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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 15, NO. 4, NOVEMBER 2000
Review of Usage-Based Transmission Cost Allocation
Methods under Open Access
Jiuping Pan, Yonael Teklu, Saifur Rahman, Fellow, IEEE, and Koda Jun
Abstract—This paper presents an overview of usage-based
methods of transmission cost allocation under open access. Allocation of transmission costs involves both technical and regulatory
issues, and as a result, the methods available in the literature
differ in their definition and measure of the “extent of use” of
transmission resources. The primary objective of this paper is to
provide a summary of recent techniques used for designing fair
and equitable access fees for the recovery of fixed transmission
costs. The discussion is thus organized under two major subtopics:
algorithms for transmission usage evaluation and alternative
pricing strategies. Numerical examples are provided to show the
results using different methods.
Index Terms—Cost allocation methods, open access, pricing
strategies, usage of transmission resources.
I. INTRODUCTION
C
OST allocation is a major issue in transmission open
access faced by the electric power industry. According
to the U.S. Federal Energy Regulatory Commission (FERC),
transmission will continue being regarded as a natural monopoly, whereby transmission providers will be required to
offer the basic transmission service in conjunction with a
number of mandatory and/or voluntary ancillary services [1],
[19]. Basic transmission service refers to the “path provision”
function of the transmission grid while ancillary services, such
as operating reserves, regulation, load following and voltage
control, are the functions necessary for maintaining the reliability of the bulk-system as well as undertaking commercial
transactions across the grid [7].
The cost of the basic transmission services corresponds primarily to the fixed transmission cost that is also referred to as
the transmission capacity cost, or the existing system cost, or
the embedded transmission facility cost. Electric utilities traditionally allocate the fixed transmission cost among the users
of firm transmission service based on Postage-Stamp Rate and
Contract Path methods [20]. In the postage-stamp rate method,
transmission users are not differentiated by the “extent of use”
of transmission facilities but charged based on an average embedded cost and the magnitude of transacted power. Contract
path method, on the other hand, assumes that the transacted
power would be confined to flow along an artificially specified
path through the involved transmission systems. Accordingly,
the transaction will be charged a postage-stamp rate that may be
calculated either separately for each of the transmission systems
or as a grid average. In reality, however, the actual path taken by
a transaction may be quite different from the specified contract
path thus involving the use of transmission facilities outside the
contracted systems.
MW-Mile methodology may be regarded as the first pricing
strategy proposed for the recovery of fixed transmission costs
based on the actual use of transmission network [5], [6]. In this
method charges for each wheeling transaction are based on the
measure of transmission capacity use. This is determined as a
function of the magnitude, the path and the distance traveled by
the transacted power. Since the charge for basic transmission
service is usually the largest component of the overall charge of
transmission services, a considerable amount of research effort
has focused on the development of usage-based cost allocation
schemes, and various implementations of MW-Mile methodology have been proposed in the literature [10], [18], [22].
Allocation of ancillary services is a rather complicated
problem. Unlike the basic transmission service, the cost of
ancillary service often involves several cost components. For
instance, the cost of operating reserve may involve capacity
cost, energy cost and opportunity cost. Moreover, the costs
of some ancillary services may vary greatly as a function
of time, location, and level of system load. Although some
newly proposed cost allocation methods can determine the
contributions to real power losses and reactive power support
from individual users, very few publications are available
for the allocation of regulation, load following and operating
reserves. These ancillary services are usually distributed among
the transmission users in proportion to their scheduled/metered
generation or demand. Efforts are currently underway in the
industry to encourage the development of metrics and the
creation of competitive markets for ancillary services [7], [12].
The primary objective of this paper is to provide a summary
of recent techniques used for designing fair and equitable access fees for the recovery of fixed transmission costs. Real-time
congestion pricing strategies associated with transmission constraints in a competitive electricity market are not included. The
paper is organized under two major subtopics: algorithms for
transmission usage evaluation and alternative pricing strategies.
Numerical examples are provided to compare the results using
different methods.
II. MW-MILE METHODOLOGY
Manuscript received March 22, 1999; revised September 3, 1999.
J. Pan, Y. Teklu, and S. Rahman are with the Alexandria Research Institute,
Virginia Polytechnic Institute and State University, Alexandria, VA 22314 USA.
K. Jun is with the Mathematical Engineering Group of R&D Center, Tokyo
Electric Power Company, Yokohama, 230-8510, Japan.
Publisher Item Identifier S 0885-8950(00)10351-7.
In the original MW-Mile methodology, DC power flow formulation was used to estimate the usage of firm transmission
services by wheeling transactions, and the procedure for multitransaction assessment may be outlined as follows [5].
0885–8950/00$10.00 © 2000 IEEE
PAN et al.: REVIEW OF USAGE-BASED TRANSMISSION COST ALLOCATION METHODS UNDER OPEN ACCESS
Step 1) For a transaction , the transaction-related flows
, are first
on all network lines,
calculated using DC power flow model considering
the nodal power injections only involved in that
transaction.
Step 2) The magnitude of MW flow on every line is mul(in miles) and the cost per
tiplied by its length
MW per unit length of the line (in $/MW-Mile),
and summed over all the network lines as
(1)
The above process is repeated for each transaction
, including one comprised of the utility’s native
generations and loads. Finally, the responsibility of
transaction to the total transmission capacity cost
is determined by
(2)
MW-Mile methodology ensures the full recovery of
fixed transmission costs and reflects, to some extent,
the actual usage of transmission systems.
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within a distribution company. The concepts of distribution
factors can also be used for transmission congestion cost
allocation in competitive electricity markets as shown in [13].
B. AC Flow Sensitivity Indices
Similar to the application of DC flow distribution factors, the
sensitivity of transmission line flows to the bus power injections
can also be derived from AC power flow models. One such example can be found in [24] where the contributions of each generation bus to all transmission line MW flows were directly estimated via a set of coefficients named Line Utilization Factors
(LUFs) as shown below.
(3)
The numerical values of LUFs can be calculated using standard AC power flow Jacobian with some minor simplifications.
The concept of Reactive Power Adjustment Factor (RPAF)
was introduced in [23] as a measure of the impact of unit MVA
load change or a transaction on the total generation reactive
power output. The formulation of RPAF is shown below involving only the sensitivity indices of network reactive power
losses to the active and reactive injections together with appropriate scaling factors.
III. TRANSMISSION USAGE EVALUATION
Accurate knowledge of transmission usage is essentially important in the implementation of usage-based cost allocation
methods. On one hand, due to the nonlinear nature of power
flow equations, it is theoretically very difficult to decompose the
network flows into components associated with individual customers. On the other hand, from an engineering point of view,
it is possible and acceptable to apply approximate models or
sensitivity indices to estimate the contributions to the network
flows from individual users.
(4)
is the transmission network reactive losses,
where
and
are the unit active and reactive load at bus . Scaling
factors and are used to reconcile the difference between
the total system reactive power losses and the total incremental
reactive power losses while scaling factors and are used to
and
are consistent with
ensure that the load increments
specified power factor at the given bus.
A. Distribution Factors
Distribution factors based on DC power flows can be used as
an efficient tool for evaluating transmission capacity use under
various open access structures [11]. These distribution factors,
i.e., Generation Shift Distribution Factors (GSDFs) and Generalized Generation/Load Distribution Factors (GGDFs/GLDFs)
have been used extensively in the domain of power system security analysis to approximate the relationships between transmission line flows and the generation/load values. The application
of distribution factors for assigning transmission payments may
offer transmission providers three alternatives to allocate the
total fixed transmission costs among different users, i.e., based
on transaction-related net power injections, only to generators,
and only to loads.
In [5], GSDFs were used in conjunction with linear programming to identify the maximum transaction-related flows
for cases in which transactions were specified by bounded
generation and load injections. In [11], GGDFs were applied
directly to estimate the contribution by each generator to the
line flow on the transmission grid while GLDFs were used to
allocate the sub-transmission network charges over the loads
C. Full AC Power Flow Solutions
More precise cost information is often needed in the assessment of wheeling transactions requiring full AC power
flow solutions or OPF studies. In a single-transaction case, the
“differencing approach” can be used which only involves two
AC power flow or OPF studies, one without the transaction
(base case) and one with the transaction (operating case)
[6]. However, the problem becomes a greater challenge in
a multi-transaction case because of the nonlinear nature of
power flow models and also the interactions among different
transactions. Recently, a power flow based multi-transaction
assessment methodology was introduced in [21], which involves the following three main study steps.
Step 1) Perform two power flow simulations, one for the
base case (no transactions) and one for the operating
case (including all the transactions) to determine the
combined impacts caused by the transactions on the
system. These impacts may include MW/MVAR line
flows, reactive power output of generators and real
power losses replacement from the slack bus.
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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 15, NO. 4, NOVEMBER 2000
Step 2) For each transaction
, investigate two
power flow cases: in one case only transaction is
included and in the other case all transactions except
for are included. Comparing the results of these two
simulations with the base case gives marginal and
incremental impacts of each individual transaction
on the system.
Step 3) The problems of “fair resource allocation” are then
solved to distribute the MW/MVAR line flows, reactive power output of generators, and real power
losses to each transaction. The formulation below
shows an example on how the reactive power sup, can be distributed to
port from generator , i.e.,
each transaction by minimizing the sum of squared
difference between the actual allocation and the marginal and incremental values.
(5)
,
,
are the actual allowhere
cated, marginal and incremental reactive power support for transaction respectively. This method is
suitable for an open market model consisting of one
or more pools, and the study objective is to determine the impact of a transaction on the base operating condition.
D. Power Flow Decomposition
Power Flow Decomposition (PFD) algorithm is a network
solution for allocating transmission services among individual
economical transactions on the system [1]. It can determine, for
each transaction, the following: i) the usage of transmission network (both real and reactive flow components), ii) the net power
imbalance and iii) the contributions from participating generators to real-power-loss compensation. The algorithm is initially
designed for the application in a bilateral contract based market
model but can also be used for wheeling transaction assessment
[1], [20].
The PFD algorithm is based on superposition of all transactions on the system and decomposes the network flows into
components associated with individual transactions plus one
interaction component to account for the nonlinear nature of
power flow models. Assuming there are totally transactions
on the system, the AC power flow solutions can then be decomposed into:
(6)
(7)
where
is the vector of total complex power injected into the
system,
is the vector of complex power injected into the system
in response to the transaction , and
is the vector of complex power caused by the interaction among transactions.
Similar definitions hold for the complex valued flow matrices
,
and
. It has been shown that the calculation of the major contribution of each transaction to the network
flows is independent of the interaction effects among different
transactions. Theoretically, only a small percentage, in the order
of 5% of a given transaction, is in the interaction component
under normal operating conditions. Thus, interaction components can be assigned to individual transactions in proportion
to the scales of transacted power.
This study suggests a revised PFD formulation with distributed slack bus that involves an iteration process to allocate
the net current imbalance caused by each transaction among
distributed slack buses and then applies the formulation with
single slack bus to determine the network flows. Test results
have shown that the revised PFD procedure can satisfy both
the equality criterion and the economic dispatch rule while
preserving the same basic assumptions.
E. Tracing Algorithms
Two tracing algorithms, i.e., the Bialek and the Kirschen, are
available. Both are designed for the recovery of fixed transmission cost in a pool based market. The basic assumption used
by tracing algorithms is the proportional sharing principle. In
Bialek tracing algorithm, it is assumed that the nodal inflows
are shared proportionally among the nodal outflows. Kirschen
tracing algorithm assumes that, for a given common (a set of
contiguous buses supplied by the same set of generators), the
proportion of the inflow traced to a particular generator is equal
to the proportion of the outflow traced to the same generator.
1) Bialek Tracing Algorithm: Bialek tracing algorithm
has two versions: upstream-looking algorithm and downstream-looking algorithm [14]–[16]. The upstream-looking
algorithm will allocate the transmission usage/supplement
charge to individual generators and apportion the losses to
the loads, and conversely, the downstream-looking algorithm
will allocate the transmission usage/supplement charge to
individual loads and apportion the losses to the generators.
The algorithm is constructed on a matrix formulation and
therefore enables the use of linear algebra tools to investigate
numerical properties of the algorithm. Extensive studies have
shown its capability and efficiency in allocating transmission
usage/supplement charge among different generators or loads
under normal operating conditions. The algorithm can also provide solutions to the questions as how much of the power output
from a particular generator/station goes to a particular load or
how much of the demand of a particular load comes from a
particular generator/station. In addition, the topological distribution factors are always positive, thus eliminating many problems resulting from counter flows. Minor errors may be incurred
when the lines are heavily loaded due to the assumptions used
in the problem formulation.
2) Kirschen Tracing Algorithm: The Kirschen algorithm
also has two versions designed for identifying the contributions
from either the individual generators or loads to the line flows
[4], [9]. In general, this algorithm shares many useful functions
and attractive features with the Bialek tracing algorithm.
PAN et al.: REVIEW OF USAGE-BASED TRANSMISSION COST ALLOCATION METHODS UNDER OPEN ACCESS
This algorithm is based on a set of definitions: domains (set
of buses getting power from a particular generator), commons
(set of contiguous buses getting power from the same set of generators) and links (branches connecting commons). The state of
system can then be represented by a directed graph consisting
of commons and links, with the direction of flow between commons and the data about generations/loads in commons and
flows on the links. A recursive procedure is used to calculate
the contributions from the generators (or loads) to the commons,
to the links, and to the loads (or generators) and the line flows
within each common.
Kirschen tracing algorithm is able to work well under various system-loading conditions because no additional assumptions are used in the problem formulation. On the other hand, it
is a simplified approach since the contributions from the generators (or loads) to a particular common will be proportionally
assigned to the loads (or generators) and line flows within that
common.
IV. ALTERNATIVE PRICING STRATEGIES
This section considers alternative transmission pricing strategies under open access. In particular, we will discuss three key
issues in implementing usage-based cost allocation. These include unused transmission capacity, MVA-Mile methodology,
and pricing of counter flows.
A. Unused Transmission Capacity
Unused or unscheduled transmission capacity is defined as
the difference of facility capacity and the actual flow on that
facility. In the original MW-Mile methodology [5], the usage of
transmission facilities is measured by absolute flow values, and
the transmission facility costs are allocated in proportion to the
ratio of flow magnitude contributed by a particular transaction
and the sum of absolute flows caused by all transmission users.
The following equation may give a more general expression of
MW-Mile rule.
(8)
where
is the cost allocated to transaction ,
is the embedded cost of facility ;
is the magnitude of flow on facility caused by
transaction ;
and represent the sets of transmission facilities and
transactions on the system.
The above pricing rule ensures the full recovery of all the embedded costs and assumes, inherently, that all transmission users
have to pay both for the actual capacity use and for the unused
transmission capacity. There are a number of reasons calling for
alternative pricing rules on the allocation of unused transmission
capacity [1]. First, this pricing rule does not encourage more efficient use of transmission systems because no matter how the
line capacity utilized the total costs will be recovered. Second,
the cost allocation procedure can seem to be unfair to some users
when they have to share the cost of an expensive transmission
1221
facility for which only a small portion of the facility capacity has
been utilized. On the other hand, adequate transmission margin
is required to maintain system reliability [2], [8].
One possible solution is to revise the MW-Mile formulation
by charging the transmission users based on the percentage utilization of the facility capacity,
, instead of the sum of flows
contributed by all users [18]. That is, transmission users will be
charged only for the actual capacity use but not for the unscheduled capacity.
(9)
This revised formulation cannot get full recovery of the fixed
transmission costs since the total flows are usually smaller than
the facility capacities under normal system conditions. The total
ignorance of the reliability value of transmission margin under
system contingency conditions is its main drawback.
A combined pricing rule was proposed in [18] and also suggested in the discussion of [9], which divides the cost allocation
, proportional
into two components. The first component,
to the utilized facility capacity, would be allocated to transmission users based on the actual usage. The second component,
, which is a portion of the difference between the total embedded costs and the costs recovered by utilized transmission
capacity, would be distributed among all users for system security reserve, in proportion to the transacted power. This combined pricing rule can be expressed by (9), (10) and (11). The
parameter can be used to determine the level of cost recovery
for the unused transmission capacity.
(10)
(11)
More advanced solution requires the evaluation of reliability
value of transmission margin to different customers. Reference
[2] presented a conceptual procedure for embedded cost recovery based on the measures of capacity-use and reliability
benefit. The reliability benefit is calculated for each line with
respect to a particular transaction considering the probability
of disconnection between the sending buses and the receiving
buses involved in that transaction. Reference [8] proposed a
well-designed reliability based approach where the revenue of
each circuit is obtained by two parts: one part that considers
the system use under normal state and the second part that consider the system under contingency conditions. Comprehensive
reliability studies are involved in this method to determine the
expected value of power flow variations and then an importance
index is calculated for each line with respect to a particular
transaction. These indices show how each transaction use the
capacity margin of each line under contingency conditions.
B. MVA-Mile Methodology
It has been recognized that the use of transmission resources
is best measured by monitoring both real power and reactive
power given the line MVA loading limits and the allocation of
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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 15, NO. 4, NOVEMBER 2000
TABLE I
TRANSMISSION DATA AND BASE CASE FLOWS
Fig. 1. Five-bus test system.
reactive power support from generators and transmission facilities. Consequently, the basic concepts of MW-Mile methodology can be extended to include the charging for reactive power
flows resulting in the so-called MVA-Mile methodology [17].
Besides full AC power flow studies, the network usage due
to reactive power flows can be determined using sensitivity approaches, decomposition formulations and tracing methods. For
instance, the decomposition formulation proposed in [1] can decompose the network flows into components, both real and reactive, associated with individual transactions. Electricity tracing
algorithms can also be used to the reactive power flows. With the
Bialek tracing algorithm, a fictitious node is added in the middle
of each line to model the different natures of line reactive power
losses [14], [17]. The newly developed Kirschen tracing algorithm uses real and imaginary currents to trace complex power
flows between generators and loads [4].
TABLE II
TRANSACTION-RELATED FLOWS AND CHARGES (T1)
TABLE III
TRANSACTION-RELATED FLOWS AND CHARGES (T2)
C. Pricing of Counter Flows
Counter flow is the flow component contributed by a particular transaction that goes in the opposite direction of the net
flow. In the original MW-Mile formulation as well as some
usage-based allocation pricing rules, the impact of each transaction on the flows is measured by the magnitude so that all
transmission users are required to pay for the use of path-provision service, irrespective of the flow directions. However, in
view of the contributions of counter flows in relieving the congested transmission lines, any usage-based tariff that charges for
counter flows needs to be carefully reviewed. For this regard, the
zero counter-flow pricing method suggests that only those that
use the transmission facility in the same direction of the net flow
should be charged in proportion to their contributions to the total
positive flow [18]. On the other hand, proposals of giving a negative charge or credit to the users producing counter flows may
not be easily accepted by the transmission service providers.
V. NUMERICAL EXAMPLES
This section presents an illustrative example based on a
five-bus test system to show the results using different cost
allocation methods. The five-bus test system is depicted in
Fig. 1 and Table I gives the transmission data including the
base case flows and the transmission revenue requirements as
used in [1]. In the base case, the loads at buses 3, 4 and 5 are
(45 MW, 15 Mvar), (40 MW, 5 Mvar) and (60 MW, 10 Mvar),
respectively. The generation from bus 2 is fixed as 20 MW and
bus 1 is the system slack bus.
A. Evaluation of Wheeling Transactions
As with [1], the following two wheeling transactions are
assumed:
T1:
Injection of 5 MW at bus 1 and removal at bus 5
T2:
Injection of 5 MW at bus 4 and removal at bus 2
Tables II and III below show the transaction-related flows determined by generation shift distribution factors (GSDFs), line
utilization factors (LUFs) and power flow decomposition (PFD)
algorithm as suggested in [20]. The original MW-Mile cost allocation rule, i.e., (7), is used to distribute the revenue requirements to each transaction including one representing the base
case generations and loads. The wheeling charges calculated by
the PFD algorithm are further distinguished between the use of
MW-Mile and MVA-Mile rules.
From Tables II and III, it can be noticed that the transaction-related MW flows and the wheeling charges determined
by different methods are very close when the transmission capacity use is measured by MW flows. In particular, results from
GSDFs and PFD algorithms are almost identical since both algorithms assume the bus voltage is close to 1.0 p.u. This finding
PAN et al.: REVIEW OF USAGE-BASED TRANSMISSION COST ALLOCATION METHODS UNDER OPEN ACCESS
TABLE IV
TRANSMISSION USAGE AND CHARGES (G1)
1223
tribution of each generator to a broader area, named as common,
which may include a large number of internal lines and load
buses.
VI. CONCLUSION
TABLE V
TRANSMISSION USAGE AND CHARGES (G2)
is in general true for the evaluation of wheeling transactions because usually the amount of transacted power is relatively small
in comparison to the native flows on the system. On the other
hand, the costs allocated to both transactions would be reduced
when the transmission capacity use is measured by MVA flows.
In this simple example, the assumed wheeling transactions only
involve real power and thus their contributions to the network
reactive flows are insignificant with reference to the base case
flows.
B. Transmission Usage by Generators
Tables IV and V below show the generator-related flows for
the base case determined by generalized generation distribution factors (GGDFs), line utilization factors (LUFs), Bialek and
Kirschen tracing algorithms. The original MW-Mile cost allocation rule, i.e., equation (7), is used to distribute the revenue
requirements to each generator. Scaling factors are used in the
cases with sensitivity based methods (i.e., GGDFs and LUFs)
to ensure the total allocated cost is consistent with the required
transmission revenues.
From Tables IV and V, it can be noticed that the generatorrelated MW flows and transmission charges determined using
GGDFs and LUFs are very close, meaning there would be no
significant difference in using DC or AC sensitivity indices as
far as the MW flow is concerned. In general, the Bialek tracing
algorithm would give similar results as those from sensitivity
based methods and therefore they may be used equivalently for
the same purposes.
Both tracing algorithms result in zero charging for G2 and
full responsibility of G1 to the use of lines 1–2 and 1–3. However, very different results can be observed from the remaining
lines with different tracing algorithms. As we discussed earlier,
the Bialek method traces the contribution from each generator to
every single line while the Kirschen method identifies the con-
This paper attempts to present an updated review of recent
progress on the subject of usage-based transmission cost
allocation. Some basic conclusions and observations from this
study may be summarized as follows.
• It is necessary to develop an appropriate method that could
allocate the costs of transmission services based on the
actual usage by different users.
• The design of usage-based cost allocation methods involves two major issues: accurate and efficient algorithms
for transmission usage evaluation and fair and equitable
pricing rules.
• Cost allocation procedures should be technically easy for
implementation and transparent to transmission users.
• As far as the MW flow is concerned, the transaction-related (or generator-related) flows and transmission
charges for the recovery of fixed transmission costs
determined by different algorithms are quite similar.
• The choice of algorithms used for the evaluation of transmission use depends mainly on the study objectives and
the market structures.
• There is still no a general agreement on the measure of
the “extent of use” of transmission network capacity, especially the value of transmission capacity margin and the
charge for reactive power flows.
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Trans. on Power Systems, vol. 13, no. 4, pp. 1407–1412, Nov. 1998.
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 15, NO. 4, NOVEMBER 2000
Jiuping Pan received B.S. and M.S. degrees in power engineering from Shandong University of Technology (SUT), P. R. China. He joined the faculty of SUT
in 1982 and is currently completing his Ph.D. degree in electrical engineering at
Virginia Tech. His main research interests include generation and transmission
planning, power system modeling and analysis, decision-making methods and
power system reliability studies.
Yonael Teklu received B.S. and M.S. degrees in electrical engineering form
Addis Ababa University, Ethiopia, and Virginia Tech in 1981 and 1995 respectively. He is currently working toward a Ph.D. degree at Virginia Tech. His
research activities involve energy systems planning, renewable and distributed
generation systems.
Saifur Rahman (S’75–M’78–SM’87–F’98) is the Director of Alexandria Research Institute at Virginia Tech where he is a Professor of Electrical Engineering. He also directs the Center for Energy and the Global Environment at the
university. Dr. Rahman is currently serving on the Power Engineering Society
Governing Board as the Vice President for Education/Industry Relations. He
serves on several PES committees and subcommittees including the Education
Committee, Energy Development Subcommittee and Customer Products and
Services Subcommittee. He is also a Member-At-Large of the IEEE-USA Energy Policy Committee. He has published over 200 papers on conventional and
renewable energy systems, load forecasting, uncertainty evaluation and system
planning.
Koda Jun received B.S. and M.S. degrees in electrical engineering from
Yokohama National University, Japan, in 1988 and 1990 respectively. He
joined Tokyo Electric Power Company in 1990 and is currently a Research
Engineer at Mathematical Engineering Group of R&D Center with focus on
the methods of real time electricity pricing. From August 1997 to August 1998,
he was a Visiting Researcher at Virginia Tech.