Exhibit 99.468 CLEARING PRICES COMPUTATION FOR INTEGRATED GENERATION, RESERVE AND TRANSMISSION MARKETS Shangyou Hao Dariush Shirmohammadi Perot Systems Corporation Los Angeles, CA, USA Abstract: In a competitive electricity market, trading and scheduling for electric energy, transmission and reserve related services are often the centerpieces of market functions. The operation of these three markets may reside in centralized pools, system operators or power exchanges. However, they are often conducted separately and sequentially in practice. This paper sets forth a new formulation to determine schedules and clearing prices for integrated electric energy, transmission and reserve markets simultaneously. The formulation yields locational market clearing prices when transmission congestion is present. Example results based on the new formulation are presented. I. INTRODUCTION Complex interactions between daily generation schedules, transmission constraints and reserve requirements need to be accounted for in determining schedules and clearing prices of a competitive electricity market. The delivery of electric energy is not possible without the use of transmission system and capacity reserves. In many established electricity markets energy scheduling, transmission congestion and reserve management are decomposed into component products, allowing these products to be traded or scheduled in centralized power pools, system operators or power exchanges. However, these component products are often traded and scheduled separately and sequentially in practice. For example, in the California [1], day-ahead energy schedules are determined by Scheduling Coordinators; Transmission congestion is managed by the Independent System Operator (ISO); and unloaded capacities along with capacity price bids are then submitted into regulation, spinning, non-spinning and replacement reserve markets. Each market is independently priced and scheduled at different time. Similar arrangements exist in the electricity markets of New York [2], PJM [3] and others around the world. In the power pool of England and Wales, dispatch orders and prices for energy are determined using unconstrained system marginal price that is set at the highest offer price of generating units being [4]. However, when transmission constraints are detected, constrained dispatch program is executed and schedules are adjusted. The rescheduling costs are then charged to consumers as transmission service uplift. Many have studied formulations and algorithms of generation scheduling and pricing methodologies. Ma[5] reviewed different dispatch algorithms such as merit order dispatch, sequential and joint dispatch of energy and reserve. He proposed a joint dispatch algorithm that minimized costs and incorporates several zonal interface constraints to account for inter-zonal trading. Hybrid method of solving for multi-commodity schedules is investigated by Cheung [6] for the interim ISO New England. Post [7] investigated how energy schedules can be determined by a central power pool to minimize total generation costs while individual bidders construct their bids to maximize profits. Guan [8] discussed the limitation of using ramp rates in Unit Commitment algorithm and proposed a concept of realizable schedules. Auction design and schedule issues related to using different objectives were studied in [9]. Sheble [10] proposed a framework for coordinating financial and physical electricity markets. In [11], Cadwalader recognized the need for security-constrained, economic dispatch methodologies for computing market equilibrium of these component markets. He pointed out that pricing is the integral part of the market equilibrium along with he schedules that maximize the bidders' profits or utility. However, in the proposed formulation, clearing prices are still the by-products of an OPF cost minimization problem and derived from the dual variables of the solution. Chattopadhyay [12] discussed the modeling requirement for price based generation scheduling and examined the importance to add transmission constraints in scheduling energy and reserves. The formulations studied so far are based on variations of unit commitment of OPF models. While traditional unit commitment or dispatch techniques can be used to minimize bidding costs, locational clearing prices for generation capacity and transmission are difficult to compute. On the other hand, while OPF techniques have been deployed to compute transmission prices, it has difficulties for scheduling reserves and enforcing clearing pricing rules. Our objective is to set forth a new formulation that solves for schedules and clearing prices for electric energy, transmission and reserve capacity markets simultaneously. This should lead to better economic efficiency and reduced transaction costs due to the integration of the component markets and simplification of market processes. The paper has five main sections. After the introduction, Section II lists the notations used in this paper. The proposed 1 formulation is described in detail in Section III. We will also discuss the features and properties of the new formulation. Section IV presents application examples. Section V contains a summary of the paper. II. NOTATIONS K: Number of generators. X: Generation energy output vector, dim(X) =K. Y: Generation reserve capacity vector, dim(Y) =K. C: Bidding price (function of X and Y) vector, dim(C) =K. Qmax: Maximum generation vector, dim(Qmax) =K N: Number of buses in the network model. M: Number of branches in the network model. Ox: Voltage angle vector due to energy schedule only, dim(0) =N. Oy: Voltage angle vector due to reserve use, dim(Oy) =N. Dx: Energy demand vector, dim(Dx) =N. Dy: Reserve demand vector, dim(Dy) =N. Px: Energy clearing price vector at each bus, dim(Px) =N. Py: Reserve capacity clearing price at each bus, dim(Py) =N. Px(b): Energy clearing price for generators, dim(Px(b)) =K. Py(b): Reserve capacity clearing price for generators, dim(Py(b)) =K. Fx: Branch flow vector due to energy schedule only, dim(Fx) =M. Fy: Branch flow vector due to reserve schedule only, dim(Fy) =M. Fxy: Branch flow vector due to both energy schedule and reserve used, dim(F(xy) =M. Fmax: Branch flow maximum limit vector, dim(Fmax) =M. Bx: Branch congestion cost vector of energy schedule, dim(Bx) =M. By: Branch congestion cost vector of reserve schedule, dim(By) =M. B: DC network admittance matrix (symmetric) ignoring branch resistance, dim(B) =NxN. A Network incidence matrix, dim(A) =NxM. I: Diagonal matrix with diagonal elements being the reciprocal of branch admittance, dim(IB) =MxM. J: Indices for identifying balanced generation and demand resources. III. FORMULATION A. Market Structures Various pricing and scheduling rules have been developed in order to address unique issues facing each market. However, there are some common attributes for the established electricity markets. To set up our new formulation, we make a few assumptions about the market structures used in this paper. These assumptions are intended to elaborate the proposed algorithm and solution; however, the algorithm and solution are not necessarily limited by the assumptions. Specifically, we consider the following market rules: - One reserve market is assumed and the impact of ramp rate is ignored. - The DC transmission system model is uded and the B matrix is symmetric (no phase shifters). - No double auction is considered for simplicity. This means that demands are treated as inelastic. - Schedules of different time periods are independently calculated. This means that hourly generation schedules are determined independently. - Both the energy and capacity demands are know. - Market operators are payment neutral. This means that the net payment is zero for market operators. The congestion related network surplus, if any, is paid to transmission owners. - Clearing prices principles apply to the markets. When there is no congestion, uniform clearing prices are used for all bidders. We assume that bidders submit to the market operator a monotonically increasing and non-negative price curve as a function of output quantity. This curve specifies the minimum price that the bidders will accept for the unit to operate at that level. The curve will also be used by the market operator to schedule reserve capacity and to compute reserve clearing prices. Further, the energy payment from the reserved capacity, when being called upon during real-time operation, will be equal to or more than that of the forward energy clearing prices. As shown in Figure 1, a generator can potentially receive three payments:forward energy, reserved capacity and real-time energy if being called. For a marginal unit whose forward energy schedule is x, total schedule is x+y, and real-time instructed output is z, the three payments are represented by areas of OECX, ABCD and CGZX, respectively. [GRAPH] B. Proposed Formulation 2 The proposed formulation is a minimization problem as follows: Solve for P(x1) P(y1) X(1) Y(3) 0(x3) B(x) and B(y) that Minimize (P(x1) D(z) + P(y1) D(y)) (1) Subject to: B 0(z) = X - D(z) (2) B 0(y) = Y - D(y) (3) 0(z1) = 0 (4) 0(y1) = 0 (5) X(1) Y(1) P(x1) P(y), B(x3) B(y) > 0 (6) - F(0(x)) - I(B) A(t) 0(z) [ILLEGIBLE] (7) F(0(z)+0(y)) = I(B) A(1) [ILLEGIBLE] F(max) (8) C(X) [ILLEGIBLE] (9) C(X+[ILLEGIBLE]C(X) [ILLEGIBLE] (10) X + Y [ILLEGIBLE] (11) B P(z) - [ILLEGIBLE] B(z) = 0 (12) B P(y) - A[ILLEGIBLE] = 0 (13) E(kcj(k)) (x(k) - d(k)) = 0 (optional) (14) E(kcj(k)) (y(k) - a(k)) = 0 (optional) (15) C. Discussions 1. Objective The objective in (1) represents the total payment by consumers. This payment is computed as the inner product of the demand vectors with the clearing price vectors. The same clearing prices are used to pay suppliers and charge consumers. Consequently, the total payment from consumers is the same as the payment credited to generators when transmission congestion is not present. The use of total consumer payment minimization tends to reduce both generation payment and transmission congestion costs. 2. Constraints The DC network model for the transmission system is represented by (2) and (3) which describe network balance for energy and reserve capacity schedules, respectively. Voltage angels of reference bus are set using (4) and (5). Eq.(6) ensures that all price and schedule variables are positive. Transmission branch flow limits are enforced by (7) and (8). These limits are applicable to both energy schedules and total schedules (energy and reserve). For simplicity, we assume flow direction is known and flow constraints are not bi-directional. Behaviors of profit maximizing bidders are modeled by (9) and (10). These constraints ensure that the energy and reserve clearing prices are no less than their bids. Consequently, all generators are sufficiently compensated with the final clearing prices. Eq.(11) is used to enforce generation output limit. We use (12) and (13) as network price constraints. They are critically important in that they link the clearing prices at different buses to satisfy the network surplus requirements. Network surplus is defined as the difference of total payment received from demand users and credited for suppliers. When there is no transmission congestion, constraints (12) and (13) will ensure that the clearing prices at all buses are identical and the network surplus is zero. If B(x)=0, (12) becomes: B P(x)=0 The rank of B admittance matrix in n-1. Thus the solution for P(x) must lie in the null space of B. Using the property of B matrix, we can obtain: P(x) = p [1,1,1, ...1](t) (16) Where p is a scalar. Hence, all clearing prices are identical. Without these constraints, the solution can lead to different clearing prices when there is no transmission congestion. When transmission lines are constrained, we will show later that network surplus is maintained and market operator receives adequate revenue from the resulting clearing prices. The motivation for introducing the network price constraints stems from the solution process used in traditional OPF formulation. The gradient vector of Langrangian with respect to the bus angel yields the necessary optimality condition to an OPF problem. This condition is the basis of locational marginal prices in the OPF formulation and sets forth many desired properties between the locational prices and branch congestion prices. In order to inherit these desired properties for the computed prices, we therefore impose this optimality condition in the original OPF problem as the new network price constraints. Eqs. (14) and (15) are optional market separation constraints. These constraints, if enforced, ensures that a set of energy schedules or capacity reserves are balanced for market participants. These can be used in modeling bilateral trading arrangement. In California and Texas, for example, energy schedules for each scheduling coordinator must be balanced. Additional constraints can be incorporated to deal with the requirements of specific market rules. For instance, when a unit participants only in the reserve or energy market, the energy variable (x) or reserve variable (y) can be constrained to be zero. D. Properties of the New Formulation 3 PRICE CLARITY AND SIMPLICITY: The explicit use of pricing variables provides price clarity to markets. With the traditional method of scheduling, prices are often computed as the by-products of the solution process. In contrast, the new formulation uses prices as control variables for scheduling and no separate process is needed for clearing price computation. With these prices, each bidder's profit is maximized. In addition, opportunity costs are often needed for compensation for redispatched or constrained generators by market operators. Use of opportunity costs has been very controversial and often adds to price ambiguity. With the new formulation, there is no need for computing these opportunity costs. COMPETITION FOR TRANSMISSION USAGE: The formulation allocates transmission to energy and reserve use according to the economic bid data rather than heuristics. Therefore, market operators no longer need to guess the amount of transmission that sets aside for reserve use. REDUCED TRANSACTIONS COSTS: A large amount of transactional costs are incurred for market participants and operators as the process of market operations becomes more complex. With this formulation, transactions for market operators and participants are straightforward and associated transaction costs can be reduced. For instance, market participants need only submit one bid curve for all three markets, thus simplifying the data processing and management. Furthermore, iterations between the constrained and unconstrained market prices can be eliminated. MODELING OF DISTRIBUTED RESERVE REQUIREMENT: The proposed formulation allows modeling of the distributed reserve requirements at different locations. Although the reserve requirements are often proportional to energy demand, there are cases that some areas may have more reserve requirements. GENERATOR PAYMENT ADEQUACY: The total payment received by any generator is equal to or more than its costs computed using its bid curve. Since on-marginal units are paid at higher clearing prices, it suffices to show that marginal units can fully recover their bidding costs. As shown earlier in Figure 1, the total payment credited to the marginal unit is represented by areas of OECX, ABCD and CGZX, and is greater than its bidding cost (area OCFZ). NETWORK SURPLUS ADEQUACY LEMMA: The network surplus is always positive and is exactly the sum of branch congestion prices multiplied by their flows. PROOF: Taking the inner product of (2) with Px leads to: [FORMULA OMITTED] (17) Substituting (12) into (17), [FORMULA OMITTED] (18) Substituting (7) into illegible [FORMULA OMITTED] (19) Similarly, we can show: [FORMULA OMITTED] (20) COROLLARY: When there is no congestion, the total consumer payment is the same as that total payment credited to generators. This can be derived by setting Bx=O and By=O in the above lemma. IV. APPLICATIONS This section presents numerical results of applying the new formulation for computing clearing prices and schedules for integrated electricity markets. The looped network used by the example is shown in Figure 2. The network has 3 buses and 5 generators. For simplicity, all three branches have equal impedances. The bid price curve is represented as co + c1*q where q is the output quantity. The bid parameter, energy and capacity demands used in the example are listed in Tables 1 and 2. Table 3 shows 5 result sets with different demand and network parameters. The parameter changes from the base case are in bold fonts. These results are discussed below. No market separation constraints are applied in the example. [GRAPH] 4 Table 3: Example Results DESCRIPTION BASE CASE CASE A CASE B CASE C CASE D - ---------------------------------------------------------------------------------------------------------------------------- Energy price at Bus 1 (Ps1) 27.5325 26.5185 27.6481 27.5325 27.6481 Energy price at Bus 2 (Ps2) 27.5325 27.7778 28.4722 27.5325 28.4722 Energy price at Bus 3 (Ps3) 27.5325 29.0370 29.2963 27.5325 29.2963 Reserve price at Bus 1 (Py1) 0.7792 0.6704 0.6704 1.0823 0.3741 Reserve price at Bus 2 (Px2) 0.7792 0.8056 0.8056 1.1898 1.3611 Reserve price at Bus 3 (Py3) 0.7792 0.9407 0.9407 1.2972 2.3481 Energy schedule of Unit 1 (X1) 30.0000 30.0000 30.0000 30.0000 30.0000 Energy schedule of Unit 2 (X2) 37.6623 32.5926 38.2407 37.6623 38.2407 Energy schedule of Unit 3 (X3) 18.4416 19.2593 21.5741 18.4416 21.5741 Energy schedule of Unit 4 (X4) 5.0649 5.5556 6.9444 5.0649 6.9444 Energy schedule of Unit 5 (X5) 8.8312 12.5926 13.2407 8.8312 13.2407 Reserve schedule of Unit 1 (Y1) 0.0000 0.0000 0.0000 0.0000 0.0000 Reserve schedule of Unit 2 (Y2) 3.8961 3.3519 3.3519 5.4117 1.8704 Reserve schedule of Unit 3 (Y3) 2.5974 2.6852 2.6852 3.9658 4.5370 Reserve schedule of Unit 4 (Y4) 1.5584 1.6111 1.6111 2.3795 2.7222 Reserve schedule of Unit 5 (Y5) 1.9481 2.3519 2.3519 3.2429 5.8704 Energy demand at Bus 3 (D3) 50.0000 50.0000 60.0000 50.0000 60.0000 Reserve requirements at Bus 3 (A3) 3.0000 3.0000 3.0000 8.0000 8.0000 Energy branch flow from 1 to 2 (Fx2) 14.7186 12.5926 13.2407 14.7186 13.2407 Energy branch flow from 2 to 3 (Fx2) 13.2251 12.4074 16.7593 13.2251 16.7593 Energy branch flow from 1 to 3 (Fx3) 27.9437 25.0000 30.0000 27.9437 30.0000 Reserve use from 1 to 3 (Fx3) 0.3160 0.0000 0.0000 2.0563 0.0000 Flow limit from 1 to 3 (Fmax3) 30.0000 25.0000 30.0000 30.0000 30.0000 Congested branch energy cost (Bx3) 0.0000 3.7778 2.4722 0.0000 2.4722 Congested branch Reserve cost (Bx3) 0.0000 0.4056 0.4056 0.3222 2.9611 Energy network surplus 0.0000 94.4444 74.1667 0.0000 74.1667 Capacity network surplus 0.0000 0.0000 0.0000 0.6626 0.0000 Total consumer payment 2761.0390 2817.1796 3168.7074 2771.5227 3185.1519 In Base Case, transmission constraints are inactive, resulting in uniform clearing prices for both energy and reserve markets, as well as a zero network surplus. Although the transmission constraints are inactive, the network price constraints are still playing an important role. Before solving for the schedules, transmission flows are unknown and congestion is undetermined. Simply allowing different locational prices are computed without any transmission limitation. On the other hand, if we use pre-defined congestion and restrict tradings between locations, we may not fully capture the economic efficiency due to the inter-locational trading. To confirm this, we remove the network price constraints in the base case and solve for the prices and schedules. In the new solution (not shown in Table 3), the objective is reduced to be 2707.89, and the different energy clearing prices at the three buses are computed as (26.00, 28.37, 28.81). If 28.81 is chosen as the clearing price, the total energy payment from consumers alone will be 2881 -- a less optimal solution. In case A, we derate the flow limit of Branch 3 from 30 to 25. Branch 3 becomes congested since the unconstrained flow is 27.9437. This leads to reduction of output in Bus 1 and increase of more expensive units in Buses 2 and 3. Consequently, higher zonal clearing prices at Buses 2 and 3 are computed. Let's examine the energy price at Bus 3. When energy is delivered from Bus 1 to Bus 3, two thirds flow through Branch 1 and one third goes through the parallel path on Branches 1 and 2. At market equilibrium, we note that [FORMULA OMITTED]. The clearing price at Bus 2 is a combination of the clearing price at Bus 1 and the transportation cost from Bus 1 to Bus 3. The network surplus 94.4444 is the difference between demand payment and generator credit payment. It can also be computed by multiplying the total flow of Branch 3 with the branch congestion price. In Case B, we examine the solution behavior when the energy demand at Bus 3 increases from 50 to 60. the objective function is increased by 407.0084. This increase is due to three factors: network surplus, cost increase for additional generation, and additional payment due to the price increases. Because of the increased demand, energy clearing prices at all buses have increased and the largest increase occurs at bus 3. However, reserve prices remain the same as in Case A. Case C is rather interesting. We increase the reserve demand at Bus 3 from 3 to 8. Branch 3 is unconstrained for energy schedules. Hence, uniform energy clearing prices are computed for all three buses. However, there is not enough transmission to support the reserve use from 1 to 3. Therefore, a congestion price of 0.3222 is assessed to the capacity reservation for this branch. Consequently, different clearing prices for reserve are computed and a network surplus of 0.6626 (the product of reserve usage 2.0563 and congestion price 0.3222) is computed due to the insufficient transmission for reserve. Finally, we simultaneously increase the reserve demand and energy demand at Bus 3 as shown in Case D. Branch is constrained for energy delivery. This results in different energy and reserve clearing prices for all three buses. The largest price increases for reserve is also at Bus 3. Because the energy demand is the same as in Case B, the energy clearing prices are the same as in case B. V. CONCLUSIONS In this paper we proposed a new formulation that solves for schedules and clearing prices for integrated electric energy, transmission and generation capacity reserve markets simultaneously. The direct use of price control variables and innovative network price constraints are the most significant aspects of the formulation. Moreover, we incorporated a DC transmission network models and yields locational clearing prices when transmission congestion is present. The new formulation has several advantages over traditional prices and scheduling methods. We overcome the shortcomings of clearing price computation in the traditional unit commitment and optimal power flow techniques by using price based dispatch methods and innovative price constraints. Because prices are used as control variables, post processing for price calculation is no longer required and there are no price ambiguity to market participants. All bidders can easily verify that their profits are maximized. Furthermore, competition for transmission allocation between energy and reserve market is addressed. The new formulation offers the ability to integrate three different, but inter-related, markets for better economic efficiency as well as for reducing market transactions costs. The formulation can be adopted for real market applications. VI. REFERENCES [1] H. Singh and A. Papalexopoulos, "Competitive Procurement of Ancillary Services by an Independent System Operator," IEEE Trans. on Power Systems, Vol. 14, No. 2, May 1999, pp. 498-504. [2] New York Independent System Operator, Day Ahead Scheduling Manual, New York Independent System Operator, Sep. 1999,//www.nyiso.com. [3] PJM Interconnection, L.L.C., Operating Agreement Accounting -- Manual M-28, June 01, 2000,//www.pjm.com. [4] NGC Settlement Limited, "Introduction to Pool Rules," Electricity Pool of England and Wales, April 1993. [5] X. Ma, D. Sun, and K. Cheung, "energy and Reserve Dispatch in a Multi-zone Electricity Market," IEEE Trans. on Power Systems, Vol. 14, No. 3, Aug. 1999, pp. 913-919. [6] K.W. Cheung, P. Shamsollahi, D. Sun, J. Milligan and M. Potishnak, "Energy and Ancillary Service Dispatch for the Interim ISO New England Electricity Market," Proceeding of Power Industry Computer Application Conference, May 1999, Santa Clara, pp. 47-53. [7] L. Post, S.S. Coppinger, and G.B. Sheble, "Application of Auctions as a Pricing Mechanism for the Interchange of Electric Power," IEEE Trans. on Power Systems, Vol. 10, August 1996, pp. 1580-1584. [8] G. Xiaohong, G. Feng, and A. Svoboda, "Energy Delivery Capacity and Generation Scheduling in the Deregulated Electric Power Market," Proceeding of Power Industry Computer Application Conference, May 1999, Santa Clara, California, pp. 25-30. [9] S. Hao, A. Papalexopoulos, G. Angelidis and H. Singh, "Consumer Cost Minimization in Power Auctions," Proceeding of Power Industry Computer Application Conference, Columbus, Ohio, May 1997. [10]G.B. Sheble, "Price Based Operation in an Auction Market Structure," Presented at the IEEE/PES Winter Meeting, New York, New York, Feb. 1996. [11]M.D. Cadwalader, S. Harvey, S.L. Pope and W.W. Hogan, "Reliability, Scheduling Markets, and Electricity Pricing," Putnam, Hayes & Barlett, inc., Cambridge, Massachusetts, May, 1998,//ksgwww.harvard.edu/people/whogan. [12]D. Chattopadhyay, "Daily Generation Scheduling: Quest for New Models," IEEE Trans. on Power Systems, Vol. 13, No.2.,May 1998,pp.624-629. VII. BIOGRAPHIES SHANGYOU HAO received his B.S. degree from Wuhan Institute of Hydraulic and Electrical Engineering, China, in 1982, and his M.S. and Ph.D. degrees in Electrical Engineering from Ohio State University in 1984 and 1988, respectively. He was with the Pacific Gas and Electric Company from 1988 to 1997, working on development of analytical methodologies for California electricity industry restructuring. He has been with Perot Systems Corporation since 1997, developing information system and business protocols for the California ISO and Power Exchange. DR. DARIUSH SHIRMOHAMMADI is the Director of energy Infrastructure Services with Perot Systems Energy Group. He has been with Perot Systems since 1996 where he has been developing and integrating information technology solutions for market operations and settlements of emerging energy market players worldwide including the California Independent System Operator and California Power Exchange. Dariush has around 25 years of experience with the electric utility industry mainly in the development and implementation of methodologies and computer models for operations, planning, costing, pricing and automation of electric power systems. His career path includes positions as researcher for two years with Hydro Quebec, transmission planner for three years with Ontario Hydro, systems engineer, transmission planner, automation engineer, and the Director of the Energy Systems Automation Organization with Pacific Gas and electric Company for 11 years and the principal consultant with Shir Power Engineering Consultants, Inc., for more than a year. Dariush has authored numerous technical paper and reports all around the world. Dariush has a Ph.D. in Electric Power Engineering from the University of Toronto. 6