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Arabian Journal for Science and Engineering

, Volume 39, Issue 6, pp 4789–4804 | Cite as

Joint Energy and Reactive Power Market Considering Coupled Active and Reactive Reserve Market Ensuring System Security

  • Hamed Ahmadi
  • Asghar Akbari ForoudEmail author
Research Article - Electrical Engineering

Abstract

Reactive power market is usually held as independent from energy and reserved active power markets; however, active and reactive power are in close relation due to a variety of mediums such as load flow equations, current limitations on the network lines, and synchronous generator capacity curve. Therefore, reactive power market conditions can affect active and reactive power markets. A new structure for joint energy and reactive power market (JERPM) is proposed in this article to resolve the difficulties pertaining interactions between active and reactive power markets. Holding a new market called joint active and reactive power reserved market (JARPRM) is proposed afterwards. Some revisions have been made in lost opportunity cost calculations in JERPM, and availability cost payment is also omitted from the model here. The objective function of JARPRM market is to minimize the costs of simultaneous active and reactive power production, and the costs of energy not supplied. This market is run using voltage stability constraints for all possible contingency incidents. The level of reserved power required by the system is determined accordingly. The proposed market model is simulated on a 24-bus IEEE-RTS network and the results are compared to traditional independent markets.

Keywords

Reactive power market Energy market Reserve market Joint markets Voltage stability 

List of symbols

Sets and indices

i, k

Index for buses

u

Index for unit generators

j

Contingency index

s

Index for loads

N

Total number of buses

NB

Total number of buses which have generators

NUi

Total number of units connected to ith bus

NL

Total number of buses which have loads

M

Total number of contingency incidents

(i,u)

uth unit generator connected to ith bus

Constants

ai

Price factor proposed by generator for being available

m1i

Price factor proposed by generator for implementation in under excitation mode (absorbed reactive power)

m2i

Price factor of incurred losses in coil, proposed by generator for implementation in (Q base, Q A) zone

m3i

Price factor of lost opportunity, proposed by generator for implementation in (Q A, Q B) zone

ρp(i, u)

Marginal cost proposed for producing active power

\({\hat{\rho}_{p(i, u)}}\)

Price proposed for active power production availability

\({\hat{\rho}_{q1(i, u)}}\)

Prices proposed for being available to absorb reactive power in zones (0 to Q Min)

\({\hat{\rho}_{q2(i,u)}}\)

Prices proposed for being available to produce reactive power in zones (Q A to Q base)

VOLLk

Value of lost load for the loads on bus K

Yik

Admittance between buses i and k

\({\delta _{ik}}\)

Angle of admittance between buses i and k

Pis

Active power consumed by loads connected to ith bus

Qis

Reactive power consumed by loads connected to ith bus

XS(i,u)

Synchronous reactance

VSMDesired

Minimum desired value for VSM index at contingency incidents

Variables

\({\rho _{p( {\rm MCP})}^{\rm sep}}\)

Higher accepted price for active power production in separate active power market

\({\rho _{p( {\rm MCP})}^{\rm sim}}\)

Higher accepted price for active power production in JERPM

PG(i,u)

Active power produced

\({P_{{\rm G}( {i,u})}^{\rm sep}}\)

Active power produced in separate active power market

\({P_{{\rm G}( {i,u})}^{\rm sim}}\)

Active power produced in JERPM

ρq0

Higher accepted price for reactive power availability in separate reactive power market

ρq1

Higher accepted price for reactive power absorption in zones of (0 to Q Min) in separate reactive power market

ρq2

Higher accepted price for reactive power production in zones of (Q A to Q base)in separate reactive power market

ρq3

Higher accepted price for reactive power production in zones of (Q B to Q A) in separate reactive power market

Q1(i,u)

Reactive power absorbed in zones of (0 to Q Min)

Q2(i,u)

Reactive power produced in zones of (Q A to Q base)

Q3(i,u)

Reactive power produced in zones of (Q B to Q A)

W0(i,u)

Binary variable which state the uth unit is selected for production or being on standby in separate reactive market

W1(i,u)

Binary variable which state the uth unit is working inside zones of (0 to Q Min)

W2(i,u)

Binary variable which state the uth unit is working inside zones of (Q A to Q base)

W3(i,u)

Binary variable which state the uth unit is working inside zones of (Q B to Q A)

\({{\rm RP}_{G(i,u)}^{j}}\)

Active power reserve required to produce by uth unit at jth contingency incident

RP(i,u)

Maximum required active power reserved capacity to produce by uth unit connected to ith bus

\({{\rm RP}_{(i,u)}^{\rm max}}\)

Active reserved amount determined in independent reserved active power market

\({{\rm RQ}_{1(i,u)}^j }\)

Reactive power reserve required to absorb by uth unit at jth contingency incident

\({{\rm RQ}_{2(i,u)}^j}\)

Reactive power reserve required to produce by uth unit at jth contingency incident

RQ1(i,u)

Maximum required reactive power reserved capacity to absorb by uth unit connected to ith bus

RQ2(i,u)

Maximum required reactive power reserved capacity to produce by uth unit connected to ith bus

\({{\rm ENS}_k^j}\)

Energy not supplied for bus k at contingency incident jth

Ui

Voltage for bus i

\({\theta _{i}}\)

Angle of voltage for bus i

S(i,k)

Apparent power through the line between buses i and k

Z(i,u)

Binary variable which states the uth unit connected to ith bus is selected for production active power

Ia(i,u)

Armature persistent mode current

Ef(i,u)

Exciting voltage

Functions

EPFi

Expected payment function for generator connected to ith bus

TRC

Total reactive power production cost in separate reactive power market

LOCi,u

Lost opportunity cost

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Copyright information

© King Fahd University of Petroleum and Minerals 2014

Authors and Affiliations

  1. 1.Electrical and Computer Engineering FacultySemnan UniversitySemnanIran

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