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					International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
        INTERNATIONAL JOURNAL OF ELECTRICAL
ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
          ENGINEERING & TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 3, Issue 1, January- June (2012), pp. 44-57
                                                                          IJEET
© IAEME: www.iaeme.com/ijeet.html
Journal Impact Factor (2011): 0.9230 (Calculated by GISI)
                                                                      ©IAEME
www.jifactor.com




 EFFECT OF REACTIVE POWER VALUATION OF GENERATORS
        IN DEREGULATED ELECTRICITY MARKETS
                                       Archana Singh
                              Electrical Engineering, H.B.T.I.
                                   Kanpur-208002,India
                                 archanasingheed@in.com

                                    Prof. D.S.Chauhan
                                      Vice Chancellor
                                  Uttarakhand University
                                     Uttarakhand,India
                                  pdschauhan@gmail.com

                                    Dr.K.G.Upadhyay
                         Professor & Head,M.M.M.E.C.,Gorakhpur


ABSTRACT

In a deregulated electricity market, Independent System Operator (ISO) meet contracted
transaction in secure manner for reactive power provision. It is differently done in
deregulated electricity market of different countries .In the paper, a reactive power
procurement market model is proposed along with reactive power valuation. Reactive
power valuation is concerned with social and technical aspects of generators .It is
discussed with IEEE-24 bus results.


Keywords: Deregulation, Procurement of reactive power, Generator capability curve,
Reactive power valuation.

I. INTRODUCTION
IN the early 1990s, with the restructuring of industry eminent, researches have been
started to review pricing of real and reactive power in an economically efficient way. The
new emphasis of the market of electricity created a focus on separate reactive power
pricing in the literature. Reactive power provision is considered by Independent System


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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
Operator (ISO) in order to meet contracted transaction in deregulated electricity
markets[1]. The various ways are discussed as applied in various countries for meeting
reactive power requirement by ISO in the deregulated electricity markets[2]. It is
suggested in recently published FERC report that an efficient pricing and procurement
scheme for reactive power should encourage investment in the infrastructure needed to
maintain the reliability of the transmission system and provide incentives for the reliable
and efficient production and consumption of reactive power from the available
infrastructure[3]. In main countries like USA, UK, Australia, for procurement of reactive
power services, the ISO enters into contracts with the reactive power providers. The New
York ISO (NYISO) compensate generators based on embedded cost pricing for their
reactive power services, and also imposes a penalty for failing to provide reactive
power[4]. The generator receives payment at the market clearing price for reactive power
compensation[5]. In NERC, reactive power provision from generators is mandated within
a power factor range 0.9 lagging to 0.95 leading. Beyond these limits, the generators are
paid for their reactive power including a loss opportunity cost payment [6]. In UK, the
Transmission System Operator (TSO)-National Grid Company (NGC) invites half-yearly
tenders from generators for “obligatory reactive power services” which correspond to the
reactive power as each generator is required to provide, and “enhanced reactive power
services” for generators with excess reactive power capabilities[7]. In Australia, apart
from generators, synchronous condensers also receive payments for providing reactive
power. All reactive support providers get availability, enabling, usage and compensation
payment mechanism[8]. Any reactive power market has different certain characteristics
in terms of economic and physical properties of active power market. For optimum level
of remuneration and charging of reactive power, economic theory states that reactive
power injection or absorption should be by its spot price[9].
 With this reactive power valuation can be done which is related to the comparative
importance of reactive power source for system security and voltage stability. This paper
presents a proposal of reactive power procurement market model with reactive power
evaluation considering economical and technical aspects of generators in a deregulated
electricity market. SAF is maximized along with reactive power cost minimization.

II. REACTIVE POWER PROCUREMENT MODEL

Currently, most power system operators primarily relying on operational experience to
arrive at reactive power dispatches based on the power flow studies, However, there are
several complex issues involved in reactive power management in deregulated electricity
markets which need to be taken into account to arrive at better solutions. These issues
include market power being exercised by some reactive power service providers,
considering the localized nature of reactive power support; the effect of reactive power
on active power generation and on system security; and the possibility of reactive power
price volatility when it is in the same time-frame as the spot energy market. In this
section a detailed discussion is presented on the reactive power procurement model, and
limitations of the model will be highlighted. Procurement of reactive power services
through competition and long-term contracts between the ISO and service providers
(generators) is an alternate way for reactive power management in deregulated electricity



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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
markets[10,11]. Reactive power market has been considered more as a local market than
a system-wide market [12].
In the reactive power procurement, first reactive power offers from the reactive power
providers are called and based on the received bids , an optimization model is solved,
which maximizes a societal welfare function subject to various system
constraints[13].The optimization model with cost minimization yields the required
reactive power for each generator along with the price components [14].
    A. Structure of Reactive Power Offers from Generator:
   Based on the classification of reactive power production costs, an offer structure can
be
Formulated (also shown in figure 1.)




                Figure 1 Reactive Power Offer Structure of a Generator
The various parameters shown in the figure are:
1. Availability price offer (a0, $/h): A fixed component to account for that portion of a
supplier’s capital cost that can be attributed to reactive power production.
2. Cost of the loss offer (m1, m2, $/MVAr-h): A approximately linearly varying
component for the increased winding losses in the under- and over- excitation ranges,
respectively.
3. Opportunity offer (m3, $/MVAr-h/MVAr-h): A quadratic component for the lost
opportunity cost in order to increase its reactive power production when a supplier is
constrained from producing its scheduled real power.
B. Reactive Power limits of Synchronous Generator
The MVA rating of Synchronous Generator can be found from point of intersection of the
two curves formed with its armature and field winding heating limits (Figure2.).




               Figure 2 Determination of Reactive Power limits from Generators

 It is shown in the capability curve that the generator requires minimum QBase for its
auxiliary equipment. For the operating point say, at (PA, QBase) lying inside the limiting
curves, the generator may increase its reactive generation from QBase up to QA without
readjustment of PA. But this will lead to increased losses in the windings and so cost of
losses is increased. So three operating regions for a generator are defined
    • (When QG=Q1 lies between 0 and Qmin,it is considered as Region-1)

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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
   • (When QG=Q2 lies between QBase and QA, it is considered as Region-2 )
    (When QG=Q3 lies between QA and QB , it is considered as Region-3)
C. Marginal Benefit of Reactive Power Supply from Synchronous Generator:
Reactive Power output from a provider is classified into three regions ( Qmin , 0),
( QBase , QA ) and ( QA , QB ). It is considered as three components: Q1, Q2 or Q3 respectively
and generator will provide their respective offer bids. Accordingly, only one of the binary
          W ,W or W3
variables 1 2          can be selected. Using the elementary mathematics we can derive
the following cost function:
To minimize:
          NG NH
                                                                                   1
Cost =∑∑ ρ0.W i,h −ρ1.Wi,h.Q i,h +ρ2.W i,h(Q i,h −Q ,i,h +ρ2.W i,h(Q i,h −Q ,i,h) + ρ3.W i,h (Q23,i,h)−(Q2Ai,h)
              ( 0,     1,   1,        2,    2,     base       3,    3,     base         3,                 , 
      i=1 h=1                                                                      2
        (1)
                                                          W
In eqn (1), if any generator is selected then 0,i ,h will be 1 irrespective of its amount of
reactive power output.
W1,i , h W2,i ,h        W                                 (W ,W ,W ) ∈ {0,1}
         ,        and 3,i ,h are binary variables i.e.  1,i ,h 2,i ,h 3,i ,h        .
                                                                 W
If hth supplier connected to ith bus is selected then 0,i ,h will be equal to one so only one
                                  W ,W or W3,i ,h
of the binary variables 1,i ,h 2,i ,h                  will be selected. It means only then
W1,i , h + W2,i ,h + W3,i ,h = 1
NG is group of generator and NH is representation of each supplier at a bus.
 Q1,i , h Q2,i ,h       Q                                Q       to 0 Qbase,i ,h Q A,i ,h       Q
          ,       and 3,i ,h represent the regions( min,i ,h          ),(       to        )and ( A,i ,h to
Q B ,i , h         Qi ,h = Q1,i ,h + Q2,i ,h + Q3,i ,h
            )i.e.
 The system constraints are as follows:
The equality constraints of the OPF problem are as follows:
  NHi

  ∑P
  h=1
        G,i,h   − PDi − ∑| Vi || Vj || Yij |cos(θij +δ j −δi) = 0;∀i, h∈NG
                        j∈N
                                                                                              (2)
 NHi

 ∑Q     Gi,h   − QDi − ∑| Vi || Vj || Yij | sin(θij +δ j −δ i) = 0; ∀i, h ∈NG
  h=1                  j∈N
                                                                                              (3)
Where, N is the total number of buses in the system;
PGi, QGi, PDi , QDi are the active and reactive power generation and demand on bus i.
                                                                                •
Yij∠θ ij is the element in the bus admittance matrix. V = Vi∠δ i is the bus voltage at bus i.
The inequality constraints are
    1. Generation limits:
        PGi , min ≤ PGi ≤ PGi , max i ∈ G                                          (4)
    2. Reactive limits:
                                                    max
                                              QGg ≤QGg , ∀g



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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
                                                            Where
                    max
                   QG = (Vt Eaf / XS )2 − (P )2 −Vt 2 / XS for P < PR
                                            G                   G


                   or    (Vt Ia )2 − (P )2 for P > PR
                                       G        G
                                                                                                             (5)
            m in
Q Gg ≥Q            ,∀g
            Gg
                                                                                                             (6)
3. Voltage Limits

  Vi , min ≤| Vi |≤ Vi , max, ∀i                                                                             (7)
4. Transmission Limits:
IPijI ≤ Pij , max i ≠ j and ∀ i , j                                                                          (8)
                                                                                   2
Where                      Pij =| Vi || Vj || Yij | cos(θ ij + δ j − δ i ) − | Vi | | Yij | cos θ ij

5. The constraints of generators for reactive power compensation
                               W2,i ,h .Qbase ,i ,h ≤ Q2,i ,h ≤ W2,i , h .QA,i ,h
                                                                                                       (9)
     W3,i ,h .QA,i ,h ≤ Q3,i ,h ≤ W3,i ,h .QB ,i ,h
                                                                                                         (10)
    W1,i ,h + W2,i ,h + W3,i ,h ≤ 1
                                                                                                         (11)
    W1,i ,h + W2,i ,h + W3,i ,h = W0,i , h
                                                                                                         (12)
6. Constraints for determination of uniform price offers of generators
   W0,i ,h .a0,i ,h ≤ ρ0 ; ∀i, h ∈ NG
                                                                                                         (13)
W1,i ,h .m1,i , h ≤ ρ1∀i, h ∈ NG
                                                                                                         (14)
(W2,i ,h + W3,i ,h ).m2,i , h ≤ ρ2∀i, h ∈ NG
                                                                                                         (15)
   W3,i ,h .m3,i ,h ≤ ρ3∀i, h ∈ NG
                                                                                (16)
 As shown above, reactive power procurement model is formed based on the marginal
contributions of reactive power from generation cost minimization. In the result, the
Lagrange multipliers that represent the marginal benefit/contribution of each reactive
power source with respect to reactive cost minimization are λg,γg and µ g. λg denotes the
sensitivity of the objective function to a change in system demand. Simply stated λ
denotes the change in the system cost for a 1MW in the system demand. The multiplier µ
and γ are associated with the generator limits and these are of significance only when a
generator limit is a binding constraint.
D. Societal Advantage Function
Once the reactive power, ancillary service limits and the marginal benefits of each
provider with respect to reactive generation cost are determined, and reactive power
offers are received, the ISO is in a position to carry out a procurement market settlement
where its sole objective is to maximize a societal advantage function. The proposed SAF
is formulated considering benefits accrued from reactive power services with respect to
expected payment by the ISO. SAF is considered on a zonal basis and can be expressed
as follows:



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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
SAFK = −∑ ρ0K + ∑(cLµg − ρ1K )Q1g + ∑(cLλg − ρ2K )(Q2g −Qbaseg ) + ∑((cLγ g − ρ2K )(Q3g −Qbaseg ) − 0.5ρ3K (Q3g − QAg )2 
                                                                                                                         
         g∈K      g∈K                   g∈K                           g∈K

(17)

In eqn(17),the subscript g denotes set of generators in the zone K considering that the
system is divided into zones. The variables ρ1k (in $/MVAr-h) and ρ2k (in $/MVAr-h)
are the under- and over-excitation prices for reactive power in the zone k, respectively;
similarly ρ3k(in $/MVAr-h/MVAr-h) is the zonal uniform opportunity price component.
The variable ρok (in $/h) is the zonal availability price component. The constant CL is a
“loadability” cost parameter (in $/MWh) denoting the economic worth of increasing the
system loadability. It is taken as 100$/MWh in this paper.
The proposed procurement algorithm is based on the following OPF model:
 Maximize SAF as given in eqn (17) with following constraints
  1) Load flow (2), (3)
  2) Reactive Power Generation limits (4), (5), (6)
  3) Bus Voltage limits (7)
 4) Power Transfer limit (8)
5) The constraints of generator (9), (10), (11), (12) and
6) Constraints for price offer (13), (14), (15), (16).
   The solution of the above procurement model yields the set of contracted generators as
well as the zonal uniform price components after its maximization of societal advantage
function.

III. IMPLEMENTATION AND RESULTS

Reactive power procurement scheme is tested on the IEEE 24 bus (RTS) system [17]
shown in figure3.. There are 32 synchronous generators, 1 synchronous condenser
(located at bus 14) and 17 constant –power type loads. The participants of decoupled
reactive power market are supposed to submit their four components of the offer prices
(a0, m1, m2, m3) [18].The participants are also required to send their Qmin , QBase , Qmax .In
this paper, Qbase = 0.1× Qmax and QA = 0.8 × QB are considered. This is a constraint
optimization problem and can be modeled as non-linear programming (NLP) problem. In
this paper, Fmincon is used to solve nonlinear constrained objective. Fmincon finds the
minimum of constrained nonlinear multivariable function. The first step is to calculate
λ, γ and µ for each generator by solving the OPF model. All Qg values are in p.u.
with respect to a base value of 100MVA.




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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME




                     Figure 3 IEEE 24-Bus RTS system

Table 1 shows offer data for all the generators. The solution is given in Table 2. It is clear
that Qg can only take one of the three values corresponding to the region of operation of
respective generator and so regions are shown in the table 3. The second step is to solve
OPF that maximizes Societal Advantage function using values of first step and Qg. The
final solutions of OPF problem are given in Table3, where the total cost payment to
generators is given along with final price offers as uniform availability price, under-
excitation price and over-excitation price respectively. The optimal value of the objective
function SW is 134 $/h.
  Table 1: Reactive Power contract offer prices of 24 Bus (RTS)IEEE system
  Bus no.         Unit no.      a0,u ($/h)
                                  i
                                             m1i ,u ($/MVAr- m2,u ($/MVAr- m3,u ($/MVAr-
                                                              i                i


                                                      h)            h)        h/MVAr-h)
          1          1              0.96             0.86         0.86           0.46
          1          2              0.94             0.82         0.82           0.45
          1          3              0.85             0.79         0.79           0.39
          1          4              0.83             0.82         0.82           0.40
          2          1              0.50             0.54         0.54           0.28
          2          2              0.42             0.42         0.42           0.35
          2          3              0.69             0.68         0.68           0.39
          2          4              0.65             0.62         0.62           0.37
          7          1              0.75             0.61         0.61           0.43
          7          2              0.80             0.75         0.75           0.36
          7          3              0.70             0.65         0.65           0.32
         13          1              0.68             0.50         0.50           0.31
         13          2              0.70             0.54         0.54           0.39
         13          3              0.75             0.60         0.60           0.50
         14          1              0.94             0.81         0.81           0.00
         15          1              0.65             0.60         0.60           0.30
         15          2              0.50             0.58         0.58           0.25
         15          3              0.60             0.73         0.73           0.38
         15          4              0.55             0.61         0.61           0.27
         15          5              0.52             0.50         0.50           0.26

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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
        15        6           0.51                 0.51            0.51             0.27
        16        1           0.50                 0.50            0.50             0.30
        18        1           0.90                 0.85            0.85             0.48
        21        1           0.80                 0.75            0.75             0.41
        22        1           0.42                 0.42            0.42             0.17
        22        2           0.50                 0.48            0.48             0.20
        22        3           0.45                 0.42            0.42             0.38
        22        4           0.48                 0.44            0.44             0.35
        22        5           0.49                 0.45            0.45             0.33
        22        6           0.55                 0.46            0.46             0.32
        23        1           0.90                 0.85            0.85             0.48
        23        2           0.95                 0.89            0.89             0.55
        23        3           0.86                 0.80            0.80             0.45
       Synchronous Condenser (SC)

  Table 2: After cost minimization and SAF maximization, the values of λ, γ, µ and QG

Bus        Lagrange multipliers from                      Classification of        QGm     QGmin
                                                                                     ax
 es           cost minimization                            regions of QG
havi        λ          γ         µ            QG          Q1         Q2        Q
 ng                                                                            3
Gen
erat
ors
 1       .04961      .04958        0       4.07709         0        4.07709    0    10       0
                        9
 1       .04961      .04958        0       4.07709         0        4.07709    0    10       0
                        7
 1       .04961      .04958        0      -0.78852     -0.78852        0       0    30      -25
                        8
 1       .04961      .04958        0      -0.78852     -0.78852        0       0    30      -25
                        8
 2       .05085         0       .04968    8.640155         0       8.640155 0       10       0
                                   7
 2       .05085         0       .04968    8.640155         0       8.640155 0       10       0
                                   7
 2       .05085         0          0          -           -            0       0    30      -25
                                          6.752158     6.75215
                                                          8
 2       .05085         0          0          -           -            0       0    30      -25
                                          6.752158     6.75215
                                                          8
 7      .050398      .05112        0      16.43847        0        16.43847    0    60       0
 7      .050398      .05112        0      16.43847        0        16.43847    0    60       0
 7       .05039      .05112        0      16.43847        0        16.43847    0    60       0
 13      .05017         0          0      32.59147        0        32.59147    0    80       0

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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
 13      .05017         0          0      32.59147         0       32.59147 0       80       0
 13      .05017         0          0      32.59147         0       32.59147 0       80       0
 15      .04780         0       .04804        6            0           0    6       6        0
                                   5
 15      .04781         0       .04804         6           0           0       6     6       0
                                   5
 15      .04781         0       .04804         6           0           0       6     6       0
                                   5
 15      .04781         0       .04804         6           0           0       6     6       0
                                   5
 15      .04781         0       .04804         6           0           0       6     6       0
                                   5
 15      .04781         0       .04804        80           0           0    8       80      -50
                                   5                                        0
 16     .045239         0       .05085        80           0           0    8       80      -50
                                   1                                        0
 18      .04756         0       .04657    72.89843         0       72.89843 0      200      -50
                                   5          8                        8
 21     .0489983        0          0          -           -            0    0      200      -50
                                          7.458590     7.45859
                                                          0
 22     .0495877     .04783        0          -           -            0       0    16      -10
                                          6.413298     6.41329
                                                          8
 22     .0495877     .04783        0          -           -            0       0    16      -10
                                          6.413298     6.41329
                                                          8
 22     .0495877     .04783        0          -           -            0       0    16      -10
                                          6.413298     6.41329
                                                          8
 22     .0495877     .04783        0          -           -            0       0    16      -10
                                          6.413298     6.41329
                                                          8
 22     .0495877     .04783        0          -           -            0       0    16      -10
                                          6.413298     6.41329
                                                          8
 22     .0495877     .04783        0          -           -            0       0    16      -10
                                          6.413298     6.41329
                                                          8
 23     .0510717     .05181        0      11.95780        0        11.95780 0       80      -50
                                              6                        6
 23     .0510717     .05181        0      11.95780         0       11.95780 0       80      -50
                                              6                        6
 23     .0510717     .05181        0      21.72790         0       21.72790 0      150      -25
                                              9                        9


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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
Table 3: Final reactive power offer prices and generator reactive power cost payment
       Generator Payment cost after its cost minimization ($/h)           6.3352e+004
                Availability price(ρ0)(MCP for a0) in$/h                      0.96
        Under-excitation price(ρ1)(MCP for m1) in$/MVAr-h                     0.89
         Over-excitation price(ρ1)(MCP for m2) in $/MVAr-h                    0.89
     Opportunity price (ρ3)(MCP for m3) in $/MVAr-h/MVAr-h                    0.00

Limitations: In the above model results are obtained by considering that all the generators
will contribute in power generation. However, this may not always be the case as in case
of distributed generation some of the generators may not take part in the power
generation based on some criterion.
Hence, it is necessary to consider the health of the generators while they take part in the
distribution generation. To address this, in the next section presents reactive power spot
pricing and thereafter, reactive power valuation is presented.
A. Reactive Power Spot Pricing
A power system which is described as set of generators and loads connected through
transmission network usually work in its optimal steady state optimal operation point. For
the case when load increases its reactive power demand in small amount then maintaining
optimal condition, the rest of system shall change to supply the additional demand. The
incremental cost is known as the reactive power spot price which is denoted as σi at a
node i. This incremental system costs can be separated in two kinds, one related to
system losses (σli) and another related to voltage security (σsi).
B. Reactive Spot Prices Computation at generator Buses and load buses
If a reactive power sources either generator or SVC with enough reactive margin is
connected at the bus, the reactive spot price will be the derivative of the equipment
operating cost curve which is related to the internal losses associated with the generation
or absorption of reactive power of generator. The reactive marginal price will be:

              ∂c j (Q j ,V j )       ∂V j ∂c j (Q j ,V j )
       σj =                      +                                                     (18)
                   ∂Q j              ∂Q j       ∂V j
   Where c j (Q j , V j ) is the loss cost function and derivative of this with the sensitivity
    ∂V j
           which is variation in the generation plant voltage with change in injected
    ∂Q j
   reactive power depend upon injected reactive power Q j and terminal voltage V j .
The reactive power spot price σ i at load bus I for increasing the reactive power load with
assumption that the rest of the loads remain constant and no reactive generation
equipment is connected at load bus I, can be decomposed first reason for increment of
reactive power generation, second for increment of the system active power losses and
third reason for possible re-dispatch caused by some system constraints which is as
shown below.
                         ∂P
         σi = ∑Wijσ j + λ l + ∑σNk,i                                              (19)
              j∈G        ∂Qi Nk


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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME

Wij is the weight factor responding for amount of increment of each reactive power
generation equipment for reactive demand increment in the absence of system
                                                               ∂Pl
constraints. λ is the system marginal active power price.          is the network active
                                                               ∂Qi
power losses increment caused by reactive load increment. σ Nk ,i shows marginal
contribution of the system constraint Nk to the system operation costs. If constraint Nk is
active then this term is non-zero.
Reactive spot price can be decomposed into a losses component and a security
component which is shown as follows:
                        ∂P
     σ li = ∑ Wijσ j + λ l                                               (20)
            j∈G         ∂Qi
    σ si = ∑ σ NK ,i                                                         (21)
            Nk
The security component of the reactive spot price will be obtained from the solution of
the optimal reactive dispatch. Each operational security constraint Nk specifically can be
written as

    rNk ( Pi ,Qi ,Vi , K ) ≥ RNk                                             (22)
Where rNk a function of the network variables and constant is related RNk to the strength
of the constraint.
 C. Reactive Power Valuation
There are many methods for sources reactive power valuation considering system
security and voltage stability like Voltage Sensitivity (VS), PV curves ,Back –up
generation and equivalent Reactive Compensation(ERC) methods. Voltages Sensitivities
(VS) show the effect an additional injection of real or reactive power at a bus has on real,
reactive, or complex power flow on a particular line or interface.
Mathematically, it can be written as
dQG  ∑ dQGi  ∑ dSLi 
                                   −1

     =               and the numbers could be obtained from the Jacobian
 dSL  dV  dV 
                    
matrix.
Sum ∑VSLi represents the sensitivity of each load to all generators MVar output.
Sum ∑ VSGi represents the sensitivity of each generator in MVar to the marginal change
of all loads.
The Sum ∑ VSGi indicates the most valuable generator in regulating the voltage in the
system and reacting to the load variation. The ∑VSLi indicates the load that requires
more system reactive power resources than other loads.
The Bus Marginal Loss Sensitivities QLS and PLS are used to calculate the sensitivity of
a real power loss function, P losses, to bus real and reactive power injections. Stated
                              dP          dP
mathematically, it calculates Losses and Losses , where PL and QL are the real and
                               dPL         dQL


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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
reactive power injections at the load bus. It indicates how losses would change if one
more MW or MVar of power were injected at the load bus.
             n
                VSGi
    QLSGi = ∑          .QLS Li                                            (23)
            L1 ∑ VS Li
                      n
                           VSGi
    PLSGi = ∑                      .PLS Li
                      L1   ∑ VS Li
                                                                            (24)
This means that we find the sum how each generator contributes to the losses sensitivities
at load buses.Cost based marginal reactive power value of every source can be by
considering the following equation [18].
 RPVGi = [VSGi . f (CQGi ) + QLSGi + PLSGi ].SP;
                                                                            (25)
In the above equation,
 RPVGi is marginal reactive power value, f (CQGi ) are the generator’s active power
losses as a function of produced reactive power, MW/MVar; VSGi is Generator’s voltage
sensitivity of ith bus, in MVar units; QLSGi , PLSGi - Q and P losses sensitivities of ith bus,
in MW; and SP is the spot price of active power in $/MW;This means that reactive power
value of each generator is the sum of active power losses, due to the marginal load
change and generator respond to it, multiplied by active power spot price in the system at
that moment.
Hence, as address above the new cost function can be framed as
To minimize,
     NG     NH
                                                                                                                       1
Cost = ∑    ∑(ρ .W0    0,i ,h   − ρ1.W1,i,h .Q1,i,h + ρ2.W2,i,h (Q2,i,h − Qbase,i,h + ρ2.W3,i,h (Q3,i,h − Qbase,i,h ) + ρ3.W3,i,h (Q23,i,h ) − (Q2 A,i,h ) + RPVGi
                                                                                                                                                          
     i =1   h=1                                                                                                        2


          (26)
    Where RPVGi = marginal reactive power value and is defined as in eqn(25).
The new cost function will take care of social and technical aspects. It is worth noting
that, the result obtained above will now be the best case results, as we assumed that all
the generators will contribute in the reactive power generation. However, in the new cost
function, some of the generators will not take part due to the valuation considerations.
Still the above obtained results give us an estimate of the system.
    IV. CONCLUSION
The main objective of this paper is to consider the health of the generators in the reactive
power procurement market model in a deregulated electricity market. The social
advantage function is modified in the paper and detailed are produced to that how
reactive power valuation is important, in the design of reactive power procurement
model.




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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME

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[8] National Electricity Market Management Company (Australia)(1999), National
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[9] M.C. Caramanis,et al.,(1982),Optimal pricing: practice and theory,IEEE Transactions
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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
[18] J.B.Gill,T.G.S.Roman,J.J.A.Rios and P.S.Martin(2000),”Reactive Power Pricing:
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BIOGRAPHICAL NOTES

Dr. D.S.Chauhan is Professor, Department of Electrical Engineering, IT, Banaras Hindu
University, Varanasi, U.P.,India. Presently he is Vice-Chancellor of Uttarakhand
University, UK. He is engaged in teaching and research activities since the last 35 years.
His fields of interest are Power System restructuring, Power Quality, HVDC, Neural
Network. Dr. D.S.Chauhan has published several papers in various national, international
conferences and journals. He is a fellow of IE(India),fellow of IETE(India) IETE(India
and senior member of IEEE.

Archana Singh is Assistant Professor in the department of Electrical Engineering, HBTI,
Kanpur, India. is engaged in teaching and research activities for the more than eight
years. Her fields of interests are Restructured Electricity Market, Reactive Power Pricing,
Power Trading. She is Associate Member of IE (India) and life time member of ISTE
(India).




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