Skip to main content
SpringerLink
Log in

A Benders decomposition algorithm for a multi-area, multi-stage integrated resource planning in power systems

  • Special Issue Paper
  • Published:
Journal of the Operational Research Society

Abstract

The aim of this paper is to propose an integrated model for resource planning in power systems by taking into account both supply and demand sides options simultaneously. At supply-side, investment in generation capacity and transmission lines is considered. Demand side management (DSM) technologies are also incorporated to correct the shape of the load duration curve in terms of peak clipping and load shifting programmes. A mixed integer non-linear programming model is developed to find the optimal location and timing of electricity generation/transmission as well as DSM options. To solve the resulting complex model, nonlinearity caused by transmission loss terms are first eliminated using the piecewise linearization technique. Then, a Benders decomposition (BD) algorithm is developed to solve the linearized model. The performance of the proposed BD algorithm is validated via applying it to the 6-bus Garver test system and a modified 21-bus IEEE reliability test system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5

References

  • Alguacil N, Motto AL and Conejo AJ (2003). Transmission expansion planning: A mixed-integer LP approach. IEEE Transactions on Power Systems 8 (3): 1070–1077.

    Article  Google Scholar 

  • Álvarez López J, Ponnambalam K and Quintana VH (2007). Generation and transmission expansion under risk using stochastic programming. IEEE Transactions on Power Systems 22 (3): 1369–1378.

    Article  Google Scholar 

  • Antunes CH, Martins AG and Brito IS (2004). A multiple objective mixed integer linear programming model for power generation expansion planning. Energy 29 (4): 613–627.

    Article  Google Scholar 

  • Becerra-Lopez HR and Golding P (2008). Multi-objective optimization for capacity expansion of regional power-generation systems: Case study of far west Texas. Energy Conversion and Management 49 (6): 1433–1445.

    Article  Google Scholar 

  • Benders JF (1962). Partitioning methods for solving mixed-variables programming problems. Numerische Mathematik 4 (4): 238–252.

    Article  Google Scholar 

  • Binato S, Veiga M, Pereira F and Granville S (2001). A new Benders decomposition approach to solve power transmission network design problems. IEEE Transactions on Power Systems 16 (2): 235–240.

    Article  Google Scholar 

  • Bulent Tor O, Nezih Guven A and Shahidehpour M (2008). Congestion-driven transmission planning considering the impact of generator expansion. IEEE Transactions on Power Systems 23 (2): 781–789.

    Article  Google Scholar 

  • Castillo E, Conejo AJ, Pedregal P, García R and Alguacil N (2001). Building and Solving Mathematical Programming Models in Engineering and Science. Wiley: New York.

    Book  Google Scholar 

  • Cordeau JF, Pasin F and Solomon M (2006). An integrated model for logistics network design. Annals of Operation Research 144 (1): 59–82.

    Article  Google Scholar 

  • Das PK, Chanda RS and Bhattacharjee PK (2005). Combined generation and transmission system expansion planning using implicit enumeration and linear programming technique. IE(I) Journal-EL 86 (1): 110–116.

    Google Scholar 

  • Delgado RM (1985). Demand side management alternatives. IEEE Conference 73 (10): 1471–1489.

    Google Scholar 

  • Gellings CW (1985). The concept of demand-side management for electric utilities. IEEE Conference 73 (10): 1468–1470.

    Google Scholar 

  • Haddadian H, Hosseini SH, Shayeghi H and Shayanfar HA (2011). Determination of optimum generation level in DTEP using a GA-based quadratic programming. Energy Conversion and Management 52 (2): 382–390.

    Article  Google Scholar 

  • Hobbs BF (1995). Optimisation methods for electric utility resource planning. European Journal of Operational Research 83 (1): 1–20.

    Article  Google Scholar 

  • Huang YH and Wu JH (2008). A portfolio risk analysis on electricity supply planning. Energy Policy 36 (2): 627–641.

    Article  Google Scholar 

  • International Atomic Energy Agency (IAEA) (2001). WIEN Automatic System Planning (WASP) Package, A Computer Code for Power Generation System Expansion Planning, Version WASP-IV User's Manual. IAEA: Vienna, Austria.

  • Kannan S, Slochanal SMR and Padhy NP (2005). Application and comparison of metaheuristic techniques to generation expansion planning problem. IEEE Transactions on Power Systems 20 (1): 466–475.

    Article  Google Scholar 

  • Kannan S, Baskar S, McCalley JD and Murugan P (2009). Application of NSGA-II algorithm to generation expansion planning. IEEE Transactions on Power Systems 24 (1): 454–461.

    Article  Google Scholar 

  • Kucukyazicı B, Ozdamar L and Pokharel S (2005). Developing concurrent investment plans for power generation and transmission. European Journal of Operational Research 166 (2): 449–468.

    Article  Google Scholar 

  • Liu G, Sasaki H and Yorino N (2001). Application of network topology to long range composite expansion planning of generation and transmission lines. Electric Power Systems Research 57 (3): 157–162.

    Article  Google Scholar 

  • Ma H and Shahidehpour M (1998). Transmission-constrained unit commitment based on Benders decomposition. Electrical Power and Energy Systems 20 (4): 287–294.

    Article  Google Scholar 

  • Malik AS (2001). Modeling and economic analysis of DSM programs in generation planning. Electrical Power and Energy Systems 23 (5): 413–419.

    Article  Google Scholar 

  • Malik AS (2007). Impact on power planning due to demand-side management (DSM) in commercial and government sectors with rebound effect—A case study of central grid of Oman. Energy 32 (11): 2157–2166.

    Article  Google Scholar 

  • Meza JLC, Yildirim MB and Masud ASM (2007). A model for the multiperiod multiobjective power generation expansion problem. IEEE Transactions on Power Systems 22 (2): 871–878.

    Article  Google Scholar 

  • Murugan P, Kannan S and Baskar S (2009). NSGA-II algorithm for multi-objective generation expansion planning problem. Electric Power Systems Research 79 (4): 622–628.

    Article  Google Scholar 

  • Reliability Test System Task Force (1979). IEEE reliability test system. IEEE Transactions on Power Systems 6: 2047–2054.

  • Seifi H, Sepasian MS, Haghighat H, Foroud AA, Yousefi GR and Rae S (2007). Multi-voltage approach to long-term network expansion planning. IET Generation, Transmission, Distribution 1 (5): 826–835.

    Article  Google Scholar 

  • Sepasian MS, Seifi H, Akbari Foroud A and Hatami AR (2009). A multiyear security constrained hybrid generation-transmission expansion planning algorithm including fuel supply costs. IEEE Transactions on Power Systems 24 (3): 1609–1618.

    Article  Google Scholar 

  • Shahidehpour M and Fu Y (2005). Benders decomposition: Applying Benders decomposition to power systems. IEEE Power Energy Magazine 3 (2): 20–21.

    Article  Google Scholar 

  • Sheen JN (2005). Fuzzy financial analyses of demand-side management alternatives. IEE Proceedings—Generation, Transmission, Distribution 152 (2): 215–226.

    Article  Google Scholar 

  • Sirikum J, Techanitisawad A and Kachitvichyanukul V (2007). A new efficient GA-Benders’ decomposition method: For power generation expansion planning with emission controls. IEEE Transactions on Power Systems 22 (3): 1092–1100.

    Article  Google Scholar 

  • Stoll HG (1989). Least-cost Electric Utility Planning. John Wiley & Sons: New York.

    Google Scholar 

  • Tanatvanit S, Limmeechokchai B and Shrestha RM (2004). CO2 mitigation and power generation implications of clean supply-side and demand-side technologies in Thailand. Energy Policy 32 (1): 83–90.

    Article  Google Scholar 

  • Tang L, Jiang W and Saharidis GKD (2012). An improved Benders decomposition algorithm for the logistics facility location problem with capacity expansions. Annals of Operation Research. DOI 10.1007/s10479-011-1050-9.

  • Unsihuay-Vila C, Marangon-Lima JW, Souza ACZ, Perez-Arriaga IJ and Balestrassi PP (2010). A model to long-term, multiarea, multistage, and integrated expansion planning of electricity and natural gas systems. IEEE Transactions on Power Systems 25 (2): 1154–1168.

    Article  Google Scholar 

  • Unsihuay-Vila C, Marangon-Lima JW, Souza ACZ and Perez-Arriaga IJ (2011). Multistage expansion planning of generation and interconnections with sustainable energy development criteria: A multiobjective model. Electrical Power and Energy Systems 33 (2): 258–270.

    Article  Google Scholar 

  • Üster H, Easwaran G, Akçali E and Çetinkaya S (2007). Benders decomposition with alternative multiple cuts for a multi-product closed-loop supply chain network design model. Naval Research Logistics 54 (8): 890–907.

    Article  Google Scholar 

  • Westermann D and John A (2007). Demand matching wind power generation with wide-area measurement and demand-side management. IEEE Transaction on Energy Conversion 22 (1): 145–149.

    Article  Google Scholar 

  • Zhou M, Li G and Zhang P (2006). Impact of demand side management on composite generation and transmission system reliability. PSCE conference 819–824, Baoding, China, October 29–November 1.

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran

    M Jenabi & S M T Fatemi Ghomi

  2. Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

    S A Torabi

  3. Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran

    S H Hosseinian

Authors
  1. M Jenabi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S M T Fatemi Ghomi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S A Torabi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S H Hosseinian
    View author publications

    You can also search for this author in PubMed Google Scholar

Appendix

Appendix

illustration

figure a

Additional Indices

n :

Index for counting number of new generation facilities

ℓ:

Index for counting number of new line

Parameters

RM :

Reserve margin (%)

r :

Discount rate

du m t :

Duration time of block m (h) at stage t (h)

lg et t :

Loss coefficient of generation of the et at stage t (%)

lg nt t :

Loss coefficient of generation of the nt at stage t (%)

D i, m t :

Demand during operating mode m at stage t in node i (MW)

IT i, j t, l′ :

Cost of constructing candidate transmission line l′ between nodes i and j at stage t ($)

IG nt, i t :

Investment cost of generation technology nt in node i at stage t ($/MW)

GC nt, m, i t :

Variable generation Cost of nt in operating mode m of stage t in node i ($/MWh)

GC et, m, i t :

Variable generation cost of et in operating mode m of stage t in node i ($/MWh)

x nt :

Typical capacity size of candidate generator of type nt (MW)

Γi, jl′:

Susceptance of the candidate line l′ between nodes i and j

Γi, jl:

Susceptance of the existing line l between nodes i and j

ɛ i, j l′ :

Conductance of the candidate line l′ between nodes i and j

ɛ i, j l :

Conductance of the existing line l between nodes i and j

α et t :

Equivalent availability of et at stage t (%)

α nt t :

Equivalent availability of nt at stage t (%)

DSM Cd, it:

DSM costs for implementing DSM programme d in node i at stage t ($)

SDS Md, m, it:

Power saved after implementing DSM programme d in node i at stage t (MW)

:

Total installed generating capacity of et at node i (MW)

N i, j l :

Number of existing lines between nodes i and j

:

Maximum power flow between nodes i and j via existing line l (MW)

:

Maximum power flow between nodes i and j via candidate line l′ (MW)

:

Maximum number of candidate line l′ that can be installed at stage t

:

Maximum number of DSM programmes implementable at stage t

UG nt t :

Maximum generation capacity of nt that can be installed at stage t

Variables

Y ℓ, i, j t, l′ :
X n, nt, i t :
DSM d, i t :
G n, nt, m, i t :

Utilization capacity of the nt at operating mode m of stage t in node i (MW)

G n, et, m, i t :

Utilization capacity of the nt at operating mode m of stage t in node i (MW)

f ℓ, i, j, m t, l′ :

Power-flow on line ℓth of type l′ connecting i and j at operating mode m of stage t

f i, j, m t, l :

Power-flow on line(s) of type l connecting i and j at operating mode m of stage t

θ i, m t :

Nodal angle at operating mode m of stage t in node i

U m, i t :

Unserved energy in node i at operating mode m of stage t

λ i, m t :

Dual variable corresponding to node balance constraints

δ i, j, m t, l :

Dual variable corresponding to second Kirchhoff's law for existing lines constraints

δ1ℓ, i, j, mt, l′:

Dual variable corresponding to second

δ2ℓ, i, j, mt, l′:

Kirchhoff's law for candidate lines constraints

μ1et, mt, i:

Dual variable corresponding to existing generation capacity constraints

μ2n, ,nt, mt, i:

Dual variable corresponding to candidate generation capacity constraints

β1i, j, mt, l, s:

Dual variable corresponding to transmission capacity constraints of line type l

β2ℓ, i, j, mt, l′, s:

Dual variable corresponding to transmission capacity constraints of line type l′

w1i, j, mt, l:

Dual variable corresponding to constraints number 34

w2ℓ, i, j, mt, l′:

Dual variable corresponding to constraints number 35

σ1i, j, mt, σ2i, j, mt:

Dual variables corresponding to stability constraints

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jenabi, M., Fatemi Ghomi, S., Torabi, S. et al. A Benders decomposition algorithm for a multi-area, multi-stage integrated resource planning in power systems. J Oper Res Soc 64, 1118–1136 (2013). https://doi.org/10.1057/jors.2012.142

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1057/jors.2012.142

Keywords

Search

Navigation