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Day-ahead multi-objective procurement of voltage control ancillary service in dynamic wind-solar incorporated deregulated power system

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Abstract

The ancillary services are becoming more important due to the increasing integration of non-dispatchable and intermittent renewable energy sources. Such behavior under deregulation necessitates the procurement of these services suitably. This paper presents the multi-objective procurement of voltage control ancillary service in a dynamic pool deregulated system that is contingent to wind and solar power generation uncertainties. The shunt capacitors bid to supply this service and their switchings, although restricted due to life expectancy, depend on locational marginal prices. An improved multi-objective artificial electric field algorithm, which adopts the concept of Pareto-based non-dominated sorting, is presented to co-optimize total cost and voltage deviation. The particle’s positions are updated through randomly picked Pareto solution to enhance exploitation capability. The sign and reorder mutation operations are employed to maintain diversity in the population, improve exploration, and evade local optima trap. The performance is investigated for different levels of wind and solar penetration on IEEE 30-bus and IEEE 118-bus test systems. The convergence of presented algorithm is analyzed and compared with other algorithms through statistical metrics and associated boxplots.

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Abbreviations

AEFA:

Artificial electric field algorithm

AS:

Ancillary services

I-MOAEFA:

Improved multi-objective AEFA

LMP:

Locational marginal price

MOAEFA:

Multi-objective AEFA

MOPSO:

Multi-objective PSO

PDF:

Probability density function

PSO:

Particle swarm optimization

PV:

Photovoltaic

RES:

Renewable energy sources

SO:

System operator

VAr:

Reactive power

VCAS:

Voltage control ancillary service

\(C_\textrm{R}\), \(C_\textrm{P}\) :

Reserve and penalty cost functions

\(C_\textrm{gps}\), \(d_\textrm{s}\) :

Active power generation cost and cost coefficient of \(s\textrm{th}\) solar unit

\(C_\textrm{gpu}\), \(C_\textrm{gqu}\) :

Active and reactive power generation cost of \(u\textrm{th}\) thermal unit

\(C_\textrm{gpw}\), \(C_{gqw}\) :

Active and reactive power generation cost of \(w\textrm{th}\) wind unit

\(C_{opu}\), \(C_\textrm{opw}\) :

Opportunity cost of \(u\textrm{th}\) thermal unit and \(w\textrm{th}\) wind unit

\(C_\textrm{vsh}\), \(C_\textrm{dsh}\) :

Reactive power supply cost and depreciation cost of \(sh\textrm{th}\) shunt capacitor

E :

Expectation of available power power

LMP, IC :

Locational marginal price and investment cost of capacitor

\(N^{-}\), \(N^{+}\) :

Number of discrete bins on left and right side of scheduled power

\(N_\textrm{b}\), \(N_{s\mathrm h}\), \(N_\textrm{pq}\) :

Number of buses, shunt capacitors, and load buses

\(N_\textrm{u}\), \(N_\textrm{w}\), \(N_\textrm{s}\) :

Number of thermal, wind, and solar units

\(P_\textrm{R}\), \(P_\textrm{gw}\) :

Rated and scheduled active power from \(w\textrm{th}\) wind unit

\(P_\textrm{S}\), \(P_\textrm{gs}\) :

Rated and scheduled active power from \(s\textrm{th}\) solar unit

\(P_\textrm{gu}\), \(Q_\textrm{gu}\) :

Active and reactive power generation from \(u\textrm{th}\) thermal unit

\(P_\textrm{gw}^{a\mathrm l}\), \(P_\textrm{gs}^\textrm{al}\) :

Available active power from \(w\textrm{th}\) wind and \(s\textrm{th}\) solar unit

\(P_\mathrm{wn+}\), \(P_\mathrm{sn+}\) :

Available wind and solar power output more than scheduled power

\(P_\mathrm{wn-}\), \(P_\mathrm{sn-}\) :

Available wind and solar power output less than scheduled power

\(Q_\textrm{R}\), \(Q_\textrm{gw}\) :

Rated and scheduled VAr from \(w\textrm{thth}\) wind unit

\(Q_\textrm{c}\), \(Q_\textrm{sh}\) :

VAr capacity and output of shunt capacitor

\(R_\textrm{c}\), \(I_\textrm{std}\) :

Certain irradiance point and standard solar irradiance

\(S_\textrm{jk}\) :

Line flow between buses j and k

\(V_\textrm{p}\) :

Voltage magnitudes of \(p\textrm{th}\) bus

\(\varDelta Q_\textrm{sh}\), \(R_\textrm{p}\) :

Change in shunt capacitor’s output and efficiency rate of reactive power

\(\bar{S_\textrm{u}}\), \(\bar{S_\textrm{w}}\) :

Maximum apparent power of \(u\textrm{th}\) thermal unit and \(w\textrm{th}\) wind unit

\(\gamma \), \(\beta \) :

Scale and shape parameter for Weibull PDF

\(\mu \), \(\sigma \) :

Mean and standard deviation of Log-normal PDF

\(a'_\textrm{u}\), \(b'_\textrm{u}\), \(c'_\textrm{u}\) :

Reactive power cost coefficients of \(u\textrm{th}\) thermal unit

\(a_\textrm{u}\), \(b_\textrm{u}\), \(c_\textrm{u}\) :

Active power cost coefficients of \(u\textrm{th}\) thermal unit

\(d_\textrm{w}\), \(d'_\textrm{w}\) :

Active and reactive power cost coefficient of \(w\textrm{th}\) wind unit

\(f_{sn-}\), \(f_{sn+}\) :

Relative frequency of \(P_{sn-}\) and \(P_{sn+}\) occurrence

\(f_\textrm{s}\), \(f_\textrm{w}\) :

Probability of available solar and wind power, respectively

\(f_\textrm{v}(v)\), \(f_\textrm{I}(I)\) :

Weibull and Log-normal PDFs

\(f_\mathrm{wn-}\), \(f_\mathrm{wn+}\) :

Relative frequency of \(P_{wn-}\) and \(P_{wn+}\) occurrence

\(k_\textrm{R}\), \(k_\textrm{P}\) :

Reserve and penalty cost coefficient

n :

Number of switching for capacitors

t, \(N_\textrm{T}\) :

Time interval in hours and total time period

v, I :

Speed of the wind and solar irradiation

\(v_\textrm{in}\), \(v_{o}\), \(v_\textrm{r}\) :

Cut-in, cut-out, and rated wind speed

\(E_{k}\), \(Q_{k}\) :

Electric field and charge of \(k\textrm{th}\) agent

\(F_{k}\), \(M_{k}\) :

Total force and inertial mass on \(k\textrm{th}\) agent

K, \(K_{0}\) :

Coulomb constant and its initial value

\(N_{a}\), \(N_\textrm{ob}\), D :

Number of agents, objectives, and non-dominated solutions

\(O_{j}\) :

Objective function

\(P_\textrm{best}\) :

Set of agents with best fitness value and biggest mass

\(P_{m}\), \(P_{s}\) :

Reorder and sign mutation probability

\(V_{k}^{\prime }\), \(V_{k}^{\prime \prime }\) :

Updated velocity using sign and reorder mutation operator

\(X_{Gb}\), \({\textbf {X}}_\textrm{Gbest}\) :

Global best value and set of non-dominated solutions

\(X_{k}\), \(V_{k}\), \(a_{k}\) :

Position, velocity, and acceleration of \(k\textrm{th}\) agent

\(\bar{d}\), \(\mu _{j}\) :

Average of all distances \(d_{a}\) and membership function

\(d_{a}\), \(d_{n}\), \(d_{x}\) :

Euclidean distance between adjacent, boundary, and extreme solutions

\(fit_{k}\), \(p_{k}\) :

Fitness value and position of best fitness value attained by \(k\textrm{th}\) agent

i, \(i\textrm{max}\) :

Current iteration number and total number of iterations

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Acknowledgements

This work was carried out with the financial support from the Department of Science and Technology (DST) under Innovation in Science Pursuit for Inspired Research (INSPIRE) Fellowship Code- IF170542.

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  1. Thapar Institute of Engineering and Technology, Patiala, India

    Akanksha Sharma & Sanjay K. Jain

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Sharma, A., Jain, S.K. Day-ahead multi-objective procurement of voltage control ancillary service in dynamic wind-solar incorporated deregulated power system. Electr Eng 105, 1431–1446 (2023). https://doi.org/10.1007/s00202-023-01749-y

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