978-1-4244-9074-5/10/$26.00 ©2010 IEEE 2010 Annual IEEE India Conference (INDICON)

Impact on Nodal Pricing with Different Generators’ Reactive Power Cost Models in Pool Based Electricity

Markets Ashwani Kumar#1, Punit Kumar*2

#Department of Electrical Engineering, NIT Kurukshetra Associate Prof. Department of Electrical Engineering, NIT Kurukshetra, India

1ashwa_ks@yahoo.co.in *Rajashtan State Electricity Board

A. E. in Rajasthan State Electricity Board, Jaipur, India 2punit_pce007@yahoo.com

Abstract— In this paper, the impact on nodal price determination of real and reactive power considering different reactive power price cost calculation methods for generator reactive power has been presented. The impact of FACTS controllers has also been considered taking their cost function into account. The comparison of fuel costs, reactive power cost, and cost of FACTS devices, and their impact on nodal price determination has been presented for different cases of reactive power cost models. The effectiveness of the proposed approach has been tested on IEEE 24-bus Reliability Test System (RTS). Keywords—Real and reactive power pricing, nodal price, cost model, FACTS devices, Pool model

I. INTRODUCTION Transmission price issue has gained considerable attention in the price based competitive emerging electricity markets. Along with the real power transmission pricing, with the growing interest in determining the costs of ancillary services needed to maintain the quality of supply, the spot price for reactive power has also gained great importance. Various models and approaches for determining spot pricing have been proposed in [1-18]. The concept of spot pricing was introduced in the late 1970’s. Schweppe et al. [2] utilized the concepts of classical economic dispatch and DC load flow to obtain the essential parts of spot price and provided the foundation and starting point for later research. In [2], authors developed model introducing reactive power pricing and revealed that the Lagrangian multipliers corresponding to node power balance equations in OPF represent the marginal costs of the node power injections [6]. The account of the reactive power production cost by introducing MVAR cost curves, which are a part of MW incremental cost curve was given in [7]. The wheeling marginal cost of reactive power is described in [9]. Many authors addressed the problem of spinning reserve pricing, congestion alleviation cost, and security components of spot price in [10-14, 16-18].

Many investigations have been carried out for appropriate pricing of reactive power [19-25]. A simple approach was presented to reactive power planning and combines the issue

with reactive power pricing so as to recover the cost of installed capacitors using OPF approach [19]. Lamont and Fu [22] introduced opportunity cost as a reactive power production of generator however, the computation of the cost is difficult. The role of FACTS controllers on transmission pricing have been presented by many authors [28-30]. Recently Shrestha and Feng presented simulation studies on the effects of TCSC on the spot price of real and reactive power using heuristic method to determine the location of TCSC [31].

In this paper, impact on nodal prices have been determined considering three different reactive cost model for generators’ reactive power cost models. The impact of FACTS devices have been incorporated with their cost model. The comparison has been given for different cases for IEEE 24-bus reliability test system.

II. REACTIVE POWER COST MODEL FOR GENERATOR REACTIVE POWER

Three methods have been considered to evaluate the cost of reactive power of generators.

A. Method-1: Triangular approach [31] This method of reactive power cost calculation is

essentially based on the formulation for active power cost, in which the active power is replaced by reactive power using the triangular relationship.

( ) cQbQaQCost ′′+′′+′′= 2 $/hr (1) where, a’’, b’’, c’’ are constants depending on power factor (cos θ) and are calculated as follows from power triangle.

a’’ = ap sin2 θ, b’’ = bp sin θ, c’’ = cp.

B. Method-2: Maximum real power based approach If a generator produces its maximum active power (Pmax),

then its cost for generating active power equals cost (Pmax). In such a situation, no reactive power is produced and therefore, S equals Pmax. To generate reactive power Qi by generator i which has been operating at its nominal power (Pmax), it is required to reduce its active power to Pi such that:

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iii PPPQPP −=Δ−= max22

max , ΔP represents the amount of active power that will be reduced as a result of generating reactive power, Cost(Pmax) : cost of producing active power equal to Pmax in one hour, Cost(Pmax −ΔP) : cost of generator when producing both active and reactive power with the amounts Pi and Qi , respectively. Cost(Pmax) − Cost(Pmax −ΔP) : Reduction in the cost of active power due to compulsory reduction in active power generation (ΔP) which happens due to generating reactive power with the amount of Qi .

( ) ( ) ( )ii PPCostPCostP

PPQCost −−Δ−= maxmaxmax

max $/hr (2)

C. Method-3: Maximum apparent power based approach The reactive power production cost of generator is called

opportunity cost reactive power output may reduce active power output capacity of generators which can at least serve as spinning reserve, therefore causes implicit financial loss to generators. For simplicity, we consider the opportunity cost approximately as:

( ) ( ) ( ) kQSCostSCostQCostGiGGGi *22

max max−−= ($/h)(3)

where SGi,max is the nominal apparent power of the generator at bus i; QGi is the reactive power output of the generator at bus i; K is the profit rate of active power generation, usually between 5% and 10%.

III. COST MODEL OF FACTS DEVICES Static model of FACTS devices viz. SVC and TCSC have

been well explained in [33-34]. The cost functions for SVC and TCSC are taken as follows [32]: SVC: ( ) 38.1273051.00003.0 2 +−= SSFCost $/KVAR (4)

TCSC: ( ) 22.1882691.00003.0 2 +−= SSFCost $/KVAR (5) S is the operating range of the FACTS devices in MVar. They must be unified into US$/Hour. Normally, the FACTS devices will be in-service for many years. However, only a part of its lifetime is employed to regulate the power flow. In this paper, five years is applied to evaluate the cost function. Therefore the average value of the investment cost is calculated as:

( ) ( )5*87601

fcfc = $/hr

IV. ACTIVE AND REACTIVE NODAL PRICE DETERMINATION FOR POOL MARKET MODEL

The results without and with FACTS devices have been obtained for a pool model based electricity market. The objective function can be represented as:

(a) Objective function ( ) ( ) ( )iii FCostQCostPCost ++∑ (6)

The objective function consist three cost components as cost of real power, cost of reactive power, and cost of FACTS

devices. These can be represented as: Where i ε NG (no. of generator)

pipipi cPbPaPCost ++= 2)( $/h (7)

Cost of reactive power has been obtained with the three methods as explained in section II. (b) Equality constraints: Power flow equation

( )ijijijijjiijiij BGVVGVP δδ sincos2 +−= (8)

( ) ( )ijijijijjishijiij BGVVBBVQ δδ cossin2 −−+−= (9)

( )ijijijijjiijjji BGVVGVP δδ sincos2 −−=

(10)

( ) ( )ijijijijjishijjji BGVVBBVQ δδ cossin2 +++−=

(11)(c) Power Injection at buses

idigi PPP =− NBi ∈∀ (12)

idigi QQQ =− NBi ∈∀ (13)

∑−∑=∈∈ TBiij

jiFBiij

iji PPP NBi ∈∀ (14)

∑−∑=∈∈ TBiij

jiFBiij

iji QQQ NBi ∈∀ (15)

(d) Power generating limits maxmin gigigi PPP ≤≤ (16)

maxmin gigigi QQQ ≤≤ (17)

(e) Power Balance equation

01

=−−∑=

lossdi

Ng

igi PPP (18)

01

=−−∑=

lossdi

Ng

igi QQQ (19)

(e) Transmission limits maxmin jijij PiPP ≤≤ (20)

(f) Voltage limits maxmin iii VVV ≤≤ (21)

(g) Phase angle limits maxmin iii δδδ ≤≤ (22)

(h) Reactive Power Capability Curves limit ( )222

atgg IVQP ≤+ (23)

The optimization problem is solved using the GAMS 21.3 / CPLEX 9.0 solver [35-36] and utilizing interfacing with MATLAB 6.5.

V. RESULTS AND DISCUSSIONS The results have been determined for IEEE-24 bus system

for a pool model without and with FACTS devices. The results have been obtained for different cases as follows- Case 1: Results without FACTS devices for all methods Case 2: Results with FACTS device (SVC) for all methods Case 3: Results with FACTS device (TCSC) for all methods

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(Case-1): The results of the marginal cost for real and reactive power for Case 1 using different methods of reactive power model is shown in Figs. 1 to 3. It is observed from Fig. 1 to Fig. 3 that the marginal cost of real power is minimum at bus 22 (32.927 $/MWh). At each bus the marginal cost of real power is different with a maximum value of 96.704 $/MWh. The marginal cost of reactive is both positive and negative. The negative reactive power marginal cost represent that the Lagrange multiplier is negative corresponding to that bus. It is also observed that the marginal cost of real and reactive power is minimum for Method-3 as given in Table I.

Fig. 1 Marginal Cost of real and reactive power (Case-1, Method-1)

Fig. 2 Marginal Cost of real and reactive power (Case-1, Method-2)

Fig. 3 Marginal Cost of real and reactive power (Case-1, Method-3)

TABLE I RESULTS FOR IEEE-24 BUS SYSTEM FOR CASE-1

Method-1 Method -2 Method -3 Fuel Cost (US $/h) 114042.317 113956.926 112497.608 Q cost (US $/h) 5039.563 4329.931 1783.560 Total cost (US $/h) 119081.880 118286.86 114281.168

(Case-2): The results for Case 2 are shown in Fig. 4 to 6. It is observed from Figs. 4 to 6 that the marginal cost of real power is minimum at bus 22 and the values is 32.89 $/MWh. At each bus the marginal cost of real power is different with a maximum value of 109.78 $/MWh. The marginal cost reduces at each bus with SVC. The minimum cost is obtained for method 3 as given in Table II. SVC is optimally connected at bus 3. SVC cost is obtained minimum for method 1 as reactive power support is obtained minimum for this case.

TABLE II RESULTS FOR IEEE-24 BUS SYSTEM (CASE-2)

Method-1 Method -2 Method -3 Fuel cost (US $/h) 114097.659 113660.366 111965.021 Q-cost (US $/h) 5223.998 4860.480 642.519

Cost of SVC (US $/h) 1.452 3.753 4.517 Total cost (US $/h) 119323.109 118524.60 112612.057

QSVC (MVAR) 0.5 1.295 1.560

Fig. 4: Marginal Cost of real and reactive power with SVC (Method-1)

Fig. 5: Marginal Cost of real and reactive power with SVC (Method-2)

Fig. 6: Marginal Cost of real and reactive power with SVC (Method-3)

(Case-3): The results of the marginal cost for real and reactive power for Case-3 is shows in Fig. 7 to 9. TCSC is optimally connected at line no. 7 between bus 3 and bus 24. For TCSC, the limit of Xc is selected between 0.2XL to 0.7XL p.u. From Figs.7 to 9, the marginal cost of real power is minimum at bus 22 (55.60 $/MWh) by Method 1 and a maximum value of 113.68 $/MWh by Method-2. At bus 6, reactive power marginal price is negative. The minimum cost is obtained using method 3 as given in Table III. Cost component for FACTS device TCSC is found lowest for Method 1 as the support of reactive power is obtained lowest for method 1 compared to other methods.

TABLE III RESULTS FOR IEEE-24 BUS SYSTEM (CASE-3)

Method -1 Method -2 Method -3 Fuel cost (US $/h) 111958.279 111469.489 110152.932 Q-cost (US $/h) 3994.098 2570.038 117.262 Cost of TCSC (US $/h) 3.115 4.411 4.291 Total cost (US $/h) 115955.492 114043.94 110274.484

QTCSC (MVAR) 0.892 1.265 1.230

Fig. 7: Marginal Cost of real and reactive power with TCSC (Method-1)

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Fig. 8: Marginal Cost of real and reactive power with TCSC (Method-2)

Fig. 9: Marginal Cost of real and reactive power with TCSC (Method-3)

VI. CONCLUSIONS In this paper, reactive power cost model for generators’

reactive support have been considered for nodal price determination. FACTS devices with their cost model have been incorporated in the problem. The total cost have been obtained minimum with method 3. The cost component of reactive power is obtained minimum using method 3 for all the cases. It is observed that reactive power cost component is important to consider for nodal price determination.

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