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

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## 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

- NU
_{i} Total number of units connected to

*i*th bus- NL
Total number of buses which have loads

- M
Total number of contingency incidents

- (
*i*,*u*) *u*th unit generator connected to*i*th bus

## Constants

*a*_{i}Price factor proposed by generator for being available

*m*_{1i}Price factor proposed by generator for implementation in under excitation mode (absorbed reactive power)

*m*_{2i}Price factor of incurred losses in coil, proposed by generator for implementation in (

*Q*_{base},*Q*_{A}) zone*m*_{3i}Price factor of lost opportunity, proposed by generator for implementation in (

*Q*_{A},*Q*_{B}) zone*ρ*_{p(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})- VOLL
_{k} Value of lost load for the loads on bus

*K**Y*_{ik}Admittance between buses

*i*and*k*- \({\delta _{ik}}\)
Angle of admittance between buses

*i*and*k**P*_{is}Active power consumed by loads connected to

*i*th bus*Q*_{is}Reactive power consumed by loads connected to

*i*th bus*X*_{S}(*i*,*u*)Synchronous reactance

- VSM
^{Desired} 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

*P*_{G(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

*ρ*_{q0}Higher accepted price for reactive power availability in separate reactive power market

*ρ*_{q1}Higher accepted price for reactive power absorption in zones of (0 to

*Q*_{Min}) in separate reactive power market*ρ*_{q2}Higher accepted price for reactive power production in zones of (

*Q*_{A}to*Q*_{base})in separate reactive power market*ρ*_{q3}Higher accepted price for reactive power production in zones of (

*Q*_{B}to*Q*_{A}) in separate reactive power market*Q*_{1(i,u)}Reactive power absorbed in zones of (0 to

*Q*_{Min})*Q*_{2(i,u)}Reactive power produced in zones of (

*Q*_{A}to*Q*_{base})*Q*_{3(i,u)}Reactive power produced in zones of (

*Q*_{B}to*Q*_{A})*W*_{0(i,u)}Binary variable which state the

*u*th unit is selected for production or being on standby in separate reactive market*W*_{1(i,u)}Binary variable which state the

*u*th unit is working inside zones of (0 to*Q*_{Min})*W*_{2(i,u)}Binary variable which state the

*u*th unit is working inside zones of (*Q*_{A}to*Q*_{base})*W*_{3(i,u)}Binary variable which state the

*u*th unit is working inside zones of (*Q*_{B}to*Q*_{A})- \({{\rm RP}_{G(i,u)}^{j}}\)
Active power reserve required to produce by

*u*th unit at*j*th contingency incident- RP
_{(i,u)} Maximum required active power reserved capacity to produce by

*u*th unit connected to*i*th 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

*u*th unit at*j*th contingency incident- \({{\rm RQ}_{2(i,u)}^j}\)
Reactive power reserve required to produce by

*u*th unit at*j*th contingency incident- RQ
_{1(i,u)} Maximum required reactive power reserved capacity to absorb by

*u*th unit connected to*i*th bus- RQ
_{2(i,u)} Maximum required reactive power reserved capacity to produce by

*u*th unit connected to*i*th bus- \({{\rm ENS}_k^j}\)
Energy not supplied for bus

*k*at contingency incident*j*th*U*_{i}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

*u*th unit connected to*i*th bus is selected for production active power*I*_{a(i,u)}Armature persistent mode current

*E*_{f(i,u)}Exciting voltage

## Functions

- EPF
_{i} Expected payment function for generator connected to

*i*th bus- TRC
Total reactive power production cost in separate reactive power market

- LOC
_{i,u} Lost opportunity cost

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