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Analysis of Merits of Hybrid Wind/Photovoltaic Concept for Stand-Alone Systems
John A. Castle, James M. Kallis, Sally M. Moite, and Neil A. Marshall Hughes Aircraft Company This paper appears in: 15th IEEE Photovoltaic Specialists Conference Publication Date: May 1981 On page(s): 738-744 CH1644-4/81/0000-0738
Abstract Methods for evaluating the merits of hybrid wind/photovoltaic systems for use in stand-alone applications were developed. The optimum mix of wind and photovoltaic power with an electrochemical storage system, with or without fossil fuel generator backup, depends upon the individual subsystem economics. A computer code was developed to calculate the optimum subsystem-sizes that minimize the levelized energy cost. The actual merits of a hybrid system over a pure photovoltaic or wind system depend upon many factors: load profile; wind regime; insolation; cost and availability of backup power; the relative costs of wind rotor area, array area, and storage; and subsystem efficiency factors. Examples of optimized hybrid systems for a range of photovoltalc costs and estimated wind and storage costs are shown for an Ely, Nevada. application. where backup power is allowed to supply 5% of the total annual load.
© 1981 IEEE.
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ANALYSIS OF MERITS OF HYBRID WIND/PHOTOVOLTAIC CONCEPT FOR STAND-ALONE SYSTEMS
John A. Castle,'''James M. Kallis, Sally M. Moite, and Nel1 A. Marshall Hughes Aircraft C~any
ABSTRACT
Methods for evaluating the merits of hybridwind/photovolta1c systems for use in stand-alone applications were developed. The optimum mix of wind and photovolta1c power with an electra. chemical storage system, with or without fossil fuel generator backup. depends upon the ind1vidual subsystem economics. A computer code was developed to calculate the optimum subsystem-sizes th~t mlni~ize the levelized energy cost. The actual merits of a hybrid syst~~ over a pure photovoltaic or wind system depend upon many factors: load profile; wind regime; insolation; cost and availability of backup power; the relat1ve costs of wind rotor area, array area, and storage; and subsystem efficiency factors. Examples of optimized hybrid systems for a range of photovoltaic costs and estimated wind and storage costs are shown for an Ely, Nevada. application, where backup poweris allowed to supply 5l of the total annual load.
INTRODUCTION
Photovoltaic (PV) systems are presentlyeconomically utilized for small remote stand-alone power systems. As the life-cycle costs of these systems have decreased relative to those of alternative power generation systems, i.e•• fossil fueled generators. the sizes of viable PV systemshave increased.
For stand~alone apllcations we believe storage costs will ultimately represent the major economic restraint to further market penetration of PV systems into higher load applications. The merits of combining both wind power and PV power to minimize the storage requirements and hence system costs are addressed in this paper. Based uponthe current technical and economic status of such systems, we have focused on relatively small overall systems which may have near-term econ~ic application.
For some locations, the availability of fuel cannot be relied upon. [n such cases. stand-alone hybrid wind/photovoltaic systems utilizing auxil iary backup power may have application. The use of backup power to supply up to 5% of the total annual load has been shown in earlier investigations at Hughes to substantially reduce the storage requirements c~ared with those of • 100% standalone system. Such a system could have merit f~ a reliability and cost standpoint, while greatlyminimizing the necessary fuel supply. The example system evaluated In this paper uses backup powerto supply up to 5% of the load.
Prior Work The merit of the hybrid system has been inves
tigated previously.(l) and (2) report preliminary investigations involving hybrid windl photovolta1c systeAS for remote sites and for desert areas. (3) reports an analysis of a hybrid wind/solarthermal-electric power system.
Present Investl£ation The presen investigation extends the prior
work 1n the systemization and automation of methods for evaluating hybrid wind/pv systems versus pure wind or pure pv systems. In particular, the paper describes the follOWingadvancements:
1. Development of quantitative criteria for the evaluation of the merit of the hybrid conceptfor a specific application.
2. Development of a method for evaluation of the solar/wind resource for a given site and load profi leo
3. Development of an automated hybrid systemoptimization method for trading off wind versus photovoltaic versus storage.
4. Application of these methods to the determination of an optimllll hybrid system for an example of a load profile at a site 1n the western United States desert.
Statement o~ the Problem The objective is to supply a specified load
at a specified site with a combination of wind and photovoltaic power. The problem is to find the most cost-effective way to match the supply and dem~d. The demand, i.e •• the load profile, may be a function of the time of day and/or the season of the year. Each of the sources of supply, i.e •• the available wind power and insolation, varies as a function of the time of day and season of the year. In general, the demand profile will not match the profile of either of the sources of supply. This mismatch can be compensated for by the inclusion of storage in the system. The factors in a hybrid system are as follows:
1. Subsystem design parameters (e.g., tilt angleof the pv array and cut-in wind speed of the wi nd machi ne). '
2. SUbsystem relative sizes (i.e., mix of wind, photovoltaic. and storage).
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CHI~/811OOQO.(1738 $00." ce 1981 IEEE
3. SUbtystem relative CO$ts (1.e., S/m2 of arr~, S/m of rotor, and S/kWh of $torage).
4. Site (i.e., diurnal and seasonal variations of tnsolation and wind).
5. Load profile (i.e., diurnal and seasonal var 1atl ons).
The large number of parameters ~lkes it diffi cult to determine I priori whether a given site and load comprise a good candidate for a hybrid system, i.e., whether a hybrtd system is better than I pure-photovolta1c or pure-wind SY5ten.
ApproachThe following step-by-step approach was
developed:
1. Select the subsystem des1gn parameters, and specify the site. Then the normaliled hourly electric outputs of the wind and photovoltalcsubsystems can be calculated, independent of the load.
2. Specify the load profile. Then the relative sizes of the wind and photovoltaic subsystems that provide the best match to the load prof11e can be calculated. and the merit of a hybrid system for the specified site and load can be evaluated.
3. Optimize the sY5tem, accounting for the subsystem relative costs. The relative subsystems1zes calculated by the load-matching cri terion provide a means for making an initial estimate of the optimum system.
GENERAlIZEO TECHNICAL CONCEPT
The conceptual hybrid photovoltaic/wlnd energyconversion system (WECS) model was mechanized as an ac system, as shown in Figure 1. An alternative ae system, summing converted photovoltaic powerand the output from a compatible ac aerogenerator,would be equally acceptable.
The aerogenerator would be of the pennanentmagnet/ac alternator type, preferably a multiphase device, similar to automotive units. The bridge rectifiers are usually integral with the alternatori diodes are included to depict block1ngand break-awAy action for both subsystems.
In the simplif1ed system. the "on-char~· voltage of the energy· storage battery detenainesthe potential Df the dc bus. This potential is a function of te-perature. battery state of charge.and net charging current. This potential is monitored and li~ited by the charge control algorithm of the regulator.
The use of a lead-calcium battery, designed for deep daily cycling. has been assumed. These cells, manufactured by several of the major US suppliers, require a float voltage of approxi~ately 2.4 volts per cell at 250C ambient. Assuming a 120 vdc system, a 60-cell ser1es strin! would typically be employed
The regulator maintains the requisite float level, once recharging has been accompliShed. Quasi-current sources, such as photovoltaics. are _ore functionally compatible ~ith shunt. than with
, series. regulators. However, series devices can be employed with equal facility. Series regulators are traditionally used with WECS alternators, which are typically stiff voltage sources. A 1~diss1patlon sw1tching regulator. of either the free-running or pulse-w1dth-modulat10n type, coul d be ill1) ll!llented.
For the 120 vdc system, the de bus _ill swingbetween about 144 volts (2.40 Volts per cell (VPS))and 105 volts (1.75 YPC). depending upon the endvoltage point. This variation from float voltageto the discharge end-point 1s accommodated in the 1nverter window. The dc-to-ac inverter .ay be either single or three phase. Without sustainingbackup power or a hard utility tie. forcedcOGmUtated inverters with their own internal precision e~cttation are mandatory. Phase-lock circuits are additionally required if the inverter is to be synchronized to the 60 Hz utility line or a backup engine-generator.
The system operation depends on whether the instantaneous power generated by the hybrid systemis greater than or less than the load. If the power generated is greater than the load, then the surplus is added to storage until the storage is full. Any remaining power generation that the storage cannot accept 1s curtailed and/or dumped,depending upon the type of voltage-regulation control system used. If the hybrid power is less than the load. then the deficit 1s drawn from storage until the storage is at 1t$ mfni.um level. An~ r~aining part of the load that cannot be supplled by the hybrid system is supplied by a backupfossil-fueled generator.
LOAD AA.TCHING
A system for which the outputs of the wind and photovoltalc subsystems provide the diurnal and seasonal power output profile that best matches the load profile is likely to be close to the .1nlmum-storage system. Amethod for calculatingthe best-match sizes of the wind and photoyolta1csubsystems is described below.
load-Independent Normalized Variables The electric outputs of the wind. photo
voltaic, and storage subsystems are approxiIMte11proportional to their sizes. Defining the following:
T • duration of I period of fnterest (for a onefear period e~pressed in hourly increments, T • 8760 hrs,
i • ti-e increment (for hourly time increments for one year: i· I, 2, .... 8760).
Then the hourly electric output of the photovoltaic SUbsystem can be expressed as the product p. W (il. where
P • area of array (m 2) and
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c
w(1) : Average output of the photovoltaic subsystem per unit ~rray area in the i'th time increment (kWh/m ).
Thus ~(i) determines the shape of the photovolta1c output profile, and P detennines its magnitude.In the same way, the hourly output of the wind subsystem can be expressed as the product W. lII(i), where
Wm area of rotors (m2) and
w(i) average output of wind subsystem p~r unit area in i'th time increment (kWh/mf).
The normalized quantities wei) and wei) depend o~ the subsystem design parameters and the site, but are independent of the load. Tney can be calculated by an hour-by-hour slmulat10n code, and these two sets of 8760 values of w(i) and wei) can be stored in the computer.
Reduction to a Numerical Analysis Problem The best-match areas of the photovoltaic
array, P, and wind rotor. W. are calculated as the solution to the following numerical analysis problem. We wish to fit a function of time 1(1). defined as the average load in the i'th time increment (kWh). with a linear combination of two other functions of time. '11'( 1) and (j) (i). In other words. we wish to find the values af the parameters P and Wthat prov1de the best fit to l(i). as illustrated in Figure 2:
i.(1) '" P·w(i) + W,w(i) (1)
Thus the load-matching calculation has been reduced to a numerical analysis problem, for which solutions are available.
Best-Fit Criterion Several criteria for the best fit could be
used. One best-fit criterion. minimization of the sum of the squares of the deviations, enablesformulas for the best-fit parameters to be derived in closed form. For this reason, the least-squares criterion has been selected for the present purpose. There is no other reason for selecting the least-squa~s criterion. In fact, this cri terion probably over-estimates the importance ofthe frequent large, brief bursts of available wind power shown in Figure 2. A criterion such as mini~1zatlon of the magnitudes of the deviations, rather than their squares, would be preferablein this regard. Amore compelling consideration, however, appears to be the insight and computational efficiency resulting from a closed-form solution. as is possible with the least-squares criterion.
Solut10n for the Best-Fit Parameters The best-fit-parameters P8F and WaF in the
least-squa~s sense are given Dy:
(2)
l:f • t .". - PSF t f • n 2 (3)
tf • 1f • W
where
and
In these formulas, f(i) is an analyst-selectableweighting function, and the summations are taken from i:l to izT.
These formulas enable an estimate of the best load-matching mix of the photovoltalc and wind subsystems by arithmetic operations on the precal cu1ated arrays 11 ( i) and Ill( i ) • They can be performed relatively quickly and inexpensively with a digital computer.
Criteria for Merit of Hybrid SystemThese formulas also can be used to derive
quantitative criteria for the merit of the hybrid system, relative to a pure photovaltaic or purewind system, in a particular application. Since the aforementioned load-matching problem is strictly a mathematical problem. it is possiblethat a physically unrealistic solution could be obtained. In particular. one or both of the bestfit subsystem areas PBE and WaF could be negativefor a specific case. This prObably would indicate that the hybrid system has no advantage over a pure photovoltalc or pure wind system for these specific subsystem design parameters, site, and load profile. Therefore quantitative criteria for the merit of the hybrid system are that PaF and WaF be positive. _
Modified Formulation Calculations showed that the foregoing formu
lation underestimates by a factor of 2-3 the size of the system required to supply the annual load. Therefore, although the foregoing formulation is useful for explaining the method. a modification is needed for actual system sizing.
The modified method involves selecting a system scale to meet the load. and then using a least-squares fit to choose the ratio of wind to photovolta1c power generation. The variables used are as follows:
l .: 1:1(1) Total load for a year.
D~Ew(i) Sum of specific wind power generation for one year.
n!!l:~(i) Sum of specific photovoltaic power generation for one year.
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L.L, O·O,n·D. L·C, L·n, n·D Sums of products for one year. e.g •• L•n >: ~ 1 (i) w( 1) •
Modification factor for load to account for desired fraction expected economic benefit of overslting generating system to reduce storage. etc.
Modification factor for wind power to account for conversion losses, non-utilization of power spikes, etc.
Modification factor for photovolta1c power to account for conversion and storage losses, etc.
Size of photovoltaic array that will meet load. defined by
Po klTn • let L. (6)
Size of wind machine that will meet load. defined by
W k {l .. k~ l. (7)wo
t Ratio used to define the design sizes of the wind and photovoltaic systems
p .. t Po (8)
W " (l-t) Woo (g)
There is merit in adding photovoltaic power to a wind ~ystem if t > O. There is merit in adding wind power to a photovoltaic system if t < 1.
From the definitions above,
P Ie.,.. n + W lew 0" Ie 1 L .... (10)
Thus, whatever value t has, the selected systemis automatically scaled to satisfy the load.
The best-fit ratio t, which minimizes the sum of the squares of the deviations of power produced from the load, is
t = ~[Pok... n (1}-W k w(i)] [k,l({)-W/ww{i)] (ll)wo SF 1:[ Pok ... 11" (i) - Wok", w(i) ] 2
A hybri d system has merit if 0 < t Bf < 1. £qullt1on (14) shows that t 8F > 0 if the oifference between the power generatea by the photovoltaiconly system and that generated by the wind-only system 1s positively related to the difference between the load and the power generated by the wind-only system. In this case, the inclusion of photovoltaic power 1s advantageous. The cri terion for there to be merit to adding wind power to a photovoltaic system (tBF < 1) is similar.
OPTlMIZAT ION
The load matching methods described above are useful for assessing-whether a hybrid systemis promising and for initial sizing of the wind and pv subsystems. However. the final sizing must be achieved by considering the costs of system components, as well as their perfonmance.
The stand-alone power system described here is optimized to minimize th~ leve11zed cost of energy used by the load subject to having the wind! photovoltaic part of the system supply at least 95~ of the load. The costs of wind machines, array, storage, and power conditioning equipment are included in the levelized energy cost calculation. The sizes of the solar array and storagelind the number of wind machines are determined by the optimization.
Conditions for OptimizationThere is a tradeoff between the wind machine
area. array area and storage capacity needed to provide 95% of the electricity for a load. For example. a system could use more wind machine area and reduce the amount of array area. or increase the use of storage in order to reduce the wind machine area.
Figure 3 shows a tradeoff between wind machine area and storage for fbed array area. It would be expected that when, for example, the store is very large. it can be reduced without changingthe power supplied to the load if the wind machine size is increased by a small amount. It would also be expected, that. if the store is small, it would take a large ilDount of wind machine area to compensate for a reduction in the storage size.This relationship determines the shape of the curve in the figure which bounds the shaded feasible region where the renewable energy system (RES)fraction is greater than or equal to .95.
Curves of constant cost are parallel straightlines under the assumption of constant unit costs for the storage and wind ~achfnes; costs decrease towards the origfn. System 0 in the figure, the lowest cost system that produces a .95 fraction, is located at the point of tangency of a cost curve and the .95 fraction curve. This system also has the lowest levelized energy cost curve though o lies below the constant cost curve at 0, and is curved downwards.
The condition for optimizat1on is that the .95 fraction curve (or surface in the threeM
variable optimization) is tangent to a constant levelized energy cost curve at the optimum and that the curves actually have the shapes indicated in Figure 3.
Choice of Variables for Optimization If the wind ~ach1ne area and the storage size
are variables in the opti~lzltion, it is likely that the optimization routine will ·sticK- at a point like N on the .95 fraction curve. Optimization programs explore by making small changesin each variable individually. At N. these changes
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lead either to J~er RES fractions than .95 or to higher leve11zed costs (unfilled arrows In F.igure 4).
If the cost of the system and the fraction of the system cost used to buy wind machines are the variables, there ts a better chance that one of the exploration directions (filled arrows) leads to a feasible point _ith improved levelized cost. With these variables, the optimization routine 1s less likely to stIck far away from the optimum.
Computer Optimization The Hughes-developed computer program, HWPVS,
simulates the annual performance of a hybrid wind/ photovoltalc system, given design parameters and hourly weather data for the design location. The program has an optimization option which uses a pattern search algorithm. The three optimization variables used for this study were: first. the levellzed annual pa~ent for wind machines. photovoltaic arrays and storage batteries; second, the fraction of this paJment used for wind machines and arrays; and third. the fraction of the wind machine and array p~ent used for wind machines. The optimization converges after about 200 systemevaluations and uses two Minutes of central procesor time on an IBM 370.
The array tilt angle also was optimized by stopping the sizing optimization after 50 steps, selecting the tilt angle (between 25 and 55 degrees at l.5-degree intervals) which gave the largestRES output to the load, and then continuing the size Optimization.
RESULTS
The site for the example of the wind/ photovoltaic system described here is Ely, Nevada. Typical Meteorological Year data were used for simulations and optl.1zat1ons. Table 1 shows the wind and solar resource at this site and the performance of the wind and solar generators.
Table 2 lists performance and price data for system components based on estimates of current installed prices. Price estimates are for small systems and low vol~ production. Maintenance costs were not estimated.
Table 3 is a comparison of optimally sized systems for Ely for array prices of $600, $1,000, and $1.600 per sq~are meter, As the array price rises to Sl,OOO/m , the fraction of energy supplied by the wind machine increases f~ .38 to .56. Array generating capacity is replaced by wind generating capacity and a somewhat larger stor~ge battery. As array price rises to SI,600/~ , arraygenerating capacity is replaced by increasing _ind generating capacity more than proportionately and by significantly increas1ng the size of the storage. For this system the wind ~achine's fraction is .82.
figure 5 shows the effect of varying the part of system energy suppl1ed by the wind "'achine when the RES fraction is ,9S. For an array pr1ce of
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Sl,600/mf per square meter, a system without wind machines is 24l more expensive than the hybrid system. The wind-only system is S4~ more expensivethan the hybrid system. For an array pr1ce of sl.ooo/;2 a photovoltaic-only system is 37l more expensive than the hybrid system, and a wind-only syst~ is 2Q% more expensive. For an array price of Sl.600/nf· there is only a 3% cost difference between the optimized hybrid system and the windonly system, and the pure photovoltaic system is 64l more expensive than the hybrid system. With the inclusion of 11fe cycle O&M costs these percentages would be expected to change with a bias favorlng greater utilization of the photovoltaic subsystem.
One deficiency in this investigation is the use of constant battery storage life and cost inputs. With decreasing storage capacity achieved through the hybrid concept and increased use of back-up power, the stress on batteries increases through increased deep cycling. This will impactbattery cost and/or life.
CONCLUSIONS
1) A method has been developed herein for systemizing and automating the design of a hybrid wind/photovoltaic electric power system. A computer code has been developed to size and optimize, for minimized level1zed energy cost, a w1n~ photovoltaic/storage system. At the designer' option, the method can design a totally stand-alone system or a system with backup power from a fossi1fuel generator.
l) The optimum mix. with or without the benefit of fossil-fuel generator backup power, depends upon the individual subsystem economics, as well as site-specific climatic characteristics. The storage requirements. and hence cost benef1ts of a hybrid system, increase with reduced availability of backup power. With decreasing availability of low-cost, fossil-fuel, backup power, the economic viability of the hybrid system is enhanced. The example presented allowed 5i of the annual load to be supported by backup power.This 51, while-small. allows the use of a storage systeM perhaps 1/5th the size required if no backup power were available.
3) The investigation confirmed the conclusion arrived at in previous analyses: there is merit in combining photovoltaic and wind-power generationfor stand-alone applications. The cost benefit derives f~ reduced storage requfrements. Therefore it is concluded that the present downward trend in photovoltaic array systeN costs will ~ake the use of hybrid PV-wind systems an attractive alternative for many stand-alone power requirements in areas with moderate wind regimes and goodinsolation.
REFERENCES
1. I. Stambler, -Hybrid Power Syst~ Explored-, Industrial Research/Development. pp. 106-108, February 1980.
FIGURE 2. ILLUSTRATION OF THE LDAD-MATCHING PROBLEM
Systems-, Solar Energy, Vol. 18, pp. 73-74, 1976.
C\ n
LOAD
2. P.E. Payne and J.L. Sheehan, -Hybrid Alternate Energy System-. AllIed can Chemi cal Soci etyCatalog Mo. 8412-0513-2/79-0779-051, pp.251-254, 1979.
3. J.W. Andrews, -Energy-Storage RequirementsReduced in Coupled Wind-Solar Generating
~ ~ I %
~ i!i
WIND OUTPUT
PH010YOLTAle 0U1J'UT
FIGURE 1. HYBRID PHOTOVOLTAIC!WIND POWER sYSTEM
LOMR COST AND UYELIZED ENERGY COST
LEVELll£D EMERGY COST· CONSTANT
STORE
FIGURE 3. COMPONENT SIZE OPTIMIZATION
FIGURE 4. SEAROi DIRECTION FOIl oPTIMIZATION
3 ......--------------__.
FIGURE 6. RES LEVELlZED ENERGY COSTS FOR ELY, NV RENEWABLE ENERGY SYSTEM FRACTION .95
0 0
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