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Research Proposal

Research Proposal. AJ van Staden, 93387807, MEng (Electrical). An Optimal Control Model for Load Shifting in a Water Pumping Scheme with Maximum Demand Charges. Problem. Little evidence of closed-loop optimal control for load shifting with TOU and MD charges.

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Research Proposal

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  1. Research Proposal AJ van Staden, 93387807, MEng (Electrical) An Optimal Control Model for Load Shifting in a Water Pumping Scheme with Maximum Demand Charges

  2. Problem Little evidence of closed-loop optimal control for load shifting with TOU and MD charges. Table: Optimal control based load-shifting.

  3. Research Design Hypothesis: A closed-loop optimal control model can be used for load shifting problems in industrial applications; including customers that are charged on TOU and/or MD. Objective: Determine the closed-loop load shifting (scheduling) strategy that yields the maximum potential of the cost saving under both TOU and MD charges for a specific application. Case study: Rietvlei water purification plant; charged on both TOU and MD.

  4. Research Design - Activities Open-loop Closed-loop Expect MD charges to play the most significant role in optimization.

  5. Case study – Rietvlei purification Randwater R 2.98/kL Garsfontein (R3) 60 Ml Randwater R 2.98/kL Klapperkop (R2) 120 Ml Valve (V1) Boreholes 10 ML/day R 0.30/kL 175 kW 10 ML/day/pump OB1 OB2 Rietvlei 25ML/day R 1.03/kL Rietvlei 20ML/day R 1.03/kL OB3 Boreholes (R4) 1.1ML Focus of the case study 300 kW 22 ML/day/pump 275 kW 10 ML/day/pump On 30% Off 15% On 40% Off 20% K1 G1 On 65% Off 45% On 50% Off 35% IB1 IB2 IB3 IB4 IB5 K2 G2 Rietvlei Dam Ranges from 37 to 75 kW motors K3 G3 back-up back-up Rietvlei Purification Plant Fountain Rietvlei (R1) 2 ML (70% of total capacity) Rietvlei Fountain 5 ML/day Gravitational flow Rietvlei Purification 40 ML/day Gravitational flow

  6. Klapperkop Pumps - Indicative In peak and standard Times (6h00 to 22h00) Integrated maximum demand intervals Undesirable maximum demand “set” for the month Current Schedule K2 K1 Option 1 – Many short periods on pump K2. K2 k1 Lower integrated maximum demand Option 2 – Short overlaps between pumps. K2 K1 6h 7h 8h 9h 10h 11h 12h 13h 14h

  7. Preliminary Results Rudimentary tuning of current control strategy i.e. narrowing the K2 switching band. Table: Monthly costs with MD savings.

  8. Formulation T = total time interval e.g. 1440 minutes (for a day). N = total number of pumps. P = kW rating of each pump. c = kWh costs function. Cmax = Maximum demand charge e.g. R 50/kW. u =state of pump e.g. 1 is on, and 0 is off. I = Number of maximum demand intervals. TOU based objective function MD based objective function Some constraints Reservoir must not get empty. Reservoir must not overflow. At least one of the Klapperkop pumps must run. At least one of the Garsfontein pumps must run.

  9. Major Challenge MD Optimization is not linear. • Consider near-optimal approaches to “linearize” e.g. • Maximum demand limit [new reference, Coulbeck, Orr]. • Reduced gradient algorithm – penalty towards end [14]. • Continuous variable [10] –trying to adapt to this application. • Others? • Alternatively, consider non-linear techniques e.g. • Dynamic programming. • Matlab fminmax – struggling to limit x to binary values. • Matlab fmincon – struggling to limit x to binary values. • Matlab fgaolattain - TODO • Neural networks. • Others?

  10. References Optimal control based load-shifting. [5] S. Ashok, R. Banerjee, “An optimization model for industrial load management,” IEEE Transactions on Power Systems, vol. 16, no. 3, pp. 879-884, Nov. 2001. [6] S. Ashok, “Peak-load management in steel plants,” Applied Energy, vol. 83, no 5, pp 413-424, May 2006. [7] E. Gomez-Villalva, A. Ramos, “Optimal energy management of an industrial consumer in liberalized markets,” IEEE Transactions on Power Systems, vol. 18, no. 2, pp. 716-723, May 2003. [8] A. Middelberg, J. Zhang, X. Xia, “An optimal control model for load shifting – with application in energy management of a colliery,” To be published. [9] J. Zhang, X. Xia, “Best switching time of hot water cylinder –switched optimal control approach,” Proc. of the 8th IEEE AFRICON Conference, Namibia, 26-28 Sept. 2007. [10] K. W. Little, B. J. McCrodden, ‘‘Minimization of raw water pumping costs using MILP,’’ Journal of Water Resources Planning and Management, vol. 115, no. 4, pp. 511–522, July 1989. [11] W. Jowitt, G. Germanopoulos, “Optimal pump scheduling in water-supply networks,” Journal of Water Resources Planning and Management, vol. 118, no. 4, pp. 406-422, July 1992. [12] G. McCormick, R.S. Powell, “Optimal pump scheduling in water supply systems with maximum demand charges,” Journal of Water Resources Planning and Management, vol. 129, no. 5, pp. 372-379, Sept. 2003. [13] V. Nitivattananon, E.C. Sadowski, R.G. Quimpo, “Optimization of water supply system operation,” Journal of Water Resources Planning and Management, vol. 122, no. 5, pp. 374–384, Sept. 1996. [14] G. Yu, R.S. Powell, M.J.H. Sterling, “Optimised pump scheduling in water distribution systems,” Journal of Optimization Theory and Applications, vol. 83, no. 3, pp. 463–488, Dec. 1994.

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