ORIGINAL ARTICLE
A probabilistic transmission pricing methodology considering transmission reliability margins
V.Vijay Venu •A.K.Verma
Received:12April 2010/Published online:3September 2010
ÓThe Society for Reliability Engineering,Quality and Operations Management (SREQOM),India and The Division of Operation and Maintenance,Lulea University of Technology,Sweden 2010
Abstract This paper posits on a reasonable quantification of the intrinsic reliability offered by an existing transmis-sion network structure for a given t of power transac-tions.We rely on the concept of transmission reliability margins in the lines,which act as safety nets to protect system curity in the face of aleatory uncertainties in the availability of transmission lines and epistemic uncertainty in accounting for the load demand patterns.This is pro-pod to be ud as an equitable basis to charge the urs of transmission network,generation and load consumption entities alike,over and above the usage charges levied according to the ‘extent-of-u’normative.Using the tan-dem combination of deterministic and probabilistic load flow studies in conjunction with power flow tracing pro-cedures,we p
ropo a step-by-step procedure to arrive at a novel transmission pricing methodology.A six-bus Roy Billinton Test System (RBTS)is employed to illustrate the conceptual feasibility and the computational procedure.Keywords Deregulation ÁPower flow tracing Á
Probabilistic load flows ÁTransmission reliability margin ÁTransmission pricing
1Introduction
The advent of deregulation in the power ctor has initiated the transition of centralized monopolistic systems towards a competitive market structure of unbundled generation,transmission and distributed rvices.In order to realize the value addition of unbundled rvices,it is esntial that proper regulatory frameworks be in place that competently address the issues arising out of decentralization,chief among them being transmission pricing strategies.
Transmission pricing must be designed in a fair and transparent manner that is economically equitable to all the market players,not only with the intent of appropriate revenue reconciliation strategies that recover system-wide transmis-sion investment and operational costs,but also with the goal of increasing market efficiency.Transmission pricing paradigms (Shirmohammadi et al.1996)that translate transmission costs into overall transmission charges usually include rolled-in transmission
pricing (bad on ‘extent-of-u’criterion,evaluated differently as in postage stamp methodology,con-tract path methodology,distance bad MW-mile methodol-ogy and power flow bad MW-mile methodology)and incremental transmission pricing (such as short-run and long-run incremental and marginal cost pricings applicable only to transactions catering to new customers).
Yu and Patton (2000)suggested the adoption of reli-ability indices such as expected unrved energy (EUE)and loss of load expectation (LOLE)to calculate reliability cost charges,which are then added to the regulated fixed charges derived from the ‘extent-of-u’unreliability costs were deemed as the basis to nd appropriate transmission price signals.Kim and Singh (2001)propod the concept of embedded costs including reliability benefits (taking into account the constraints of
V.V.Venu (&)
Reliability Engineering Group,Department of Electrical Engineering,Indian Institute of Technology Bombay,Mumbai 400076,India e-mail:vvv@ee.iitb.ac.in
A.K.Verma
Department of Electrical Engineering,Indian Institute of Technology Bombay,Mumbai 400076,India e-mail:akv@ee.iitb.ac.in搬家要注意什么
Int J Syst Assur Eng Manag (Apr-June 2010)1(2):113–119DOI 10.1007/s13198-010-0023-8
transmission line capacity)to allocate charges for each wheeling participant bad on reliability indices derived for the transactions.A relationship between capacity-u and reliability benefits was also shown.
A composite generation and transmission reliability evaluation method was ud by Li et al.(2005)to establish a unit incremental reliability value with capital investments. Reliability component was incorporated into the rate designs for wheeling and native customers.It was shown that the reliability component in the price design provided an incentive signal to both the utility and its customers to share their responsibility in the transmission system reliability.
Silva et al.(1998)considered the operation of trans-mission system under both normal and contingency con-ditions as a basis for allocating reliability costs to urs. Variants of procedures to quantify reliability contributions of market participants were put forward by Hur et al. (2004a,b),Chung et al.(2005),Kim et al.(2006),Lee-preechanon et al.(2007),and Monf and Jaefari(
2009) for reliability differentiated transmission pricing.Advo-cated in the papers is the usage of powerflow tracing procedures and load outage impact factors arising out of transmission line uncertainty owing to plausible contin-gencies.Our paper relies on their underlying fundamental conceptualization to advance such approaches by also considering additional sources of uncertainty,thus evolv-ing a new probabilistic transmission pricing methodology with considerations to transmission reliability margins.
2Propod conceptualization and methodology
漫与
indirect函数的使用方法The propod probabilistic transmission pricing methodol-ogy has its roots in the conceptual foundation provided by the minal works of Hur et al.(2004a,b)where explicit con-siderations to system reliability werefirst made in the transmission embedded cost allocation.This was achieved through the espousal of quantifying generators’contribution (using powerflow tracing procedures)to transmission reli-ability margins(TRMs)under line contingencies as dictated by the deterministic n-1criterion.In their works,a prob-abilisticflavour was added by implanting forced outage rates (FORs)of transmission lines in the subquent calculations. In doing so,only aleatory uncertainties in the availabilities of transmission lines have been addresd.We propo the additional inclusion of considerations for epistemic uncer-tainties due to random variations in the load demand patterns thr
ough the deployment of probabilistic loadflow studies. Aleatory uncertainty,also referred to as irreducible uncer-tainty,aris becau of natural,unpredictable variation in the performance of the system under study.Epistemic uncertainty is due to a lack of knowledge about the behavior of the system that is conceptually resolvable.
The utilized model of TRM of a line is the difference between its total transmission capacity and the megawatt power flow that it can carry for a given load profile.It should be pointed out here that the TRM employed in the prent study is the existing TRM after the scheduled transactions have taken place and not the planned TRM t aside for the Available Transfer Capability(ATC)unud transmis-sion capacity after carrying out energy transfer schedules is taken as the existing TRM.Ideally speaking,the system should be he transactions must be scheduled)in such a way that the existing TRMs match with the TRMs as pre-t from the ATC calculations.TRMs are greatly affected by transmission line outages and hence this scenario is best cap-tured by the usage of Line Outage Impact Factors(LOIFs)as also ud by Chung et al.(2005)and Kim et al.(2006).
LOIF is a linear nsitivity factor quantifying the impact of contingencies.It reprents the powerflow change on a line due to the outage of one of the remaining lines.It is distinctly different from the typic
ally ud Line Outage Distribution Factor(LODF)which gives the percentage of flow from the outaged its pre-outageflow)that ends upflowing on another line.
LOIF i;k¼
j f k
i
j
i
;8j f k
i
j[j f0i j
0;8j f k i j j f0i j
(
ð1Þ
where LOIF i,k is the line outage impact factor of line i due to the outage of line k,f i k is the powerflow on line i after the outage of line k,and f i0is the pre-outageflow on line i.The Line Outage Reliability Impact Factor(LORIF)can then be obtained as:
LORIF i;k¼ðLOIF i;kÞÃð"A kÞð2Þ
where"A k is the unavailability of line k.This expression is normalized to capture the relative impact of failure of line k on line i as follows,assuming that there are n lines in the transmission system:
NLORIF i;k¼
ðLOIF i;kÞÃð"A kÞ
ðLORIF i;1þLORIF i;2þ:::þLORIF i;nÞ
借呗利息怎么算的ð3Þi.e.,
NLORIF i;k¼
LORIF i;k
P
j¼1
n
j¼k
LORIF i;j
B B
@
1
C C
A
ð4Þ
According to our assumed notion of TRM,basic TRM of a line i from the ba ca loadflow solution is calculated as: TRM i¼TTC iÀBCPF ið5Þwhere TTC is the total transmission capability(line thermal rating),and BCPF is the ba ca powerflow.According
to the MW-mile pricing rule(Shirmohammadi et al.1996), transmission usage cost(TUC)is given as:
牵牛花一天的变化
TUC i¼
f i
TTC i
ÃFC ið6Þ
where f i is the powerflow on line i,and FC i is thefixed cost(embedded cost)of line i.On the similar lines of formulation,basic transmission reliability margin cost, TRMC,can be devid as postulated by Hur et al.(2004b), where it is noted that conventional methods bad only on the capacity-u for allocating costs are not equitable in that they overlook transmission rerves as the inherent nature of transmission infrastructure.
TRMC i¼TRM i
TTC i
ÃFC ið7Þ
Costing of reliability margins in the wake of the impact of n-1line contingencies is captured as weighted TRMCs, with NLORIFs being the weighting factors as below: TRMCLO i¼
X
k¼1
n
k¼i
ðNLORIF i;kÃTRMC kÞð8Þ
where TRMCLO i is line i’s transmission reliability margin cost considering line outages.Thefirst component of total transmission pricing in line i,TTP1i is now given as: TTP1i¼TUC iþTRMCLO ið9Þ
Carrying out a probabilistic loadflow(PLF)study with assumed distributions of bus injections for the ba ca can yield the probability of powerflows in transmission lines being greater than their respective rated thermal verload probabilities.The studies were carried out by us in detail in an earlier paper(Vijay Venu and Verma2009).PLFs are conducted for each of the n-1 line contingencies and the overloading probabilities, P(f i[TTC i),are computed.Percentage overloading probability increa(POPI)with respect to the ba ca for each ca is computed.
今生相伴POPI i¼½Pðf i[TTC iÞj lcÀPðf i[TTC iÞj bc
½Pðf i[TTC iÞj bc
ð10Þ
where the subscripts lc and bc stand for line contingency and ba ca,respectively.Normalization is done by calculating the relative percentage increa in probability of line overloads for the n-1contingency cas,yielding Normalized POPI(NPOPI).
TRMCPLF i¼
X
k¼1
n
k¼i
ðNPOPI i;kÃTRMC kÞð11Þ
where TRMCPLF i is the transmission reliability margin costing considering probabilistic loadflow studies,and NPOPI i,k is the Normalized POPI in line i for the outage of line k.The cond component of total transmission pricing in line i,TTP2i is now given as:
TTP2i¼TUC iþTRMCPLF ið12ÞNet Transmission Pricing,NTP is a weighted summation of the two components of total transmission pricing:
NTP i¼a1TTP1iþa2TTP2ið13Þwhere a1and a2are the weightage factors such that a1?a2=1and are chon by the regulatory agencies depending upon the significance they wish to attach to the two different modes of evaluating TRM TRMLO and TRMPLF.
申请办理Powerflow tracing methods basically rely on the pro-portional sharing principle,which assumes nodal
inflows as being shared proportionally in nodal outflows(Bialek 1996;Kirschen et al.1997;Wu et al.2000).Topological generation distribution factors are calculated,which indi-cate the portion of generation in debt to a generator that flows in a line.The upstream-looking algorithm analys nodal inflows while its dual,the downstream-looking algorithm,analys the nodal outflows.The upstream-looking algorithm applied to the grossflows determines how the power output from each of the generators would be distributed between the loads.The downstream-looking algorithm applied to the netflows determines how the demand of each of the loads would be distributed between individual generators.
Generators and loads can now be charged for trans-mission line utilization bad on the powerflow tracing calculations as below:
TC Gx;i¼a3ðNTP iÃU Gx;iÞð14Þwhere TC Gx,i is the transmission cost assigned to generator x due to the usage of line i,and U Gx,i is the per unit usage of generator x in line i.This relation can be ud as a stand-alone basis if the regulatory policy is such that the total transmission costs are attributable only to generators.In such a situation,a3is1.
TC Ly;i¼a4ðNTP iÃU Ly;iÞð15Þwhere TC Ly,i is the transmission cost assigned to load y due to the
usage of line i,and U Ly,i is the per unit usage of load y in line i.This relation can be ud as a stand-alone basis if the regulatory policy is such that the total transmission costs are attributable only to loads.In such a situation,a4 is1.However,if the regulatory policy is such that the total transmission costs are attributable both to the generators and the loads,then a3and a4must be accordingly chon such that a3?a4=1.A detailedflowchart for the pro-pod probabilistic transmission pricing methodology is shown in Fig.1.
3Illustrative ca study
The procedure conceptualized as earlier to formulate a probabilistic framework for transmission pricing is demon-strated with the help of a ca study using Roy Billinton Test System (RBTS).RBTS (Billinton et al.1989)is a six-bus test system with two generator bus and four load bus.The system peak load is 185MW and total installed generating capacity is 240MW,comprising 110MW at bus 1(four units)and 130MW at bus 2(ven units).There are nine transmission lines connecting the six bus and five bulk load points as shown in Fig.2.Only transmission corridors are considered for this identical parallel transmission lines between a pair of bus are lumped together and their parameters are adjusted accordingly.Upon the input of pertinent system data,three studies are simultaneously conducted—deterministic load flow study,probabilistic load flow study and power flow tracing study.The results from the studies are intertwined along way to get the transmission pricing,which costs are dis-tributed between the generators and the loads bad on the propod conceptualization.The flowchart shown in Fig.1depicts this quence of steps in an easily understandable way.
Table 1gives the normalized LORIFs,where the sum-mation of values in each row amounts to unity,except for tho of the radial line,line 7.The impacted lines are given row-wi and the outaged
lines column-wi.Though the system is n -1incure becau of the prence of a radial line (which isolates bus 6from the rest of the system in ca of a contingency),in keeping with the widely held practice of conducting reliability studies on this standard-ized benchmark system,we prerve the standard bus configuration presuming alternative means of meeting the load demand at bus 6locally in the event of a contingency in line 7.This also has the implication of assigning zero
TRMC considering both the n -1contingency analysis
and the probabilistic load flows.
Monte Carlo simulation bad PLF study is then carried out,where repeated trials of the dc deterministic load flow are carried out to determine the probability distributions of line flows.For each of the 100,000iterations of the Monte Carlo simulation performed,a t of bus loads and gener-ations are pudo-randomly generated and analyzed using the dc load flow equations that establish linear relationship between power flows and nodal power injections.A large number of line power flows are obtained,from where the requisite statistical information of probability of line overloads is
extracted.
Table 1Normalized LORIF for line outages Impacted line #Outaged line L1L2
L3
L4L5L6
L7
L1–
0.99270000.00730
L20.7715–0.21120.00430.01300
L30.33040.6641–00
0.00550L40.32310.58320–
0.06450.02310.0061L500.807500.0300–0.16250
L60.59870
0.16410
0.2371–0L7000000–L7
–
Table 2Probability of line overloads for line outages
Impacted line #Outaged line L1L2
L3
L4
L5
L6
L7
L1
–
肉肉花怎么养0.47290.21790.15820.160.17760.1236
L20.6231–0.33530.04450.07350.05720.066
L30.60270.6514–0.26470.21510.23490.224L40.48480.0820.3309–0.21660.23410.0673L50.00530.07170.6770.1806–
0.13430.0052
L60.28190.00110.14020.20480.1344–
0.0047L7
0.00560.00510.005
0.00530.00520.005
–
Table 3Relative %increa in probability of line overloads for line
outages Impacted line #Outaged line L1L2
L3
L4
L5L6
L7
L1–
0.84990.13180
00.01830L20.6780–
0.32200
L30.41940.4712–0.05930.00650.02760.0160L40.40130.02150.2562–0.14840.16490.0076L500.05730.65800.1653–0.11940
L60.37850
0.17970.27030.1716–
0L7
–
