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Stochastic economic analysis of FACTS devices on contingent transmission networks using hybrid biogeography-based optimization

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Abstract

Flexible AC transmission systems (FACTS) devices have advantages of enhancing AC system controllability and stability, increasing power transfer capability and relieving congestion. Finding the best sizing and siting of them is obligatory to obtain the maximum benefit. In this paper, the optimum planning is done for determining the suitable sizing and siting of the FACTS devices during their lifetime span. The proposed planning approach is implemented to the networks, which are suffering from the contingency to demonstrate that how proper sizing and siting of the FACTS devices are able to deal with the existing problems in such networks. In fact, the maximum social welfare, reducing load shedding cost and construction cost of the new branches besides of the technical issues such as voltage improvement are the main concerns of the present work. To accomplish these aims accurately and reduce the computation time, a hybrid approach, consisting of mathematical and heuristic methods, is proposed for solving the proposed planning problem. The mentioned algorithm is a combination of biogeography-based optimization (BBO) as a heuristic algorithm and nonlinear programming as a mathematical approach. Furthermore, since the stochastic natures of renewable energy sources and load variations contribute to the optimum decisions, the stochastic formulation has been considered in the planning problem using the efficient point estimation (\( 2m + 1 \)) scheme. Finally, the proposed planning approach is tested on different test systems, namely IEEE 14-bus, IEEE 57-bus and IEEE 300-bus, in order to verify its effectiveness from a different point of views.

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Abbreviations

l :

Index for load

n, m :

Indices for node

g :

Index for generator

h :

Index for hour

y :

Index for year

s :

Index for scenario

f :

Index for FACTS devices

j :

Index for uncertain variable in (\( 2m + 1 \)) scheme

\( \omega \) :

Index for habitat

\( \varphi \) :

Index for SIV in each habitat

iter:

Index for iteration

NPV:

Index for net present value of the variable

FACTS:

State with FACTS devices

NOFACTS:

State without FACTS devices

exp:

Superscript for expected value of the variable

Max:

Superscript for maximum amount of the variable

Min:

Superscript for minimum amount of the variable

new:

Superscript for updated variable

BBO:

Biogeography-based optimization

\( A,B \) :

Shape and scale of the Weibull distribution

\( P_{\text{wr}} \) :

Rated power of the wind

a, b, c :

Coefficients of bid function of the interruptible loads

\( v_{\text{i}} \) :

Cut-in speed

\( v_{\text{r}} \) :

Rated speed

\( v_{\text{o}} \) :

Cut-out speed

\( N_{\text{TCSC}} \) :

Number of the TCSC

\( N_{\text{SVC}} \) :

Number of the SVC

\( N_{\text{scen}} \) :

Number of the scenarios

\( n_{G} \) :

Number of the generators

\( n_{l} \) :

Number of the load

\( n_{\text{lifetime}} \) :

Lifetime of the FACTS devices

rate:

Rate of interest

\( {\text{price}}^{\text{shed}} \) :

Price of the load shedding ($/MW)

\( L_{\text{int}} \) :

Set of the interruptible load

\( \alpha \) :

Fixed coefficient in BBO algorithm

\( v \) :

Velocity of wind

\( P_{w} \) :

Wind output power

\( P_{g} \) :

Generator output active power (MW)

\( Q_{g} \) :

Generator output reactive power (MW)

\( P^{\text{load}} \) :

Active load in each node (MW)

\( Q^{\text{load}} \) :

Reactive load in each node (MW)

\( P^{\text{fc}} \) :

Forecasted active power in each node (MW)

\( P^{\text{shed}} \) :

Active shed power in each node (MW)

\( C_{\text{Gen}} \) :

Cost function of the diesel generator

\( {\text{Cost}}_{\text{TCSC}} \) :

Investment cost of the TCSC per kVAr

\( {\text{Cost}}_{\text{SVC}} \) :

Investment cost of the SVC per kVAr

\( {\text{Cost}}_{\text{Install,FACTS}} \) :

Total investment cost of the FACTS devices

Ben:

The obtained benefit of the TRANSCO

\( S_{\text{SVC}} \) :

SVC capacity in MVAr

\( S_{\text{TCSC}} \) :

TCSC capacity in MVAr

Bid:

Interruptible load bid

V :

Voltage magnitude of each node

\( I^{\text{line}} \) :

Line current

prob:

Probability of each scenario

lmp:

Locational marginal price ($/MW)

\( \chi \) :

Location of the particular concentration in (\( 2m + 1 \)) scheme

\( \xi \) :

Standard deviation of the particular variable

\( \lambda \) :

Standard control moment of the uncertain variable

w :

Weight of the calculated concentration

x :

Decision variable in each habitat in BBO algorithm

\( \mu_{\text{BBO}} \) :

Emigration rate in BBO algorithm

\( \lambda_{\text{BBO}} \) :

Immigration rate in BBO algorithm

\( f_{\text{wind}} \) :

Probability density function of the wind speed

\( f_{\text{load}} \) :

Probability density function of the load

\( F(.) \) :

Active power balance

\( G(.) \) :

Reactive power balance

\( N(.) \) :

Normal distribution

\( f \) :

Probability distribution density of particular uncertain variable

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Authors and Affiliations

  1. Department of Electrical Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran

    Sina Ghaemi, Farid Hamzeh Aghdam & Amin Safari

  2. Center for Energy Science and Technology, Skolkovo Institute of Science and Technology, Moscow, Russia

    Meisam Farrokhifar

Authors
  1. Sina Ghaemi
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  2. Farid Hamzeh Aghdam
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  3. Amin Safari
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  4. Meisam Farrokhifar
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Correspondence to Amin Safari.

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Ghaemi, S., Hamzeh Aghdam, F., Safari, A. et al. Stochastic economic analysis of FACTS devices on contingent transmission networks using hybrid biogeography-based optimization. Electr Eng 101, 829–843 (2019). https://doi.org/10.1007/s00202-019-00825-6

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