacts reported earlier are obtainedunder the linear pricing model in (3). An important question tobe addressed is under what condition on the pricing model andwhat distribution on the imbalance ∆i, that we can observesimilar types of local and global impacts? In the following,we answer the question and generalize the previous results.

Theorem 2. Assume that for any 1 ≤ i ≤ N , the imbalance∆i follows a symmetric distribution with mean zero andvariance σ2

i , and they are mutually independent. Denote theprice function as ps = p(x). The following statements aretrue:

(1) If p(x) is increasing w.r.t. x, then for any 1 ≤ i ≤ N ,given a fixed σ2

−i, E[ABCi] monotonically increases as σ2i

increases. In other words, Corollary 1 holds for any pricefunction that is increasing w.r.t. x.

(2) If p(x) is differentiable for all x except the origin, i.e.,p′(x) exists for all x ∈ R\ {0}, and either

p(0+) = p(0−),

p′(ξ1) + p′(−ξ1) < p′(ξ2) + p′(−ξ2), ∀ξ1 > ξ2 > 0,(8)

orp(0+) > p(0−),

p′(ξ1) + p′(−ξ1) ≤ p′(ξ2) + p′(−ξ2), ∀ξ1 > ξ2 > 0,(9)

then for any 1 ≤ i ≤ N , given a fixed σ2i , E[ABCi]

monotonically decreases as σ2−i increases. In other words,

Corollary 2 holds for any price function satisfying (8) or (9).

Remark: (i) Results in Corollary 1 and 2 are special casesof Theorem 2 under assumptions of Gaussian distributionfor ∆i and the pricing model in (3). In particular, the pricefunction in (3) satisfies the condition in (9). (ii) Theorem 2generalizes previous results to a larger class of pricing models.For example, we can observe local and global impacts underthe two price functions given in Fig. 3. We note that the pricefunction on the left is continuous at ∆ = 0 while the rightone is discontinuous at ∆ = 0. (iii) This theorem applies toany ∆i following symmetric distribution with zero mean.

−1 −0.6 −0.2 0.2 0.6 1

20

25

30

∆ (MWh)

ps ($/MWh)

pd

× 104

(a) b1 = b2 = 1

−1 −0.6 −0.2 0.2 0.6 1

20

25

30

∆ (MWh)

ps ($/MWh)

pd

× 104

(b) b1 = 1.2378, b2 = 0.6638

Fig. 3. Nonlinear pricing function p(x) = pd × (1{x>0}(a1xk + b1) +

1{x<0}(−a2(−x)k + b2) + 1{x=0}) with a1 = 0.0034, a2 = 0.0005,pd = 20, and k = 1

2, where 1{·} is the indicator function. Note that to show

the nonlinear relationship more clearly, we vary ∆ from -10GWh to 10GWh.

IV. EXPERIMENTAL RESULTS

A. Experiment SettingsScenarios and Experiment Procedure. We simulate an

electricity market with 10 utilities. In the electricity market,

6

-50 0 50Forecasting Error(MWh)

0

200

400

600

800

1000

Num

ber

of O

ccur

ance

Fig. 4. The histogram of load fore-casting error for a utility using ANNmodel.

0 10 20 30 40 508

10

12

14

16

Renewable Penetration(%)

Nor

mal

ized

ST

D(%

)

Fig. 5. The normalized standarddeviation for the utility with vari-ous renewable penetration in activedistrict.

0 10 20 30 40 5035

36

37

38

39

Renewable Penetration(%)

AB

C($

/MW

h)

Fig. 6. The mean of ABC forthe utility with various renewablepenetration in active district.

0 10 20 30 40 50

35.03

35.04

35.05

35.06

35.07

35.08

35.09

Renewable Penetration(%)

AB

C($

/MW

h)

Highest ABCLowest ABCAveraged ABC

Fig. 7. The mean of ABC forother utilities with fixed renewablepenetration in active district.

each utility participates in both day-ahead and real-time marketoperations. The spot price is obtained from the pricing modelin (3) and the parameters in [18]. For each hour, the ABC iscomputed according to (2) and the retail price for the activedistrict is set as the same as the ABC, following real-timepricing scheme for the retail customers. As in our experimentswe aim to measure the cost-saving of the active district, wehave used the total electricity cost of the active district as themetric, which is defined as the product of the retail price andresidual demand.

Experimental Data. We use the hourly day-ahead pricedata from the PJM market to conduct the experiments [5].The mean of the day-ahead price is 35$/MWh. The hourlyelectricity demands are obtained from 10 utilities in the PJMmarket and the electricity consumptions from these 10 utilitiesare scaled to have the same mean (2GWh). We incorporaterenewable energy supply sources by the wind power tracefrom the PJM market and scale it down to obtain differentlevels of renewable penetration in active district. We define therenewable penetration in the active district as the ratio betweenaverage renewable generation and peak demand of activedistrict. Unless otherwise specified, we assume the utilitieshave 30% of its demand coming from the active district,and the renewable penetration in active district is fixed at10%. Meanwhile, weather information including temperature,humidity, pressure, and wind speed are gathered from thePennsylvania State Climatologist [4] to perform load forecast-ing.

B. Impact of Renewable Uncertainty

Purpose: As new types of retail customers with localrenewable sources in electricity supply chain, active districtsexhibit large fluctuations in their net demand due to theuncertainty from renewables. Previous analysis highlights thenegative impact of renewable uncertainty on the load fore-casting accuracy, but it remains unclear to what extent thisrenewable uncertainty can affect the load forecasting accuracy.This subsection aims to answer this question.

Nowadays, various load forecasting tools have been em-ployed to perform the day-ahead prediction. For example,similar day method, Artificial Neural Network (ANN), andregression analysis are used in ISO-NE [1]. In our experi-ments, we use an ANN model to conduct load forecasting,and the load forecasting errors are obtained by subtracting the

forecasted demands from the true demands. Note that in theexperiments, we do not preset a model for the load forecastingerrors.

The artificial neural network, which is composed of anumber of interconnected neurons with different connectionweights, was first developed by researchers to mimic thestructure of the human brain. Through a learning processbased on the training data set, ANN adjusts the connectionweights among neurons and generates a mapping between theinputs and the outputs. Once the ANN is trained, it can thenbe utilized to predict target value based on the input data.In our experiments, the training of a three-layer feedforwardneural network is performed by Neural Network Toolbox inMATLAB [9] using the Levenberg-Marquardt algorithm. Thetarget value is the load consumption, and the input data to trainthe ANN model include the weather information, the holidayinformation, the 24-hour-ahead load consumption and the 48-hour-ahead load consumption.

Observations:We observe that the load forecasting errors in our ex-

periments do not follow normal distribution. To see this,in Fig. 4 we plot the histogram of forecasting error fora utility. The distribution is symmetric, and the mean andstandard deviation of the samples are 0.7659 and 9.7391,respectively. We then use the Lilliefors Goodness-of-Fit Testto perform the normality test on the load forecasting errorsamples. It turns out that the null hypothesis (i.e., “the data arenormally distributed”) is rejected at the 5% significant level.This observation demonstrates the robustness of our analysis.Namely, for our main results to hold, the load forecastingerrors need not necessarily follow a normal distribution. Asstated in Theorem 2, the main results extend to any forecastingerrors that follow a symmetric distribution with zero mean.In addition, we note that there are correlations in the loadforecasting errors among different utilities, and the largestcorrelation coefficient is 0.76 in the experiments.

We define the normalized standard deviation as the standarddeviation of load forecasting error in all hours normalized bythe mean of actual load. As shown in Fig. 5, the load fore-casting error increases as the renewable penetration continuesto grow in the active district. In particular, we can observean increasing normalized standard deviation from roughly8% under no renewable condition to around 17% when therenewable penetration reaches 50% in active district. We notethat although the mean absolute percentage error (MAPE)

7

is commonly used as a measure of prediction accuracy ofa forecasting method in statistics, here we use normalizedstandard deviation instead, since the variance is commonlyused to model the load forecasting error in the power systemliterature [7], [17], [19], [23].

C. Impact of Increasing Load Forecasting Error

Purpose: As suggested in Sec. III, the increasing loadforecasting error in one utility will increase the ABC of thisutility and decrease the ABC of all other utilities on the samemarket. In this subsection, we conduct experiments to verifyour theoretical results. Toward this end, we vary the renewablepenetration of the active district in one utility from 0% to 50%,while fixed the renewable penetration of the active district inall other utilities and measure the ABCs. We note that eachpoint in the following figures is the average ABC of the utilityunder 17520 different executions (2 years hourly data).

Observations: Fig. 6 shows the average of ABC for theutility with active district as its retail customer under differentlevels of renewable penetration. The result depicts that asrenewable penetration increases, the ABC increases as well.Note that when the renewable penetration reaches 50% inactive district, the ABC of the utility increases by more than10% as compared to the case with no renewable penetration.This observation further verifies the result in Corollary 1 on thelocal impact of uncertainty in distributed renewable generation.

Fig. 7 demonstrates the decrease of the ABC for otherutilities (we have plotted the results for the utilities withthe highest ABC, the lowest ABC, and the average ABC ofother 9 utilities to keep the figure clear). This decrease isconsistent with the analysis in Sec. III, that the increasingload forecasting error in one utility can benefit other utilitiesby reducing their ABC. As compared to the amount of increasein the ABC of the utility with active district (10% with 50%penetration), the decrease in the ABC of the others is ratherminor (0.1% decrease with 50% penetration, on average).From Fig. 5, we know that as the renewable penetration inactive district increases from 0% to 50%, the load forecastingerror of the utility will increase from 8% to 17%. Theoretically,we can compute from (6) that the ABC of this utility willincrease by 10% and the ABC of other utilities will decreaseby 0.08% under our simulation setting (Please refer to theexperiment settings in Sec. IV-A, we use the mean of pd andDi to approximate the ABC when σ−i takes two differentvalues, and calculate its relative change in percentage). In otherwords, the simulation result matches the theoretical result. Wenote that the local impact only affects one utility, while theglobal impact can affect all other utilities in the electricitymarket. In this sense, the global impact is significant as well.

D. Implication on the Cost-saving of the Active District

Purpose: The increase in the ABC of the utility eventuallyleads to the increase in the retail price for customers. In thisway, even though the active district increases the renewablepenetration and reduces its electricity demand, it will observeless cost-saving as compared to the case without renewableuncertainty, since the increased retail prices caused by the

renewable uncertainty partially offset the benefit of the re-newable generation. To evaluate the impact of the renewableuncertainty on the cost-saving of active district, in this sub-section, two different scenarios are considered: 1) the utilitypredicts the day-ahead demand with ANN prediction method;2) the utility has accurate day-ahead demand prediction. Thetwo scenarios differs in the utility’s ability to predict the futuredemand. The second scenario serves as the benchmark to studythe impact of renewable uncertainty.

We define the cost-saving as η(x) = Cm−C(x)Cm

, where Cm isthe cost of active district without renewable energy and C(x) isthe cost of active district with different renewable penetrationlevels (x ∈ {5%, 10%, ..., 50%}). We denote ηANN (x) andηAP (x) as the cost-saving with ANN prediction methodand accurate prediction, respectively. Then the cost-savingreduction is formally defined as ηAP (x) − ηANN (x). Smallcost-saving reduction indicates a small impact of renewableuncertainty on the cost-saving of active district.

10 20 30 40 500

20

40

60

Renewable Penetration(%)

Cos

t Sav

ing(

%)

10 20 30 40 500

5

10

15

Cos

t Sav

ing

Red

uctio

n(%

)

ANN PredictionAccurate PredictionCost Saving Reduction

Fig. 8. The percentage of cost-saving and cost-saving reduction in activedistrict

Observations: Results in Fig. 8 depict that the cost-savingof active district increases with high renewable penetration.This is reasonable as the renewable generation is free ofcharge and the more renewable generation, the less electricityactive district needs to buy from the utility. However, the cost-saving reduction in active district is increasing as renewablepenetration in active district increases, which demonstrates thenegative impact of renewable uncertainty. The uncertainty ofrenewable increases the ABC of the utility and consequentlythe retail price, which partially offset the benefit of renewablegeneration in active district.

E. Impact of Increasing Renewable Penetration in MultipleUtilities

Purpose: Previous experiments have focused on the sce-narios that increase of renewable penetration occurs only inone utility, while other utilities on the same market havefixed renewable penetration. In practice, multiple utilitiesmay simultaneously suffer larger load forecasting error dueto increase of renewable penetration. In this subsection, weconsider the scenarios that multiple utilities have increasingrenewable penetration and investigate the changes in their

8

ABCs3. More specifically, we assume that utilities in themarket can be categorized into two groups, with 6 of thembelong to group-1 and 4 of them belong to group-2. In thisexperiment, we consider two scenarios for comparison. Inthe first scenario, group-1 utilities have an annual increasein renewable penetration at 5%, while group-2 utilities havean annual increase at 10%. At year 0 all the utilities do nothave renewables at all and their renewable penetration start toincrease year by year. By year 5, the group-1 utilities have25% renewable penetration and group-2 utilities have 50%renewable penetration. In the second scenario, group-1 utilitiesdo not increase their renewable penetration, while group-2utilities have an annual increase at 10%.

0 1 2 3 4 5Year

36

37

38

39

40

AB

C($

/MW

h)

Group-2 Utility in Scenario 2Group-1 Utility in Scenario 2Group-2 Utility in Scenario 1Group-1 Utility in Scenario 1

Fig. 9. The mean of ABC for different groups of utilities.

Observations: Fig. 9 shows the mean of ABC for the twogroups of utilities in different scenarios. In the first scenario(shown in solid line), we can observe that as renewablepenetration increases year by year, all the utilities in the marketsuffer an increasing ABC. In particular, the utilities with higherrenewable penetration have higher ABCs. This result depictsthe significance of the local impact. In the second scenario(shown in dash line), we can observe that the ABC of group-1 utilities decrease slightly, which demonstrates the existenceof global impact from the group-2 utilities. In addition, wenote that the ABC of group-2 utilities in scenario 1 is slightlysmaller than that in scenario 2. This is because in scenario1 the renewable penetration in group-1 utilities also increaseand they have global impact on the group-2 utilities.

V. CONCLUSION

In this paper, we investigated the impact of the uncertaintyfrom distributed renewable sources in active districts on theefficiency of the deregulated electricity supply chain. Our com-prehensive study demonstrated that the distribted renewableuncertainty can lead to (i) an increase in the average buyingcost per unit electricity of the utility serving the active district,termed as local impact, and (ii) a decrease in the averagebuying cost per unit electricity of other utilities in the sameregional market, termed as global impact. Putting together,

3We note that when all the utilities increase the renewable penetration, thetotal demand will decrease and it may lead to a lower day-ahead price, whichwill decrease their ABC. In this paper, we do not consider this case andassume that the day-ahead price is not affected by the decreasing demand.

these observations revealed the potential inefficiency in theoperation of the current deregulated electricity market that wasdesigned for the cases with low uncertainty in both supply anddemand. An interesting future direction is then to investigatehow to redesign the market operation to be robust against thisdemand side uncertainty.

APPENDIX APROOF SKETCH OF LEMMA 1

Proof: Recall from (1) that the actual demand Di for aparticular hour of utility i is settled in two timescales: (i) anamount of Di −∆i is settled in day-ahead operation at pricepd, and (ii) the remaining amount ∆i is settled in real-timeoperation at the spot price ps expressed in (3). Since ∆i takessymmetric values in φ(δi, σ

2−i), summing over these two cases

will result in a fixed day-ahead market settlement pd. Thus,the increase in δi will only affect the real-time settlement.• When ∆i = δi > 0, the total mismatch ∆ followsN(δi, σ

2−i)

where the variance σ2−i is fixed under the

setting of Lemma 1. For large δi > 0, ∆ tends to takelarge positive values. As spot price ps is increasing w.r.t.∆, large positive ∆ leads to large positive ps (and indeedlarge positive ps−pd according to (3)). Thus, in real-timeoperation, the utility i will buy electricity at a statisticallyhigh price to settle the positive mismatch δi.

• When ∆i takes the symmetric value −δi < 0 (of thesame magnitude), the total mismatch ∆ ∼ N

(−δi, σ2

−i).

Following similar arguments, the utility i will sell atstatistically low spot price to settle the negative mismatch.

In the first case, utility i will buy δi amount of electricity ata price that is higher than pd and proportional to δi, denotedas ps1. In the second case, it will sell δi amount of electricityat a price that is lower than pd and proportional to (−δi),denoted as ps2. Hence, the real-time settlement cost of utilityi, summing over these two equally-likely cases, i.e., δi(ps1 −ps2) is positive and increasing w.r.t. δi, and thus φ(δi, σ

2−i)

increases as (the magnitude) δi increases.

APPENDIX BPROOF SKETCH OF LEMMA 2

Proof: Following similar arguments in the proof sketch ofLemma 1, we know that σ2

−i affects φ(δi, σ2−i) only through

the real-time settlement. Meanwhile, when ∆i = δi > 0 isfixed4, the total imbalance ∆ follows a normal distributionwith mean δi and variance σ2

−i. Let’s begin with the followingtwo simple cases to see the intuition:• If a1 = a2, b1 = b2 in the pricing model, then the spot

price ps is a linear continuous function in ∆. Fig. 10shows the spot price function and the distribution of ∆.We can observe that the real-time settlement cost onaverage is invariant to the changes in σ2

−i, due to thesymmetry property in the distribution of ∆.

• If a1 = a2, b1 > b2 in the pricing model, then the spotprice ps is a linear “step” function in ∆, as shown inFig. 11. Unlike the first case, when ∆ < 0, the utility

4Similar arguments can be applied when ∆i = −δi < 0.

9

−100 −50 0 50 100

8

16

24

32

40

48 ps ($/MWh)

δi

∆ (MWh)

Fig. 10. Case 1: a1 = a2, b1 = b2.

−100 −50 0 50 100

8

16

24

32

40

48 ps ($/MWh)

δi

∆ (MWh)

Fig. 11. Case 2: a1 = a2, b1 > b2.

−100 −50 0 50 100

8

16

24

32

40

48

δi

∆ (MWh)

ps ($/MWh)

Fig. 12. ∆i = δi > 0.

−100 −50 0 50 100

8

16

24

32

40

48

−δi

∆ (MWh)

ps ($/MWh)

Fig. 13. ∆i = −δi < 0.

can buy electricity at a spot price that is much lower,indicating a gain for the utility. In other words, as longas the sign of ∆ is different from that of ∆i, utility iwill gain from the market. Increasing σ2

−i in this casewill increase the probability of utility i to gain, thus itsreal-time settlement cost will decrease.

In Lemma 2, we consider the pricing model in (3), wherea1 > a2, b1 > b2. For ease of discussion, let’s denote the slopeof the spot price function as k1 when ∆ > 0 and k2 when∆ < 0, respectively. Thus k1 = a1 > k2 = a2. In this case,summing the real-time settlement cost over two equally-likelycases, i.e., ∆i = δi > 0 and ∆i = −δi < 0, can be shownto be the same as the case when summing over ∆i = δi > 0and ∆i = −δi < 0 under the setting where k1 = k2. To seethis, let’s consider the following two cases:

• As shown in Fig. 12, if ∆i = δi > 0, when ∆ = −δ < 0,the real-time settlement cost for utility i will increase by(a1 − a2)δ as compared to the case when k1 = k2 = a1.

• As shown in Fig. 13, if ∆i = −δi < 0, when ∆ = δ > 0,the real-time settlement cost for utility i will decrease by(a1 − a2)δ as compared to the case when k1 = k2 = a2.

Now summing over these two cases results in a real-timesettlement cost that is the same as that of summing over thesetwo cases under the setting where k1 = k2. As discussedbefore, when k1 = k2, increasing σ2

−i will decrease real-timesettlement cost. Consequently φ(δi, σ

2−i) is decreasing w.r.t.

σ2−i.

APPENDIX CINTUITIVE EXPLANATION FOR GLOBAL IMPACT

In this appendix, we present the intuitive explanation forthe global impact, i.e., fixed σ2

i , E[ABCi] decreases w.r.t. σ2−i.

According to the independent assumption of ∆i and ∆−i, theE[ABCi] can be expressed as:

E[ABCi] =

∫ ∞0

∫ ∞0

ω(δi, δ−i)f∆i(δi)f∆−i

(δ−i)dδidδ−i,

where

ω(δi, δ−i) =E[ABCi|∆i = δi,∆−i = δ−i]

+ E[ABCi|∆i = δi,∆−i = −δ−i]+ E[ABCi|∆i = −δi,∆−i = δ−i]

+ E[ABCi|∆i = −δi,∆−i = −δ−i],

δi, δ−i > 0 and f∆i(·) and f∆−i

(·) are the PDF of randomvariable ∆i and ∆−i, respectively. Since δi+δ−i > 0, −(δi+δ−i) < 0, we have

E[ABCi|∆i = δi,∆−i = δ−i]

=pdDi

(Di − δi) +pdδiDi

(a1δi + a1δ−i + b1),

E[ABCi|∆i = −δi,∆−i = −δ−i]

=pdDi

(Di + δi) +pdδiDi

(a2δi + a2δ−i − b2).

If δ−i < δi, we have

E[ABCi|∆i = δi,∆−i = −δ−i]

=pdDi

(Di − δi) +pdδiDi

(a1δi − a1δ−i + b1),

E[ABCi|∆i = −δi,∆−i = δ−i]

=pdDi

(Di + δi) +pdδiDi

(−a2δi + a2δ−i + b2).

Summing the above four terms we have for δ−i < δi,

ω(δi, δ−i) = 4pd +2pdδiDi

((a1 + a2)δi + b1 − b2). (10)

Similarly, when δ−i > δi, following similar calculation wehave

ω(δi, δ−i) = 4pd +2pdδiDi

(a1 + a2)δi. (11)

Now we can observe that fixed δi, when δ−i increases, ifit is always less (or larger) than δi, from (10) (or (11)) weknow that the ω(δi, δ−i) remains unchanged. If δ−i increasesfrom δ−i < δi to δ−i > δi, the ω(δi, δ−i) decreases due to thepositive term b1 − b2. Thus ω(δi, δ−i) is non-increasing w.r.t.δ−i. Note that in this case, the gap (b1 − b2) at ∆ = 0 in thepricing model in (3) is the key factor that cause the ABCi todecrease.

Finally, we note that as σ2−i increases, the random variable

∆−i is more likely to take value of large magnitude, resultingin a large δ−i. Thus given fixed σ2

i , E[ABCi] decreases as σ2−i

increases.

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Hanling Yi received his B.Eng. degree from the De-partment of Electronic Engineering and InformationScience at University of Science and Technologyof China, Hefei, China in 2014, and is currentlypursuing the Ph.D. degree in Department of Infor-mation Engineering at the Chinese University ofHong Kong. His research interests include electricitymarket and microgrid operation.

Mohammad H. Hajiesmaili received the B.Sc.degree in Computer Engineering from the Depart-ment of Computer Engineering, Sharif University ofTechnology, Iran, in 2007, and the M.Sc. and Ph.D.degrees in Computer Engineering from the Electricaland Computer Engineering Department, Universityof Tehran, Iran, in 2009 and 2014, respectively.He was a Postdoctoral Fellow with the Departmentof Information Engineering, The Chinese Universityof Hong Kong, from 2014 to 2016. He is cur-rently a Postdoctoral Fellow with the Department

of Electrical and Computer Engineering, Johns Hopkins University. Hisresearch interests include optimization, algorithm, and mechanism design incommunication, energy, and transportation networks.

Ying Zhang received his B.Eng. degree from theDepartment of Electronic Engineering at ShanghaiJiao Tong University in 2013, and is currenty pur-suing the Ph.D. degree in Department of Informa-tion Engineering at the Chinese University of HongKong. His research interests include energy systemsand distributed optimization. He is also interested instatistical arbitrage and high frequency trading.

Minghua Chen (S’04 M’06 SM’13) received hisB.Eng. and M.S. degrees from the Dept. of Elec-tronic Engineering at Tsinghua University in 1999and 2001, respectively. He received his Ph.D. de-gree from the Dept. of Electrical Engineering andComputer Sciences at University of California atBerkeley in 2006. He spent one year visiting Mi-crosoft Research Redmond as a Postdoc Researcher.He joined the Dept. of Information Engineering, theChinese University of Hong Kong in 2007, wherehe is currently an Associate Professor. He is also

an Adjunct Associate Professor in Institute of Interdisciplinary InformationSciences, Tsinghua University. He received the Eli Jury award from UCBerkeley in 2007 (presented to a graduate student or recent alumnus foroutstanding achievement in the area of Systems, Communications, Control,or Signal Processing) and The Chinese University of Hong Kong YoungResearcher Award in 2013. He also received several best paper awards,including the IEEE ICME Best Paper Award in 2009, the IEEE Transactionson Multimedia Prize Paper Award in 2009, and the ACM Multimedia BestPaper Award in 2012. He is currently an Associate Editor of the IEEE/ACMTransactions on Networking. He serves as TPC Co-Chair of ACM e-Energy2016 and General Chair of ACM e-Energy 2017. His current research interestsinclude energy systems (e.g., smart power grids and energy-efficient datacenters), intelligent transportation system, online competitive optimization,distributed optimization, networking, and delay-constrained network coding.

11

Xiaojun Lin (S’02 M’05 SM’12 F’17) received hisB.S. from Zhongshan University, Guangzhou, China,in 1994, and his M.S. and Ph.D. degrees from PurdueUniversity, West Lafayette, IN, in 2000 and 2005,respectively. He is currently an Associate Professorof Electrical and Computer Engineering at PurdueUniversity.

Dr. Lin’s research interests are in the analy-sis, control and optimization of large and complexnetworked systems, including both communicationnetworks and power grid. He received the IEEE

INFOCOM 2008 best paper and 2005 best paper of the year award fromJournal of Communications and Networks. His paper was also one of tworunner-up papers for the best-paper award at IEEE INFOCOM 2005. Hereceived the NSF CAREER award in 2007. He was the Workshop co-chairfor IEEE GLOBECOM 2007, the Panel co-chair for WICON 2008, the TPCco-chair for ACM MobiHoc 2009, and the Mini-Conference co-chair forIEEE INFOCOM 2012. He is currently serving as an Associate Editor forIEEE/ACM Transactions on Networking and an Area Editor for (Elsevier)Computer Networks Journal, and has served as a Guest Editor for (Elsevier)Ad Hoc Networks journal.