Components of nodal prices for electric power systems - Power ...

48 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 1, FEBRUARY 2002TABLE VIDEMAND, GENERATION AND NODAL PRICES FOR IEEE 30-BUSSTANDARD TEST SYSTEMa total reactive power balance equality in (2), or evaluatethe real and reactive power losses in reactive nodal priceof (25).dent elements, e.g., power losses, which are not explicitly handledin (24) and (25). Since power loss (real or reactive powerloss) is not an independent factor in the objective function orconstraints, it cannot be directly expressed as a component ofnodal prices.If it is necessary to evaluate effect of real power loss, (2) canbe reorganized in the following way. Deleting one real powerbalance equation at any bus, we instead add the total real powerbalance equalityV. CONCLUSIONThis paper proposes a methodology directly to link eachconcerned factors to the nodal prices, i.e., we break downeach nodal price into a variety of parts corresponding todifferent factors, such as generations, transmission congestion,voltage limitations and other constraints. Different from theac power flow which cannot generally be identified to itssources or routes, this paper shows that the nodal prices cantheoretically be traced to each factor based on the marginalconditions from the economics viewpoint. The decompositionis unique, and components of each nodal price are identicalto their increment costs or benefits for total system. Thesedetail information for nodal prices can be used not only toimprove the efficient usage of power grid, energy resources andcongestion management, but also to design a reasonable pricingstructure of power systems, or to provide economic signals forgeneration–transmission investment [11]. Several numericalsimulations have been used to demonstrate our approach.If the decomposed components are all required to be positive,the components can be recalculated by first letting the negativecomponents be zero, and then proportionally allocating thenodal prices to the positive components depending on their contributions(values).Although this paper uses OPF-based model with static constraintsas an example to demonstrate the decomposition of thenodal prices which are actually based on the short-term marginalcost principle, the nodal prices incorporating the long-term investmentas well as dynamical constraints can be decomposedin the same manner provided that the long-term expansion planningmodel or dynamical constraints are adopted instead of thestatic OPF model. For example, the values or prices of controldevices such as PSS and AVR can also be evaluated as the sameway as (24) and (25) if the transient stability constraints are consideredin OPF [10].plossinto (2), where and are the summations of realpower generations and loads, respectively, and ploss is total realpower loss which is a function of . Then the powerloss is explicitly expressed in the reformulated by (1)–(3), whichare theoretically equivalent to the original (1)–(3). From the dualtheory of mathematical programming, there generally exists anonzero Lagrangian multiplier for the new equality at anyoptimal solution of the reformulated (1)–(3).Take real power loss ploss as an independent factor, i.e.,assume ploss tradable. In other words, the total real powerbalance equality should be added into . Then there is a termin the components of nodal priceof (24), which corresponds to real power loss and canbe viewed as the value of real power loss. As the same way,we can also evaluate the value of the reactive power loss asin real nodal price of (24) whenone reactive power balance equality of any bus is replaced byREFERENCES[1] F. C. Schweppe, M. C. Caramanis, R. D. Tabors, and R. E. Bohn, SpotPricing of Electricity. Boston, MA: Kluwer, 1988.[2] W. W. Hogan, “Contract networks for electric power transmission,” J.Regulatory Econ., vol. 4, pp. 211–242, 1992.[3] R. J. Kaye, F. F. Wu, and P. Varaiya, “Pricing for system security,” inProc. IEEE Winter Power Meeting, 1992, Paper 92-WM-100-8.[4] S. Oren, P. Spiller, P. Varaiya, and F. F. Wu, “Nodal prices and transmissionrights: A critical appraisal,” Electricity J., vol. 8, no. 3, pp. 24–35,1995.[5] M. L. Baughman, S. N. Siddigi, and J. W. Zarnikau, “Advanced pricingin electrical systems,” IEEE Trans. Power Syst., vol. 12, pp. 489–502,Feb. 1997.[6] D. Sun, B. Ashley, B. Brewer, A. Hughes, and W. Tinney, “Optimalpower flow by Newton approach,” IEEE Trans. Power Apparat. Syst.,vol. PAS-103, pp. 2864–2880, Oct. 1984.[7] R. Shoults and D. Sun, “Optimal power flow based upon P–Q decomposition,”IEEE Trans. Power Apparat. Syst., vol. PAS-101, pp. 397–405,Feb. 1982.[8] L. Chen et al., “Mean field theory for optimal power flow,” IEEE Trans.Power Syst., vol. 12, pp. 1481–1486, Nov. 1997.[9] L. Chen et al., “Surrogate constraint method for optimal power flow,”IEEE Trans. Power Syst., vol. 13, pp. 1084–1089, Aug. 1998.