CALCULATION OF NODAL AND ZONAL COEFFICIENTS TO INCORPORATE IN THE PORTUGUESE TARIFFS FOR USE OF THE
TRANSMISSION NETWORK
João Tomé Saraiva Maria Teresa Ponce de Leão André Sá Manuel João Aguiar jsaraiva@fe.up.pt mleao@fe.up.pt mee01026@fe.up.pt maguiar@inescnporto.pt Abstract – In this paper we describe the studies and the
main results obtained with a consultancy study conducted to evaluate nodal and zonal coefficients to incorporate in the Portuguese tariffs for the use of the transmission system.
According to the Tariff Regulation these coefficients should signal good or bad connection points and should mainly reflect transmission losses. To compute them, we analyzed several generation/load scenarios of the system, computed the components of nodal marginal prices and performed classification studies in order to define zonal coefficients in the 400 kV, 220 kV, 150 kV and 60 kV connection points with the distribution grids.
1. INTRODUCTION
Recently, the Power Systems Unit of INESC Porto - a non profitable private research institute linked to several Portuguese Universities – conducted a consultancy study under a contract with the Portuguese Energy Regulatory Board in order to compute nodal loss coefficients to incorporate in the Tariffs for Use of the Transmission Network. According to the Tariff Regulation these coefficients multiply the power terms of the Tariff for Use of the Transmission Network to be paid by the new connections during the first year. These coefficients have values higher or lower than 1,0 signaling connection points having an impact in losses in terms of their increase or decrease. They were already referred in the Tariff Regulation approved in 1998 and in force in the first regulatory period from 1999 to 2001.
They were kept in the revised regulation approved in 2001 and currently in force till 2004 although their values were always fixed at 1,0 for all nodes of the transmission network.
Despite t heir limited impact in time, the fact they mainly
reflect active losses, and the referred tariffs are currently set according to a Postage Stamp approach, their calculation was never considered important. This means the current tariffs don’t incorporate any kind of geographical differentiation except a voltage level one.
The study was conducted using several operation scenarios of the transmission grid for the year of 2001. Each of these scenarios was studied using an enhanced DC OPF model including power flow constraints and an estimate of active transmission losses. From these simulation exercises it was possible to derive nodal marginal loss coefficients for each analyzed scenario. In a second step, t hese coefficients were grouped using clustering techniques, name ly the Fuzzy C - Means approach, to identify sets of nodes of the network and the related zonal coefficients. The paper describes the Portuguese regulatory and tariff systems, describes some loss allocation methods referred in the literature, details the calculation of nodal loss coefficients and the clustering analysis in order to generate meaningful zones and finally presents an overview of the obtained results.
2. PORTUGUESE REGULATORY SYSTEM 2.1. Regulatory System
The Portuguese Energy Regulatory Board – ERSE – Entidade Reguladora do Sector Eléctrico – was originally created in 1995 in the scope of new legislation that contributed to induce competition in the electricity sector.
Meanwhile, in 2002 its responsibility was enlarged since it was assigned the responsibility of regulating the gas sector.
Therefore it is now the Regulatory Board for the Energy Services – ERSE, Entidade Reguladora dos Serviços Energéticos. Among its original responsibilities (as in Decree Law 187/95 of June 27, 1995) we can refer:
- the preparation and publication of the Tariff Regulation, establishing the structure of the tariffs, the formulas to be used in order to compute tariffs for several services, the identification and preparation of economic and account information required to set the tariffs, and the responsibility to set those tariffs every year;
- to prepare a set of aspects to be included in the Quality of Service Regulation;
(1) João Tomé Saraiva (jsaraiva@fe.up.pt) and Maria Teresa Ponce de Leão (mleao@fe.up.pt) are with the Electrotechnique and Computer Department of Faculdade de Engenharia da Universidade do Porto, Portugal and INESC Porto, Campus da FEUP, Rua Dr. Roberto Frias, 4200-465 Porto – Portugal.
(2) André Fernando Sá concluded his master in the Electrotechnique and Computer Department of Faculdade de Engenharia da Universidade do Porto, Portugal and is currently Energy Manager in Textil Riopele, Portugal, mee01026@fe.up.pt
(3) Manuel João Aguiar is a master student in the Electrotechnique and Computer Department of Faculdade de Engenharia da Universidade do Porto, Portugal and is also with the Power Systems Unit of INESC Porto.
- to prepare and to issue the Commercial Relations Regulations and the Regulation of the Access to the Networks and Interconnections;
- to obtain information from the regulated entities as well as preparing inquiries, solving conflicts and setting fines.
Regarding the Tariff Regulation, its first version was in force from 1999 till 2001, that is, during the first regulatory period.
By the end of 2001, the regulations under the responsibility of ERSE were revised and a new version of the Tariff Regulation was passed to be in force from 2002 till 2004, that is, in the second regulatory period.
According to this Tariff Regulation:
- the transmission activity is regulated according to a Cost of Service/Rate of Return – CoS/RoR, strategy. The transmission company sends each year an estimate of its costs and investments for the next year as well as the actives to be re munerated at a 9% rate. ERSE has the power to accept or not those costs, investments and actives and, once accepted, it sets the tariffs for the use of the transmission network;
- the distribution activity is regulated according to an incentive price cap mechanism. In the year previous to the beginning of a new regulatory period, the economic and technical performance of this activity is studied in order to compute a reasonable departing set of values for the tariffs for the use of the distribution system. On subsequent years these tariffs evolve according to a pre - determined rule usually known as RPI-X. The regulation includes incentives or penalizations related to Quality of Service (dependent on the Annual Energy not Supplied) and on the technical performance of the grid (dependent on the annual active losses).
2.2. Tariff System
The tariffs currently in force in Portugal are additive in the sense that the amounts to be paid at a certain level are determined by the addition of several terms corresponding to different regulated activities. The tariff system comprises:
- a Tariff for Energy and Power – TEP - to be paid by non eligible consumers or by eligible consumers that didn’t change of supplier. This tariff remunerates generation activities as well as the investment in new power stations;
- a Tariff for the Global Use of the System – TUGS - paid by all clients, eligible or non eligible. It pays costs related with the National Control Center, with Ancillary Services and with the budget of the Regulatory Board. It also includes the remunerations due to the overcosts of small hydros, cogeneration stations and wind parks as well as overcosts from the electricity systems of the Atlantic islands of the archipelagos of Açores and Madeira;
- a Tariff for Use of the Transmission Network – TURT - with terms for Extra High Voltage and for High Voltage networks. This tariff remunerates the costs of the transmission provider regarding new investments and maintenance. It is paid by all clients connected at the Extra High Voltage level or below that level, respectively;
- a Tariff for Use of the Distribution Network – TURD – with terms for high voltage (typically 60 kV), medium voltage (typically 30 and 15 kV) and low voltage
(230/400 V). These tariffs remunerate the investment, maintenance and operation costs of distribution networks. Each client pays the tariffs for the voltage level it is connected to and above that one;
- a Tariff for the Commercialization of Networks – TCR – paid by all clients and remunerating the metering and billing activities regarding the use of networks;
- a Tariff for the Commercialization on Regulated Clients – TCSEP – paid by all non eligible clients and by eligible ones that didn’t change of supplier. This tariff remunerates the metering and billing activities regarding supplying energy and power.
The application of these tariffs leads to the following payments:
- eligible clients that changed of supplier pay the TUGS, TURT, TURD and TCR. These clients pay energy and power according to bilateral contracts or according to prices in the day-ahead market;
- regulated clients, that is, non eligible clients and eligible ones that didn’t change of supplier pay TEP, TUGS, TURT, TURD, TCR and TCSEP.
In particular, TURT is composed of prices for active contracted power, for active peak power and for reactive injected and consumed power. TURT values are established according to a Postage Stamp approach per voltage level, meaning that there are constant values for these four tariff variables in all nodes at 400 kV, for one side, and at 220 and 150 kV nodes, for the other. This also means that there is no geographic discrimination of those tariffs, eventually leading to a cross subsidy situation inside each voltage level. In 2002, the peak power term of this tariff was responsible for 90% of the regulated remuneration of the transmission activity while the reactive energy terms had neglectable contributions.
The Tariff Regulation incorporates a mechanism to induce some level of geographic discrimination of TURT. This mechanism corresponds to nodal or zonal factors that multiply the monthly active power to be billed. The Tariff Regulation indicates that these coefficients can be higher or lower than 1,0 signaling a bad or a good interconnection point of a new consumer with the grid. These factors should reflect losses and congestion problems in the 400/220/150 kV grid. Although included in the Tariff Regulation since 1998, these coefficients were never computed, so that the Regulatory Board used unit values for all of them. Recently, the Power Systems Unit of INESC Port concluded a consultancy study aiming at proposing nodal and zonal factors to incorporate this information. When dealing with this issue, it shouldn’t also be forgotten the next implementation of the Iberian Electricity Market between Portugal and Spain.
3. OVERVIEW ABOUT LOSS ALLOCATION METHODS
3.1. Proportional Allocation
The literature includes a large number of publications on loss allocation methods. The simplest approach simply allocates the cost of losses between generators and loads
according to a pre-fixed share between these two activities and considering a proportion regarding each particular generation or load [1, 2]. If the share between generators and loads is Perc % and (100-Perc)%, then the amounts to assign to generator i or to load j are given by (1) and (2). Based on this, the nodal generator allocation coefficients are all equal, and the nodal load allocation coefficients are also equal meaning that we are not transmitting any locational signal.
= ∑
k i gi
,
loss Pg
. Pg Ploss 100.
P Perc (1)
∑
= −
k j lj
,
loss Pl
. Pl Ploss 100 .
Perc
P 100 (2)
3.2. Allocation Using the Impedance Matrix
Some approaches express the system active losses in terms of nodal currents and the bus impedance matrix [3, 4]. These approaches depart from (3), and substitute nodal voltages by impedances multiplied by currents as in (4). After some calculations, it is obtained (5) that can be decomposed node by node. For node k the losses to be allocated are given by (6). This expression indicates there are couplings between nodal currents showing the non linear nature of this problem.
= ∑
= N 1 k
* k k.I V al Re
Ploss (3)
= ∑ ∑
= =
N 1 k
N 1 j kj j
* k. Z .I I al Re
Ploss (4)
= ∑ ∑
= =
N 1 k
N 1 j kj j
* k. R .I I
al Re
Ploss (5)
= ∑
= N 1 j kj j
* k k Real I . Z .I
Ploss (6)
3.3. Incremental Allocation
Several approaches perform the loss allocation considering the results from a set of power flow studies solved sequentially [5, 6, 7]. These approaches admit that an infinitesimal change in a bilateral transaction or in a generation or demand from the pool also leads to an infinitesimal change of active losses. This change is computed using (7) in which the derivative of active losses regarding the injected power in node j is usually known as the Incremental Transmission Loss, ITL, of that node.
j N
1
i j
P P . Ploss
Ploss ∂
∂
= ∂
∂ ∑
= (7)
If one considers a bilateral contract between nodes r and s, the active losses to be allocated to it are given by (8). In this case, to allocate losses one should increase the generation and/or demand in each node by steps, update the generation powers using (9) and solve a new power flow study to update the operation point of the system. The main drawback of this approach is due to the fact that it requires defining an order to consider each transaction. This priorization is not immediate and can be interpreted as a subjective decision not transparent and unacceptable in a market environment.
contract s
r
P P . Ploss P
Ploss
Ploss ∂
∂
−∂
∂
= ∂
∂ (8)
∑
∑ +
= = allcontracts i,rs
N 1
j contract,ij
i P Ploss
Pg (9)
3.4. Marginal Allocation
Marginal allocation methods are described for instance in [2]. This paper uses the previously referred ITL coefficients obtained as results from a power flow study. Based on these ITL coefficients, the losses to allocate to generator i or to load j are given by (10) and (11).
i i gi i
gi Pg
Ploss . Pg ITL . Pg Ploss
∂
= ∂
= (10)
i i li i
li Pl
Ploss . Pl ITL . Pl Ploss
∂
= ∂
= (11)
However, the sum of these loss terms allocated to generators and to loads does not correspond to the total amount of losses. This requires a normalization step using the real amount of losses to be allocated. The final allocation depend on the bus selected to reference+slack.
Besides, there can exist positive and negative ITL coefficients reflecting increasing and decreasing impacts on the losses from increasing the injected power.
3.5. Allocation Based on OPF Results
Several other publications as [8] suggest the use of OPF results to compute coefficients reflecting congestion and losses. These coefficients are terms usually included in the expressions of short term marginal prices, STMP. For node k the STMP is defined by (12) as the impact on the objective function Z of the optimization problem from varying the load in node k, for a given load scenario, topology and components in operation.
lk
k P
Z
∂
= ∂
ρ (12)
STMP can be obtained by solving the optimization problem (13) to (17). This problem aims at minimizing generation costs (13) subjected to a global balance equation (14) as well as to generator constraints (15), Power Not Supplied limits (16) and to branch capacity ranges (17).
∑ + ∑
= ck.Pgk G. PNSk Z
min (13)
∑Pgk+∑PNSk =∑Plk (14)
max k k min
k Pg Pg
Pg ≤ ≤ (15)
k
k Pl
PNS ≤ (16)
( )
∑ + − ≤
≤ bk k k k bmax
bmin a .Pg PNS Pl P
P (17)
In this model Pgk is the generation in node k having variable cost ck, PNSk represents the output of the fictitious generator connected to bus k to simula te Power Not Supplied, G is the penalty specified for PNS, Pgmink and Pgmaxk are the generation ranges, Pbmin and Pbmax are
the transmission limits of branch b and abk is the DC sensitivity coefficient translating the impact in the flow in branch b from changing the injection in node k by one unit.
This model can be enhanced by considering an iterative process to include an estimate of transmission losses. This step is important since transmission losses contribute to increase the geographic discrimination of nodal marginal prices thus turning more realistic its evaluation. Following the ideas in [8], losses in branch ij were approximated by (18) in which gij is the branch conductance and θij is the phase difference along branch ij.
) cos 1 .(
g . 2
Lossij≈ ij − θij (18)
The estimate of transmission losses was included according to the following algorithm:
i) Solve problem (13) to (17) and set iteration counter itr at 1;
ii) Built the nodal injection vector and compute voltage phases using the inverse of the DC model bus admittance matrix;
iii) Estimate branch losses using (18) and add half of the losses in branch ij to each of the loads in its extreme buses;
iv) Solve problem (13) to (17) considering the new load vector and increase itr by 1;
v) Built the nodal injection vector and compute voltage phases using the inverse of the DC model bus admittance matrix;
vi) Check convergence by comparing voltage phases between two consecutive iterations. If convergence was not yet reached return to iii).
The expression for the Short Term Marginal Price in node k, for a given set of operational conditions is model dependent and, for the above formulation, is given by (19). This means that the nodal marginal loss coefficient, MLC, reflecting load changes is given by (20).
ik
j lik
mn ij lik i i
ik P
. P P
. Loss ∑ +σ
∂ µ ∂
∂ + γ ∂ + γ
=
ρ (19)
ik
ik Pl
1 Loss
MLC ∂
+∂
= (20)
In this expression, ρik is the nodal marginal price at node k for a given load scenario i, γi is the dual variable of (14), Plik is the active load at node k in scenario i, Pmn is the active flow from node m to node n, µij is the dual variable of an active branch limit constraint in scenario i, σik is the dual variable of the Power Not Supplied limit constraint in node k in scenario i and Loss represents the active losses in all system branches at scenario i.
This model has a major drawback due to the fact that it requires inverting the DC model admittance matrix in order to compute the abk coefficients. This means that one has to eliminate a line and a column of that matrix corresponding to selecting a reference and slack node. This is important when talking about the compensation of the marginal variation of losses, since they will be balanced in the reference node. If this node does not coincide with the node where it is the marginal generator, the nodal prices and the nodal loss coefficients will be affected by this fact. This means that the use of this model requires identifying the marginal generator
and then selecting the corresponding node to reference and slack. This identification is not always straightforward because the marginal generator function can be distributed by several machines or the marginal generator can change whenever the operation conditions are modified.
4. CLASSIFICATION APPROACH – FC MEANS ALGORITHM
In order to identify zones to aggregate system nodes considering the nodal loss coefficients, we used the Fuzzy C Means algorithm detailed in [9]. In brief, this algorithm uses concepts from Fuzzy Set Theory admitting that there are points to classify that are not adequately and fully explained by a single cluster. This means it is adopted an iterative procedure that uses an initial set of membership values of each point to each cluster, so that condition (21) holds. In this expression, i represents a point in the set to be classified, c is the specified number of clusters and µij is membership degree of point i to cluster j.
∑=c µ =
1
j ij 1 (21)
Then, the algorithm computes the coordinates of the centroids (22), that is, points representing the characteristics of the elements in each cluster. Once these coordinates are available, the membership values are updated using (23) and the convergence is checked comparing the membership values in two consecutive iterations. The use of this algorithm requires specifying the number c of clusters and the value of the parameter m. One can conduct a number of classification studies for different c values and then select the clustering result that better improves a Quality Partition Index. Regarding the m parameter, it is used to filter the information of points having low membership degrees to some clusters, so that the larger m, the harder or less fuzzy the final partition is.
( ) ( )
∑
∑
=
=
µ
= Nµ
1 k
m jk N
1
k k
m jk j
x .
v (22)
( ) ( )
∑= −
= −
µ c
1 j
m 1 2 jk
m 1 2 jk jk
d
d (23)
5. APPLICATION TO THE NATIONAL TRANSMISSION NETWORK
5.1. General Description and Main Assumptions
The simulations were conducted using 8 generation/load scenarios made public by the Portuguese transmission company [10] for the year 2001. These scenarios include peak and valley hours for Spring, Summer, Autumn and Winter dry conditions. To characterize more completely the operation conditions of the network in 2001 we prepared some extra scenarios corresponding to full summer and winter hour conditions as well as peak, full and valley winter hours assuming a wet hydrological scenario. The final 13 scenarios are coded as:
- PS and VS – peak and valley spring hours;
- PDS, FDS and VDS – peak, full and valley summer hours in dry conditions;
- PA, VA – peak and valley autumn hours;
- PDW, FDW and VDW – peak, full and valley winter hours in a dry hydrologic situation;
- PWW, FWW and VWW - peak, full and valley winter hours in a wet hydrologic situation.
The full spring and autumn scenarios were not explicitly considered since the corresponding hours were allocated to the peak and valley spring and autumn scenarios. The duration of each scenario was calculated based on the provisions of the Tariff Regulation regarding the number of peak, full and valley hours in a week. As an example, the number of valley hours in summer is 76, out of 168 hours in a week so that the VSM scenario as a duration given by (24).
h 71 , 4 990 .8760 168 M 76
DurationVS = = (24)
For each of these scenarios, it was run the DC OPF problem detailed in section 3.5 in order to compute the marginal nodal coefficients. The simulations considered some basic assumptions that will be detailed in the next paragraphs:
- in the first place, the Portuguese generation system is a mixed hydro-thermal one. This means that its operation and simulation requires some water management module or knowledge about the Value of Using Water. Neither that module nor the Value of Using Water in several reservoirs was available. To overcome this problem, and in order to obtain generation results from the simulation software in each scenario consistent with the data in the scenarios, we substituted constraints (15) for hydro stations in the DC OPF model by constraints as (25). In
this constraint Pgk is the generation in generator k,
sc ,
Pgk is the generation value included in the data for scenario sc for that station and ∆g is a small variation allowed to affect the final value of Pgk;
g sc , k k g sc ,
k Pg Pg
Pg −∆ ≤ ≤ +∆ (25)
- in order to overcome the dependence of the marginal nodal loss coefficients from the reference+slack bus, and for each scenario, we identified the marginal generator by increasing the load in several buses by 1 MW and checking the generator that supplies this increase. Once this generator is identified, the corresponding bus is selected for reference+slack;
- it was considered that all system components were ideal in the sense that the study did not consider outages through an year of simulations. The incorporation of reliability issues can be done adopting a Monte Carlo Chronological module that would sample outages according to failure rates and would simulate the reparation of components considering repair rates.
5.2. Results Obtained For Some Nodes and Scenarios Table I presents the values of the nodal marginal prices,
ρk, and nodal loss coefficients, MLC, obtained for some nodes of the 400 kV network for four of the thirteen scenarios that were analyzed: PS, VS, PWW and VWW scenarios. The last two columns of this table include the average values of the nodal marginal prices and the nodal marginal loss coefficients weighted by the duration of each scenario. The complete results of this study can be obtained in reference [11].
Table I – Some results obtained for nodes of the 400 kV network.
PS VS PWW VWW Average values
Node ρk
€/MW.h
MLC ρk
€/MW.h
MLC ρk
€/MW.h
MLC ρk
€/MW.h
MLC ρk
€/MW.h
MLC A.Lindoso 37,1373 0,9930 36,8899 0,9864 37,8085 1,0109 36,0108 0,9629 35,7566 0,9952 R. de Ave 37,3211 0,9979 37,0591 0,9909 37,8085 1,0109 36,2547 0,9694 35,8826 0,9987 Palmela 36,5980 0,9786 36,6414 0,9797 36,6616 0,9803 36,9443 0,9878 35,6768 0,9935 C. Sines 35,7800 0,9567 35,8160 0,9576 35,8270 0,9579 36,1982 0,9679 34,9836 0,9741 Pego 37,2047 0,9948 36,8134 0,9843 37,0863 0,9916 36,8137 0,9843 35,8299 0,9976 Fanhões 37,3175 0,9978 37,1426 0,9931 37,3840 0,9996 37,4258 1,0007 36,1544 1,0067 Rio Maior 37,2770 0,9967 37,1061 0,9921 37,3558 0,9988 37,1220 0,9926 36,0698 1,0043 Recarei 37,3254 0,9980 37,0750 0,9913 37,7045 1,0081 36,3023 0,9706 35,8867 0,9989 Falagueira 37,5110 1,0030 37,0019 0,9894 37,2861 0,9970 36,9922 0,9891 36,0261 1,0030 F.Alentejo 37,6514 1,0067 37,2370 0,9956 37,6433 1,0065 38,4439 1,0279 36,4116 1,0137 5.3. Results Obtained from the Classification Study
The classification study was conducted for each voltage level (400 kV, 220 kV, 150 kV and 60 kV supply points to the distribution networks) and for each of the 13 analyzed scenarios. In each case, the points to be classified were defined as
(
x,y,MLC)
in which x and y are the coordinates of the system node regarding the southwest extreme point of Portugal and MLC is the marginal loss coefficient for the scenario and voltage level being analyzed. From this study we got the following main conclusions:- for each voltage level and for each scenario, we ran the classification algorithm for different specified number of
clusters, c in Section 4. Then we computed a Quality Partition Index that indicates the most adequate number of cluster. For each voltage level, and independently of the scenario under consideration, the most adequate number of clusters was always the same. In this case, we concluded that the most adequate number of clusters was 3 for the 400 kV network, 4 for the 220 kV network and 2 both for the 150 kV network, and for the 60 kV interconnection points with distribution grids;
- as an illustration, Figure 1 presents a one line diagram of the Portuguese transmission system. It has a set of north-south and center west-center east 400 kV lines, a set of 220 kV from northeast to the center of the
country and 150 kV in the northwest and in the south.
This diagram presents the geographic location of the four clusters identified for the 220 kV network;
- the independency of the number of clusters regarding the scenarios, within each voltage level, suggested the use of the average values of the centroids to characterize each zone in an annual basis. In this sense, Table II includes the average values of the centroids weighted by the duration of each scenario;
- regarding the four clusters of the 220 kV, it should be noticed that centroid C2 has a value lower than 1,0, while the other ones are higher than 1,0. Cluster C2 includes nodes in the northeast part of the country where there is excess of generation regarding demand. Therefore, new demand in this area contributes to reduce the losses in the transmission system;
- the majority of the demand is connected to 60 kV nodes.
This is quite evident because the values in Table II tend to increase when going from 400 kV to 60 kV nodes as we are more distant from generation. Apart from that, the two centroids identified for the 60 kV nodes have average values higher than 1,0. This fact indicates that the remuneration collected by the transmission company would slightly increase by 1,6% if these multiplicative coefficients were used for all loads along a year.
Figure 1 – Four zones identified for the 220 kV network.
Table II – Average centroids of the marginal loss coefficients.
400 kV 220 kV 150 kV 60 kV
C1 0,9998 C1 1,0033 C1 1,0120 C1 1,0159 C2 1,0022 C2 0,9967 C2 1,0088 C2 1,0164 C3 0,9961 C3 1,0373
C4 1,0169
6. CONCLUSIONS
In this paper we described the studies performed in the scope of a consultancy study developed by the Power Systems Unit of INESC Porto under a contract with the Portuguese Energy Regulatory Board. This study was based in a set of generation/demand scenario s defined for 2001 and aimed at calculating nodal marginal loss coefficients to integrate in the Tariff Regulation. At the end, it was performed a classification study using the Fuzzy C Means algorithm in order to define zones of each voltage level network. The use of these coefficients will improve the geographical signals transmitted to network users in order to adopt more efficient behaviors.
References
[1] A. G. Expósito, J. R, Santos, T. G. Garcia, A. R. Velasco, “Fair Allocation of Transmission Power Losses”, IEEE Transactions on Power Systems, vol. 15, no. 1, February 2000.
[2] A.J.Conejo, J. M. Arroyo, N. Alguacil, A. L. Guijarro, “Transmission Loss Allocation: A Comparision of Different Practical Approaches”, IEEE Trans. on Power Systems, vol. 17, no. 3, August 2002..
[3] A. J. Conejo, F. D. Galiana, I. Kockar, ”Z-bus Loss Allocation”, IEEE Trans. Power Systems, vol. 16, no. 1, February 2001.
[4] D. Lima, A. Padilha, “Loss Allocation on Electric Power Networks”, in Proceedings of the VIII Symposium of Specialists in Electric Operational and Expansion Planning, VIII SEPOPE, May 2002.
[5] F. D. Galiana, M. Phelan, “Allocation of Transmission Losses to Bilateral Contracts in a Competitive Environment”, IEEE Trans. on Power Systems, vol. 15, no. 1, February 2000.
[6] F. D. Galiana, A. J. Conejo, I. Kockar, “Incremental Transmission Loss Allocation Under Pool Dispatch”, IEEE Trans. on Power Systems, vol. 17, no. 1, February 2002.
[7] C. Moyano, R. Salgado, “Transmission Loss Allocation in Pool Energy Markets: Analysis of Alternative Approaches”, in Proceedings of the VIII Symposium of Specialists in Electric Operational and Expansion Planning, VIII SEPOPE, May 2002.
[8] M. Rivier, I. J. Perez-Arriaga, “Computation and Decomposition of Spot Prices for Transm ission Pricing”, 11th Power Systems Computation Conference, PSCC, Avignon, 1993.
[9] J. D. Bezdek, K. Sankar, Pattern Recognition with Fuzzy Objective Functions Algorithms, Plenun Press, New York, 1981.
[10]REN – Rede Eléctrica Nacional, SA, “Characterization of the National Transmission Network in December 31th 2001”, (in Portuguese), March 2002.
[11]J. T. Saraiva, A. F. Sá, M. J. Aguiar, M. T. Ponce de Leão, “Studies On the Definition of Nodal Loss Coefficients”, (in Portuguese), Final Report for ERSE - Portuguese Energy Services Regulatory Board, Power Systems of INESC Porto, Porto, October 2003.
João Tomé Saraiva got his degree, PhD, and Agregado degrees from Faculdade de Engenharia da Universidade do Porto, FEUP, in 1985, 1993 and 2002 where he is currently Associate Professor. In 1985 he joined INESC Porto – a private research institute – where he was head researcher or collaborated in sprojects related with the development of DMS systems, qualit y of service in power systems and tariffs for the use of networks. Several of these projects were developed under consultancy contracts with the Portuguese Electricity Regulatory Agency.
André Fernando Sá was born in August 1977 and concluded his Master in Electrotechnical and Computer Engineering from FEUP in July 2000 and in December 2003. He worked in Schneider Electric Portugal from 2000-2002, in the Power Systems Unit of INESC Porto in 2003, and he is now the Energy Manager in Textil Riopele, Portugal.
Maria Teresa Ponce de Leão received her Licenciado and Ph.D. degrees from Faculdade de Engenharia da Universidade do Porto, FEUP, in 1980 and 1996, in Electrical Engineering. In 1983 she joined FEUP and currently holds the position of Assistant Professor. In 1987 she joined also INESC, a research and development institute. In recent years, she was involved in the development of DMS sy stems and in the evaluation of the impact of dispersed generation in distribution planning.
Manuel João Aguiar is a researcher in the Power Systems Unit of INESC Porto. He obtained is Degree in Electrical Enginnering, in 2000, from Faculdade de Engenharia da Universidade do Porto. Now he is working in is MSc dissertation.
Cluster C2
Cluster C4 Cluster C3
Cluster C1
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~ V.Fria
Caniçada V.Furnas T1_1
Oleiros
Cartella
Salamonde Venda Nova
T1_2 Alto Rabagão
Chaves Mogadouro Picote
Miranda
Valeira Guimarães
T1_3
Riba d’Ave Recarei Pocinho
Central
Pocinho BempostaAldeadavila Aldeadavila
Saucelle Régua
Tabuaço Ruivães
Ermesinde
Custóias
Vermoim Maia
Torrão Carrapatelo T2_3
Chafariz
Canelas Estarreja
T2_2
Aguieira
Pombal
Batalha
Pereiros Zêzere Bouça
Cabril
Falagueira Pracana
T1_5 Fratel Pego
Cedillo Carregado
Sacavém Q. Grande Porto Alto
Sacavém Carriche
Alto Mira Trajouce
Sines
Seixal T1_8
F. Ferro Q. Anjo
Setúbal Pegões
T1_7 Évora
Ferreira Alentejo
Ourique Neves Corvo Estói Tunes
T1_4
T2_5
T2_1
FPV4 FPV1
FPV2
T2_7 T2_10
T2_8
T2_4
Vila Chã Alto Lindoso
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~ C.Gás Valdigem
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Mourisca
Mogofores Rio Maior
Fanhões
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~ Palmela
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