tracing network ﬂows due to sources/sinks using virtual ... · tracing network ﬂows due to...

Tracing Network flows due to Sources/Sinks usingVirtual flow Concept

Surendra S, D ThukaramDepartment of Electrical Engineering

Indian Institute of Science, Bangalore-12Email: {dtram, surendra18}@ee.iisc.ernet.in

Abstract—The main component of modern utilities gearedup for open access scenario is determine marginal pricing fortransmission network usage by the different entities involved inthe power market. One important aspect is power tracing whichin turn used to determine the charge allocation for the extentof service utilized and make up for the loss component in thenetwork. The methods available in the literature have certainshortcomings. This paper presents a concept called ”Virtualflows”, which is based on superposition principle for tracing realand reactive power flows. method evaluates the injection of eachsource on the network when it is considered to act alone withthe specified power as obtained from a solved load flow or fromthe output of on-line state estimator. The combined action of allthese gives the resultant state of the network. Modern powersystems incorporate HVDC links [1] for unsynchronized bulkpower transmission. It is aimed to extend the proposed concept tosystems incorporating DC links and further to evaluate networkusage charges based on the outcome of this tracing.

I. INTRODUCTION

Power flow tracing is very much essential from the pointof transmission charges allocation and to make up the losscomponent. System losses are associated with power transferin the network. In the interconnected system, determinationof the lines involved in providing transmission services for agiven transaction period among the various entities is to bedetermined for allocating charges based on the actual usage,so that the network cost can be recovered in a equitable man-ner. Marginal pricing requires the knowledge of transmissionfacility availed by each generation and demand present in thesystem. Most of the power flow tracing methods have someamount of arbitrariness. Proportional sharing principle basedloss allocation and its variations are explained in references[2], [3], [4], [5], [6]. The tracing is done from the net flowsobtained from load flow / output of on line state estimator.The network parameters have no role in tracing the flow.Bialek el. [2], [3] explains the flow tracing from each sourceto load or vice-versa using upstream and downstream lookingmatrix. Loss allocation to generating buses is still a problemand to be relatively specified with respect to load buses.The tracing technique defined by Kirschen et.al [4] usesdomain of generation and commons to specify the real powercontributions. Further Kirschen et.al [5], using the informationabout complex network currents, the flow tracing is refined forboth real and reactive powers. Graph theory based approachfor tracing is carried out for network flows devoid of loops isgiven by Wu et.al [6]. Using the network Z-bus, Coneja et.al

[7] proposed loss allocation by using load flow information.Here system losses are attributed to buses which takes care ofrelative position of generation and loads in the network alongwith the capacity but contribution to loads from a given sourceis still a problem. Further if line shunts are not present thenZ-bus formation is difficult & charges are also allocated tocounter flows. The shortcomings of Postage stamp and Pro ratamethods are discussed in reference [8]. Postage stamp methodpractised in some markets even though simple to adopt, fails togive proper indication due to which large loads get the benefitover small loads. Pro rata method ignores the generation/loadlocation in the network and remote generations/loads benefitat the cost of others. Cost allocation to HVDC links present inthe system is not easy. This is due to the fact that the marginalcost is zero for these lines because of automatic control loopmaintains the desired power flow irrespective of variations inthe system conditions in normal state of operation.

This paper propose to use the virtual flows concept fortracing proposed by Thukaram et.al[9], in order to obtainsource contributions to loads. Principle of superposition isapplied to evaluate the virtual flows based on actual networkconditions. This is suited for on-line application in a giventransactional period. In principle this method can be equallyapplied to network with HVDC links. The proposed methodis detailed but preceded by brief look into the computationalaspects for obtaining power flow to AC system incorporatingDC links. Case studies on sample system and a real lifeequivalent 33-bus system incorporating an HVDC link, arepresented. Pricing aspect is dealt for the sample system,lastly the salient points of this approach and conclusions arepresented.

II. PROPOSED APPROACH

The initial data as a base case is to be obtained from theoutput of load flow / on line state estimator along with thetopology of network at the given transactional period. The buspower injections(generations/loads) along with the bus voltageprofiles is considered as a priori. From this data the virtualcontribution to loads from each source is evaluated usingsuperposition. The following section briefs about performingAC/DC load flow in order to get the base case data.

16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 503

Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.

A. AC/DC Load Flow

The presence of DC links in AC system requires loadflow to be performed in sequential steps as per the reference[10]. Load flow program developed by Thukaram et.al[11] isincorporated in this regard. Firstly the condition for DC systemis specified based on the control mode selected i.e. constantpower or constant current or constant voltage. From this, thevoltage along with active and reactive power requirements atthe input of DC terminal is obtained which in turn specifies theAC side requirement at the secondary of transformer feedingthe converter bridge. With this AC power flow solution isobtained as in usual case. The power fed at the converterside is represented as a equivalent load and at the AC sideof inverter as a equivalent generation. The taps of terminaltransformers at the respective converter bridges are computedand checked against practical available settings so as to obtainsatisfactory solution for the combined system. If the settingsare not satisfactory, the initial conditions of the DC system arerecast by changing the firing/extinction angles and the processis repeated. If transformer settings are within the satisfactorylimits, settings are selected to the nearest practical values at theAC-DC terminals and final power flow solution is obtained onthe combined system. Figure 1 shows the major computationalblocks for the specified approach.

System specified data

DC System Solution

AC System solution

Check for satisfactory

solution of combined

AC/DC system

Readjust DC system

initial settings

Obtain final AC/DC

combined power

flow

To virtual flows

evaluation block

YES

NO

Check for satisfactory

solution of combined

AC/DC system

Perform

Optimization if

necessary

NO

YES

Fig. 1. AC/DC Power flow computation blocks

B. Converter Representation

Figure 2 shows the general representation of a converterstation [1] present in the DC link of the AC sub system.The converter comprises of single or series connected bridgesas per voltage requirement. Mono polar or bipolar operationis possible depending upon the configuration. The converter

Vac∟ψ

1:a

Vdc

_

+Idc→

PacQac

Iac ∟ξ

AC System

Fig. 2. Converter representation

bridge is fed from AC side through the secondary of a feedingtransformer whose output can be adjusted through tap control.Similar converter is operated as a inverter on the other side ofthe DC link. Their roles can be interchanged depending uponthe direction of power transfer desired. With the selection ofproper bases for the combined system, the following perfor-mance equations for the converter are specified. DC voltageand power at the converter are,

Vdc = aVac cosα−RcIdc (1)

Pdc = VdcIdc (2)

where α as the firing angle, a feeding transformer tap settingand Rc, the commutation resistance of the converter which isa pure reactance term. With losses neglected the expressionsfor real power at the AC side is,

Pac = Pdc (3)

From the above, the expression for power factor angle at theAC side is obtained by,

Vdc = aVac cos(ψ − ξ) (4)

The reactive power requirement at the converter terminal isthen calculated by,

Qdc = Pac tan(ψ − ξ) (5)

the power factor angle between AC side voltage and currentis (ψ − ξ = θ). For inverter present at the other end of theconverter, the expression for DC voltage is same as in equation(1) but α being replaced by extinction angle γ, whose polarityopposite to the converter voltage. For proper operation of thelink such that no commutation failure occurs, the condition tobe met is,

α+ µ ≤ 1800 − γ0 (6)

where, µ being the commutation overlap angle and γ0 is theminimum required extinction angle. The AC power require-ment at the input of the inverter is similarly calculated by thevalid assumptions made as earlier wherein AC active poweronly being negative and the expressions Pac and Qac beingexpressed in terms π − ϕ, where ϕ being the power factor atthe AC side of inverter transformer.



C. Concept of virtual flows

As mentioned in the previous section the virtual flows areto be determined from the output of on-line load flow / stateestimator. After obtaining satisfactory AC/DC load flow solu-tion for the network, the virtual flow block is activated. Therequired parameters for computation are the bus voltage pro-files, real and reactive power injections/withdrawals from allthe buses along with the parameters of the network elementssuch as transformer tap positions and line parameters of theconnected AC network for which the power flow is obtained.The DC link is now equivalently represented as two loads onthe either side of the AC system to which it is connected suchthat converter power flowing into the DC system is taken as aload. At the inverter side the received power being representedas power injection to the respective system bus (negative load).Figure 3 represents the steps involved in computing the virtualflows from the sources present in the network. The computing

1: Get the required data from the o/p of loadflow / state estimator

2: Obtain admittance matrix of the

connected network [Ybus]

5: Convert all the bus powerinjections from each source to

equivalent currents

6: Inject equivalent current from ithgenerator

into modified network

7: Obtain the voltage profile developed in the networkdue to this injection & calculate the resulting currents in

all the branches of the network

8 : Evaluate the virtual flows contributed fromith generator using the base case bus voltageprofile and corresponding branch currents

obtained from previous step

3: Convert all the loads to equivalent admittancesConvert all the negative loads to equivalent

negative admittances

4 : Include all the load admittances into thenetwork [Ybus ] matrix to form modified

[Ybus ]mod

matrix

10: Select next

generator

9: All generators

covered

Stop

NO

YES

Fig. 3. Major computational blocks for proposed approach

blocks are briefly explained with network having g generatorbuses, r load buses and remaining as switching buses withzero generation/load.

1) The required data from the output of load flow / stateestimator is read. The bus voltage vector for this base

case is [V 0] and the admittance matrix of the networkbeing [Ybus].

2) Convert all the complex loads into equivalent admit-tances.

YLr = S∗Lr/|VLr|2 (7)

r = 1 .... d (number of loads) where SLr, VLr :loadpower and voltage at rth bus.

3) Include all the loads admittances into network [Ybus]matrix to form modified matrix say [Y mod

bus ].4) Convert all the complex generator power injections into

equivalent currents.

IGi = [SGi/VGi]∗ (8)

i = 1 .... g (number of injections) where SGi, VGi :businjected power and voltage at ith bus.

5) Form injection current vector [IGi] with all elementszero except the one corresponding to ith generator beingnon zero. Find the partial bus voltages developed in thenetwork due to this injected current alone by solving thefollowing network equation by LU decomposition.

[IGi] = [Y modbus ][Vgi] (9)

With [Vgi] the partial bus voltage vector for ith generatorcurrent injection(virtual action). Using this, partial cur-rents in the all network branches due to correspondinggenerator can be found by usual manner.

6) The contributions to line flows (partial contributions)from the given generator is found out by using the basecase bus voltage profile and by corresponding networkcurrents determined from previous step.

7) Repeat steps from 6 to 8 so as to cover all generators.8) Contribution to a particular load from a given generator

is evaluated by summing the partial contributions in thelines incident on the node to which load is connected.

Here the flows determined are defined to be virtual. Thesuperposition of individual contribution to network flows andloads matches with the base case result.

D. Illustrative sample systems

To demonstrate the virtual flow concept, a sample 5 bus sys-tem comprising of 2 generators and 3 loads as shown in Figure4 is considered. Shunt reactor of 2.0 p.u(400kV,100MVA base)is connected to load bus 5.

1

~

3

~

2

4

5

Fig. 4. Sample 5 bus system with 3 loads



The network parameters are given in Table I. Table II showsbase case data as obtained from solved power flow along withthe bus voltage profiles(p.u). Table III indicates the power flowin the lines of the network for base case. The partial voltagesdeveloped at network buses, when each of the source injectingequivalent current(individual action) into the modified networkis given in Table IV. It can be noted that the respective partialbus voltages developed from each source sums to original busvoltage profile.

TABLE ITRANSFORMER, LINE DATA FOR THE SAMPLE NETWORK IN (P.U)

Bus Element (R & X) B/2 Tap1-3 Transformer (0.002, 0.02) —– 1.0002-4 Transformer (0.002, 0.02) —– 1.0003-5 Line (0.004, 0.04) 0.5 —–4-5 Line (0.004, 0.04) 0.5 —–

TABLE IIGENERATION, LOAD(MW& MVAR) BUS VOLTAGES FOR BASE CASE

Bus Generation/Load Voltage(p.u)1 (305.40, 82.60) (1.000+j 0.000)2 (200.00, 79.70) (0.998-j0.067)3 (-100.00, -50.00) (0.977-j0.059)4 (-100.00, -50.00) (0.975-j0.104)5 (-300.00, -150.00) (0.939-j0.138)

TABLE IIIFLOWS (MW & MVAR)IN ALL THE LINES OF THE NETWORK FOR BASE

CASE

Line Forward flow Reverse flow Loss1-3 (305.44, 82.58) (-303.44, -62.56) (2.00, 20.02)2-4 (199.99, 79.71) (-199.06, -70.44) (0.93, 9.27)3-5 (203.35, 12.67) (-201.47, -86.91) (1.88, -74.24)4-5 (99.08, 20.49) (-98.48, -107.64) (0.60, -87.14)

TABLE IVPARTIAL BUS VOLTAGE PROFILES DEVELOPED DUE TO INDIVIDUAL

CURRENT INJECTION

Partial voltage developed all in p.uBus Injection at Bus-1(p.u) Injection at Bus-2(p.u)

(3.054-j0.826) (1.942-j0.929)1 (0.633+j0.113) (0.367-j0.111)2 (0.560-j0.063) (0.437-j0.003)3 (0.610+j0.053) (0.367-j0.111)4 (0.560-j0.063) (0.415-j0.040)5 (0.566-j0.040) (0.374-j0.096)

TABLE VCONTRIBUTIONS TO LINE FLOWS (MW & MVAR)IN THE LINES OF THE

NETWORK FROM SOURCE AT BUS 1

Line Forward flow Reverse flow Loss1-3 (305.40, 82.60) (-303.40, -62.58) (2.00, 20.02)2-4 ( 0.00, 0.00) ( 0.00, 0.00) (0.00, 0.00)3-5 (236.94, 40.84) (-241.02, -75.10) (-4.08, -34.26)4-5 (-57.31, -29.08) ( 53.64, -27.66) (-3.67, -56.75)

The partial contributions to line flows from the two sourcesare shown in Table V and Table VI respectively. The negative

loss term in these tables gives information about counter flowsfrom the corresponding generators. It can be inferred that thesuperposition of voltage, line currents and power holds good.

TABLE VICONTRIBUTIONS TO LINE FLOWS (MW & MVAR)IN THE LINES OF THE

NETWORK FROM SOURCE AT BUS 2

Line Forward flow Reverse flow Loss1-3 (0.00, 0.00) (0.00, 0.00) (0.00, 0.00)2-4 (200.00, 79.70) (-199.07, -70.43) (0.93, 9.27)3-5 (-33.59, -28.12) ( 39.42, -11.83) (5.83, -39.95)4-5 (156.34, 49.66) (-152.19, -80.02) (4.15, -30.36)

TABLE VIICONTRIBUTIONS TO LOADS(MW & MVAR) FROM INDIVIDUAL

GENERATORS

Source ↓ Load bus-3 Load bus-4 Load bus-5Gen. bus-1 (-66.45, -21.74) (-57.31, -29.08) (-187.38, -102.76)Gen. bus-2 (-33.59, -28.12) (-42.73, -20.77) (-112.77, -91.85)

Total (-100.05, -49.86) (-100.04, -49.86) (-300.15, -194.61)

Finally the contribution to loads from each sources arepresented in Table VII (loads indicated as negative powerinjections at respective buses). It can be inferred that all thegenerators will share some portion of each and every loadof the network in some proportion which may be significantor otherwise. This is evident from the Table VII. The tracingtechniques detailed so far in literature traces the output of gen-erators to only loads which are in its reach. Some generatorsmay not contribute to a particular load. Table VIII comparesthe proposed method with the technique explained by Kirschen[4], w.r.t real power contributions from each source to loads.The compared method, traces the output of source-1(bus-1)to loads at buses 3 and 5 & loads at buses 4 and 5 getscontributions from source-2(bus-2).

TABLE VIIICONTRIBUTIONS TO LOAD FROM SOURCES A COMPARISON

Source By proposed method By Kirschen MethodL3 L4 L5 L3 L4 L5

Gen. bus-1 66.4 57.3 187.3 100.0 —- 201.5Gen. bus-2 33.6 42.7 112.7 —- 100.0 98.5

Total 100.0 100.0 300.0 100.0 100.0 300.0

E. Transmission Usage Charge Allocation

In this section the pricing aspect has been dealt from the out-come of tracing using virtual flows. Charges for transmissionfacilities availed by each generating unit based on real powerflows is evaluated and compared with the tracing obtainedfrom Kirschen method. Table IX and Table X indicates thecharges for each generator. Here the reference is the net flowdirection in each lines as per the base case load flow. Negativevalues indicates counter flow components. Lines/transformersof the sample network are identical in every aspect and withthe assumption of equal transmission cost the results arepresented. The cost of transmission facility for both lines are



TABLE IXLINE USAGE(MW) AND CHARGES FOR SOURCE AT BUS-1

Lines Proposed method Kirschen method1-3 305.40 305.402-4 00.00 00.003-5 236.94 203.354-5 -57.31 00.00

Total charge 255980.00 279700.00

TABLE XLINE USAGE(MW) AND CHARGES FOR SOURCE AT BUS-2

Lines Proposed method Kirschen method1-3 00.00 00.002-4 200.00 200.003-5 -33.59 00.004-5 156.34 99.08

Total charge 173050.00 149080.00

taken at Rs.1000/MW and transformer cost is 25% of the linecost on similar terms. The proposed method allocates morecharges to generating unit at bus-2. Some portion of the loadat bus-4 is allocated to this generator and extra allocated chargeis compensated. Further, sources which are producing counterflows in a given line are not charged. As for as virtual flowsare concerned, if there is any counter flow/flows in a givenline, then these counter flows are made zero and non counterflows are accordingly modified as explained. Assuming in anyline the partial flow components due to four sources being pl1,pl2, −pl3 & −pl4, then the non counter components pl1 & pl2are respectively modified as per equation (10) and line usagecharge are allocated to these two components only.

p′

l1 = pl1{1− (|pl3 + pl4|)/(pl1 + pl2)}p

′

l2 = pl2{1− (|pl3 + pl4|)/(pl1 + pl2)}(10)

F. 33 Bus UPSEB equivalent system with an HVDC link

The determination of contributions to loads is applied to reallife 400kV, 33 bus equivalent of UPSEB (Utter Pradesh State)with a DC link between buses 17(Rihand-400)and 18(NCR-400). It comprises 7 transformers and 37 transmission lines.Two series connected bridges are located on either side of thelink which is configured for bipolar operation. The single linediagram of the system is shown in Figure 5. The details ofsystem generation/loads, HVDC system results from on-lineload flow are given in Tables XI & XII respectively.

TABLE XIGENERATION/LOAD DETAILS FOR THE UPSEB SYSTEM

Generating units Loads7 21

MVA (7399.5+j2326.0) (-7169.0-j4279.2)Shunt reactors 15 -1666.3 MVA

For determining virtual flows, the DC link is expressedequivalently by two complex loads on either side of the busesto which it is connected. The sending end power is equivalentto a positive load, whereas at the receiving end it is taken asnegative load (injection). Though the DC line carry only real

TABLE XIIDETAILS OF HVDC LINK

Sending end Receiving endMVA (-1547.9-j887.0) (1504.2+j915.8)

Transformer 465MVA 460MVArating 219kV 216kVTap 0.9625 0.975Vdc 1030.3kV 1001.4kV

Resistance 9.60960 OhmAngles α = 15.78o, γ = 18.00o

power, reactive power is required at the input of bridges forproper operation. Pricing aspect can be dealt on similar linesas explained in the previous section. The virtual flows areevaluated as explained in previous section. The net flows aswell as virtual flows in the AC lines connected to HVDC linksare presented in Tables XIII and XIV. It can be verified fromthese two tables that the net flows in the lines matches with thesuperposition of corresponding virtual flows. The contributionto DC link from either side of the terminal from all sourcesof the system is presented in Table XV. This gives powerinjection to DC line by each sources. Only the values of virtualcontributions from the sending has to be taken into account forpricing purpose. The loads specified in the tables also includescompensation and shunt reactor MVA if any.

TABLE XIVNET FLOWS(MW & MVAR) IN THE LINES ADJACENT TO DC LINK

Lines Flows1-17 (1800.3, 467.8)

11-18 (756.0, 440.5)32-17 (473.5, 10.3)17-25 (715.0, -115.0)18-33 (459.9, 138.2)18-8 (1795.0, 31.0)

TABLE XVSOURCE CONTRIBUTIONS (MW & MVAR) TO EITHER SIDE OF DC LINK

Source↓ Converter end Inverter End(at bus 17) (at bus 18)

RHND-GEN ( -486.9, -4.3) (310.2, 7.8)OBRE-GEN ( -214.2, -57.3) (153.1, 16.8)ANPR-GEN ( -371.8, -51.6) (254.8, 8.7)SNGRLGEN ( -472.2, -18.8) (310.6, -0.4)LAKHWGEN ( -5.9, -76.4) (118.6, -42.8)SRINGGEN ( -10.3, -53.8) ( 80.2, -35.8)NCR–GEN ( 13.5, -148.5) (276.3, -120.6)

Total (-1547.8, -410.7) (1503.8, -166.3)

III. CONCLUSION

A approach for evaluating source contributions to line flowsand loads is presented. By using the network modified admit-tance matrix and by sparse LU decomposition it is possible toevaluate virtual flows from the on-line load flow data. Partialcontributions are to be determined for each sources presentin the network. Repeated evaluation of virtual flows can beavoided if there is no considerable change in load/generationpattern. Generating units producing counter flows are iden-tified in a transaction. Each generating unit will be entitled



Fig. 5. 33 bus 400 kV equivalent UPSEB system with single DC link

TABLE XIIIVIRTUAL FLOWS(MW & MVAR) IN THE LINES ADJACENT TO DC LINK

LinesSource↓ 1-17 11-18 32-17 17-25 18-33 18-8

RHND-GEN (1800.0, 468.6)) (0, 0) (-1052.0, -274.1) (251.5, 4.8) (-53.7,-48.1) (363.9, 55.9)OBRE-GEN (0, 0) (0, 0) (288.8, 55.9) (74.6, -0.1) (-24.5,-26.0) (177.6, 42.8)ANPR-GEN (0, 0) (0, 0) (518.1, 45.4) (146.7, -5.5) (-43.7,-39.9) (298.5, 48.7)SNGRLGEN (0, 0) (0, 0) (685.8, 11.5) (214.2, -6.7) (-55.0,-46.7) (365.6, 46.2)LAKHWGEN (0, 0) (0, 0) ( 12.4, 46.9) (6.0,-29.3) (-27.4,-10.3) (146.1,-32.5)SRINGGEN (0, 0) (0, 0) ( 13.0, 32.7) (2.3, -20.9) (-19.6, -5.7) ( 99.8,-30.1)NCR–GEN (0, 0) (756.0, 440.0) (7.0, 91.4) (19.7, -57.0) (683.7,315.1) (343.4, -100.4)

Total (1800.0, 468.6) (756.0, 440.0) (473.2,10.1) (715.0,-114.7) (459.8, 138.4) (1794.9, 30.6)

to collect charges from each and every loads. The counterflow information is useful in managing network congestion tosome possible extent. In the presence of HVDC links in theAC system, this technique can be employed after obtaining theload flow / state estimation results for the combined AC/DCsystem for obtaining the extent of utilization of links by thesources. From the results it can be inferred that each and everysource is responsible to meet the load demand to some extent.This finds potential applications in areas such as bilateral &multilateral transaction evaluation, loss allocation and reactivepower optimization.

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