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Value assessment method for expansion planning of generators and transmission networks: a non-iterative approach

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Abstract

In the context of efficient generation expansion planning (GEP) and transmission expansion planning (TEP), value assessment method (VAM) is the critical topic to discuss. Presently, two well-known VAMs, min-cut max-flow (MCMF) and load curtailment strategy (LCS), are used for GEP and TEP. MCMF does not follow electrical laws and is unable to calculate congestion cost (CC) and re-dispatch cost (RDC). LCS calculates both, but in iterative way, thus takes a long time to provide solution. In the constrained network, multiple quantities like demand/energy not served (D/ENS) and generation not served (GNS), wheeling loss (WL), CC and RDC are existing together and thus have to be calculated together to encounter the loss in all aspects. Existing methods show limitations in this regard and do not calculate all above described quantities simultaneously. Thus, in this paper, a non-iterative VAM (NVAM) is presented based on electrical laws, which calculates value of the present and the planned systems by incorporating all system quantities of D/ENS, GNS, WL, CC and RDC together. Due to non-iterative batch approach, it is quite faster compared to the above-mentioned traditional VAMs, i.e., MCMF and LCS. Furthermore, comparative results on IEEE-5 bus and IEEE-24 bus power systems show its higher efficiency. The MATLAB code of the introduced NVAM is provided in “Appendix” for further development by the researchers.

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Abbreviations

BBIM:

Bus-branch incidence matrix

CC:

Congestion cost

CMRD:

Constrained market with reduced demand

CN:

Constraint network

ELD:

Economic load dispatch

EMRD:

Economic market with reduced demand

ENS:

Energy not served

DNS:

Demand not served

GNS:

Generation not served

HOU:

Hypothetical optimal unconstrained

RD:

Re-dispatch

RDC:

Re-dispatch cost

TEP:

Transmission expansion planning

GEP:

Generation expansion planning

LCC:

Life cycle costs

LCS:

Load curtailment strategy

MCMF:

Min-cut max-flow

MCS:

Monte Carlo simulation

NMC:

New marginal cost

ODNS:

Other buses than demand buses

OGNS:

Other buses than generator buses

UMTD:

Unconstrained market with targeted demand

VAM:

Value assessment method

WL:

Wheeling loss

AC :

Alternating current

DC :

Direct current

MW :

Megawatt

\(\mathbf A \) :

Bus-branch incidence matrix

B :

Total number of buses in the network

b :

Linear cost coefficient of generator

C :

Cost in $

\(\mathscr {C}_{i,s}\) :

Capacity of \(i\mathrm{th}\) line connected to bus ‘s’

c :

Quadratic cost coefficient of generator

\(C_C\) :

Congestion cost

\(C_\text {ED}\) :

Economic dispatch cost

\(C_\text {UED}\) :

Uneconomic dispatch cost

\(C_\text {RD}\) :

Re-dispatch Cost

\(c(q_{S-L})\) :

Sum of the capacities of all the elements defining the \(q_{S-L}\) cut, in MW

\(\mathscr {D}\) :

Demand at bus represented by subscript

\(\mathbf {D}\) :

Vector of demand

d :

Number of demand buses

\(\{d\}\) :

Set of demand buses

\(\mathscr {F}\) :

Power flow vector

\(\mathscr {F}_{S \rightarrow L}\) :

Flow in transmission line from node S to node L (in MW)

\(\mathscr {F}_{i,s}\) :

Flow in \(i\mathrm{th}\) incoming/outgoing line of bus s (in MW)

\(\mathscr {G}\) :

Generation in MW and nature is represented by subscript/superscript

\(\mathbf {G}\) :

Vector of generation

g :

Number of generators

\(\{g\}\) :

Set of generators

\({{\ell }}^{{{\mathrm{cut}}}}_s\) :

The amount of real power curtailed (DNS) at bus s

\(\mathbf{l}^{{{\mathrm{cut}}}}\) :

Vector of load curtailment

\(\lambda \) :

Marginal cost \(\$/\mathrm{MW}\)

\(\varLambda \) :

WL in MW

m :

Number of m incoming lines

\(\{m\}\) :

Set of m incoming lines

n :

Number of outgoing lines

\(\{n\}\) :

Set of n outgoing lines

\(\omega \) :

Re-dispatch cost $/MW

\(\mathbf {P}\) :

Power injection vector

\(\mathscr {P}\) :

Power transfer distribution function matrix

Q :

Set of all such \(q_{S-L}\) cuts

\(q_{S-L}\) :

Set of elements whose removal from the graph breaks all directed paths from node S to node L

\(\zeta \) :

Congestion cost in k$/MW

\(\bigtriangleup \) :

DNS in MW

\(\bigtriangledown \) :

GNS in MW

ED:

Economic dispatch of generators

k :

Index for constrained incoming lines

l :

Index for constrained outgoing lines

max:

Maximum

min:

Minimum

opti:

Optimal state of associated variables

over:

Over flow in lines

p :

Index for incoming lines

q :

Index for outgoing lines

red:

Reduced generation

s :

Bus index

sup:

Supplied generation/demand in constrained network

UED:

Uneconomic dispatch of generators

un:

Unconstrained

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Author information

Authors and Affiliations

  1. University of Information, Science and Technology, St. Paul the Apostle, Ohrid, Macedonia

    Neeraj Gupta, Mahdi Khosravy & Ninoslav Marina

  2. Department of Plant Engineering, Tata Motors Ltd., Mumbai, India

    Kumar Saurav

  3. Oakland University, Rochester, MI, USA

    Ishwar K. Sethi

Authors
  1. Neeraj Gupta
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  2. Mahdi Khosravy
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  3. Kumar Saurav
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  4. Ishwar K. Sethi
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  5. Ninoslav Marina
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Corresponding author

Correspondence to Neeraj Gupta.

Appendix: MATLAB code of NVAM function

Appendix: MATLAB code of NVAM function

1.1 Description of the input and output

FlowTr

Flow in transmission lines in unconstrained network, each column in this matrix is with respect to a particular demand scenario

Capacity \(\_\) Tr

Capacity of all lines arranged in a column, where number of column is equal to the number of demand scenarios taken

GenOpti

Economic load dispatch of the generators in unconstrained network, where each row subject to a particular generator and number of column equal to the number of demand scenarios

gen \(\_\) b

A column vector representing linear cost coefficient correspond to generators available in the network

gen \(\_\) c

A column vector representing quadratic cost coefficient correspond to generators available in the network

Incidence \(\_\) mat

As per the description in Eq. (17)

TDNS

Total DNS in the constrained network

TGNS

Total GNS in the constrained network

WL, CC & RDC

As for the description in the manuscript

1.2 Default values to test the function

figure a

1.3 NVAM function

figure b

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Gupta, N., Khosravy, M., Saurav, K. et al. Value assessment method for expansion planning of generators and transmission networks: a non-iterative approach. Electr Eng 100, 1405–1420 (2018). https://doi.org/10.1007/s00202-017-0590-7

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