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dispersed solar power systems.
through an end- user decision analysis in which the reliability of dispersed system reliability and the role of utility prices in
Special math needed for explanations: 
None The purpose of this analysis is to identify the major
Many electric utilities are considering or implementing The purpose of power system planning is the develop- solar energy 
programs as part of their system diversification of a rational program to provide , in an orderly and
depends on the impact these dispersed systems have on cross-subsidization, the only costs of reliability that the
Key Words-Dispersed solar system, Cost/benefit analysis, Solar today's climate of increasing electric energy costs, the issue
(FERC) has promulgated rules that prohibit utilities from Typically, end users only consider the reliability of the
policies, in addition to fossil fuel prices which are end users present demands of different amounts and 
dura- escalating, are providing incentives for the use of tion, the costs to the entity of providing reliability differ
0018-9529/82/0800-0308$00.75
University of Florida, Gainesville 
Barney L. Capehart 
University of Florida, Gainesville 
Clyde F. Kiker 
University of Florida, Gainesville
electric rates. of the appropriate criterion for system reliability is receiving considerable attention . This discussion has 
a direct
photovoltaic and other dispersed solar energy systems by across end users. But typically these costs of serving 
different customers are not reflected in electric power rates _
IEEE TRANSACTIONS ON RELIABILITY, VOL. R-31, NO. 3, AUGUST 1982
Special mathematics needed to use 
results: None Results useful to : Reliability theoreticians and electrical utility planning policy issues that will influence both the costs 
and penetration rate of dispersed solar systems. The primary focus is
Purpose: Present a system 
analysis of dispersed solar energy systems.
of reliability. We conclude that benefits and costs of electric power discussion of policy issues related to power system reliabili- 
reliability for the end user should be considered in establishing reliability ty with dispersed solar systems and the implications of
total interconnected electrical system reliability. Any potential end user -actually considers result from outages. These
ducted by the Electric Power Research Institute [1] showed has been of prime importance. In the broadest sense,
addressed from the perspective of end users' demands and the social costs formulating these decisions. The paper concludes with a
Interconnected Solar Energy Systems
alternative levels of reliability are equal to the marginal
costs of providing these levels of reliability 15-8]. In
236 utilities involved in solar programs. The Public Utility reliability reports to the delivery of power to end user
Regulatory Policies Act (PURPA) of 1978 required within specified tolerances of intermittent service. As a
positive and negative impacts, but this evaluation must be duration of interruptions, and of past levels of reliability
J. Walter Mion
engineers Abstract-The electrical power system reliability criteria and rate struc- an end-user decision analysis in which alternative levels of
tion to satisfy conservation goals and requirements to economic manner, electrical power to final users. Many fac- 
reduce dependence on imported oil. A 1980 survey contours are considered in the planning process , and reliability
solar energy technologies as a substitute for fossil fuels. In any electrical utility is to assure that customers are supplied
with virtual certainty [2-4]. A contrasting view of reliability 
is based on the economic criterion that the total system _
electricity must always meet any level of system demand
standards and rates for interconnected dispersed solar systems. alternative reliability standards for the interconnection of
tures adopted by regulatory commissions and utilities have important im- reliability for dispersed systems and total system reliability
pacts on the design, cost, and market penetration rate of photovoltaics and are explicit considerations. A discussion of the main
Planning, Pricing and Public Policy Issues for Reliability of
bearing on policies governing the use of interconnected
based on a broad view of system reliability. Under the
308
is designed so that the marginal benefits to end users from
and utility electrical supply are considered. Broad issues of public policy are
1. INTRODUCTION
traditional engineering view of reliability, the supply of
2. PLANNING FOR SYSTEM RELIABILITY
utility 
The acceptance, however, of solar energy technologies except to the largest industrial users. As a result of this
utilities to examine conservation strategies which include regulated entities serving the public the ultimate objective of
addition, the Federal Energy Regulatory Commission the service reliability they need and are willing to pay for.
up rates or purchase agreements. These major federal is spread across all end users served by the utility [5]. Since
system customers.
1982 IEEE
tial solar energy program must be evaluated in terms of its costs are a function of the rate, timing, magnitude, and
other dispersed solar electrical systems. The implications of alternative elements in reliability planning are followed by an 
ill- levels of reliability for dispersed generating facilities are examined lustrative model of end-user investment decisions for
©
discriminating against solar electric systems in either back- electric service they receive while the cost of that reliability
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tical purposes this is the requirement for a "near perfect In assessing the reliability of dispersed solar systems it is
power from periodic insolation. It is assumed that end are the capital costs of dispersed solar system designs with
usually a system failure of one day in ten years; for prac- depending on timing, purpose, and benefits of the power.
of planning power systems. Planning is divided into three associated costs and benefits from alternative levels of
system planning process usually consists of the following reliability from the dispersed system and from the utility
and storage capacity thereby controlling the availability of cost of that reliability. For an end user the marginal costs
In light of this dual planning framework, the critical analysis with no discounting.
3. Solar capacity costs are a function of reliability.
issue is "What level of reliability should, or will be, 5. Total end-user costs are the sum of the cost of
you assume that all demand placed on a system must be served demand is its 2-part nature: both quantity and reliability.
vice to the customer, the system expansion plan must ac- consider an illustrative end-user investment model for
alternative system expansion plans, examination of system reliability consistent with its own risk preferences and
13]. In effect the full burden of risk due to different levels number of objectionscan be raised against this criterion and
network will be only slightly affected by the 
interconnection of dispersed systems . This is because the costs of native levels of power and reliability.
capacity planning since the transmission and distribution
3. UTILITY PRICING AND END USER RELIABILITY
users will own the dispersed systems. Although it is possible- improved reliability ratings while the marginal benefits are
solar systems with the utility complicates the planning pro- summarized as a comparison of the marginal benefits from
recent federal and state regulations have restricted utility benefit to the end user from the availability of power.
Historically, electrical system reliability in the USA has 
been based on an engineering view of reliability which A frequency overlooked aspect of end-use electricity
ble that utilities could own and operate dispersed systems, the savings in power not purchased from the grid and the
cess. Dispersed system users can install both generating a particular level of electricity reliability with the marginal
the load facing the utility will become more uncertain. This
participation. Depending on the aggregate amount of Clearly the optimum level of reliability will differ across
thus expands to include both utility planners and dispersed some time interval.
should have the lowest possible occurrence of outages. A resulting from insufficient power to meet demand.
from the generating units to the end users. The overall seems appropriate to allow end users to select the level of
availability.
system [3]. essential that the factors which determine a customer's de- The integration of photovoltaic and other 
dispersed mand for reliability be considered. In brief, this can be
and that all users be exposed to the lowest possible occur- Final users not only demand different quantities of 
elec- rence of power outages [3-5]. This reliability criterion is tricity but they also require different levels of reliability
expansion plan, and finally, analyzing these results and the utility. In order to clarify the relationship between utility
1. End users attempt to minimize total cost for altering
count for the uncertainty of load forecasts, daily and dispersed systems.
2. Power output from solar systems and end-user
distribution system. Generation system planning determines depending on the final use of the electrical power . With
the most economical and reliable network to deliver power from that reliability. Clearly with dispersed solar systems it
system users. Both groups are capable of planning for 
generating capacity and reliability.
INVESTMENT
the availability of backup power to dispersed system users, the utility.
4. The decision framework considered is a one-period
selected?" On the basis of precedent, the engineering view power purchased from the grid at alternative levels of
reliability and economic consequences of each alternative remove some of the burden for near perfect reliability from
of reliability is on the utility. these objections merit further elaboration. Telson [5], Kauf- The trend toward 
centralized power generating man [2], and Munasinghe [7, 8] have all argued that the
Transmission and distribution system planning determine reliability level that is consistent with the benefits derived
seasonal variations in load, equipment failures, and fuel
dispersed capacity installed and the provisions governing users and will be influenced by the rate structure used by
uncertainty will be reflected mainly in generating assumptions
ensuring safety on the system is small relative to the 
cost of changes in generating capacity. The planning process power demand are stationary stochastic processes over
MILON ET AL.: RELIABILITY OF INTERCONNECTED SOLAR ENERGY SYSTEMS 309
would suggest that both central and dispersed systems reliability, solar capacity and operating costs, and the loss
mines the minimum-cost mix of generating units to serve uniform reliability and rate structures that do not differ- the 
projected magnitude and duration of system load. tially price reliability, end users have no means of selecting a
facilities since the early 1900s has led to a particular way engineering view of reliability only indirectly considers the
major areas: generation system, transmission system, and reliability. End users of electricity desire different reliability
steps: preparation of a load forecast based on expected that equates the cost of reliability to the end user with the
peak demand and energy requirements, identification of benefits. This would allow the end user to select a level of
formulating the recommended plan. To assure reliable ser- and dispersed system reliability to the end user, it is useful to
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for minimizing (1) require : price schedule allows the end user to weigh the costs of different levels of power reliability 
against the benefits. End
a coordinating mechanism in system planning that forces
end user would have little incentive to invest in dispersed
[p - bl[OE{qd}/Or] = [OB(r)/Sr] Kd, for L(.) = 0° ing to pay both a capacity credit and an energy credit for
PI,c
small changes in E{qd} due to changes in reliability, the
enhance investment opportunities. Similarly, dispersed
stems from avoiding losses and power purchases while the must be resolved on technical standards. The buyback
With the utility backup service approaching 100 percent that determines dispersed system payback; andI, these
(b) power from a dispersed solar system will significantly
310
r
price pc. From (2), the first order condition reduces to: probability of meeting demand or an explicit rationing
Notation
-E{qd})
W
(4a)
literature concentrates on two alternative approaches to
which is a convex function with a unique minimum reflection- 
ing nonincreasing returns for end-user cost with respect to r 
and Kd.
reliability (eg industrial users) are more likely to invest in
insufficient electricity to meet demand. Assuming that the cost alternative(s) that satisfies a desired level of reliability.
backup service to dispersed system end-users at a constant reliability constraint which imposes restrictions on the
users with a high value (large potential loss) for power
decentralized decision makers to consider the system-wide
solar system reliability, and the loss to the end user from to the utility, rather the end user must determine the least
+ Kd[aB(r)/ar] + aL/ar = 0
+ B(r) + aL/ Kd = 0
Q
cost. For a more detailed discussion of utility pricing and
An additional consideration in dispersed system 
investment decisions is the revenue from sales of excess power to _
(residential). As a result the utility price schedule serves as
system reliability. Power would be drawn from the 
dispersed system whenever it was available and the end user _
IEEE TRANSACTIONS ON RELIABILITY, VOL. R-31, NO. 3, AUGUST 1982
On the condition that 8p#(r)/ar > 0 and aLI ar < 0, the 
(1) end user would consider: a) the cost ofreliability pur- 
chased from the utility, b) the loss resulting from alter- 
Eq (1) states that total cost to the end user is composed of native levels of power reliability, and c) the cost of 
pro- the cost of purchases from the utility, the variable cost of viding reliability through the dispersed system . The end
could be expressed as:
(5)
The end user's objective is to minimize total cost, C, pc(r)[9E{qJ}/ r] + E{qc}[apc(r)/ar]
reliability see [9].
reliability are greater than the marginal avoided power
Kd
(3) effects of dispersed system decisions. The economy
Consider first the situation where the utility provides determining reliability charges in electric tariffs: either a
costs stem from the concomitant investment in reliability rates, however, are influenced by many economic factors
[Pc- b] [ aSE{qd}/Sar] - aOL/Oar = [(aSB(r)/Sar] Kd,4
SC/Sr = pc[SE{qc}/ Or] + b( SE{qd}/ Sri
would rely on the utility for backup at other times. Both
C = pc E{qc} + b E{qd} + B(r)Kd + L(Q - E{qc}
reliability, the loss approaches zero and ( 4a) reduces to: buyback rates will depend on several characteristics of 
individual utility systems. For example, a utility that is will-
where the 1.hs of (4a) represents the marginal benefits the utility. This of course requires compatibility with the
the risk and the cost of reliability are shifted to the utility.
whether the marginal costs of changes in dispersed system peak periods will complement the utility system .
q. 
qd
solar system output, the capital cost for a selected level Of user is no longer able to shift the risk and cost of reliability
solar system capacity cost 
solar system operating cost 
total cost to end user 
solar system output capacity 
loss function 
price of electricity from the grid 
total end-user electrical demand 
electrical demand from the grid 
output from a solar system 
system reliability
B 
b
reflect the cost of alternative levels of power reliability,
- b[aE{qd}/ar] - aL!ar = [aB(r)/ar] Kd.
(2) dispersed system reliability than users with a low value
and the rhs the marginal costs of reliability. The benefits grid to maintain transmission integrity and is an issue that
costs. With small differences between pc and b and with
p(r). Substituting pC(r) into (1), the first order conditions
L
extreme occur at an internal point, first order conditions Unlike the constant price structure, the reliability-based
SC! SKd = Pd SE{qc}/ SKd] + b[ SE{qd}/ SKd]
The economic decision for the end user is to determine systems that supply power with high reliability during
An alternative approach is to allow the utility price to
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4. PUBLIC POLICY IMPLICATIONS
ty of interconnected or ty of inteconnectedoperation" established by stte 
utilit commssios.his s amajo isse o conenton sncecould preempt all but the most expensive dispersed systems.
. .
sdl me ib c reliability because of smaller sized units, fuel diversity, fast 
should reflect imprvemetsiyemrliabliand flexible installation, and grid connections closer to end dispersed systems that reduce peak demands and thereby
times during the load cycle is a primary determinant of the This gives a flexibility in response to system load changes
are less precise but nonetheless important. "discriminatory" rate based on the reliability of end user
This discussion is the recognition that the reliability of the needed to add new system capacity is relatively short 
com- dispersed system in providing power to the grid at different walls to that of a new coal or nuclear central station unit.
.
Buyback rates that reflect these effects on utility system In assessing these policy aspects of interconnected
demand might be appropriate. On the other hand, rates
dividually or if systems will be grouped generically accord- also allows construction and siting near the end-use loads.
be a welcome addition.
ing to supply characteristics such as the availability and Overall service reliability could be improved if dispersed
of base demand with a stochastic peak demand from inerpil.aku. evc ol rooeedue n beem di.in a di nancial investment decisions that are consistent with the planning dispersed systems would clearly be n the objectives of the utility. situation that would 
eventually force another utility ~~~~Some additional policy aspects of dispersed solar customers to pay higher rates. In this instance, the
variability of insolation. It seems apparent that regulatory systems could supply power to the grid during system
201 and 210 of PURPA and recent rules from FERC [11]. customers within the same class, might have widely varying
volatility of end user dem'and and directly reports to 
Iong voltiltyof.nduse.dman addretlyreatet log decreased or eliminated. An incentive price reflecting this term planning. A utility system that faces a certain erosion
interconnected dispersed solar systems focuses on sections customers. Different customer classes, or even different
of alternative levels of reliability. This has led to the charge
promote a coordinated planning effort between the utility fuel diversity attributable to dispersed solar systems could
A different aspect of the reliability issue reports to the with certainty until the concept of reliability based pricing is
- .
.
indirectl benefit other customers. Theeffectiveuseofgenerating units in electrical systems is the large disturbance 
in system capacity caused by loss of the unit due to a 
forced outage . In many cases a reserve margin equal to the
systems will have to demonstrate their reliability level in- its customers. The dispersed nature of the solar systems
and end users.
.crld question thatrempnsihoweer, iswther
solar systems for both the utility and the end users [10]. capacity planning process. Several writers [3, 5, 7] have
rates for utility power can encourage
.
argued that reliability standards have been imposed with 
insufficient consideration for the economic costs and benefits _
nthat electric utilities-are "gold plated" [13] with reliability At 
the present time the policy debate on the reliability of characteristics that greatly exceed the needs of many
tionsystmwile otetialenduser 
cerned with the reliability of their onsite systems. .air
.
.
reliability investment
Most interconnected dispersed solar electrical systems would needs for electrical reliability. A framework for integration of
use locations. One of the problems of having large
reliability will promote an efficient integration of scattered dispersed solar systems it is important to consider the
On the issue of dispersed system demand that 
jeopar- the FERC rules backup rates must be "just and the FERCrules backup.rates must be "just and says utility reliability by presenting a stochastic peak 
de- reasonable" and a utility may not charge a dispersed end
rate. It is not yet clear whether individual dispersed that can be utilized to the advantage of both a utility and
.
t
MILON ET AL.: RELIABILITYOF INTERCONNECTED SOLAR ENERGY SYSTEMS 311
user a different rate than other customers in a similar class command, one solution is the use of load management through
a direct control device. In terms of overall system planning unless significant differences in cost of service 
can be this could promote load-leveling since off-peak use for demonstrated. This reliability consideration deals with the backup could be increased while on-peak use could be
qualify as small power producers [12], that is, power pro- dispersed systems that employs an explicit price to account
ducers with less than 80 MW of capacity using a renewable... for reliability factors would allow rational end users to select 
fuel source. Under this status, dispersed systems must meet a reliability level consistent with their needs. As a result this
by the end users that benefit overall system efficiency.
w
courage reliability investments by end users and will not reliability problems due to oil embargos or coal strikes, the
At the
An additional aspect of the reliability issue concerns 
size of this large unit must be maintained for reliability utility buyback rates from dispersed systems. The FERC purposes. Smaller dispersed units with non-coincident 
rules identify a number of factors that must be considered power outputs could reduce tsneed f ornclrer v 
~~~~~~~~~power outputs could reduce this need for a 
large reserve in determining buyback rates. But the most important for margin. Also, with smaller, dispersed units, the time
.
iniecl beei ote cutmr.Teefcieueo
based only on supply characteristics will do little to en- peaks or generating unit shutdowns. Finally, in terms of
rates for backup power to dispersed system users. Under implemented, at least on an experimental basis.
utilities would clearly like to require as high a level 
of .cust ill respondto p res tharefect lther- reliability as possible to preserve the integrity of the distribu- 
ar priciplly on -customers will respond to price structures that reflect alteration system while potential end users are mainly con- naiv leel oreiblt.Tsqutoncntbeawrd
P
,~~~~~~~~~~~~systems ,,
-
"reasonable standards to ensure system safety and 
reliabili- could translate into lower costs for dispersed system 
capaci- aton eishe by stateutility ty and storage. Rigid adherence to strict reliability standards
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Barney L. Capehart (S'65, M'67, SM' 72) received the BS and MEE
[3] 5. Walldorf L. Mark,"Thelectricity industry-pastand Science, and serves on the Administrative Committee of the IEE Systems,
power system reliability levels," Bell Journal of Economics, vol on various foreign assistance programs. His research interests are in the
US Congress, House of Representatives , Committee on 
Interstate and Foreign Commerce, Are the Electric Utilities Gold
J. Endrenyi, Reliability Modeling in Electric Power Systems, John avsry Committee.
capacity," for Electric Power Research Institute, 1978 October. in both the Food and Resource Economics Dept. and the Agricultural [7] 
M. Munasinghe, "A new approach to power system planning,"
Office, 1979 April.
Plated? A Perspective on Electric Utility Reliability, 96th 
Congress , First Session, Washington, DC, US Government Printing
Economics and Regulation, edited by MA Crew, Boston: DC Manuscript TR81-166 received 1981 April 13; revised 1981 August 22.
present," in The National Electric Reliability Study, 1981 April, Man and Cybernetics Society. He is a member of the AIIE National prepared 
for the US Department of Energy.
for electrical power generation systems," The Bell Journal Of Dr. Clyde F. Kiker; Dept. of Food and Resource Economics; University
systems," Public Utilities Fortnightly, vol 107, 1981 Jun, pp
economic and technical aspects of dispersed energy systems including
of Florida, Gainesville, Florida 32611 USA.
AIIE, a Fellow of the American Association for the Advancement of
[8] M. Munasinghe, M. Gellerson, "Economic criteria for optimizing the Univ. of Florida. He has served on the Univ. of Kentucky faculty and
the Univ. of Oklahoma in 1961, 1962, and 1967 respectively. Since 1968
[6] Decision Focus, Inc., "Costs and benefits of over-under Dr. Kiker holds the rank of associate professor and has appointments
5. CONCLUSIONS
312
recognize
Dr. Barney L. Capehart; Dept. of ISE: University of Florida; Gainesville,
degrees in electrical engineering, and a PhD in systems engineering from
[5] ML Telson, "The economics of alternative levels of reliability
[1] M. Laliberte, E. DeMeo, "Solar update," EPRI Journal, vol 6,
[13]
he has been with the Dept. of Industrial and Systems Engineering at the
[2] A. Kaufman, "Reliability criteria - A cost benefit analysis," New Univ. of Florida where he is presently a Professor. His main research area
IEEE Trans. Power Apparatus and Systems, vol PAS-99, 1980 Engineerng Dept at the Univ. of Florida. He received his BS and MS in
May/Jun, pp 1198-1206. agricultural engineering and PhD in Food and Resource Economics from
persed perseystems systems that complement the utility system. A direct interfacing alternative energy systems with electrical utilities. Dr. 
Milon at- A drei that,.implement theutility system. tended the London School of Economics and the Univ. of Virginia and 
recognition of the need for a flexible approach to rela- received his PhD degree from Florida State Univ.
10, 1979 Spring, pp 353-365.
-
Florida 32611 USA.
1981 Jun, pp 12-15.
[9] MA Crew, PR Kleindorfer, "Some elementary considerations photovoltaics and biomass.
Reporter, vol 2, 1980 Nov/Dec, pp 705-752.
Economics, vol 6, 1975 Autumn, pp 679-694.
users will help fulfill this responsibility.
Heath, 1979, pp 143-160.
Federal Energy Regulatory Commission, " Small power 
production and cogeneration facilities: Regulations 
implementing section ** r210 of the public utility regulatory policies act of 
1978," Federal Register, vol 45, 1980 Feb 25.
[11] RHJH Lock, "Encouraging decentralized generation of 
electricity : Implementation of the new statutory scheme," Solar Law
The end-user investment model illustrated the significance Dr. J. Walter Milon; Dept. of Food and Resource Economics; University
[41
REFERENCES
Wiley and Sons, 1978.
of major public policy issues that will significantly
[101 JW Milon, "Electric rate reform and alternative energy
The purpose of this analysis was to highlight a 
number of major public policy issues that will significantly 
influence both the costs and the penetration rate of 
dispersed solar systems . The policy making process should 
explicitly [12] recognize Ithat the goals of end users and 
the utility concerning standards of reliability and the 
availability of backup power may differ. Actual problems 
that will be encountered in the process of integrating 
dispersed solar systems with electric utilities are more 
complex than described here . However, if efficient use 
of dispersed solar systems is of concern, utility rates that 
reflect thecosts of reliability would allow end users to 
select the appropriate reliability level consistent with the benefits to the end user.
IEEE TRANSACTIONS ON RELIABILITY, VOL. R-31, NO. 3, AUGUST 1982
ty standards reflecting different values of reliability to end
* ***
15-20.
Seepage 307for details.
of reliability and backup power availability in the decision of Florida, Gainesville, Florida 32611 USA.
AUTHORS
to invest in dispersed system reliability. State utility com- J. Walter Milon is assistant professor of natural resource economics in
framework that will encourage end users to utilize dis- current research centers on the technical and regulatory issues involved in
is energy systems analysis. Dr. Capehart is a Senior Member of IEEE and
of reliability and regulation," in Problems in Public Utility
Energy Committee and serves on several local, state and federal energy
York State Department of Public Service, OR Report 759, 1975 
August.
missions will have the responsibility for establishing a the Dept. of Food and Resource Economics at the Univ. of Florida. His
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