Abstract
This paper proposes a framework to extract appropriate locational marginal prices for each type of reserve (up-/down-going reserves at both generation- and demand-sides). The proposed reserve pricing scheme accounts for the lost opportunity of selling the convertible products (energy and reserve). The fair prices can be obtained for capacity reserves applying this framework, since this framework assigns the same prices to the same services provided at the same location. The proposed reserve pricing scheme provides all the market participants with the appropriate signals to modify their offers according to the system operator requirements. The pricing problem is decomposed to different hourly sub-problems considering the bounding constraints. To show the effectiveness of the proposed algorithm, it is applied to the IEEE reliability test system and the results are discussed.
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Abbreviations
- \(C(\ )\) :
-
Generalized objective function
- \(com(\ )\) :
-
Reserve commitment indicator; 1 means the regarding reserve is committed and 0 means not committed
- \(DT(\ )\) :
-
Shutdown time counter
- \(GMP(\ )\) :
-
Generation marginal price
- i :
-
Index for unit
- \(ILS(\ )\) :
-
Involuntary load shedding
- j :
-
Index for bus
- msf :
-
Index for segment in linearized cost function
- \(outg(\ )\) :
-
Unit outage indicator
- \(p(\ )\) :
-
Generation of each segment in cost function
- \(pg(\ )\) :
-
Generation of a unit
- \(pd(\ )\) :
-
Demand at a bus
- \(R_d^{dn} (\ )\) :
-
Demand-side down-going reserve
- \(R_d^{up} (\ )\) :
-
Demand-side up-going reserve
- \(R_g^{dn} (\ )\) :
-
Generation-side down-going reserve
- \(R_g^{up} (\ )\) :
-
Generation-side up-going reserve
- t :
-
Index for time
- \(u(\ )\) :
-
Unit status indicator; 1 means on and 0 means off
- x :
-
Reactance of a line
- \(y(\ )\) :
-
Start-up indicator
- \(z(\ )\) :
-
Shut-down indicator
- \(\lambda _g^{up} (\ )\) :
-
Lagrange multiplier of maximum available generation-side up-going reserve constraint
- \(\lambda _d^{up} (\ )\) :
-
Lagrange multiplier of maximum available demand-side up-going reserve constraint
- \(\lambda _g^{dn} (\ )\) :
-
Lagrange multiplier of maximum available generation-side down-going reserve constraint
- \(\lambda _d^{dn} (\ )\) :
-
Lagrange multiplier of maximum available demand-side down-going reserve constraint
- \(\gamma (\ )\) :
-
Lagrange multiplier of pre-contingency load-generation balance constraint
- \(\gamma k (\ )\) :
-
Lagrange multiplier of post-contingency load-generation balance constraint
- \(\mu ^{\max }(\ )\) :
-
Lagrange multiplier of maximum output limit
- \(\mu ^{\min }(\ )\) :
-
Lagrange multiplier of minimum output limit
- \(F_i^{min} \) :
-
Generation cost at the minimum output of unit i
- \(IC(\ )\) :
-
Involuntary load shedding price
- \(MSR(\ )\) :
-
Maximum sustainable ramp rate
- Nc :
-
Number of optimization binding constraints
- Nd :
-
Number of buses
- Ng :
-
Number of units
- Nl :
-
Number of lines
- Nx :
-
Number of optimization independent variables
- Nu :
-
Number of optimization control variables
- NSF :
-
Number of segments in linearized cost curves
- \(Q(\ )\) :
-
Offered rate for reserve which takes the same subscripts and superscripts as R
- \(R^{of} (\ )\) :
-
Maximum offered reserve which takes the same subscripts and superscripts as R
- \(RD(\ )\) :
-
Ramping up limit of a unit
- \(RMP(\ )\) :
-
Reserve marginal prices which takes the same subscripts and superscripts as R
- \(RU(\ )\) :
-
Ramping down limit of a unit
- \(SDC(\ )\) :
-
Shutdown cost
- \(sl(\ )\) :
-
Slope of each segment in the linearized cost curve
- \(SUCF(\ )\) :
-
Start-up cost function
- T :
-
Number of hours in the time span
- BG :
-
Bus-to-unit incidence matrix
- BGK :
-
Post contingency bus-to-unit incidence matrix
- \(EMP(\ )\) :
-
Vector of energy marginal prices
- \(f^{max}\) :
-
Vector of upper limits of line and transformer flows
- \(fK^{max}(\ )\) :
-
Vector of post-contingency upper limits of line and transformer flows
- GSF :
-
Generation shift factors matrix
- \(GSFK(\ )\) :
-
Post-contingency generation shift factors matrix
- \(Outg(\ )\) :
-
Unit outage matrix
- \(PD(\ )\) :
-
Demand vector
- \(PG(\ )\) :
-
Generators real power output vector
- \(RD(\ )\) :
-
Demand-side reserve vector
- \(RG(\ )\) :
-
Generation-side reserve vector
- X :
-
Inverse of DC-LF matrix
- \(\lambda \) :
-
Vector of general Lagrange multipliers
- \(\Phi (\ )\) :
-
Vector of Lagrange multipliers for pre-contingency line flow constraints
- \(\Phi k(\ )\) :
-
Vector of Lagrange multipliers for post-contingency line flow constraints
- \(\delta (\ )\) :
-
Bus voltage angle vector
References
Bolouck Azari, J., & Ghadimi, N. (2014). Firefly technique based on optimal congestion management in an electricity market. International Journal of Information, Security and Systems Management, 3(2), 333–344.
Bouffard, F., Galiana, F. D., & Conejo, A. J. (2005). Market-clearing with stochastic security part I: Formulation. IEEE Transactions on Power Systems, 20, 1818–1826.
Chen, J., Thorp, J. S., Thomas, R. J., & Mount, T. D. (2003). Locational pricing and scheduling for an integrated energy-reserve market. In Proceedings of 36th Hawaii international conference on system sciences, Hawaii, (pp. 54–63).
Dideban, M., et al. (2013). Optimal location and sizing of shunt capacitors in distribution systems by considering different load scenarios. Journal of Electrical Engineering and Technology, 8(5), 1012–1020.
Fu, Y., Shahidehpour, M., & Li, Z. (2005). Security-constrained unit commitment with AC constraints. IEEE Transactions on Power Systems, 20, 1538–1550.
Ghadimi, N. (2014). MDE with considered different load scenarios for solving optimal location and sizing of shunt capacitors. National Academy Science Letters, 37(5), 447–450.
Ghadimi, N. (2015). A new hybrid algorithm based on optimal fuzzy controller in multimachine power system. Complexity, 21(1), 78–93.
Jalili, A., & Ghadimi, N. (2015). Hybrid harmony search algorithm and fuzzy mechanism for solving congestion management problem in an electricity market. Complexity. 21(S1), 90–98.
Jamalzadeh, R., Zhang, F., & Hong, M. (2016). An economic dispatch algorithm incorporating voltage management for active distribution systems using generalized benders decomposition. In IEEE power and energy society general meeting (PESGM) (pp. 1–5). Boston, MA, USA.
Li, T., & Shahidehpour, M. (2007a). Price-based unit commitment: A case of Lagrangian relaxation versus mixed integer programming. IEEE Transactions on Power Systems, 20, 2015–2025.
Li, T., & Shahidehpour, M. (2007b). Risk-constrained generation asset arbitrage in power systems. IEEE Transactions on Power Systems, 22, 1330–1339.
Momoh, J. A., Yan, X., & Boswell, G. D. (2008). Locational marginal pricing for real and reactive power. In Conversion and delivery of electrical energy in the 21st century, power and energy society general meeting-IEEE, (pp. 1–6).
Nouri, A., Afkousi-Paqaleh, M., & Hosseini, S. H. (2013). Probabilistic assessment and sensitivity analysis of marginal price of different services in power markets. IEEE Systems Journal, 7, 873–880.
Nouri, A., & Hosseini, S. H. (2015). Comparison of LMPs’ sensitivity under payment cost minimization and offer cost minimization mechanisms. IEEE Systems Journal, 9, 1507–1518.
PJM Manual 06, 11, 12: Scheduling Operations. http://www.pjm.com/contributions/pjm-manuals/manuals.html.
Shahidehpour, M., Yamin, H., & Li, Z. (2002). Market operations in electric power systems: forecasting, scheduling, and risk management. New York: Wiley.
Wang, J., Encinas Redondo, N., & Galiana, F. D. (2003). Demand-side reserve offers in joint energy/reserve electricity markets. IEEE Transactions on Power System, 18, 1300–1306.
Wong, S., & Fuller, J. D. (2007). Pricing energy and reserve using stochastic optimization in an alternative electricity market. IEEE Transactions on Power Systems, 22, 631–638.
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Akbary, P., Ghiasi, M., Pourkheranjani, M.R.R. et al. Extracting Appropriate Nodal Marginal Prices for All Types of Committed Reserve. Comput Econ 53, 1–26 (2019). https://doi.org/10.1007/s10614-017-9716-2
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DOI: https://doi.org/10.1007/s10614-017-9716-2