Multi-Objective based Optimal Energy and Reactive Power Dispatch in Deregulated Electricity Markets

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 8, No. 5, October 2018, pp. 3427~3435
ISSN: 2088-8708, DOI: 10.11591/ijece.v8i5.pp3427-3435  3427
Journal homepage: http://iaescore.com/journals/index.php/IJECE
Multi-Objective based Optimal Energy and Reactive Power
Dispatch in Deregulated Electricity Markets
Surender Reddy Salkuti
Department of Railroad and Electrical Engineering, Woosong University, Daejeon, Republic of Korea
Article Info ABSTRACT
Article history:
Received Apr 9, 2018
Revised Jun 8, 2018
Accepted Jun 21, 2018
This paper presents a day-ahead (DA) multi-objective based joint energy and
reactive power dispatch in the deregulated electricity markets. The traditional
social welfare in the centralized electricity markets comprises of customers
benefit function and the cost function of active power generation. In this
paper, the traditional social welfare is modified to incorporate the cost of
both active and reactive power generation. Here, the voltage dependent load
modeling is used. This paper brings out the unsuitability of traditional single
objective functions, e.g., social welfare maximization (SWM), loss
minimization (LM) due to the reduction of amount of load served. Therefore,
a multi-objective based optimization is required. This paper proposes four
objectives, i.e., SWM, load served maximization (LSM), LM and voltage
stability enhancement index (VSEI); and these objectives can be combined as
per the operating condition. The simulation studies are performed on IEEE
30 bus test system by considering the both traditional constant load modeling
and the proposed voltage dependent load modeling.
Keyword:
Evolutionary algorithms
Load modeling
Market clearing
Multi-objective optimization
Social welfare
Copyright © 2018 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Surender Reddy Salkuti,
Department of Railroad and Electrical Engineering,
Woosong University,
Jayang-dong, Dong Gu, Daejeon, 300718, Republic of Korea.
Email: surender@wsu.ac.kr
NOMENCLATURE
a0 Availability price offer (in $).
NG Number of generators participating in the market clearing.
ND Number of load demands participating in the market clearing.
np, nq Voltage exponents.
Active power output from ith
generating unit at hour k.
RRi Ramp rate limits of ith
generating unit.
CGi(PGi) Cost function for generating the active power PGi.
BDi(PDi) Demand function at bus i.
ai, bi, ci Generator cost coefficients of ith
generator bus.
di, ei, fi Demand function coefficients of ith
load bus.
Q1,i Operating region between (Qmin < Q ≤ 0).
Q2,i Operating region between (Qbase < Q ≤ QA).
Q3,i Operating region between (QA < Q ≤ QB).
Bid price of ith
generator.
Market Clearing Price (MCP) of energy only market.
1. INTRODUCTION
Independent System Operator (ISO) collects the half-hourly/hourly supply bids from the generation
companies (GENCOs) and demand bids from distribution companies (DISCOs) for solving the day-ahead

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 8, No. 5, October 2018 : 3427 – 3435
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(DA) market clearing (generation and load demand schedule) problem. In the deregulated power industry,
establishing an effective and equitable reactive power market with the consideration of the voltage security
problem is very important to provide a reliable power system. Ancillary services are necessary to support the
transmission of electric power from producers to customers. These services are needed to ensure that the
ISOs are able to meet their responsibilities and to enhance the system maintenance, reliability and quality.
Reference [1] proposes a new structure for joint energy and reactive power market to resolve the
difficulties pertaining interactions between the active and reactive power markets. A stochastic multi-
objective optimization (MOO) algorithm for simultaneous active and reactive power dispatch in electricity
markets with wind power volatility is proposed in [2]. Reference [3] proposes a dispatching reactive power
model based on optimal power flow (OPF) by which both the cost of procuring reactive power as auxiliary
service and the losses of active power are minimized. Reference [4] deals with the obtaining, decomposition
and deduction of behavior rules of spot prices, and their influence on established contractual relationships in
a deregulated market environment which allows the power purchase agreements between consumers and
producers. A new reactive power market structure is presented in [5] to improve the reactive power market
and create fair competition between producers. An efficient stochastic framework to develop a coupled active
and reactive market in smart distribution systems is proposed in [6]. Reference [7] presents an algorithm for
procuring reactive power from reactive resources based on a reactive power pricing structure. Reference [8]
proposes two new active/reactive dispatch models to be used by System Operators in order to assign reactive
power and to validate the economic schedules prepared by Market Operators together with the injections
related with bilateral contracts. A deterministic model of complete generation-grid system to obtain the active
and reactive power spot prices and their decomposition, to deduce general rules concerning their behaviour,
and to analyze the effect of the applied constraints is proposed in [9]. A new probabilistic algorithm for
optimal reactive power provision in hybrid electricity markets is proposed in Reference [10].
The real and reactive power dispatch models used by the ISOs to assign the reactive power and to
validate the economic schedules prepared by the market operators with bilateral contracts is described in
Reference [11]. A multi-objective based day-ahead reactive power market clearing model is proposed in
Reference [12]. A joined real and reactive power market clearing in the restructured electrical systems is
presented in Reference [13]. In [14], uses multi-objective directed bee colony optimization algorithm to
optimize the combined emission and generation cost. An optimal reactive power scheduling problem in
restructured power system using the evolutionary based Cuckoo Search Algorithm is proposed in [15]. A
meta-heuristic based approach to solve the Optimal Reactive Power Dispatch problem using Crow Search
algorithm is proposed in [16].
From the literature review, it can be observed that most of the works in the literature doesn't
considers the energy and reactive markets, simultaneously. Therefore, the motivation of this paper is to clear
the market by optimizing both the energy and reactive powers, simultaneously, and considering the voltage
dependent load modeling. In this paper, it is considered that the traditional single objectives such as Social
Welfare Maximization (SWM) and Loss Minimization (LM) objectives are not feasible with voltage
dependent load modeling due to the reduction in the amount of load served (LS). A MOO is required for
solving the problems of this kind.
2. SEPARATE ACTIVE AND REACTIVE POWER MARKET CLEARING
Typically, the market clearing problem is solved by the system operator to know the accepted offers
and bids and the resulting Market Clearing Price (MCP).
2.1. Centralized separate energy market
The concept of social welfare maximization (SWM) can be applied for the centralized electricity
market with demand elasticity. The social welfare (SW) is the total surplus of generators and customers. The
system operator solves the SWM [17] objective function, and it is formulated as,
[∑ ( ) ∑ ( )] (1)
Where
( ) (2)
( ) (3)

Int J Elec & Comp Eng ISSN: 2088-8708 
Multi-Objective based Optimal Energy and Reactive Power Dispatch … (Surender Reddy Salkuti)
3429
2.2. Reactive power market clearing
The synchronous generator's capability curve [18] consists of 3 operating regions. These regions
reflect the armature, field current heatings and the under-excitation limits.
2.2.1. Reactive power bid structure
Similar to the real power, synchronous generators bids for the reactive power [18]. These bids
consist of a capacity component which is paid in advance for their readiness to absorb/ produce the reactive
power.
Expected Payment Function (EPF): The reactive power payment of generators consists of different
cost components depending upon their operating regions. EPF is a mathematical formulation of generator
reactive power cost components of generator’s expectation of payment towards utilization, capacity and
compensation components. Figure 1 depicts the EPF of a generating unit, as a function of amount of reactive
power output. The terms of EPF i.e., opportunity cost, cost of loss are presented in Reference [18].
EPF
Qmin QBase0 QBQA
a0
m2
m3Q
m1
Opportunity
Cost
Cost of
Loss
Availability
Cost
Region-I Region-II Region-III
Figure 1. Structure of reactive power offers from the generating units
Figure 1 depicts the operating regions of generator on the reactive power coordinates and these
regions are clearly presented in Reference [19]. The expected payment function (EPF) of a generator is
expressed as,
∫ ∫ ∫ (4)
Where a0, m1, m2 and m3 in the above equation represent different components of reactive power
cost offered by the generator. m1 is cost of loss price offer for operation in the under-excited mode
(Qmin ≤ Q ≤ 0) ($/Mvar-h), m2 is cost of loss price offer for the operating in region (Qbase ≤ Q ≤ QA) in
($/Mvar-h), and m3 is opportunity price offer, for operating in region (QA ≤ Q ≤ QB) (($MVar-h)/MVar-h).
The Total Payment Function (TPF) is expressed as [20], The last term in equation 5 represents the LOC
payment.
∑ [
( ) ( )
( ( ))
] (5)
3. DESIGN OF COUPLED ACTIVE AND REACTIVE POWER MARKET CLEARING
In this section, different objective functions for the coupled ARPMC are proposed.
3.1. Loss opportunity cost (LOC) formulation
The LOC of a generator plays a vital role in the reactive power scheduling and pricing [19]. To use
the LOC in Equation (7), the results of separate energy dispatch are required. Therefore, the separate energy
dispatch must be performed before the coupled ARPMC problem. Here, the LOC of a generator, which is

 ISSN: 2088-8708
3430
forced to produce the reactive power, can be expressed as [20]:
{ (6)
[ ( )] (7)
The TPF for reactive power compensation in coupled ARPMC consists only operation and
availability payments [18], and this can be expressed as,
∑ [ ( )] (8)
3.2. Load modeling
Generally, the active and reactive power loads are modeled as the constant power loads. But, they
are voltage dependent [21] in the practical real time operation. In this paper, for the sake of simplicity,
exponential load demand model is used, and it can be expressed as,
( ) (9)
( ) (10)
where np and nq are depend on composition and type of the load demand. The objective functions
considered in the centralized DA coupled ARPMC problem are as follows.
3.3. Social welfare maximization (SWM) in coupled ARPMC
In this paper, an OPF based approach is used to find the market clearing price (MCP), and to get the
active and reactive power schedules that satisfy the system operation requirements. In coupled ARPMC
model, the objective is to maximize social welfare (SW). SWM objective function can be formulated as [17],
SWM is an important objective under all system operating conditions.
maximize, ∑ ( ) ∑ ( ) ∑ ( ) (11)
3.4. Loss minimization (LM)
The goal of this objective is to find the optimal settings of control variables which result in optimum
transmission losses. The LM objective is suitable only for the constant load modeling at light loading
condition. If load demands are modeled as voltage dependent, the SWM and LM objectives lead to the load
served (LS) reduction through the voltage reduction. This LM objective is expressed as [22],
∑ * ( ( ))+ (12)
3.5. Amount of load served maximization (LSM)
The practice, the load demands are the function of voltages, therefore the voltage dependent load
modeling is utilized. The improvement of system voltages increases the amount of load served (LS). Under
the voltage dependent load modeling, the LSM objective is appropriate at light loading conditions, and it is
formulated as Equation (13). This LSM objective will never be used as an independent objective.
∑ ( ) (13)
3.6. Voltage stability enhancement index (VSEI)
To monitor the voltage stability in the system, L-index [23] of the load/demand buses is considered.
L-index/VSEI uses the information from the power flow and is in the range of 0 (no load) to 1 (voltage
collapse). L-index presents the stability of complete system, and it is expressed as,

3431
| ∑ | (14)
∑ (15)
where j = ng + 1, ..., n. The values of Fji are calculated from the Y-Bus matrix [18]. In the case of
voltage dependent load modeling, the L-index/VSEI minimization objective improves the voltage profile of
the system and hence the amount of load served (LS).
3.7. Equality and inequality constraints for the coupled ARPMC problem
3.7.1. Equality constraints
The nodal power balance constraints include the active and reactive power balance equations. They
are expressed as,
∑ [ ( )] (16)
∑ [ ( )] (17)
3.7.2. Generator constraints
The generator outputs are limited by their minimum and maximum active power outputs as,
[ ] [ ] (18)
Using the reactive power offers from the generators in different operating regions, the constraints
are formulated as,
(19)
(20)
(21)
(22)
3.7.3. Demand limits
(23)
(24)
3.7.4. Constraints on MCPs
(25)
(26)
(27)
3.7.5. Generator reactive power constraints
√( )
( )
(28)
√( ) (29)

 ISSN: 2088-8708
3432
The minimum limit of reactive power generation ( ) is given by,
(30)
3.7.6. Security constraints
(31)
| | (32)
(33)
where is power flow in a line/MVA flow, is maximum power flow/thermal limit of the
transmission line connected between the buses p and q. In this paper, the single objective optimization
problem is solved using the Genetic Algorithm (GA), and the Strength Pareto Evolutionary Algorithm 2+
(SPEA 2+) algorithm is used to solve the coupled ARPMC problem. The fuzzy min-max approach [22] is
used to determine the best-compromise solution [24].
4. SIMULATION RESULTS AND DISCUSSION
Here, IEEE 30 bus system [25] is considered to test the effectiveness and feasibility of the proposed
centralized day-ahead (DA) coupled ARPMC problem. Five generator active powers, 21 power demands, 6
generator bus voltage magnitudes, 4 transformer taps and 9 bus shunt admittances are considered as the
control variables. Here, the exponential (i.e., voltage dependent) load modeling with np = 1 and nq = 2 are
utilized [18]. In this paper, they assumed as QBase = 0.1∗Qmax; QA is restricted by armature or field heating
limit; QB = 1.5∗QA.
4.1. Case study 1: Solving the coupled ARPMC problem using the constant load modeling with light
loading condition
Table 1 presents the control variables and objective function values for the Case Study 1 considering
the single and multiple objectives with constant load modeling. When the SWM objective is optimized
independently then the obtained SW is 602.88 $/hr, which is the optimum value, but VSEI and losses are
deviated from the optimum. When LM objective is optimized independently, then the obtained optimum loss
is 2.8977 MW, but the obtained SW and VSEI are not optimum. In the same way, when one objective
function is optimized independently, then the other objectives are deviated from the optimum value.
Therefore, there exists a conflict between the optimum objective values when one objective is optimized
independently.
Table 1. Optimum Objective Function Values and Control Variables for Case Study 1
Objective & Control
variables values
Single Objective ARPPC MO ARPPC
SWM LM VSEI SWM & LM
PG1 (MW) 162.49 62.87 106.53 77.23
PG2 (MW) 49.67 72.10 67.99 64.44
PG5 (MW) 24.35 44.78 28.08 41.25
PG8 (MW) 26.78 33.42 34.60 34.96
PG11 (MW) 12.81 25.69 10.40 29.99
PG13 (MW) 12.89 29.48 26.04 25.73
V1 (pu) 1.0206 1.0488 1.0947 1.0934
V2 (pu) 1.0565 1.0424 1.1000 1.0959
V5 (pu) 1.0088 1.0294 1.0994 1.0759
V8 (pu) 1.0424 1.0247 1.0994 1.0847
V11 (pu) 1.0959 1.0953 1.0994 1.0888
V13 (pu) 1.0347 1.0965 1.0994 1.0988
Generation (in MW) 288.99 268.34 273.64 273.60
Amount of Load Served (in MW) 278.38 265.45 267.58 269.85
Generation Cost (in $/hr) 1336.75 1452.42 1346.83 1415.14
Demand Cost (in $/hr) 1939.63 1868.65 1891.58 1905.85
Social Welfare (in $/hr) 602.88 416.24 544.75 490.71
Total System Losses (in MW) 10.6041 2.8977 6.0629 3.7451
VSEI 0.12296 0.10702 0.06133 0.08647

3433
In this case study, SWM and LM objectives are selected as the appropriate objectives for the DA
multi-objective coupled ARPMC problem. As it is the normal operating condition, the VSEI value is away
from the voltage collapse point, so there is no need to optimize the VESI objective. Figure 2 depicts the
Pareto optimal set of SWM and LM objectives for multi-objective based coupled ARPMC problem for case
study 1. In this paper, SPEA 2+ algorithm is used to obtain the Pareto optimal front. The best-compromise
solution can be obtained by using the fuzzy min-max method. The obtained best-compromise solution has the
social welfare of 490.71 $/hr, and the loss of 3.7451 MW, and this is the better compromise solution as
compared to the single objective coupled ARPMC problem.
Figure 2. Pareto optimal front of SWM and LM objectives for case study 1
4.2. Case Study 2: Coupled ARPMC with voltage dependent load modeling at light loading condition
Table 2 depicts the control variables and objective function values obtained when the single and
multiple objectives are optimized with voltage dependent load modeling. When the social welfare
maximization objective is optimized individually, then the obtained optimum SW is 580.64 $/hr, and it is less
than the social welfare obtained by constant load modeling, and load served (LS) is 259.46 MW, which is
less than the load served by the constant load modeling. In this case, the SWM leads to reduction in voltages
and therefore, the reduction in the amount of load served (LS). Due to this reason, the SWM should not be
optimized individually. When the LSM objective is optimized individually, then the amount of load served
(LS) is 314.90 MW, but the social welfare has decreased to 537.97 $/hr. As explained earlier, the LSM
objective cannot be used as an independent objective.
Table 2. Optimum Objective Function Values and Control Variables for Case Study 2
Objective & Control Variables Values
Single Objective ARPMC MO ARPMC
SWM LSM VSEI SWM & LSM
PG1 (MW) 144.89 120.08 158.36 132.50
PG2 (MW) 49.13 66.40 44.06 65.57
PG5 (MW) 23.94 47.50 45.15 36.95
PG8 (MW) 24.55 34.53 25.48 34.71
PG11 (MW) 15.07 28.07 10.06 10.32
PG13 (MW) 12.3 25.55 12.57 17.65
V1 (pu) 0.9529 1.0718 1.0971 1.0768
V2 (pu) 0.9959 1.0988 1.0912 1.0613
V5 (pu) 0.95 1.1 1.0912 1.0796
V8 (pu) 0.9541 1.1 1.1 1.0671
V11 (pu) 0.95 1.0988 1.1 1.0542
V13 (pu) 0.9512 1.0994 1.0941 1.0583
Generation (in MW) 269.87 322.13 295.68 297.70
Total System Losses (in MW) 10.4092 7.231 7.6954 8.0654
Generation Cost (in $/hr) 1278.40 1558.88 1412.36 1405.21
Demand Cost (in $/hr) 1859.05 2096.85 1970.38 1967.91
Social Welfare (in $/hr) 580.64 537.97 558.02 562.70
Amount of Load Served (in MW) 259.46 314.90 287.98 289.63
VSEI 0.29138 0.10192 0.07499 0.15043
When the VSEI objective is optimized individually, then the obtained optimum value is 0.07499,
which is away from the voltage collapse point. Hence, there is no need to optimize VSEI at this operating
2 3 4 5 6 7 8 9
420
440
460
480
500
520
540
560
580
Total System Losses (MW)
SocialWelfare($/hr)
Social Welfare maximization and Total System Loss minimization
X: 3.745
Y: 490.7

 ISSN: 2088-8708
3434
condition. Therefore, the SWM and LSM objectives are considered to be the appropriate multiple objectives
to be optimized simultaneously. The compromise solution has social welfare of 562.70 $/hr and 289.63 MW
of load served. Figure 3 depicts the Pareto optimal front of SWM and LSM objectives for the coupled
ARPMC for Case Study 2.
Figure 3. Pareto optimal set of SWM and LSM objectives for case study 2
In this paper, it has been shown that the LM and SWM objectives do not make valid single or joint
objectives with this voltage dependent load model, due to reduction of load served. SWM and LSM are best
suited objectives to be optimized simultaneously for light to moderate loading condition.
5. CONCLUSIONS
This paper has proposed a day-ahead (DA) multi-objective based centralized coupled active and
reactive power scheduling and pricing mechanism using the practical voltage dependent load modeling.
Different objective functions such as SWM, LSM, LM and VSEI are proposed. The SWM objective includes
the offer cost for generators active power production, reactive compensations and the LOC payments for
generators and beneﬁt function of customers. In this paper, it is shown that SWM and LM objectives do not
make valid single or multiple objectives with the voltage dependent load model, due to the reduction in the
amount of load served (LS). Simulation studies on IEEE 30 bus test system shows the suitable and optimum
choice of multiple objectives to be selected for a given operating condition. SWM and LSM objectives are
appropriate for unstressed loading condition to moderate loading condition, with voltage dependent load
modeling. The Pareto optimal front allows the system operator to make a better decision, by considering the
better compromised solution.
ACKNOWLEDGMENTS
This research work is based on the support of “Woosong University Academic Research Funding-
2018”.
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Social Welfare and Load Served maximization

3435
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