new models for integrated short-term forward electricity markets

478 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 2, MAY 2003

New Models for Integrated Short-Term ForwardElectricity Markets

Shangyou Hao and Fulin Zhuang

Invited Paper

Abstract—In a typical short-term forward wholesale electricitymarket where products are auctioned sequentially, one often ob-serves significant market inefficiency and price volatility—thusthe recent growing impetus in developing integrated short-termforward markets where electric energy, reserves, and transmis-sion capacity are auctioned simultaneously. Such markets neednew computational methods and models for determining marketclearing prices and physical (delivery/consumption) schedules.The purpose of this paper is to examine key aspects of currentmodeling and pricing methods in short-term forward wholesaleelectricity markets and to introduce new models suitable forclearing price-based markets of integrated trades of energy, re-serve, and transmission. Specifically, an analysis of the impactsof various pricing rules and bidding requirements on marketoperations is presented, the selection of optimization objectivesis discussed, and a new model of transmission congestion andmultiproducts simultaneous auction is introduced. Examples areused where appropriate.

Index Terms—Ancillary services, congestion management,deregulation, marginal cost, power markets.

I. INTRODUCTION

T HE FOREMOST step of electric industry deregulation inthe U.S. has been the introduction of wholesale electricity

markets for price based supply-side competition. In short-term,typically one-day ahead, this competition often takes placein the so-called short-term forward markets where wholesaleelectricity products are auctioned for every scheduling time in-terval, typically an hour, resulting in market clearing prices foreach product and physical (delivery/consumption) schedules.The physical schedules are determined for every product ofeach seller or buyer, often also for every physical location, andevery scheduling time interval. The market operator conductsan auction, or a series of sequential auctions, applying marketclearing algorithms to the bid and ask data of sellers and buyersto yield market clearing prices, which, in turn, determinethe physical (delivery/consumption) schedules. In contrast,long-term forward wholesale electricity markets in whichcontracts for monthly or yearly delivery are traded typicallyuse bid-ask matching mechanisms akin to those in conventionalstock markets.

Manuscript received December 9, 2002.S. Hao is with EEE Consulting, Inc., LLP, Walnut, CA 91789 USA.F. Zhuang is with Deloitte & Touche, Los Angeles, CA 90071 USA.Digital Object Identifier 10.1109/TPWRS.2003.810686

The operation of short-term forward wholesale electricitymarkets is like no other. The market not only has to matchoverall sale and buy quantities of electricity products, it needsto also ensure the feasibility of physical delivery/consumptionschedules over a complex electric transmission network withstringent, hour by hour limits and reliability requirements. Insuch a market, an electricity supply source is often capableof providing both energy and reserve products out of a totalproduction capacity and all energy and reserve products use thesame limited transmission capacities. In other words, multipleenergy and reserve products compete for limited productionand delivery capacities [1], [2]. In many existing short-termforward wholesale electricity markets, however, energy and re-serve products are auctioned sequentially with varying degreesof consideration for transmission limits, partially ignoringthe interaction between products. This sequential approachcan result in inefficient use of production and transmissionresources, leading to high total payment from buyers. Thesellers’ attempt to allocate limited production capacity betweensequential auctions also can contribute to significant pricevolatility [3], [4]. Further complicating such a market are thevarious uplift charges to buyers typically arising from selleror transmission owner costs not easily priced on productionvolumes. The uplifts are applied outside the auctions, tendingto mask the true prices of electricity products.

Recent standard market design discussion initiated by theFederal Energy Regulatory Commission (FERC) once againbrought into focus the deficiency of many sequential marketsand the need for short-term forward markets with integratedenergy and reserve auctions.

A fundamental design aspect of the integrated market is the si-multaneous pricing of energy and reserve products under trans-mission limits. At issue are not only how multiple products canbe auctioned together while considering transmission, but alsowhich optimization objectives are appropriate: should the auc-tion be conducted to a) minimize the bid cost characterized bysale bids; b) minimize total payment by buyers;, or c) maximize“social welfare” of all sellers and buyers and does using any ofthese objectives lead to the same auction results.

Even with a given optimization objective, there are dif-ferent approaches to modeling the auction as a mathematicalprogram. For many existing short-term forward wholesale elec-tricity markets, traditional optimal power flow (OPF) and/orunit commitment programs are used to explicitly determine

0885-8950/03$17.00 © 2003 IEEE

HAO AND ZHUANG: NEW MODELS FOR INTEGRATED SHORT-TERM FORWARD ELECTRICITY MARKETS 479

physical schedules, with marginal prices of production com-puted afterwards as a proxy for market clearing prices. Inorder to account for uplift charges not modeled in the pro-gram, manual adjustments to the marginal prices are oftennecessary to ensure revenue sufficiency for sellers. This ad-justment, in turn, may result in unintended consequences [3],[4].

In this paper, we will examine the current modeling andpricing aspects of short-term forward wholesale electricitymarkets, and to introduce new models suited for clearingprice-based markets. Specifically, an analysis of the impacts ofpricing rules and bidding requirements on market operations ispresented; the selection of optimization objectives in forwardmarket scheduling processes is discussed; and a new method ofmodeling transmission congestion and multiproducts auctions,such as energy and reserves, is introduced. Examples will beused where appropriate to illustrate the merits and differencesof the modeling alternatives.

II. M ODELS FOR SHORT-TERM FORWARD

ELECTRICITY MARKETS

A. Current Pricing and Scheduling Models

Conventional unit commitment and OPF algorithms havebeen the prevailing tools used in short-term forward wholesaleelectricity markets [5]–[9]. In these applications, the auctionsare formulated with a cost minimization objective over thescheduling horizon. In the market context, the cost functionsare characterized by the seller’s quantity-price bid curves. Thescheduling and pricing models used in New York ISO and PJM,for example, are combinations of unit commitment and OPFalgorithms using a multipass approach in conjunction with cer-tain pricing rules [10], [11]. After a unit commitment solution,the OPF model is to be used to adjust the physical schedulesto satisfy the transmission limits and compute the locationalmarket clearing prices. In California ISO, the day-ahead marketonly allocates transmission since scheduling coordinatorsperformed energy scheduling [12]. These markets auctionenergy and reserve products sequentially, energy first, reservesnext, with a mixture of optimization principles and heuristics.For instance, NYISO [13] determines hourly locational reserveclearing prices of three reserve products depending on whethertransmission constraints are binding between three reserveregions. First, the prices of marginal units in the three regionswere identified. Then clearing price of a region is set by oneof the marginal prices that pass a criterion: regions in whichspinning response would help the constraint will use the highermarginal price as clearing price, whereas regions in which spin-ning response would aggravate the constraint will use the lowermarginal price. On the other hand, PJM [10] differentiates theprimary and secondary reserves and use opportunity costs tocredit the reserve sellers based on daily total energy offer costs.The California ISO [12] identifies congestion regions based onthe binding constraints from energy market and then conductsregion-wide sequential auctions of five reserve products.

The common themes of these market models are the varyingdegrees of disjoint between energy and reserve product auctionsand the focus of cost minimization as the auction objective. Aswe will illustrate later, the disjoint between energy and reserve

production auctions leads to market inefficiency and the costminimization objective do not always result in minimum pay-ment from buyers.

B. Need for New Scheduling and Pricing Models

Although steady progress has been made and valuable expe-riences have been accumulated over the last decade, significantissues remain. In addition to the market inefficiency and priceimparity across sequential markets, we will discuss the impactof different auction optimization objectives on buyer payments,effects of bidding formats, and treatment of uplift charges.

1) One-Part Bid or Multipart Bids:Seller and buyer bids arethe most important data used in a market. Two common bid for-mats used in a short-term forward wholesale electricity marketare the multipart and the one-part bid formats. In a multipartbid, the bid data typically include a bid curve representing bidprice as a function of sale or buy quantity as well as in the caseof sale bid, some explicit nonquantity related costs such as gen-erating unit no-load cost and start-up cost. The one-part bid, onthe other hand, consists of only a price-quantity bid curve thatreflects not only the seller’s quantity-based pricing but also non-quantity-related costs.

For a market using multipart bids, the revenue sufficiencycondition for sellers is typically achieved in two steps. In thefirst step, conventional unit commitment algorithms are used tominimize total energy production and nonenergy-related costs.If necessary, OPF model can be used to satisfy transmissionlimits. Once this process yields the physical schedules, marginalsupply resources are identified and their marginal prices are theprices for the traded products. In the second step, depending onthe market design, the seller may be separately compensated fortheir actual non-MW-related costs or only to the extent of elimi-nating the seller’s revenue shortfall. This separate compensationfor sellers becomes an uplift charge to buyers. Some argue thatthe advantage of using multiparts bid format is that the overallcosts of schedules may be the smallest and multipart biddingformat encourages revelation of supplier costs.

The importance of bid formats goes beyond simple dataformat and revelation of operating data: it has major economicand operational consequences to the markets. With multipartbids, start-up and no-load costs are not included in marketclearing price calculation but as uplifts to buyers assessed aftermarket clearing. This leads to price distortion.

Uplifts behave like taxes that create economic inefficiency orwelfare loss. Fig. 1 explains this phenomenon. In Fig. 1,and are demand and supply bid curves. The market wascleared at the price . However, after the uplift charge is addedon, the effective price to the buyer is uplift. The welfareloss is the product of uplift rate,uplift, and the buy quantity

, and the negative welfare is the shaded portion where somebuyers are effectively paying more than their bids prices. In thelong run, buyers will have to raise their bids in order to avoidthe negative welfare’s, as indicated by the new dotted bid curve,which add the instability of the market. These shortcomings aremostly absent in markets using one-part bid.

In addition to the economic inefficiency, there have also beendebates on what seller costs should be compensated from upliftcharges. There are at least three different approaches in prac-tice or in the literature. First, all no-load and startup costs can


Fig. 1. Uplift effect on buyer’s welfare.

be treated as uplifts. Second, only the deficiency between sup-plier’s revenue and costs, if any, is treated as uplifts. In bothoptions, no-load and startup costs are completely ignored in de-riving the clearing prices. A third approach is to not use explicituplift. Instead, the market operator adjusts the market clearingprices heuristically after the optimization solution to ensure allsellers are revenue sufficient. With the first two approaches, itis difficult to set up pricing rules for buyers since the true coststo buyers are masked by the uplifts. While the third approachavoids this problem, the adjusted market clearing price may behigher than some sale bid prices without such bids being actu-ally awarded the full bid sale quantities. Consequently, manybelieve that one-part bid format enables a simpler market struc-ture and transparent prices, and should be used as the format forforward electricity markets.

2) Optimization Objectives:The prevailing use of uniformclearing pricing in short-term forward wholesale electricitymarkets implies that social welfare maximization is the in-tended objective of such markets. In this setting, the socialwelfare is the sum of the consumer surplus and supplier surplus.Perhaps due to historical reasons and transitional needs, how-ever, most of today’s solution tools for such markets are basedcost minimization models traditionally seen in a verticallyintegrated utility. Conventional unit commitment and OPFalgorithms with cost minimization have been used in electricitymarkets for determining day-ahead schedules and clearingprices [15]–[18]. As mentioned previously, some markets useboth OPF and unit commitment tools in a multipass process.

Concerning the optimization objective, an issue in debateis whether the minimization of production costs is the rightobjective. Recent studies in [1] and [15]–[18] suggest that, inreal systems, prices resulting from a cost minimizing strategymay not be the lowest possible prices. Different schedules,even with higher bid cost, may result in lower average priceor lower total payment for buyers. Such different schedulesmay be achieved, for example, with an alternative objective ofminimizing the total payment by buyers. Ideally, an efficientmarket would simultaneously minimize buyer payment and bidcost while clearing the market. In reality, however, this is notalways possible. Vazquez [17] illustrates that the differencesbetween the results of the two approaches are directly related tothe discrete nature of generating unit bid data. Vazquez reportsthat when linear models with one-part bids are used, bothobjectives lead to the same schedules; otherwise, the schedulesmay differ depending on the optimization objective. In general,it can be shown that when the payment minimization model

TABLE IPARAMETERS FOROPTIMIZATION OBJECTIVESEXAMPLE

TABLE IIRESULT OFOPTIMIZATION OBJECTIVESEXAMPLE

is convex, the solution of the model also minimizes the bidcost. In reality, this convexity requirement cannot always besatisfied. For example, in a three-part bid, the discrete nature ofno-load and startup costs would render the model nonconvex.Even an innocent looking minimum generation limit canintroduce nonconvexity. Romos also recognizes that traditionalscheduling approach might result in nonoptimal profits forsellers [18]. He introduces in the cost minimization problem arequirement that the marginal revenue must be the same as themarginal costs for resolving this issue.

To illustrate the impact of different optimization objectiveswhen the optimization model is nonconvex, let’s look at a simpleexample with three units in one hour selling energy withouttransmission constraint. The demand is 140 MWh and the biddata are shown in Table I. The price curve for the units is repre-sented as where is the energy output.

The optimization results using the two objectives are shownin Table II. Results in Table II show that buyers would pay $40more although the costs are minimized. In addition, the schedulepatterns of units are also different. Unit 2 is off from the costminimization and on from payment minimization. This is be-cause under payment minimization, the clearing price rule is im-plicitly modeled. When additional energy is needed under costminimization solution, it is cheaper to supply it from unit 3 toavoid the startup cost of unit 2. However, the higher price andpayment can offset the cost saving since, under clearing pricerule, the higher price is applied to all consumers (in this ex-ample, by the entire 140 MW).

3) Interactions and Coordination of Energy, Transmission,Reserve Products:In short-term forward wholesale electricitymarkets, energy and reserve products often compete for limitedproduction and transmission capabilities. Interactions betweenenergy and reserve products have been recognized as important


Fig. 2. Example profit under sequential solution.

Fig. 3. Example profit under optimal profit solution.

issues and should be modeled [19]. These interactions impactthe physical delivery schedules and clearing prices of the dif-ferent products in the following two ways.

First, a generating unit capable of selling both energy andreserves can substitute energy sale for reserve sale and vise versawithin its capacity. A rational seller would tend to allocate thelimited production capacity between different products so as tomaximize the seller’s profit. When these products are tradedsequentially, the seller often faces considerable uncertainty inthis allocation.

To illustrate this point, let’s examine the simple example inFigs. 2 and 3. Assuming a linear price curve for a generator withmaximum output being 10 MW and the energy market clears ata price of U.S.$ 30 per megawatt-hour and reserve at a priceof U.S.$ 5 per megawatt-hour. In a sequential (energy first, re-serve second) market, the solution will result in an energy saleat 10 MWh and reserve sale at 0 MWh, as shown in Fig. 2.On the other hand, the optimal solution in an integrated marketwhere the two products are auctioned simultaneously would be7.5-MWh energy sale and 2.5-MWh reserve sale, as shown inFig. 3. The seller profit resulting from the sequential market isU.S.$ 5 while from the integrated market is U.S.$ 7.5, as repre-sented by the shaded areas in Figs. 2 and 3. As can be observedfrom Fig. 3, the optimal solution for the integrated market resultin equal marginal profit rate for each product. In the example,the marginal profit rate for energy and reserve both equal U.S.$2.5 MWh. It is this equalization of marginal profit rates that willcontribute to the stabilization of multiproduct market prices. Forthe sequential market in this example, the marginal profit rate isU.S.$ 0 per megawatt-hour for energy and U.S.$ 5/MWh forreserve. This difference tends to drive the seller to withhold ca-pacity from the energy market for the reserve market, thus con-tributing to price instability.

The second way energy and reserve products interact arethrough the common delivery infrastructure: transmission.How the limited transmission capacity is allocated to differentproducts remains highly heuristic. In many of today’s markets,

commonly used approaches to handle the transmission-relatedinteractions are

i) ignoring transmission constraints in procuring reservesfrom ancillary service markets;

ii) preallocating transmission capacity for the separate useby energy and reserve markets;

iii) using sequential energy and reserve markets withregional or submarkets for reserves, with binding trans-mission constraints in each market defined by trades inthe previous markets.

These approaches result in varying degrees of inefficienciesin the economic use of transmission for energy and reserves.Further, the resulting locational prices of energy and reservesmay be distorted. Conceptually, an integrated model for the en-ergy and reserve markets with simultaneous energy and reserveuse of transmission would be required in order to overcome thelimitations of the heuristics and the inefficiency.

III. PAYMENT MINIMIZATION MODEL

A new formulation of computing locational energy prices thatwas motivated by the need discussed in the last section was pre-sented in [19] and [20]. This formulation inherits all of the prop-erties of the locational energy prices from the OPF. However,the formulation overcomes the shortcomings of clearing pricecomputation in conventional optimal power flow models. Thenew formulation differs from the OPF in three areas: using pay-ment minimization as the optimization objective, using marketclearing prices as control variables, and explicit representationof pricing constraints. Since prices are used as control variables,post processing for price calculation is no longer required. Addi-tional enhancements can be made by including nonquantity-re-lated seller costs and unit commitment decision variables.

A. New Model Formulation

The new model we propose is an integrated market of mul-tiple products with transmission constraints for scheduling overmultiple scheduling intervals. This model is formulated as thefollowing payment minimization problem:

Solve for to

Minimize

(1)

Subject to:

for all (2)

for all (3)

for all (4)

or for all (5)

(6)

(7)

(8)

(9)


where , over all , maximize the following seller profitfunction

(10)

and , over all , maximize the following buyer social wel-fare function

(11)

In the above, the subscripts have the following meaningswhere

index of buses;index of products or commodities;index of scheduling intervals;index of transmission lines or paths;index of generators;index of demands.

The variables and functions have the following meaningswhere

seller bid curve;bus-branch incident matrix;buyer bid curve;dc power flow network admittance matrix;transmission price;demand quantity for a product;bus demand vector for a product, whoseth component is the sum of all of

demands located at theth bus;power flow limit vector;no load and start-up costs;dc power flow branch admittance matrix;market price for a product;price vector for a product, with for all

as its components;power angle required to delivery a product;power angle vector of a product, withfor all as its components;supply quantity for a product;bus supply vector for a product, whosethcomponent is the sum of all of gen-erators located at theth bus;summation over all buses;summation over all products;summation over all scheduling intervals;summation over all demandsat bus ;summation over all generators at bus ;unit commitment decision variable.

The objective in (1) represents the total payment by buyers. Itincludes a component of purchase quantity dependent paymentand uplifts charges. Inequalities (2) and (4) represent limits onindividual variables, while inequality (3) models the fact thatmultiple product sales compete for the same limited supply ca-pacity. The transmission network model is represented by (6).Transmission flow limits are enforced by (7). Equation (8) re-lates the product clearing prices at different buses to transmis-sion prices. Expressions (10) and (11) reflect the objective ofsocial welfare maximization. Equation (9) is the familiar com-plimentary slackness condition for inequality constraints.

Compared to conventional unit commitment and OPF-basedmarket models, the new model is different mainly in theseaspects. First, the optimization objective is one that minimizestotal buyer payment as opposed to total seller cost. Second,it models an integrated multiproduct auction market withsimultaneous use of transmission by competing products.This integrated model enforces an optimal transmission uti-lization rule that is often not satisfied. This rule says thatcompetitive transmission prices for energy use should equalthe corresponding transmission prices for any reserve use.Third, it explicitly models clearing prices as control variablesrather than as a post-processing product. Finally, it explicitlyrepresents product and transmission pricing rules (8) and socialwelfare maximization objectives. When clearing prices areused as control variables, the interactions and coordinationbetween various products such as energy, ancillary service, andtransmission are directly modeled and accounted for.

The solution to the proposed formulation is a large-scale non-linear optimization problem with mixed integer variable. Al-though this paper does not prescribe the specific algorithm ofthe solution, some general observations are made. First, (10),(11), and (2) through (4) can be implemented as an inner loopsubproblem nested in an outer loop to solve the optimizationproblem. Second, since the functions and aretypically piece-wise linear functions in (10) and (11), a closedform of solution for the integral is available. Third, while theformulation ensures revenue sufficiency for all scheduled units,it does not ensure that the offline units are revenue sufficientsince an offline unit is not prevented to schedule at the solutionprices. The revenue deficiency of a supply resource resultingfrom being constrained off by the centralized schedule will haveto be recovered from the operating period when the resource iscommitted to sell power. Lastly, the applications of various nu-merical approaches such as branch-and-bound and Langrangianrelaxation to the proposed formulation remain to be tested espe-cially for a large-scale system.

B. Applications of the New Model

The new model allows flexible adaptations to practical marketsettings.

First, the integrated model allows simultaneous auction of re-serve and energy products subject to transmission constraints.Additional products and transmission constraints can be easilyadded. For example, the transmission constraints in (7) can beexpanded to limit product flow in both directions. Further, con-tingency power flow constraints can be added to reflect moreaccurately reserve use of transmission. In addition, flow con-straints can be imposed on both energy flow and the sum of en-ergy and reserve flows.

Obviously, this model can be modified to allow sequential orseparate operations of markets of energy and reserve markets.

Furthermore, this integrated model can be utilized for a de-centralized market operation. To accomplish this, we envisionthat system operators will solve for a master problem as definedin (1) through (11) using forecasted system and market data,and publishex antetransmission prices. Alternatively, historicaldemand function for transmission can be used for determiningex ante transmission prices. Givenex antetransmission prices,one or more localized short-term forward electricity markets


Fig. 4. Configuration and parameters for example 1.

can be operated independently to each other. This is achievedusing a subproblem formulation that solves for product pricesand schedules of energy and reserve given fixed transmissionprices. The model setup for the subproblem involves removingthe transmission constraint in (7) and freezing the transmissionprices .

IV. A PPLICATION EXAMPLE

Two numerical example of applying the new market modelis given in this section. The network configuration for the ex-ample is shown in Fig. 4. The bid parameter, branch parameter,energy, and capacity demands are listed in Table III. The bidprice curve is represented as where is the outputquantity limited by the maximum output . Subscriptsand are used to separate the energy from reserve variables.Furthermore, a startup cost of U.S.$ 300 and no-load cost ofU.S.$ 150 are assumed for all units. Branch between 3 and 4is a congested branch with a maximum flow of 100 MW. Forsimplicity, the demands are assumed inelastic, or constant. Theenergy and reserve demand vectors (in megawatts) are

and , respectively.The optimal solution results are shown in Tables IV and V.

Due to congestion, clearing prices differ at different location. Itis easy to verify that all generators are revenue sufficient. Animportant feature of the integrated energy and reserve model isthat the transmission allocation to energy and reserve productsis based on the values of the products. Out of the 100-MW trans-mission capacity, 6.15 MW are allocated to the reserve product,while 93.85 MW are to energy product. At the solution, bothproducts place the same value on the use of the constrained path,leading to fair and equitable allocation of the transmission ca-pacity to energy and reserve products.

Example 2 is used to illustrate the application ofex antetrans-mission price for decentralized markets. In this case, theex ante,transmission prices are determined by the market operator andpublished to all market participants, who, in turn, submit saleand buy bids for energy and reserve products. The market oper-ators then use the fixedex antetransmission prices together withthe sale and buy bid data to determine the prices and schedulesof energy and reserve products. In this example, 5–10% errorsin theex antetransmission prices were created to simulate the

TABLE IIIMARKET AND BID PARAMETERS FOREXAMPLES 1

TABLE IVPRICES AND SCHEDULES FOREXAMPLE 1

TABLE VPAYMENT RESULTS FOREXAMPLE 1


TABLE VIPRICES AND SCHEDULES FOREXAMPLE 2

TABLE VIIPAYMENT RESULTS FOREXAMPLE 2

forecasting inaccuracy. The resulting solution results are shownin Tables VI and VII.

Table VI shows that the prices and schedules determinedusing ex ante transmission prices deviate from the optimalsolution of Table IV. As can be observed from Table VII,however, the impact of using theex antetransmission priceson costs and payments is limited. The total demand paymentchanged by $25—about 0.1% in error. One notes that when thetransmission path price is higher than the optimal price, thereis less demand for the path. Likewise, when the transmissionpath price is lower than the optimal price, there is more demandfor the path. In hour 3, there is 1.11 MW overbooking due tothe 10% pricing error. In practice, these overbooking is eithertolerated or mitigated in real-time. The advantage of usingexantetransmission prices is that it provides market participantswith a degree of certainty in transmission prices.

V. SUMMARY

To facilitate efficient and competitive operation of short-termforward wholesale electricity markets, adequate pricing andscheduling models are required. This paper examines keyaspects of these models: the interaction between energy and re-serve products, the pros and cons of multipart and one-part bidsand the impact of optimization objectives. A new integratedmarket model with simultaneous energy and reserve auctionand transmission use was introduced.

The new model accounts for the interactions coordinationbetween energy and reserve products. It can be easily expandedto allow other products and transmission constraint undervarying market conditions, including sequential markets ormarkets usingex antetransmission prices.

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Shangyou Haoreceived the B.S. degree from Wuhan Institute of Hydraulicand Electrical Engineering, China, in 1982, and the M.S. and Ph.D. degrees inelectrical engineering from Ohio State University, Columbus, in 1984 and 1988,respectively.

He was with the Pacific Gas and Electric Company, San Francisco, CA, from1988 to 1997, working on development of analytical methodologies for Cali-fornia electricity industry restructuring. He was with Perot Systems Corporationfrom 1997 to 2002, developing information system and business process for theCalifornia ISO and Power Exchange.

Fulin Zhuang received the B.S. degree from Shanghai Jiao Tong University,China, the M.S. Eng. degree from the University of New Brunswick, Canada,and the Ph.D. degree in engineering from McGill University, Montreal, QC,Canada.

Currently, he is with Deloitte & Touche, Los Angeles, CA. He was a sys-tems engineer and supervising transmission planning engineer at Pacific Gasand Electric Company, San Francisco, CA, from 1989 through 1998. He joinedPerot Systems Corporation, Plano, TX, in 1999 and worked on application de-velopment projects at California Power Exchange, Alhambra, CA, and otherenergy market analysis and solution consulting projects.

new models for integrated short-term forward electricity markets

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