BUSINESS INTELLIGENCE USING INFORMATION GAP DECISION THEORY AND DATA MINING APPROACH IN COMPETITIVE BIDDING

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1 1 BUSINESS INTELLIGENCE USING INFORMATION GAP DECISION THEORY AND DATA MINING APPROACH IN COMPETITIVE BIDDING Me-Peng Cheong Gerald B. Sheblé Danel Berleant ABSTRACT Snce the nnetes, many electrc utltes and power networ companes have undergone and are stll experencng dynamc change n the ways of dong busness, from a vertcally ntegrated ndustry to an open maret system. The operatonal plannng actvty of a generaton company (GenCo) s no longer a cost-mnmzng process, but sees to maxmze ts net proft subject to physcal constrants and maret factors. The objectve of ths research s to develop a strategc bddng decson-mang unt that not only consders the techncal aspects of unt operaton such as capacty lmts but also ncorporates nformaton about other maret partcpants and the volatlty of the maret prces. These addtonal maret factors are sgnfcant n such an olgopoly maret because they nfluence the amount of electrcty sold and purchased, hence affectng the net proft ganed. Ths project proposes an economc model that attempts to data mne the avalable hstorcal and current maret data n a determnstc two-maret-partcpant envronment. Further stochastc analyss s performed usng the nformaton gap decson theory concept to quantfy the uncertanty that arses. The data mnng approach can also be justfed for nformaton acquston to reduce uncertanty, hence mprovng the nformaton gap model. INTRODUCTION Tradtonally, the electrc power ndustry was domnated by large utltes that manage overall actvtes n generaton, transmsson, and dstrbuton of power. The economc ncentves to provde cheaper and relable electrcty as well as to encourage effcent capacty expanson and nvestment plannng have opened up the opton to ntroduce competton n the electrcty sector. To date, almost half of the states n North Amerca are ether fully deregulated or n the transton stages, whle others are n

2 2 the applcaton process 1. The restructurng process has ntroduced ncreased competton and most GenCos no longer employ the conventonal unt commtment and economc dspatch technques to produce the optmal prce-quantty bds. Instead, GenCo s now faced wth a compettve strategc bddng envronment at a hgher uncertanty level snce every maret player has nformaton only about ts own producton actvtes and some publcly avalable nformaton such as maret clearng electrcty prces and fuel prces. In ths compettve maret mechansm, the behavor of each maret partcpant affects but does not control the maret, hence leadng to an olgopoly maret where the maret s not perfectly compettve. Maret players are faced wth uncertantes n whch electrcty can now be consdered a type commodty and ts prces are determned by maret forces. Every decson made by the maret players s dependent on factors that can be descrbed by Porter s fve forces. In ths framewor, Mchael Porter llustrates the relatonshp between compettors wthn an ndustry, potental compettors, supplers, and buyers. The fve forces are barrers to entry, rvalry among exstng compettors, product substtutes, maret power of buyers, and maret power of supplers. Optmal bddng strateges can be formulated n several ways dependng on what type of nformaton s avalable and accessble. Often tmes, GenCo models ts bddng strategy wth the ad of forecastng tools that estmate the maret-clearng prce (MCP) of the maret n the next tradng perod based on hstorcal fluctuatons n prces. A more complcated model wll try to nclude the behavor of the compettors n an attempt to outperform ther rvals. The followng sectons begn wth the data mnng approach that analyzes the behavor of the compettors polces or strateges n bddng followed by the nformaton gap decson concept to quantfy uncertantes for the dependent nput varables n the bddng model. DATA MINING Data mnng refers to the process of transformng collected raw data nto usable nformaton. Although data n ts raw form s of lmted use, t can be manpulated to realze ts potental use. Raw data can be aggregated and analyzed, together wth heurstc nowledge about the nature of the problem, provdng sgnfcant nformaton that can be acted upon n mang nformed decsons. Ths secton explans the data mnng process wth a determnstc model. The organzaton of the data mnng process comprses the forward and bacward process. The forward process ams to provde an optmal bddng strategy for GenCos (producers) that ncludes not only the physcal constrants but the 1 Source: Energy Informaton Admnstraton (EIA) as of February, 2003.

3 3 demand sde as well. Ths model generates a bd-quantty seres as the optmal decson wth the gven nformaton and the nherent structure of the model. The bacward process ams to use the output of the forward process to reverse the bddng strateges employed. The basc nformaton on the maret structure ncludes, but s not lmted to, the followng: have avalable data on system outages and forecasted loads; loads bd n hourly fashon; forecasted load s avalable n the day-ahead maret; supplers bd n mnmum generaton blocs and ncremental energy blocs wth ncreasng costs; hourly prces, loads commtted, and generaton bds are posted. The Forward Process The fundamental objectve n the forward process s to be able to generate the approprate prcequantty bddng curve wth respect to maret movements such as the prce of electrcty and fuel. In the real maret, prce and quantty are determned by the maret forces, n partcular the demand and supply for electrcty. MCP depends on fuel prce, heat rate curve (to calculate fuel cost), varable cost, operatng and mantenance cost, wheelng cost, new equpment nstallaton, future cost evoluton, demand varaton, and other economc and cost consderatons. In our project, we develop a model that conssts of the followng two components: SUPPLY: proft-maxmzng compettve producers or utlty companes (generaton companes) DEMAND: prce-tang cost-mnmzng consumers In the SUPPLY model, the fuel prce s assumed to be gven and each suppler s maxmzng proft wth the followng objectve functon: MAXIMIZE Proft = Revenue Cost Revenue orgnates from spot maret sell and blateral power sell, and cost s represented as payments for spot maret buy, unt operatng costs, startup costs, and shut down costs. MAXπ = [ ρs q( sell) + q( contract ) ρc ρs q( buy) { w, c(mn) + qg, gc + ust, st + usd, ρ, q() NG = 1 sd }] Where: ρ s, ρ c Spot maret prce and blateral contract prce for tme perod q ( ) Amount of power sold, contracted, or bought for tme perod w, ust,, usd,, Bnary varables for unt status (1=ON/startup/startup, 0=OFF/No startup/no

4 4 c(mn) shutdown) for tme perod for duraton Cost of mnmum generaton for duraton qg, Amount of power generated n addton to mnmum generaton for tme perod for duraton gc Generaton cost beyond mnmum generaton cost for duraton st, sd Startup and shutdown costs Frst of all, we generate a brea-even bd curve by excludng the hedgng component of the equaton. Revenue ( ρ s, q ( sell ) ) = Cost ( c(mn), qg, gc,, ust,, st, usd,, sd, ) In addton to the quantty sold, we need to consder that there s a fxed payment or mnmum payment charged to guarantee future flow of the commodty (electrcty) sold. Ths fxed payment can be treated as a means to recover fxed cost n the long run. Ths fxed payment s assumed to recapture the mnmum generaton and startup and shutdown costs. Deleted the followng bracet at the end R fxed, + ρ q( sell) = { w, c(mn) + qg, gc + ust, st + usd, s N = 1 sd } where R fxed, = w, c(mn) + ust, st + usd, sd The generaton cost curve should nclude the prce of fuel (gas) and the average heat rate (AHR) curve of the generatng unt. The ρ g n the followng equaton represents the prce of gas for tme perod and the AHR curve s obtaned from the nput-output (IO) curve averaged over the quantty of power generated. gc = ρ g AHR where TQ = q 2 + q + 18 AHR = TQ q 18 = q + 1+ q The updated revenue equals cost equaton:

5 5 B( q) q( sell) = qg ρ, g qg, qg, In ths equaton, ρ s has been replaced wth B q) ( because we want to fnd the relatonshp between the bd prce and the generaton level qg, for tme perod. The spot maret prce s the prce pad, and bds submtted may or may not be accepted. We also now that q sell) qg, ( = (gnorng the hedgng component) and hence our brea-even bd curve can be represented by: B( q) = ρ g qg, qg, Assumng that the prce of fuel s gven, we can produce a brea-even bddng curve for the suppler. We would then nclude the maxmum proft bd curve by fndng the frst-order-condton for the proft functon. The resultng bddng curve s shown n Fgure 1. Bd ($/ MWh) Brea-Even Max Prof t Generat on Level ( MWh) Fgure 1. The maxmum proft and brea-even bd at each generaton level. The maxmum proft s obtaned by usng the forecasted electrcty prce that maxmzes our proft. The brea-even curve s found by the equaton derved above and s dependent on the natural gas prces. Therefore, we have a range of bds at each cross secton of the generaton level. The amount to bd depends on the rs profle of the GenCo, and later sectons wll explan how to quantfy uncertanty n determnng the prce-quantty bd.

6 6 The Inducton Procedure As mentoned n the earler secton, data mnng sees to dscover hdden patterns that can nform the analyst about the strategy or types of generatng unt used. The frst data mnng approach used n ths research s the rule or decson tree nducton to deduce the pattern dscovered from the data. It produces patterns that relate to the bddng decson made or other data felds (attrbutes). The resultng patterns are typcally generated as a tree wth splts on data felds and termnal ponts (leafs). In order to study the bddng behavor of a suppler, we frst use ths rule nducton to separate the actve (when bd s submtted) bd-quantty-prce group from the passve (when no bds are submtted) group. The algorthm used for the decson tree nducton s the standard C4.5 algorthm [1,2]. Smlar to ts predecessor, the ID3 algorthm, C4.5 s a top down nducton of decson tree that employs the dvde and conquer concept. However, to select the best splttng attrbute, t uses the hghest nformaton gan rato 2 based on the entropy formula to generate decson tree. The optmal splttng attrbute chosen s the attrbute that results n the smallest tree. The general steps for C4.5 are as follows: (1) Attrbute s selected for root node and branch s created for each possble attrbute; (2) The nstances are splt nto subsets (one for each branch extendng from the node); (3) Procedure s repeated recursvely for each branch, usng only nstances that reach the branch; (4) Procedure stops when all nstances have the same class. It nfers decson tree from the tranng set to convert the learned tree nto an equvalent set of rules. We have developed a basc forward process and used the Java program (Wea3.2) to run C4.5 on the data generated by the forward process. The frst rule nducton process yelds the followng smple result shown n Fgure 2. Electrcty Prce Prce > $39 Prce $39 BID BID Fgure 2. The nduced decson tree based on the data generated from the forward process. Smple as t seems to be, ths s a strong result n that ths rule matches all the data generated from the forward process. From the compettor s vewpont, t may only rely on the forecasted electrcty prce to determne whether we, as GenCo 1, wll bd or not and adjust ts bd accordngly. However, ths set of data may over-ft the algorthm and thus more data should be used to verfy ths decson tree. Moreover, 2 Informaton gan rato s used to compensate for the number of attrbutes by normalzng the nformaton encoded n the splt tself snce the nformaton gan formula gnores the number of regons used, hence may lead to bas and over-fttng problem.

7 7 we cannot conclude that the fuel prce s nsgnfcant when t comes to bddng decson. Ths nducton process wll be extended to nclude other maret factors, such as the fuel prces and maret demand, to dscover the prce sgnals that are used to nfer the strateges employed by other maret partcpants. Snce electrcty prces, fuel prces, and other maret varables are fuzzy or uncertan, we wll next descrbe a model that helps to quantfy uncertanty n decson mang. USING INFORMATION GAP THEORY TO QUANTIFY UNCERTAINTY Informaton gap theory [3] s useful for mang decsons n cases where uncertanty s present and severe. We have developed an nfo-gap model based on the bddng model descrbed n Reference [4]. Informaton gap theory handles dstrbutons that may not be fully specfed, such as n Fgures 3a 3b. (a) GenCo 2 cost functon F 2A for G 2A. (b) GenCo 2 cost functon F 2B for G 2B. Fgure 3. The cost functons wth respect to bds for the two generators of GenCo 2. Ths problem s formulated wth two generaton companes GenCo 1 and a compettor, GenCo 2. Both GenCos are competng to sell X D megawatt-hours (MWh) of electrc energy. GenCo 1 attempts to model GenCo 2 to determne a bd for an amount and a prce that wll serve ts proft-mang nterests. Suppose that we wsh to ensure that the expected monetary value (EMV) of a bd (correspondng to the expected proft) meets or exceeds a gven mnmum value. An nformaton gap model helps to dentfy bds that meet that requrement and the uncertanty-reducng nformaton needed to ensure that other, possbly more desrable, bds meet that requrement. An example of such a potentally more desrable bd would be one that corresponds to a wde range of possble EMV values, some qute hgh and desrable and others below a mnmum tolerable EMV. For example, n Fgure 4, the bdder may enjoy a hgh EMV of 74200, at a bd of $145/MWh, but that bd may also result n an EMV of f the true

8 8 curve happens to be the lowest EMV curve shown. Fgure 4. A wde range of possble EMV values for a gven bd. Fgure 5. EMV curves correspondng to the left envelope (lowest curve), the rght envelope (hghest curve), and the horzontal average envelope of Fgure 6. An nformaton gap model for ths example problem may be specfed as follows. 1. Decson varable. Ths s our bd B 2 n $/MWh. 2. Uncertan varable. Defne a cumulatve dstrbuton functon (CDF) for the compettor s bd that serves n the role of nomnal best guess. Any CDF judged to fll ths role could be used. For purposes of llustraton we use horzontal averagng of the left and rght CDF envelopes of Fgure 3b, gvng the ntermedate curve of Fgure 6. In horzontal averagng, for each vertcal axs value y, the correspondng horzontal axs values of the left envelope, B l, and of the rght envelope, B r, are averaged, gvng a value B =(B l +B r )/2. The pont (B, y ) s on the average CDF curve, whch may be plotted as precsely as desred by usng an approprate set of values for. The average CDF serves as a nomnal best guess CDF. Accountng for weghts generalzes the averagng formula to B =(wb l +(1-w)B r )/2. Let the uncertan varable n the nfo-gap model be the weght w of the left envelope, wth the weght of the rght envelope then beng 1-w. Then Fgure 5 descrbes the EMV values calculated from the CDF envelopes of Fgures 3b and Nomnal value of uncertan varable. There seems to be no partcular reason to prefer weghtng one envelope more than the other when dong horzontal averagng, so the default nomnal value of weght w s w ~ = Uncertanty parameter. The amount of uncertanty n the model, α, s the amount of devaton from the nomnal value of the uncertan varable that s to be consdered. In ths model, that s the amount of devaton from w ~ =0.5. In the worst case, ths mght be ±0.5, gvng a range of weghts from 0 to 1. Determnng ths s the goal of the nformaton gap analyss.

9 9 5. Uncertanty model. Ths s the functon u(α, w ~ ) that descrbes the amount of uncertanty n the uncertan varable w n terms of ts nomnal value w ~ and uncertanty parameter α. Consstent wth ponts 2 4 above, we have u (α, w ~ )={w: w w ~ + α }. 6. Reward functon. The reward s the EMV of a bd. It s determned by the bd value and the EMV curve that apples. In ths problem, the EMV curve s uncertan, so the worst possble EMV curve s used to allow the reward functon to provde the mnmum EMV that the bd could be assocated wth, as requred by the nfo-gap analyss. The worst possble EMV curve s n turn determned by the leftmost possble CDF curve for the compettor s bd. Ths curve s found by horzontal averagng wth an averagng weght of w ~ + α. Usng ths curve s consstent wth the ultmate goal of desgnng the bd and any necessary nformaton-seeng actvtes to ensure at least a mnmum EMV. Thus reward functon R s defned by R( B j, w) = EMV ( B j, w F B ( B j ) + (1 w) F2 ( B )) 2 B j Where F B ) s the hghest possble envelope around the functon F 2B (.e., the left envelope n 2 ( B2 Fgure 3b), and ) s the correspondng lowest possble envelope (.e., the rght envelope). F2 B ( B2 7. Crtcal reward. Ths s the mnmum acceptable value of the reward functon, call t r c. The results of an nformaton gap analyss dffer dependng on the value assgned to r c,. 8. Robustness functon. Ths functon, ˆ α ( b, r ), returns the greatest value of uncertanty parameter α c for whch fallng below the crtcal reward r c s not possble n the model. It therefore measures the ablty of the model to delver an acceptable reward n the presence of uncertanty, hence the term robustness. Its value s therefore dependent on acceptable reward r c. It s also dependent on the bd B 2, because the reward s dependent on B 2. Fgure 6. Best-guess curve between the left and rght envelopes computed by horzontal averagng and the maxmum uncertanty α, showng that the space of plausble curves s wthn the envelopes. Fgure 7. Crtcal reward separates the EMV curves nto regons.

10 10 Fgure 7 gves nformaton about ˆ α ( b, r ) for a range of bd values, and a specfc value of r c, whch would c be a busness decson provded as a model nput. For bd values toward the left of Fgure 7 (denoted as regon X ), the EMV s above r c regardless of whch EMV curve s consdered, so r c wll be safely met for any of those bds. However t may be desrable to consder bddng hgher n order to reap the potental opportunty for greater gan due to potentally hgher EMV values such as, for example, the pea feasble EMV of $146.25/MWh for regon Y. Ths s smply an analytcal elaboraton of the ntuton that the hgher the bd the greater the proft, f the bd s successful, but the hgher the chance that a compettor wll undercut the bd resultng n no proft. Thus, bds n the range desgnated by Y n Fgure 7 are not guaranteed to have an EMV of at least r c unless new nformaton s obtaned that rules out values of w that are too close to 0 (thereby movng the worst-case EMV curve upward). The result of an nformaton gap analyss s a valdaton (or nvaldaton) of a bd value based on whether ts EMV meets mnmal requrements. However, the analyss does not tell us what the best bd s. In Reference [4], we presented a dscusson on the dfferent decson crtera used to determne the bd such as maxmzng worst-case EMVs, maxmzng expected EMVs, and convertng EMVs to utltes usng rs profles. Another approach s to see nformaton by usng the data mnng technques to reduce the uncertanty n the model. However acquston of nformaton requres an expendture of resources. Unless the new nformaton leads us to a more nformatve and robust nfo-gap model u new, whch s a subset of u(α, w ~ )={w: w w ~ + α } mentoned earler, the acquston of nformaton s of no value added to our model. CONCLUSIONS Ths research shows that data mnng usng an evolutonary technque can be used to nfer rvals strategy. Based on avalable maret nformaton, one can develop algorthms to deduce the polcy employed by compettors. More wor wll be mplemented to nclude the forecast of maret varables, such as prces. However, not all nformaton s free and the acquston cost of nformaton vares. A support tool such as the nformaton gap theory can assst n quantfyng severe uncertanty when nformaton s scarce and expensve. It helps decson maers to develop preferences, assess rss and opportuntes, and see nformaton, gven a mnmum requred level of reward. Ths mnmum level of reward could be determned by ncorporatng rs management methodologes such as value at rs or proft at rs. Understandng how to balance the cost of new nformaton wth ts benefts s an mportant next step.

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