INTERNATIONAL INTERCONNECTIONS AND ELECTRICITY DEREGULATION IN AFRICA AND THE GULF STATES

T.J. Hammons∗

References

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  9. [9] A. Majeed, H.A. Karim, N.H. Al Maskati, & S. Sud, Status of Gulf Cooperation Council (GCC) electricity grid system interconnection, Panel presentation at IEEE PES 2004 GM, Denver, CO, USA, 2004, available at www.ieee.org/ipsc, 15–23. Appendix Formulation of Simultaneous Linear Equations for the Trading Platform Let us assume that P MW of power is on offer and that there are altogether n offers and m bids. Let us also assume that a given bidder j receives power from a given seller i and that this power is Pij as illustrated in Table 7. For n offers, it can be shown that: P11 + P12 + P13 + P14 + · · · + P1m = mj =1 P1j P21 + P22 + P23 + P24 + · · · + P2m = mj =1 P2j ... Pn1 + Pn2 + Pn3 + Pn4 + · · · + Pnm = mj =1 Pnj ⎫ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭ (1.0) 381 Table 7 Power Allocation Table 1 2 3 4 TOTAL BIDS NAM SEB LEC ZESA 1 SNEL P11 P12 P13 P14 4 1 P1j 2 ZESCO P21 P22 P23 P24 4 1 P2j OFFERS 3 EDM P31 P32 P33 P34 4 1 P3j 4 ESKOM P41 P42 P43 P44 4 1 P4j TOTAL 4 1 Pi1 4 1 Pi2 4 1 Pi3 4 1 Pi4 4 1 Pij Similarly for m bids we get: P11 + P21 + P31 + P41 + · · · + Pn1 = ni =1 Pi1 P12 + P22 + P32 + P42 + · · · + Pn2 = ni =1 Pi2 ... P1m + P2m + P3m + P4m + · · · + Pnm = ni =1 Pim ⎫ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭ (2.0) If OFFER_POWER [i] is the maximum power offered by seller i and BID_POWER [j] is the maximum power requested by bidder j , then the selling and buying conditions must satisfy the following equations (3.0) and (4.0) respectively, for offers and bids. m i=1 P1i ≤ OFFER_POWER [1] m i=1 P2i ≤ OFFER_POWER [2] ... m i=1 Pni ≤ OFFER_POWER [n] ⎫ ⎪⎪⎪⎪⎪⎪⎪⎪⎬ ⎪⎪⎪⎪⎪⎪⎪⎪⎭ (3.0) n j=1 Pj1 ≤ BID_POWER [1] n j=1 Pj2 ≤ BID_POWER [2] ... n j=1 Pjm ≤ BID_POWER [m] ⎫ ⎪⎪⎪⎪⎪⎪⎪⎪⎬ ⎪⎪⎪⎪⎪⎪⎪⎪⎭ (4.0) The value of the power Pij at other positions can easily be evaluated from the qualification criterion. If the offer price from the seller I is more than the bidder price by the bidder j, then if follows that Pij = 0. It was initially stated that the cheaper power has to be shared first equally amongst all the qualified bidders. Therefore, it follows that the cost function (i.e., cost per hour) with respect to the bidder must be minimized to get the optimal solution for all the offers and bids. The cost function in this case is the product of the price of the offer power by the power allocated to the buyer from the particular seller. The unit of the cost function is therefore cents per KWh. The optimization problem for any given buyer at position j and for n sellers can then be stated as follows: Minimize: Costf = OFFER_PRICE [1] ∗ P1j + OFFER_PRICE [2] ∗ P2j + · · · + OFFER_PRICE [n] ∗ Pnj Subject to: 1. Pij = 0 when equation (1.0) is not satisfied. 2. Transmission system constraints and other wheeling constraints 3. m k=1 Pjk ≤ OFFER_POWER [j] 4. n i=1 Pij ≤ BID_POWER [j] There are two ways of solving the optimization problem of this nature: mathematically using the well-known linear optimization techniques, or by using the market rules that have been formulated. The method that was finally adopted combined the two approaches. The market rules simplified the task of incorporating system transmission and wheeling constraints. The proposed algorithm first allocates the power equally to all the successful bidders. If the power allocated is more than what the bidder requested, adjustments are made to the affected bidder. Then the transmission constraints are applied to check for any system violations. If no violation is detected, the solution is accepted. If violation is encountered, the allocated power is adjusted until no violation is observed. Using the proposed algorithm, a computer program called STEM Program Manager was written to automate and computerize the allocation of offers to successful bidders. 382

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