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Feasibility of Stochastic Voltage/VAr Optimization Considering Renewable Energy Resources for Smart Grid

  • James A. Momoh and Surender Reddy Salkuti EMAIL logo
Published/Copyright: April 21, 2016
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International Journal of Emerging Electric Power Systems
From the journal International Journal of Emerging Electric Power Systems Volume 17 Issue 3

Abstract

This paper proposes a stochastic optimization technique for solving the Voltage/VAr control problem including the load demand and Renewable Energy Resources (RERs) variation. The RERs often take along some inputs like stochastic behavior. One of the important challenges i. e., Voltage/VAr control is a prime source for handling power system complexity and reliability, hence it is the fundamental requirement for all the utility companies. There is a need for the robust and efficient Voltage/VAr optimization technique to meet the peak demand and reduction of system losses. The voltages beyond the limit may damage costly sub-station devices and equipments at consumer end as well. Especially, the RERs introduces more disturbances and some of the RERs are not even capable enough to meet the VAr demand. Therefore, there is a strong need for the Voltage/VAr control in RERs environment. This paper aims at the development of optimal scheme for Voltage/VAr control involving RERs. In this paper, Latin Hypercube Sampling (LHS) method is used to cover full range of variables by maximally satisfying the marginal distribution. Here, backward scenario reduction technique is used to reduce the number of scenarios effectively and maximally retain the fitting accuracy of samples. The developed optimization scheme is tested on IEEE 24 bus Reliability Test System (RTS) considering the load demand and RERs variation.

Keywords: optimal power flow; renewable energy resources; voltage/var control; stochastic programming; voltage stability

Appendix A: Chance Constrained Programming (CCP) [52, 53]

The Chance Constrained Programming (CCP) is a kind of stochastic optimization technique, and is suitable for solving the problems with random variables incorporated in the constraints and sometimes in the objective function as well. The constraints are guaranteed to be satisfied with a specified probability or confidence level at the optimal solution found [52–54]. The basic idea of optimization under uncertainty is to integrate the available stochastic information into the optimization problem formulation. The general CCP problem is expressed as,

(26)minimize fˉx
(27)such that Probgjx,ξ≤0,j=1,2,…,k≥α

where xϵRn is a vector of decision variables; ξ is the stochastic vector with a given PDF Φ(ξ); f(x) is the objective function; gj(x, ξ) (j=1, 2, ..., k) is the constraint function; and α is the specified confidence level of the constraint function to be satisfied.

If possible, the best method for solving the CCP problem is to convert the stochastic constraints to their respective deterministic equivalents with respect to the pre-specified confidence level. However, this does not work for most CCP problems.

Fortunately, the MCS technique provides a general approach for solving CCP problems. For any given decision x, the procedure of using the MCS to check the following constraint,

(28)Probgjx,ξ≤0,j=1,2,…,k≥α

is given below.

First, N independent random vectors ξ1, ξ2, ..., ξN are generated based on the given PDF Φ(ξ). Let N’ be the number of cases with the following inequality constraint satisfied,

(29)gjx,ξi≤0,i=1,2,…,N

In other words, N’ is the number of random vectors satisfying the constraints. Mathematically, Prob {gj (x, ξ)≤0} can be estimated by N’/N, if N is large enough. This means that a chance constraint expressed by eq. (28) holds if and only if N’/N ≥α. If random variables are included in the objective function, then the CCP will be of the following form,

(30)Probfx,ξ≤fˉ≥β

where β is the given confidence level. The detailed procedure to solve this CCP problem could be found in [54].

Appendix B: Latin Hypercube Sampling (LHS) [38, 39, 43]

The aim of LHS is to estimate the uncertainty in a problem where the variable of interest is expressed as a function of random variables as [38],

(31)y=fx

where y is the variable of interest and x are the random variables.

When the function to be evaluated is complicated and computationally intensive, investigation of interaction of variable of interest with other stochastic variables (in multi-dimension) is inevitably cumbersome. LHS has been developed as a probabilistic risk assessment tool to specifically assist this type of investigation. With multidimensional random variables, LHS creates a system state by pairing the values after sampling each random variable individually. The pairing scheme is rather simple in the case of uncorrelated random variables. A system state is found by randomly choosing one value out of the sampled values from each component without replacement. However, in case of random variables with certain correlation among them, a strategy of pairing scheme will involve use of optimization.

The sample size (n) is specified in advance. Next, the equivalent probability distribution functions of generation and load are divided into n subintervals with equal probability of 1/n. A value is randomly chosen from each and every subinterval. The procedure for implementing the LHS is presented next:

  • Step 1: Specify sample size (n).

  • Step 2: Construct discrete distribution function of load demand and power generation.

  • Step 3: Divide equivalent generation and load distribution functions into n subintervals with equal probability.

  • Step 4: Randomly sample without replacement and record a value from each and every subinterval corresponding to its distribution in that subinterval.

  • Step 5: Perform random permutations to produce pairs of generation and load demand.

  • Step 6: Use each pair in the Monte Carlo Simulation (MCS).

Appendix C

The minimum and maximum limits of power supply for IEEE 24 bus Reliability Test System (RTS) are presented in Table 5, and the minimum and maximum limits of power demand are presented in Table 6.

Table 5:

Minimum and maximum limits of power supply for IEEE 24 bus system.

BusPSmin (MW)PSmax (MW)
Bus10115.276
Bus10215.276
Bus10725100
Bus11368.95197
Bus11554.25155
Bus11654.25155
Bus118100400
Bus121100400
Bus122050
Bus123140350
Table 6:

Minimum and maximum limits of power demand for IEEE 24 bus system.

BusPDmin (MW)PDmax (MW)
Bus10195.04142.56
Bus10285.36128.04
Bus103158.4237.6
Bus10465.1297.68
Bus10562.4893.72
Bus106119.68179.52
Bus107110165
Bus108150.48225.72
Bus109154231
Bus110171.6257.4
Bus113233.2349.8
Bus114170.72256.08
Bus115307.76461.64
Bus11688132
Bus118293.04439.56
Bus119159.28238.92
Bus120112.64168.96

References

1. Pimentel D, Herz M, Glickstein M, Zimmerman M, Allen R, Becker K, Evans J, Hussain B, Sarsfeld R, Grosfeld A, Seidel T. Renewable energy: current and potential issues. Bioscience Dec. 2002;52:1111–12.10.1641/0006-3568(2002)052[1111:RECAPI]2.0.CO;2Search in Google Scholar

2. Kumbaroğlu G, Madlener R, Demirel M. A real options evaluation model for the diffusion prospects of new renewable power generation technologies. Energy Econ 2008;30:1882–908.10.1016/j.eneco.2006.10.009Search in Google Scholar

3. Jebaselvi GDA, Paramasivam S. Analysis on renewable energy systems. Renewable Sustainable Energy Rev Dec. 2013;28:625–34.10.1016/j.rser.2013.07.033Search in Google Scholar

4. Schellenberg A, Rosehart W, Aguado JA. Cumulant-based stochastic nonlinear programming for variance constrained voltage stability analysis of power systems. IEEE Trans Power Syst May 2006;21:579–85.10.1109/TPWRS.2006.873103Search in Google Scholar

5. Kimball LM, Clements KA, Pajic S, Davis PW. Stochastic OPF by constraint relaxation. Proc IEEE Bologna Power Tech Conf Jun. 2003;4:5.10.1109/PTC.2003.1304714Search in Google Scholar

6. Yong T, Lasseter RH. Stochastic optimal power flow: formulation and solution. Proc IEEE Power Eng Soc Summer Meeting Jul. 2000;1:237–42.Search in Google Scholar

7. Schellenberg A, Rosehart W, Aguado JA. Cumulant based stochastic optimal power flow (S-OPF) for variance optimization. Proc IEEE Power Eng Soc General Meeting Jun. 2005;1:473–8.10.1109/PES.2005.1489589Search in Google Scholar

8. Carrión M, Arroyo JM, Alguacil N. Vulnerability-constrained transmission expansion planning: a stochastic programming approach. IEEE Trans Power Syst Nov. 2007;22:1436–45.10.1109/TPWRS.2007.907139Search in Google Scholar

9. Birge JR, Louveaux F. Introduction to stochastic programming. New York: Springer-Verlag, 1997.Search in Google Scholar

10. Xiao Y, Song YH, Sun YZ. A hybrid stochastic approach to available transfer capability evaluation. Proc of IEEE Gener Trans Distrib Sept. 2001;148:420–6.10.1049/ip-gtd:20010478Search in Google Scholar

11. Monticelli A, Pereira MVF, Granville S. Security constrained optimal power flow with post-contingency corrective rescheduling. IEEE Trans Power Syst Feb. 1987;2:175–80.10.1109/TPWRS.1987.4335095Search in Google Scholar

12. Ochoa LF, Harrison GP. Minimizing energy losses: optimal accommodation and smart operation of renewable distributed generation. IEEE Trans Power Syst Feb. 2011;26:198–205.10.1109/PES.2011.6039007Search in Google Scholar

13. Pepermans G, Driesen J, Haeseldonckx D, D’haeseleer W, Belmans R. Distributed generation: definition, benefits and issues. Energy Policy Apr. 2005;33:787–98.10.1016/j.enpol.2003.10.004Search in Google Scholar

14. Malekpour AR, Niknam T. A probabilistic multi-objective daily Volt/Var control at distribution networks including renewable energy sources. Energy 2011;36:3477–88.10.1016/j.energy.2011.03.052Search in Google Scholar

15. Coath G, Al-Dabbagh M, Halgamuge S. Particle swarm optimisation for reactive power and voltage control with grid-integrated wind farms. IEEE Power Eng Soc General Meeting Jun. 2004;1:303–8.10.1109/PES.2004.1372803Search in Google Scholar

16. Oshiro M, Uchida K, Senjyu T, Yona A. Voltage control in distribution systems considered reactive power output sharing in smart grid. Proc Elect Mach Syst, Incheon, Oct. 2010:458–63.Search in Google Scholar

17. Keane A, Hearne T, Fallon T, Brooks D. Volt/Var control for distributed generation. Proc IEEE PES Innovative Smart Grid Technologies (ISGT Europe) Dec. 2011:1–1.10.1109/ISGTEurope.2011.6162828Search in Google Scholar

18. Bayat B, Barband SA, Ebrahimi A. Real Time Voltage Control in Distribution Network Considering Renewable Energy Sources. CIRED Workshop on Integration of Renewables into the Distribution Grid May 2012:1–4.10.1049/cp.2012.0793Search in Google Scholar

19. Di Fazio AR, Fusco G, Russo M. Decentralized control of distributed generation for voltage profile optimization in smart feeders. IEEE Trans Smart Grid Sept. 2013;4:1586–96.10.1109/TSG.2013.2253810Search in Google Scholar

20. Falahi M, Butler-Purry K, Ehsani M. Dynamic reactive power control of islanded microgrids. IEEE Trans Power Syst Nov. 2013;28:3649–57.10.1109/TPWRS.2013.2246589Search in Google Scholar

21. Zhang W, Liu W, Wang X, Liu L, Ferrese F. Distributed multiple agent system based online optimal reactive power control for smart grids. IEEE Trans Smart Grid Sept. 2014;5:2421–31.10.1109/TSG.2014.2327478Search in Google Scholar

22. Malekpour AR, Niknam T. A probabilistic multi-objective daily volt/var control at distribution networks including renewable energy sources. Energy 2011;36:3477–88.10.1016/j.energy.2011.03.052Search in Google Scholar

23. Shu Z, Jirutitijaroen P. Latin hypercube sampling techniques for power systems reliability analysis with renewable energy sources. IEEE Trans Power Syst Nov. 2011;26:2066–73.10.1109/TPWRS.2011.2113380Search in Google Scholar

24. Zhang X, Flueck AJ, Nguyen CP. Agent-based distributed volt/var control with distributed power flow solver in smart grid. IEEE Trans Smart Grid Mar. 2016;7:600–7.10.1109/TSG.2015.2423683Search in Google Scholar

25. Hong YY, Lin FJ, Lin YC, Hsu FY. Chaotic PSO-Based VAR control considering renewables using fast probabilistic power flow. IEEE Trans Power Delivery Aug. 2014;29:1666–74.10.1109/TPWRD.2013.2285923Search in Google Scholar

26. Padilha-Feltrin A, Quijano Rodezno DA, Mantovani JRS. Volt-VAR multi-objective optimization to peak-load relief and energy efficiency in distribution networks. IEEE Trans Power Deliv Apr. 2015;30:618–26.10.1109/TPWRD.2014.2336598Search in Google Scholar

27. Ahmadi H, Martí JR, Dommel HW. A framework for volt-VAR optimization in distribution systems. IEEE Trans Smart Grid May 2015;6:1473–83.10.1109/TSG.2014.2374613Search in Google Scholar

28. Anilkumar R, Devriese G, Srivastava AK. Intelligent volt/VAR control algorithm for active power distribution system to maximize the energy savings. IEEE Ind Appl Soc Ann Meeting, Addison, TX, 2015:1–8.10.1109/IAS.2015.7356832Search in Google Scholar

29. Manbachi M, Farhangi H, Palizban A, Arzanpour S. A novel Volt-VAR optimization engine for smart distribution networks utilizing vehicle to grid dispatch. Elect Power Energy Syst 2016;74:238–51.10.1016/j.ijepes.2015.07.030Search in Google Scholar

30. Patel MR. Wind and solar power systems. Boca Raton, FL, USA: CRC Press, 1999.Search in Google Scholar

31. Hetzer J, Yu DC, Bhattarai K. An economic dispatch model incorporating wind power. IEEE Trans Energy Convers Jun. 2008;23:603–11.10.1109/TEC.2007.914171Search in Google Scholar

32. Justus CG, Hargraves WR, Mikhail A, Graber D. Methods for estimating wind speed frequency distributions. J Appl Meteorol Mar. 1978;17:350–3.10.1175/1520-0450(1978)017<0350:MFEWSF>2.0.CO;2Search in Google Scholar

33. Ackermann T. Wind power in power system. England: John Wiley & Sons, Ltd., 2005.10.1002/0470012684Search in Google Scholar

34. Usalola J, Castronuovo ED. Wind energy in electricity markets with high wind penetration. New York: Nova science publishers, Inc, 2009.Search in Google Scholar

35. Bryc W. The normal distribution: characterization with applications. New York: Springer-Verlag, 1995.10.1007/978-1-4612-2560-7Search in Google Scholar

36. Surender Reddy S, Bijwe PR, Abhyankar AR. Joint energy and spinning reserves market clearing for wind-thermal power system incorporating wind generation and load forecast uncertainties. IEEE Syst J Mar. 2015;9:152–64.10.1109/JSYST.2013.2272236Search in Google Scholar

37. Reddy SS, Momoh JA. Realistic and transparent optimum scheduling strategy for hybrid power system. IEEE Trans Smart Grid Nov. 2015;6:3114–25.10.1109/TSG.2015.2406879Search in Google Scholar

38. Shu Z, Jirutitijaroen P. Latin hypercube sampling techniques for power systems reliability analysis with renewable energy sources. IEEE Trans Power Syst 2011;26:2066–73.10.1109/TPWRS.2011.2113380Search in Google Scholar

39. Yu H, Chung C, Wong K, Lee H, Zhang J. Probabilistic load flow evaluation with hybrid latin hypercube sampling and cholesky decomposition. IEEE Trans Power Syst 2009;24:1–8.10.1109/TPWRS.2009.2016589Search in Google Scholar

40. Augugliaro A, Dusonchet L, Favuzza S, Sanseverino ER. Voltage regulation and power losses minimization in automated distribution networks by an evolutionary multi-objective approach. IEEE Trans Power Syst Aug. 2004;19:1516–27.10.1109/TPWRS.2004.825916Search in Google Scholar

41. Zhang W, Liu W, Wang X, Liu L, Ferrese F. Distributed multiple agent system based online optimal reactive power control for smart grids. IEEE Trans Smart Grid Sept. 2014;5:2421–31.10.1109/TSG.2014.2327478Search in Google Scholar

42. Zakariazadeh A, Jadid S, Siano P. Stochastic operational scheduling of smart distribution system considering wind generation and demand response programs. Elect Power Energy Syst 2014;63:218–25.10.1016/j.ijepes.2014.05.062Search in Google Scholar

43. Jirutitijaroen P, Singh C. Comparison of simulation methods for power system reliability indexes and their distributions. IEEE Trans Power Syst 2008;23:486–93.10.1109/TPWRS.2008.919425Search in Google Scholar

44. Razali NMM, Hashim AH. Backward reduction application for minimizing wind power scenarios in stochastic programming. Proc Int Power Eng Opt, Shah Alam, 2010:430–4.10.1109/PEOCO.2010.5559252Search in Google Scholar

45. Villanueva D, Feijóo A, Pazos JL. Probabilistic load flow considering correlation between generation, loads and wind power. Smart Grid Renewable Energy 2011;2:12–20.10.4236/sgre.2011.21002Search in Google Scholar

46. Li X, Cao J, Du D. Probabilistic optimal power flow for power systems considering wind uncertainty and load correlation. Neurocomputing 2015;148:240–7.10.1016/j.neucom.2013.09.066Search in Google Scholar

47. IEEE Reliability Test System. IEEE Trans Power App. and Sys Nov./ Dec. 1979;98 no. 6.10.1109/TPAS.1979.319398Search in Google Scholar

48. Billinton R, Li W. Reliability assessment of electrical power systems using Monte Carlo methods. New York: Plenum, 1994:299–309.10.1007/978-1-4899-1346-3Search in Google Scholar

49. Ugranli F, Karatepe E., Power system planning for maximizing intermittent energy sources using AC model. Innovative Smart Grid Technologies Europe, 4th IEEE/PES 2013:1–5. Lyngby10.1109/ISGTEurope.2013.6695475Search in Google Scholar

50. [Online]. Available: http://www.nrel.gov/midc/Search in Google Scholar

51. Abou AA, El Ela MA, Abido SR. Spea, optimal power flow using differential evolution algorithm. Elect Power Syst Res Jul. 2010;80:878–85.10.1016/j.epsr.2009.12.018Search in Google Scholar

52. Zhang H, Li P. Chance constrained programming for optimal power flow under uncertainty. IEEE Trans Power Syst Nov. 2011;26:2417–24.10.1109/TPWRS.2011.2154367Search in Google Scholar

53. Liu B. Uncertain programming. New York: Wiley, 1999.Search in Google Scholar

54. Yang N, Wen F. A chance constrained programming approach to transmission system expansion planning. Elect Power Syst Res 2005;75:171–7.10.1016/j.epsr.2005.02.002Search in Google Scholar

Published Online: 2016-4-21
Published in Print: 2016-6-1

©2016 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Review
  3. Detection of Frauds and Other Non-technical Losses in Power Utilities using Smart Meters: A Review
  4. Research Articles
  5. Improving the Dynamic Response during Field Weakening Control of IPMSM Drive System using Adaptive Hysteresis Current Control Technique
  6. Optimal Energy Management for a Smart Grid using Resource-Aware Utility Maximization
  7. Decentralized Charging of Plug-In Electric Vehicles Using Lagrange Relaxation Method at the Residential Transformer Level
  8. Power Quality Improvement in Induction Furnace by Harmonic Reduction Using Dynamic Voltage Restorer
  9. Feasibility of Stochastic Voltage/VAr Optimization Considering Renewable Energy Resources for Smart Grid
  10. Design and Analysis of Grid Connected Photovoltaic Fed Unified Power Quality Conditioner
  11. Sympathetic Trippings Blocking in Over Current Relay Coordination Algorithm during Steady State & Transient Network Topologies
  12. Application of Multi-Objective Human Learning Optimization Method to Solve AC/DC Multi-Objective Optimal Power Flow Problem
  13. Intelligent Energy Management System for PV-Battery-based Microgrids in Future DC Homes
  14. Optimum Location of Voltage Regulators in the Radial Distribution Systems
  15. Design of Passive Power Filter for Hybrid Series Active Power Filter using Estimation, Detection and Classification Method
https://doi.org/10.1515/ijeeps-2016-0009
Keywords for this article
optimal power flow; renewable energy resources; voltage/var control; stochastic programming; voltage stability

Articles in the same Issue

  1. Frontmatter
  2. Review
  3. Detection of Frauds and Other Non-technical Losses in Power Utilities using Smart Meters: A Review
  4. Research Articles
  5. Improving the Dynamic Response during Field Weakening Control of IPMSM Drive System using Adaptive Hysteresis Current Control Technique
  6. Optimal Energy Management for a Smart Grid using Resource-Aware Utility Maximization
  7. Decentralized Charging of Plug-In Electric Vehicles Using Lagrange Relaxation Method at the Residential Transformer Level
  8. Power Quality Improvement in Induction Furnace by Harmonic Reduction Using Dynamic Voltage Restorer
  9. Feasibility of Stochastic Voltage/VAr Optimization Considering Renewable Energy Resources for Smart Grid
  10. Design and Analysis of Grid Connected Photovoltaic Fed Unified Power Quality Conditioner
  11. Sympathetic Trippings Blocking in Over Current Relay Coordination Algorithm during Steady State & Transient Network Topologies
  12. Application of Multi-Objective Human Learning Optimization Method to Solve AC/DC Multi-Objective Optimal Power Flow Problem
  13. Intelligent Energy Management System for PV-Battery-based Microgrids in Future DC Homes
  14. Optimum Location of Voltage Regulators in the Radial Distribution Systems
  15. Design of Passive Power Filter for Hybrid Series Active Power Filter using Estimation, Detection and Classification Method
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