Allocation of losses in distribution systems with embedded generation ...

Allocation of losses in distribution systems with embedded generation J.Mutale, G.Strbac, S.Curcic and N.Jenkins Abstract: Deficiencies in present-day loss allocation practices are demonstrated using as an example the substitution method presently applied in England and Wales to evaluate the impact of EG on losses. Two new loss allocation schemes are proposed; one based on the allocation of marginal losses and the other on the allocation of total losses. Loss allocation factors computed from the proposed schemes are specific to location and time of use. This is especially important for EG whose impact on losses varies in time and space. A notable feature of the proposed loss allocation coefficients is that they can be positive or negative and therefore can recognise the presence of counter-flows such as those due to the presence of EG. Application of the proposed loss allocation schemes is illustrated on a real network based 265-node generic distribution system model incorporating EG.

List of symbols

Active power injection at node i Reactive power injection at node i L Total system active power losses B, Susceptance of branch between nodes i and j G, Conductance of branch between nodes i and j '3 Voltage angle at node i vi Voltage magnitude at node i N Number of nodes i j p i Marginal loss coefficient for active power at node i ijQl Marginal loss coefficient for reactive power at node i PPi Reconciled marginal loss coefficient for active power at node i PQi Reconciled marginal loss coefficient for reactive power at node i Vector of unreconciled marginal loss coefficients P Vector of reconciled marginal loss coefficients P MLC reconciliation factor KO Vector of direct loss coefficients Y H Hessian matrix Pi Qi

1

Introduction

Electricity supply industries (ESI) worldwide are undergoing major structural changes with the fundamental objective of introducing competition and choice in electricity supply. These changes are motivated primarily by the belief that competition will bring better service, at a lower price 0IEE, 2000 ZEE Proceedkgs online no. 20000003 DOL lO.l049/ipgtd20000003 Paper fmt received 6th April and in r e d form 21st September 1999 S . Curcic was w i and ~ J. Mutale, G. Strbac and N. Jenkins are with UMIST, UK S. Curcic is now with EA Technology Limited, UK IEE Proc-Gmer. Trunsm. Distrib., Vol. 147, No. 1. January 2000

to electricity consumers. A notable feature of the emerging market-based industry structure is the separation of the generation, transmission, distribution and supply segments of the electric energy business into autonomous business units. Prices in the generation and supply segments are determined through suitable market mechanisms, whereas those in the monopoly segments of transmission and distribution are regulated. Interaction between all these business units is through commercial contracts. An essential condition for competition to develop is open access, on a nondiscriminatory basis, to transmission and distribution networks. The central issue in the concept of open access is setting an adequate price for transmission and distribution services. This is because price affects the future siting of generators and loads, and network operating costs as well as strongly influencing further development of the network. Under such a scenario, there is ever-growing pressure for all components of costs to be clearly identified and assigned equitably to all parties taking care to avoid or minimise any temporal or spatial.cross-subsidies. In parallel with the structural changes described, another equally important development is the growing penetration of embedded generation (EG) into power distribution systems. This development has been spawned by advances in generation technologies whch have rendered economic the production of small eficient generators, using both conventional and renewable energy sources. In particular, the environmental merits of renewable generation located close to customers present an extremely attractive proposition in the continuing battle against global warming. The presence of EG in distribution systems alters radically the way these networks should be viewed from both technical and commercial vantagepoints. T h ~ sis because EG effectively changes distribution networks from passive networks, with unidirectional power flows from higher to lower voltage levels, into active ones with multidirectional power flows. This change challenges the validity of traditional distribution network planning, operation and commercial practices in which dlstribution networks are treated as essentially passive systems. For the value of EG to be appropriately recognised and hence its optimal development encouraged, it is essential to factor the active nature of distribution netI

> works with EG into all technical as well as commercial operation and planning activities. This paper is primarily concerned with the treatment of variable losses under the envisaged electricity market and trading arrangements talung particular cognisance of the impact of EG. The paper begins by identifying the requirements for an ideal scheme for allocating losses. The present practice in England and Wales of evaluating the impact of EG on losses by the substitution method is then demonstrated and shown to be unsuitable for real-time energy trading, especially in the presence of EG. A more appropriate loss-allocation method based on the concept of marginal losses is then presented. A similar concept was applied to quantify, in a stochastic framework, the additional value of wind energy with respect to losses [I]. Allocation of losses by the marginal loss method proposed entails loss reconciliation on similar lines to revenue reconciliation under short-run marginal cost pricing [2]. Multiplicative reconciliation by a constant multiplier, rather than additive reconciliation, is applied. To justify and validate the choice of loss reconciliation by the constant multiplier method, another method for allocating losses based on an entirely different approach is presented. The new method relates losses directly to injections and it is therefore named the direct loss coefficient method. Case studies carried out on a 265-node realistic generic distribution system (GDS) model indicate strong agreement between the two methods. Both methods provide loss allocation factors that are location specific and vary in time. Furthermore, the loss allocation factors can be positive or negative depending on the users specific impact on losses (i.e. whether total losses are increased or reduced). This feature is essential in dealing with the impact of counter-flows such as those due to the presence of EG. The paper also presents an illustration of the characteristics and sigmfkance of applying marginal loss coefficients on the GDS with EG. The paper concludes with a brief discussion of some issues pertinent to the practical implementation of the proposed loss allocation factors.

2

Requirements for ideal loss allocation

In determining the requirements for the ideal scheme for

allocating losses it is useful to remember that the cost of losses constitutes a large component of network operating costs. Therefore the same requirements for equity and economic efficiency as prescribed for an optimal pricing strategy for transmission and distribution services [4] in a competitive electricity market are also applicable in loss allocation strategies. With this in mind, the requirements for the ideal scheme for allocating losses can be summarised as follows: Economic efJciency: Losses must be allocated so as to reflect the true cost that each user imposes on the network with respect to cost of losses. Accuracy, consistency and equity: The loss allocation method must be accurate and equitable i.e. must avoid or minimise cross subsidies between users and between different times of use. Furthermore, the method must be consistent. Must utilise metered data: From a practical standpoint, it is desirable to base allocation of losses on actual metered data. Must be simple and easy to implement: For any proposed loss allocation method to find favour it is important that the method is easy to understand and implement. 8

3

Current UK practice

Loss adjustment factors (LAFs) are currently used to gross up demanageneration to the grid supply point (GSI') to account for losses [3]. For small users, average LAFs are calculated in accordance with the voltage level. For larger users, the substitution method is used to calculate LAFs. Under this method the LAF for a user is calculateld by assessing the users impact on the total power losses. This is achieved by comparing the total losses when the uzer is connected and disconnected. There are a number of problems associated with this practice, among whch the following three are major sources of concern: the method can produce inconsistent results; LAFs calculated in this way do not prevent temporal and spatial cross-subsidies; and for large networks, application of this method is very cumbersome and impractical. The first two are illustrated on a simple distribution network shown in Fig. 1. The network is composed of a radial feeder to which three users are connected. At nodes A and B there is load of 200kW while at node C there is an EG whose output is 400kW. Node T represents the transmission network. Note that the lkeder section TA is twice the length of AB and BC. For siniplicity of illustration the calculation of losses is simplified by malung the following assumptions: All voltage magnitudes are equal to 1.0 pu. Voltage drops are negligible. Losses have no impact on the calculation of power flows. It is further assumed that line reactance is much greater than resistance. With this assumption, the formula foir line losses reduces to a simple product of line resistance and the square of the power flow through the line [2]. In the following illustrations, a base value of IOOkW is used and the resistance r is chosen to be 0.001pu. A very low value of r is chosen deliberately to maintain validity of the assumptions made in this approximate calculation. D2=200kW T A

f

i

C

D, =2OOkW

G =400k\lV

Fig. 1 Excmyle network to illustrate inconsistency of substitution meth,d Loss = 2*r + 4% = 0.001[4 + 161 = 0 . 0 2 ~= ~2kW

Approximate power flows and associated series losses for various cases are given in Table 1. The case where all the users are connected will be used as the base case. Total losses for this case amount to 2.0kW. Cases 1 to 3 represent the results of applying the substitution method by disconnecting each of the users in turn. Notice that in all three cases losses increase from 2.0 to 3.6, 4.0 and 2.8kW in cases I, 2 and 3, respectively (see Table 1). Clearly, disconnecting any of the users leads to an increase in total losses. In other words, it appears that each of the users in this example contributes to a reduction in the total system losses. According to the substitution method, which follows8t h s logic, they would all be entitled to a reward for reducing total losses. However, they are the only users resporsible for creating losses. This clearly demonstrates the incoiisistency of the substitution method. IEE Proc.-Gener. Transm. Distrih., Vol. 147, No. I , January 2000

Table 1: Power flows and associated series losses obtained by substitution method Approximate power flow (kW)

Total loss

TtoA

Case CtoB

TtoF

(kw)

0

200

400

0

2.0

400

-200

0

0

3.6

Case 2: user at node B disconnected

-200

400

400

0

4.0

Case 3: user at node A disconnected

-200

200

400

0

2.8

Base case: all users connected Case 1: EG at node C disconnected

In a reconciliation process the cost of total system losses would have to be recovered. As all the users in this example are deemed to be reducing losses, the cost of losses created by these users would have to borne by other users giving rise to cross-subsidies. The example demonstrates that the substitution method fails to meet the specified requirements for the ideal lossallocation scheme. 4

BtoA

Applying the standard chain rule, the following general system of linear equations can be established for calculating MLCs

General approachesto loss allocation

Two entirely different approaches for computing loss allocation factors, which avoid the problems of the substitution method, are presented. The fmt method is based on the concept of marginal losses whereas the second method relates losses directly to injections. The assumptions made in the examples in Section 3 do not apply in the following discussion.

4.I Marginal loss coefficients By d e f ~ t i o n marginal , loss coeficients (MLCs) measure the change in total active power losses L due to a marginal change in consumptiodgeneration of active power Pi and reactive power Qiat each node i in the network Eqn. 4 can be written in a more compact form as follows: where f i p j and f i p j represent the active and reactive power related MLCs. If a user, i.e. generator, takes part in voltage control by injecting required reactive power (PV node); there are no loss-related charges for the reactive power to be allocated. This is reflected by

Since in load flow calculations, losses are deemed to be supplied from the slack node, the loss-related charges for t h s node are zero. In other words, total power losses are insensitive to changes in active and reactive injections at the slack node i.e.

dL dL -- aps

aQs

=0

s is the slack node

(3)

Because of this assumption the choice of slack node clearly has an impact on both magnitude and polarity of MLCs. Fortunately, in distribution systems this complication need not arise as the transmission network can always be taken as the slack node. MLCs are a function of a particular system operating point. As there is no explicit relationship between losses and power injections the standard chain rule is applied in the calculation of MLCs using intermediate state variables, voltage magnitudes and angles. Therefore only a load flow solution for a particular system operating point (system state at a certain half-hour or hour) is required to compute MLCs. IEE Proc.-Gener. Transm. Dislrib.. Vol. 147, No. I, January 2000

A-b=b (5) Matrix A is the transpose of the jacobian in the NewtonRaphson load flow and can be calculated on the basis of load flow results for a particular system operating point. The vector fi represents MLCs whereas the right-hand vector b represents sensitivities of total losses with respect to voltage angle and magnitude. Total system active loss L is given by . N 1

L=7

N

G,,

[y2+ y2- 2V,4 COS(O,

-

O,)]

Therefore the entries of vector b in eqn. 5 are

E =2 80,

N

Gz3V,ysin(O, - 0,)

i = 1,.. . , N (7)

3

(8) Note that there are no equations for any voltage-controlled node as by definition the MLC with respect to reactive power for any such node is zero.

4.1.I Reconciliation: The result of applying MLCs calculated in accordance with the procedure outlined yields approximately twice the amount of losses. That is 9

N-1

(9) i=l

where [HI is the hessian matrix, A 8 and AV represent the change in operating point. Applying the following initial conditions to eqn. 15

Therefore to obtain the vector of reconciled MLCs p, a constant-multiplier reconciliation factor K~ is applied. The factor K~ is calculated as follows: KO

=

L N-1

K O

= 1.0

e;=o

i = l , ..., N - 1

(16)

obtains

(10)

f

(eo,v O )

= Lo = o

(LO

represents system losses

under flat start conditions) The vector of reconciled MLCs p is then calculated as follows: p=Ko.6 (11) Reconciled MLCs enable the allocation of the total system active power losses to individual users such that N-1

N-1

2=1

2=7

1

Where reactive power is not metered separately derived values of Q can be used based on a specified constant power factor. In such a case eqn. 12 would take the form N--l

(PPz

+ apQz)Pz= L

(17) From eqn. 16 it follows that there are no flows through the circuits which corresponds to zero initial nodal active power P and reactive power Q injections. The first derivative elements dLla8, and d L / d q are also zero at the flat start, while the hessian matrix is symmetrical and contains only the real parts of the bus admittance matrix. Therefore the total network losses can be represented as follows:

(13)

2=1

where a is a constant of proportionality between P and Q. The value of a is determined from the specified power factor.

4.2 Direct loss coefficients As the name suggests, the direct loss coefficient (DLC) method relates losses directly to nodal injections and therefore does not require reconciliation. In contrast to the MLC method which allocates marginal losses, the DLC method allocates total losses. The objective of this method is to derive a relationship such that losses can be expressed directly in terms of injections. A method for allocating losses to trades is described in [5]. Due to the complexity of AC load flow equations and their solution by iterative procedures, a closed form solution for losses is not feasible. Moreover, the formula used to compute losses contains system state variables whose values are only known after the load flow solution has converged. As already indcated, the total power losses in an AC transmission network are given by

L" T[AO AV][H][AB AVIT

(18)

It is important to point out that A8 and AV in eqn. 18 represent the final deviations from the flat start values of voltage angle and magnitude, respectively. To express losses directly in terms of nodal injections, eqn. 18 must be expressed in terms of nodal injections. T h s is accomplished by using an analogy with the well-established NewtonRaphson load flow algorithm

[A0 AVIT =

[AP

(19)

where J is an average jacobian computed from the flat start and final jacobians 9 and J,respectively i.e. 1 J = -(JO J ) (20) 2 Note that AP and AQ in eqn. 19 represent the actual nodal active and reactive power injections, respectively, as the initial P and Q values were assumed to be zero. Finally, the vector of changes in voltage angles and magnitudes on the extreme right of eqn. 18 can be replaced by the right-hand side of eqn. 19 to obtain eqn. 21.

+

L

z 1 [ne

AV] [HI [ J ]-l [P

Q1'

The first three right-hand terms constitute DLCs. Thus, the vector of DLCs is given by eqn. 22

L = f ( 0 ,V) .

N N

(14) For a given change in operating point the new total system losses can be evaluated using Taylor series expansion around the initial operating point. The operating point is defined in terms of state variables V and 8 with P and Q representing the corresponding nodal power injections. The new loss position is therefore given by

L

II

f

(e0

+ ae,VO + AV)

The assumptions and approximations made in the coinputation of direct loss coefficients give rise to small dfferences between the losses calculated from the application of l3LCs and those calculated from load flow. However, in contrast to MLCs, there is no fundamental requirement for reconciliation in the case of DLCs. This is because the 13LC method is based on allocation of total losses. Furthermore, losses are, approximately, a quadratic function of power and eqn. 14 used as the basis for derivation of DLCs !;tops at the quadratic term. 5

Application of MLCs and DLCs on &bus network

The algorithms described for calculating MLCs and DLCs were implemented and tested on the 4-bus network in Fig. 1 in Section 3. The results are shown in Table 2 depicting reconciled MLCs and DLCs for dfikrent 10

IEE Proc -Gener Transm DiJtrrb , Vol 147, No I . Januar.9 2000

Table 2: ReconciledMLCs and DLCsfor example network: spatial variation MLCs and DLCs (kW)

Total losses Node A (kW) MLCs

DLCs

MLCs

DLCs

MLCs

DLCs

Case 1

400

1.97

-0.0001

-0.0001

+0.0018

+0.0019

+0.0058

+0.0059

Case2

200

1.21

-0.0041

-0.0040

-0.0041

-0.0041

-0.0021

-0.0020

Case

EG Output

scenarios. The polarity of MLCs and DLCs should be interpreted in accordance with the following convention: Negative MLCs and DLCs for load Load is charged for increasing the total system active power loss Positive MLCs and DLCs for load Load is compensated for decreasing the total active loss in the system Negative MLCs or DLCs for EG: EG is compensated for decreasing the total active loss in the system Positive MLCs or DLCs for EG: EG is charged for increasing the total system active power loss If both load and generation are present at a particular node, MLCs (or DLCs) at this node must be applied to both provided the sign convention described is adhered to. With reference to Table 2, case 1 corresponds to the base case in Section 3, Table 1. The effect on MLCs of reducing EG output is shown in case 2. From case 1, we note that the EG at node C and load at node A pay for losses whereas the load at node B is compensated for losses. A popular misconception with regard to EG is that because the total system losses before introducing EG are hgher (compare base case and case 1 in Section 3, Table l), EG must be rewarded for reducing losses. In this regard it is important to stress that whether or not an EG should be rewarded for-loss reduction depends on both the amount and distribution of load as well as the level of EG output. By appropriate adjustment of the output of the EG, there is a point at which EG is compensated for losses as MLCs change polarity from positive to negative. This is shown in case 2 where the output of the EG has been halved. I

4 ,

Node C (with EG)

Node B

increases linearly from a negative value when EG is equal to zero and passes through zero when EG output is equal to approximately 250kW. Beyond 250kW, the MLC at node C becomes positive signalling that EG is no longer contributing to system loss reduction and is therefore required to pay for losses.

I

0.8

0.6 0.4 0.2

0

-0.2 -0.4 -0.6 -0.8

-1 -1.2I

I EG output, kW

Fig.3

-e-

Variationof reconciled marginul loss coe@cients with EG output

-W-

ndeA nodeB

-A-

nodeC

The impact of EG output on the contribution to total losses by the loads at nodes A and B is also shown in Fig. 3. The contribution of the load at node B to total losses diminishes relative to that at node A as the output of EG increases, from zero to 500kW. T h ~ strend is to be expected since node B is closer to the EG and therefore the load at this node should derive greater benefit from an increase in EG output than that at node A whch is further away. As a matter of interest, the MLC profiles at node A and B cross over when EG output equals approximately 200kW. Once EG output exceeds 400kW, MLCs at both nodes A and B become positive, indicating that loads at these nodes are paid for reducing losses. The reason for this is simple. EG output beyond 400kW must be exported to the grid causing a significant amount of losses along the route. Therefore loads at nodes A and B, located along the way, serve to reduce the amount of power flowing to the grid and hence losses. This is why the MLCs at nodes A and B are positive, correctly signifying that the loads at these nodes are paid for reducing losses. The simple example illustrates many of the attributes of MLCs and DLCs, in particular their ability to properly take account of and reward/penalise EG for its impact on losses. It is evident from Table 2 that reconciled MLCs and DLCs are practically identical. In the following Section, the application of MLCs and DLCs is demonstrated on a large real network-based distribution network model.

I

0.5 00

100

200

300

400

500

EG output, kW

Fig.2

Vuriztionof totalsystem loss with EG output

Figs. 2 and 3 summarise graphically the impact of EG on losses and their allocation to all network users. Fig. 2 presents the variation of total losses with EG output whereas Fig. 3 depicts the variation of MLCs with EG output. It is evident from Fig. 2 that minimum losses in this network occur when the EG output equals approximately 250kW. Beyond this level of output, EG ceases to have a beneficial effect on losses. This is reflected in the variation of the MLC at node C, to which the EG is connected (see Fig. 3). Notice that the MLC at this node IEE ProcGener. Transm. Distrib., Vol. 147, No. I , January 2000

6

Application on a large network

Case studies to illustrate the application of MLCs and DLCs on a large network were performed on a generic distribution system model. The GDS model includes all the 11

Table 3: Characteristicsof generic distribution network Nodes

281

Branches

322

Grid supply points

4

Conventional embedded generators

2 (2 x 10 MVA at 33 kV, 1 x 3 MVA at 11 kV)

Wind farms

3(20 x 500 kW at 33 kV, 3 x 225 kW at 11 kV a n d 3 x 2 2 5 k W a t 1 1 kV)

Cable and overhead networks

ll,33and132kV

important characteristics of a real multiple-voltage largescale mixed urban and rural distribution system. It consists of the generic distribution network including EG and databases for network description (branches and nodes) annual hourly load (active and reactive power) at each node EG characteristics for modelling EG output. The GDN includes cable and overhead networks at 11, 33 and 132kV voltage levels, with embedded conventional and renewable wind generators connected to it; (see Fig. 8 in the Appendix, Section 11). General characteristics of the GDN are summarised in Table 3. The envisaged application of MLCs requires analyses for particular system operating points as well as year-round analyses. MLCs for particular system operating points are required for half-hourly or hourly settlements. MLCs on a year-round basis can provide signals to existing and potential system users (customers, generators and suppliers) on the costshenefits they can expect based on their impact on losses. In the ideal case, each hour of the year would have associated with it its own unique set of loss allocation factors for each node. Given the expansive nature of distribution systems the amount of data that would be generated is very large. To simplify the analyses and reduce the amount of data handling the year can be split, for example, into three seasons and three characteristicdays, as shown for a generic year in Table 4. A year is now represented by nine characteristic days. Loss allocation coefficients can therefore be computed and published for these days only instead of 365 days. Table 4: Generic year Day WPe

Number of days

Winter

Working day Saturdays Sun days

81 19 20

Working day Saturdays Sundays

54 10 13

Spring/Autumn

77

Working day Saturdays Sundays

116 24 28

Subtotal

168

Total

365

To provide realistic spatial and temporal load variations, several customer types are included in the GDS. Loading of the GDS is based on load models of individual customers. Load demand is modelled for 11/0.415kV substations based on an assumed mix of individual customers supplied from these substations. Power output of conventional EG 12

Temporal variations of MLCs

-0015

' time of day, h

Fig.4 Node 9o-active power reconciled M L C and DLC profilesfor typical winter working day DLC

--C --I-

MLC

-

120

Subtota I Summer

6. I

Average MLC and DLC profiles for si&icant day!; in a week and different seasons are shown for three nodes in the GDS (Figs. 4-7). The impact of EG on losses is analysed for two extreme typical days (in terms of the load level) namely winter working day and summer Sunday. Consumers located at nodes with negative MLCls are charged for losses. Conversely, those consumers at nodes with positive MLCs are rewarded. The opposite applies for EG. It is important to note that LAFs in current use do not recognise the contribution of load to system loss reduction.

0.0141

Season

Subtotal

(e.g. diesel engine driven) is modelled deterministically. Wind farms are characterised by variable power output due to the stochastic nature of wind speed.

0.0°2

t

Fig.5 Node W-active power reconciled M L C und DLC projYesfor typical " e r S&y

Fig. 4 shows MLC and DLC profiles for a winter ,working day at node 90, to which a conventional EG is; connected. It is clear that between the hours of 7:OO and 19:OO (12 hours in total), the EG at this node is rewarded for its contribution to system loss reduction (signified by negative MLCs and DLCs during this period). However, during early hours of the day and late at night, when load is low, the EG contributes to increasing losses and therefore it is IEE Proc.-Gencr. Trunsm. Distrih.. Vol. 147, No. 1. Junuurv 2000

duly charged. This situation is radically amplified during summer Sundays when practically all day the EG contributes to increasing system losses (Fig. 5). This EG (being a conventional generator) is neither charged nor paid for reactive power as it is assumed that it participates in voltage regulation. Fig. 6 shows active power DLC and MLC profiles for the EG (wind farm) at node 178. These MLCs and DLCs indicate that the siting of the renewable EG at node 178 is more favourable than the conventional EG at node 90. ms is because during winter working days the EG at node 178 derives greater benefit than the EG at node 90 as MLCs and DLCs at node 178 are negative through out the entire day. It is important to stress that wind generators are rewarded for reducing losses due to active power output but they get charged for reactive power intake. Fig. 7 shows the reactive power related MLC and DLC profiles for the wind generator at node 178. As expected, the MLCs and DLCs remain negative during the whole day signifying that the EG is charged for reactive consumption. These examples demonstrate that MLCs and DLCs vary in time consistent with the temporal nature of load and EG output.

'

I

-0.04

3

6

9

12

15

18

21

24

-0.005

ers would be rewarded for their contribution to system loss reduction. At 17:00, the opposite situation is presented. The load is relatively large and the EG at node 90 contributes to reducing the total system loss while surrounding customers contribute to increasing the total system loss. This is reflected in the change of polarity of DLCs. and MLCs. In t h s case, EG would receive payment and demand would pay for losses. 7

Implementation

Implementation of the proposed loss allocation Coefficients can take several forms. In the simplest case, published loss allocation coefficients for each node (zone) and characteristic day would be used to compute the cost of losses for each customer based on either metered data or profiled consumption data. Any discrepancy between actual losses and losses computed from loss allocation coefficients would be settled through revenue reconciliation. Charges would nevertheless be based on published MLCs. In this implementation, MLC computations are based on load and generation output forecasts and therefore are subject to the same uncertainties as these forecasts. Furthermore, the averaging process used to generate characteristic days also constitutes another source of errors leading to some small spatial and temporal cross-subsidies. Another more accurate approach would require the MLCs to be recalculated at each half-hour (or hour as the case may be) and to use these MLCs for charging purposes. The MLCs published in advance would therefore only serve as planning guides. In this case, charges would be applied on an ex-post basis although short-term predictions are possible. Charges based on such an ex-post regime have the advantage that they do not require reconciliation. In contrast, the charging regime described in the first approach requires revenue reconciliation as it is essentially an ex-ante regime because the MLCs are known in advance. Since the computation of MLCs is a relatively trivial task, it can be argued that the second approach should be favoured, as it reflects more accurately the impact on losses of each user in real time. A further application of MLCs based on year-around analyses would be in the negotiation of bilateral forward contracts for losses. These contracts would cover the bulk of expected losses over a given time horizon and would be priced at negotiated tariffs. Only the residual losses arising from forecasting and other errors would be exposed to the spot price determined by the balancing market. This is an attractive option given that losses priced at the spot price determined by the balancing market are likely to be very expensive, as this price is likely to be very high and extremely volatile. The idea of contracting for losses in advance is touched on in [6].

time of day, h

Fi 7 Node 178-reactive power reconciled MLC rmd DLC profiles for typicai%hter working &y

6.2 Spatial distribution of MLCs To illustrate spatial distribution of DLCs and MLCs, two time-periods (i.e. operating points) were chosen, the 2nd and 17th hour in a winter working day. Each node has different loss allocation coefficients, whch can be positive or negative. At 2:OO the load is relatively low and, therefore the EG at node 90 for example, increases total system losses hence MLCs and DLCs are positive. At this operating point the EG supplies even relatively distant load, such as at nodes 78 and 120. The surrounding customers contribute to decreasing the total system losses and therefore they have positive MLCs for active power. These customIEE Proc -Gener TranJm. Dislrrb , Vol 147, No I , January 2000

8

Conclusions

It has been demonstrated that the substitution method of allocating distribution system active power losses in systems with embedded generation is inconsistent and lacks a sound economic foundation. In particular, this method gives rise to both spatial and temporal cross-subsidies. Since the method relies on assessing the impact of the latest user on losses, it has the potential to either penalise or reward EG in a more or less arbitrary manner. Furthermore, the method is cumbersome and impractical for application in an electricity market in which energy trades are settled in real time on half-hourly or hourly time intervals. Two loss allocation schemes namely marginal loss coefficient method and direct loss coefficient method that 13

overcome the deficiencies of the substitution method have been proposed. It has been demonstrated that there is strong agreement between reconciled MLCs and DLCs. Both are location specfic and vary in time. Furthermore, they can be positive or negative depending on the users particular impact on losses at any given time (i.e. whether they increase or reduce total losses). This feature is critical and its importance cannot be overstated when dealing with the impact on losses of counter-flows, such as those due to the presence of EG. Application of MLCs and DLCs has been illustrated on the generic distribution system. The results obtained clearly demonstrate that MLCs and DLCs change with time of day and from one location to another. Losses are composed of futed and variable components. This paper focused on the allocation of the variable loss component because it is in the management of variable losses that the value of EG has most significance. In a realtime energy market however, it is also important to have a mechanism for allocating futed losses in an equitable manner in real time. We are not aware of any work that deals with t h s issue adequately in the context of energy markets based on real-time settlements. Some effort must therefore be made to develop loss allocation schemes for fmed losses as fmed and variable energy losses on an annual basis can have slmilar orders of magnitude particularly in distribution networks with a large population of transformers.

9

Acknowledgments

The authors gratefully acknowledge the support 01‘ the EPSRC under grant GM83748 and the European Commission under Joule I11 Project JOR3-CT98-0201. 10

References STRBAC, G., JAYANTILAL, A., ALLAN, R.N., and JENKINS, N.: ‘Allocation of losses in electrical distribution systems with wind generation’. Proceedings of the 1996 European Union confererice on Wind energy, Goteborg, Sweden, May 1996 SCHWEPPE, F., CARAMANIS, M.C., TABORS, R.D., B13HN, R.E.: ‘Spot pricing of electricity’ (Kluwer Academic, 1989) ‘Guidance note for calculation of loss factors for embedded generators in settlement’. SSC(0P) 1 390 (revised), The Electricity Pool 01’ England and Wales, London, March 1992 FARMER, E.D., CORY, B.J., and PERERA, B.L.P.P.: ‘Optimal pricing of transmission and distribution services in electricity supply’, IEE Proc. Gener. Transm. Distrib., 1995, 142, (1) WU, F.F., and VARANA, P.: ‘Co-ordinated multilateral trades for electric power networks: Theory and implementation’. Power report PWP-031, University of Califomia Energy Institute, June, 1995 GROSS, G., and TAO, S.: ‘A loss allocation mechanism for :power system transactions’. Presented at the conference on Bulk power fystem dynamics and control IV - Restructuring, Santorini, Greece, Pagust 1998

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11. I

Appendix

Generic distribution network

Fig.8 ~

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IEE Proc.-Gener. Trunsm. Distrib., Vol. 147, No. I , Junuury 2000