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A combined optimisation concet for the design and operation strategy of hybrid-PV energy systems
Pergamon
PII: SOO38#2X( 97)000285
Solar Energy Vol. 61, No. 2, pp. 77-87, 1997 Q 1997 Published by Elsevier ScienceLtd All rights reserved. Printed in Great Britain 0038-092X197 $17.00+0.00
A COMBINED OPTIMISATION CONCEPT FOR THE DESIGN AND OPERATION STRATEGY OF HYBRID-PV ENERGY SYSTEMS+ G. C. SEELING-HOCHMUTH* EDRC (Energy for Development Research Centre), University of Cape Town, Private Bag, Rondebosch, 7700 Cape Town, South Africa Received 17
November 1995: revised version accepted 13 January 1997 Communicated by GERARD WRIXON
Abstract-This paper presents a method to jointly determine the sizing and operation control of hybrid-PV systems. Hybrid energy systems use different energy sources such as solar and wind energy and diesel gensets. They are an economical option in areas remote from the grid. In this context the correct and cost-effective system sizing as well as efficient system operation are important. The problem becomes complicated through uncertain renewable energy supplies and load demand, non-linear characteristics of some components, and the fact that optimum operation strategies and optimum sizing of hybrid system components are interdependent. The outlined approach finds an optimum operation strategy for a hybrid system by carrying out a search through possible options for the system operation control. The search is conducted over some time period using estimated weather and demand data and long-term system component characteristics. The costing of the operating strategies is evaluated and component sizes are changed by the designed algorithm according to optimum search rules. As a result an optimum system configuration is chosen by the algorithm together with an optimum operation strategy for a given site and application requirement. 0 1997 Elsevier Science Ltd.
1.
achieved when operating ranges are better preserved. Hybrid systems are an important source of electricity not only for schools, clinics, village communities but also for farms and tourist facilities in areas remote from the grid. The design and operation control problem is non-linear due to non-linear component characteristics and the complexity of the problem. The operation control problem in the literature is called the economic power generation problem (Papalexopoulos, 1993). An optimal steady state is achieved by adjusting the available controls to minimise an objective function subject to specified operating requirements. The difficulty in solving the optimum operation control problem mostly lies in the dimension of the problem (B. Jansen et al., 1993). Control strategies which can be implemented by adjusting regulator settings and circuits or hardware configuration have been researched by Barley et al., 199.5. Both the optimum control decisions and the control operation strategies reflecting field operation are modelled in this paper. Stochastic models (Braun, 1993; Dantzig and Infanger, 1993) address uncertainties in demand, component failure and weather behaviour, but can be high in computations. A more recent methodology which can solve non-linear optimisation problems are genetic algorithms (Marrison and
INTRODUCTION
When electrifying remote areas it will be difficult and expensive to reach very remote communities solely by extending the grid. To fill this gap, a hybrid system offers an off-grid energy supply and is a combination of PV, wind, diesel and sometimes micro-hydro generators, in most cases incorporating battery storage (Fig. 1). These hybrid systems can provide power for productive uses. The cost-effective, reliable design and appropriate operation of these systerns is important. When sized and run efficiently a hybrid system is often fit for long-term autonomous operation at an acceptable price. Prolonged battery and diesel lifetimes are
%
solu -
I-
‘-I
Im
Ip’IiJcnUO DC Load
Ii AC
Dkcl
4
LOad
Fig. 1. Basic PV-hybrid system set-up. ‘Paper presented at the ISES Solar World Congress, Harare. Zimbabwe, 9-16 September 1995. $Fax: +27 2 I 650 2830; e-mail: [email protected] 77
Stengel, 1994; Pohlheim. 1995) which copy the evolutionary development of the biological world. This has been applied to the design hybrid systems in Seeling-Hochmuth ( 1995 ); ( 1997); Marrison and Seeling-Hochmuth Seeling-Hochmuth and Marrison ( 1997). and is used for the algorithm to be described in this paper. Quite a few software tools assess hybrid system performance for pre-defined system configurations (Bezerra et al., 1991, Jennings, 1994; Keiderling, 1990; Protogeropoulos ef al.. 1991; Morgan, 1995; Green and Manwell. 1995: van Dijk et al., 1991). Some of the sizing approaches for hybrid systems are paper-based and employ rule-ofthumb methods (FSEC Energy Short Course, 1987, Sandia National Laboratories, 1991). Other hybrid system sizing approaches apply software tools using a simplified and linear model (Lorenz, 1988; Lilienthal et al., 1995) or a complex model but varying the design randomly within a chosen range of component sizes (van Dijk et al., 1991). Seeling-Hochmuth (1995), describes the design of hybrid systems which considers the non-linear hybrid system description and the complex interdependence of operating strategy and sizing. Marrison and Seeling-Hochmuth (1997), formulated the appropriate cost/benefit function for the optimisation of hybrid systems which is used in this paper. The approach in this paper takes the interdependency between sizing and system operation strategy into account. The model is outlined and the developed algorithm is explained. Results are given at the end of the paper, 2. HYBRID SYSTEM DESIGN 2.1. Goals The general goals of the developed design algorithm are twofold: ( 1) sizing of PV-hybrid system components; and (2) operation control of a PV-hybrid system. A suitable system design and operation control should minimise the (1) life cycle costs system reliable guaranteeing (2) while operation. The latter objective includes satisfying demand and operating the system components such as the battery and diesel generator economically, in terms of replacement and maintenance needs.
Fig. 2. Interdependence between system operation strategy.
sizing and system
2.2. Appromh Minimising operation costs and unsatisfied demand are achieved not only by selecting an appropriate system configuration, but also by finding a suitable operation strategy and suitable settings for it, taking account of the special operational requirements (Fig. 2). The operating strategy adopted in handling the hybrid system combined with the sizing choice affects system performance as well as degradation and ageing of components. The sizing of the hybrid system is encapsulated in the so-called Main Algorithm (Fig. 3) which models the configuration and mix of system components for the initial system installation. The decision variables are the size of the capacities of diesel generator, PV, wind, battery, cables etc., and number of components, relevant installation heights or angles, and the controller settings. The system component mix is initially chosen randomly. The control settings and costs of operation strategies for a certain component mix are investigated by the imbedded subalgorithm and then passed back to the main
Fig. 3. Main and sub-algorithm.
79
Hybrid-PV energy systems
algorithm. The quality of the obtained system performance from the component mix is evaluated. After that the components are varied according to optimal search rules in the optimisation algorithm. The different system configurations are compared and optimal ones are recommended. Each main problem is associated with sub-problems which model possible system operations. The sub-algorithm is provided with the following information by the main algorithm: the system configuration, the local weather data or the renewable energy outputs, the demand, the costs for maintenance, overhaul, replacement, refuelling, and administration. The system model contains all relevant component descriptions of energy generation, conversion and distribution, and component wear. The sub-algorithm assesses the possible operating strategies with regard to life cycle costs and performance efficiency. The sub-algorithm decides which operating strategies and settings are recommendable and passes them on to the main algorithm. Different operation strategies can be envisaged. Some will always use the renewable energy sources plus the energy stored in the battery to cover demand, and switch on the diesel only if this is not possible. Or the diesel is always employed to cover demand and other energy sources are used as a back-up. In some operating strategies, the diesel, once it is switched on, is required to run for some time period. Or the diesel is only run if it has a capacity load above a certain amount. Other strategies switch on the diesel when the battery is discharged to a certain level, or only use renewable energy sources to charge the battery once it has reached a certain level of charge. Many other strategies have been researched (e.g. Barley et al., 1995). In addition to these field operating strategies, an ideal or optimum resource allocation of the available capacities can be investigated to meet the demand for electricity and vice versa, based on demand, weather and component performance estimates. Possible extension of the subproblems would be to include controllable loads to better meet supply with available demand and to allow for long-term fuel-resource, maintenance. component replacement and expansion scheduling. 2.3. output The output of the sizing and operation control algorithm is a set of component sizes for a
given application together with recommendations for system operation. The component sizes are restricted to values which reflect existing component sizes on the markets. A sensitivity analysis can be carried out to assess the impact of changes in demand, availability of renewable energies, probabilities of component failure and fuel prices. 3. HYBRID 3.1.
SYSTEM
MODEL
Introduction
The quantitative model used for describing the hybrid system contains the following elements: (1) Decision variables. Decision variables are the unknowns that are to be determined by solving the model. A specific decision is made when decision variables take on specific values. Decision variables concern component sizes, component numbers and installation settings and operating decisions: amount of battery charge or discharge current (x&, diesel output power (Xdiesel), position of switches (.~si) and routing decisions (xRi), Objective function. The objective function (2) changes value as a result of changes in the values of the decision variables. The objective function measures the desirability of the consequences of a decision. In this approach, the objective function describes a) initial equipment costs, and b) fuel and other operating costs discounted over the project planning period according to cost/benefit calculations (Marrison and Seeling-Hochmuth, 1997). (3) Constraints. The constraints restrict the range of the decision variables as a result of technological, socio-economic, legal or physical constraints on the system. The constraints in the presented approach are given by technical characteristics of battery and diesel operation and by matching demand and supply. 3.2 System component models 3.2.1. PVlwind. With weather data from the site, component output characteristics and installation details like angle and height, the energy output is calculated based on the models explained in (Schuhmacher, 1993). 3.2.2. Diesel. The diesel power output and the length of its running time is non-linearly related to fuel consumption (Morris, 1988). The
HI)
CJ L
Seelmg-Hochmuth
diesel current is the product of maximum possible nominal diesel current Idleselnaxand the diesel output decision variable .xdlese,:
at time r: fbat,max= max[O,min[l,,, ,(i ISOC,,, +(SOc‘--SOC,,,).(
ldiesel
= ~dieselmax
(1)
.ydiesel
Fuel consumption levels for different diesel sizes can be entered by the user as data points for each available diesel genset type or by scaling an entered fuel consumption curve up or down. The arising fuel consumption costs during operation are calculated as follows: fuel-costs = cost/litre . litre used = cost/litre ‘1, =lo, I
SOC(t+ l)=SOC(t)~o+Z,,,(t)~
At .r&,(t)) (3)
G is the self-discharge rate, q the charging efficiency and Z,,, the charge/discharge current. During discharge, yeis assumed to be 1. When charging, q is 0.85 to 0.65, depending on the charging current. When gassing starts at a critical state of charge SOCcrit(1,,,), q drops to 0.3 to 0.01. The battery’s state of charge is limited between maximum and minimum state of charge. The latter depend on battery type, battery current, temperature, and the battery’s age and condition. The state of charge limits produce maximum possible ranges of charge acceptance (SO&,, - SOC), discharge depth which can influence the (SOC-SOC&n), maximum possible battery current rate Zi,at,max
l-cf))iAt]]
(4)
The amount of Ibat,maxdepends on the battery’s state at each time instant. The battery’s state is described by the amount of the battery’s state of charge, by the sign of the battery current (negative sign: discharge; positive sign: charge) as well as the history of the battery. /,,,,X is given by manufacturers as around 20% of the value of nominal capacity. (’ is zero during discharge and 1 during charge. The battery current Ihat is given by decision variable _ybat times maximum possible charge or discharge current Iba,,maxat time t:
(2)
where corrfactor accounts for increases in fuel needs during start-up. Running the diesel with a low capacity factor increases fuel consumption and wear. The fuel consumption is higher than normal during a cold start of the diesel, especially under low capacity factors. Many such starting periods in a short time contribute to increased diesel wear. 3.2.3. Other energy sources. Micro-hydro generators and their performance can be modelled as well. battery model is 3.2.4. Battery. The explained in detail in Schuhmacher ( 1993). Energy losses occur when charging a battery. The battery efficiency drops further when the battery is ageing or is not operated correctly. The battery’s state of charge (SOC) is computed as follows:
SO(‘)
Ibat =vxbat
(5)
lbat,max
3.2.5. fnwrter. The inverter input current. required to satisfy the AC load current IAcioad when drawn from the inverter, is given as: I,,, =
iACload
u,,t(
ud,
e$L
1
(6)
where p*,~
i/p
rILv
= Pinv
(7)
-o/p
Manufacturers give the inverter efficiency ejj& over the inverter output power. These can be entered into the algorithm by the user or be taken from default values. The characteristic inverter curves are non-linear. If the inverter is to be sized as well, a decision variable linvmean has to be introduced which indicates the AC current regime with the most efficient operating range of the inverter. An example for possible values could be 60% of the diesel output linvmean power or maximum range of AC load current etc. 3.2.6. Batterq’ charger. The output power P o,p of the battery charger equals the input power Pi,p times the efficiency losses e& during the energy conversion: ‘O:p =
‘i/p
(8)
eflbc
where pilp
=
XRD
(9)
zdiesel uac
XRn stands for the percentage of diesel current allocated to the battery charger. (1 -xi& goes to the transfer switch between inverter, diesel and AC loads. It follows that the amount of the diesel current going to the battery charger is given by: XRD
ldiesel
= Ibc - DC
The manufacturers
udc/(uac
‘effb,
(lo)
give characteristic curves of
Hybrid-PV
battery chargers as efficiency losses efsb, versus output power. In such a curve e& depends non-linearly on the DC output power, and therefore non-linearly on the DC output current of the battery charger Z,_,. Again, the user can enter the data points of the characteristic curve or use default data points. When the operation and sizing algorithm has to choose the size of the battery charger as well, a variable I bcmeanis introduced which indicates in which current regime the maximum efficiency range for the energy conversion should lie. 3.2.7. Transfer switch. The transfer switch models the switch positions “inverter off - diesel can supply the AC loads” and “inverter on diesel does not supply the AC loads”. The switch is modelled as X,(,itch)= 1 for inverter on, and 0 for inverter off. If a parallel inverter is used, then X, E [O,l ] and both the diesel and the inverter can supply the AC load at the same time. 3.2.8. ACJDC load mix. If DC appliances are used, XR(outing) denotes the percentage of the DC bus current which is directed to the DC devices. ( 1 -xR) goes through the inverter (see Fig. 1). 3.2.9. Loads. Most common loads are 12, 24, or 36 V appliances or 220 V AC appliances. The estimated power consumption should be given in one hour to 15 minute intervals, for the length of a week, month or year. 3.3. Powerflow The system model is based of current flows through the efficiency losses. At the AC flow arriving can be described
on a description system including load the current as follows:
where zinc = ( 1 - xR >
+eff
(Ire - Ibat
‘(“acludc)‘zdiesel
.XRD)
(12)
is the current produced from the renewable energy sources. Z,, depends on the renewable component sizes chosen by the main algorithm. The demands, ZACload and IDCload,are known. The arriving current flow description at the DC-load is I,,
I DCsupply
= XR
All these variables are time-dependent. Another DC bus and multiple parallel battery and inverter devices can be included in the energy flow description. 3.4. Sizing and control setting decisions The sizing and control settings being optimised by the main algorithm concern sizes and numbers of component, installation angle and height, and controller settings. 3.5. Operation decisions The operation decision variables are collected in a vector called n whose components have to be determined by the chosen operation strategy or found in an optimisation procedure. The components of x represent routing and operation decisions:
( &cl uctc) . zdiesel . XRD)
(13)
(14)
X(t)=[XbatXdieselXSXRXRDl~t)
x = Vx(t)
for all t
(15)
The hybrid model was formulated based on the decision vector x. Within this model different operating strategies can be formulated. As an example, the operation strategy “using renewable energy sources whenever possible” is formulated as follows for an AC load only system: Routing to DC bus: x,=0, as there is no DC bus. Inverter switch position: X, = 1 (inverter on) when renewable and stored energy are enough to satisfy the demand, otherwise it is 0 (inverter off ). Battery current [%]: xbat = sign(Z,,,,). The battery current is calculated based on the rules of the operation strategy. When the diesel is employed to cover demand, the battery is charged by renewable energy and diesel. If enough renewables are there to satisfy the demand. then any oversupply of renewables is stored in the battery. I batch
= nlin[k
WGax
xs f Ik -DC
-_ (lac/effv) -
( 1 -- & )?
SOC)lAt]
( 16)
The battery is discharging if needed to supply the demand in conjunction with the renewable energy sources: I batdls
= min[O?max(&e
-
(zac/effinv)
-(SOC-SOC,i,)/At)].
(I,., - ibat
+ e%
81
energy systems
%.
(17)
Diesel output power [%]: Xdiesel=0 if enough renewable energy and energy stored in the batteries are available to cover the demand,
82
(2 d
otherwise it is the normalised power as Xdiesel
=
min[zdiesmax. +
kc
DC
beding-HochmuOl
diesel output
lacl.oad udc/(
(/,c
c%x )lil~d,esmax (18)
Where rent to battery charge
Zbc_ DC,the battery charger output curthe DC bus, charges the battery if the can accept further charge next to the from the renewable energy sources.
&-DC =min[max[(SOC,,, (zdiesmax
-
zacLoad
- SOC)IAt -Z,,,O], )
t”ac ’e.c>:“dcl
(19) Diesel routing to battery charger: if the renewable and stored energy are not enough to cover the demand, then the diesel covers the load and simultaneously charges the battery if it can accept charge
/At
-
Ire 1
udc /( uac
d&c
)l/zdiesel
( 20 )
If enough renewable and stored energy is available to cover the demand then xRD=O. Similarly, the other operating strategies are implemented. For the optimum or ideal operation strategy, the optimal vector x, denoted x*, is to be found for all instances in the time period investigated such that a minimum of the objective cost functions is achieved over that time period. 3.6. Cost function The output of minimising the objective functions are the desired decision variables for operation control settings, sizing and possibly demand management. 3.7. Initial costs The initial equipment costs are related to the size of the supply devices. The problem of minimising the initial costs is expressed as: MIN
noT TYPE. Cosf~(fype)~~,,~~, (21)
The matrix TYPE has on its diagonal a list of variables called “typei” which represent the component sizes of every component category to be optimised. Such categories are “Diesel”, “PV”, “Wind Turbine”, “Inverter”, “Battery”, “Cable”, “Converter”, “Battery Charger” etc. The optimal size can be chosen from a list of permissable sizes. TYPE is zero everywhere outside the diagonal. For example, for the com-
ponent category “PV”. the diagonal of TYPZ: can contain a value (in IQ’,)such as 40, 48. 5.1 etc. which can be changed by the optimisation process. The vector 110stands for the numbers of the component types selected for each category. The vector Costs contains costs per unir dimension prompted for the corresponding equipment types. These costs include installation, and balance of systems costs. The result of the optimisation procedure yields an optimal vector for no and !~pt (containing the diagonal values of TYPE). called type* and no*. The vectors type* and no* together indicate the optimal system configuration in Lerms of componeni sizes available on the market and the number of each component type required in the system. The minimisation of equipment costs can only be carried out in connection with the subalgorithm which deals with the operation requirements of the system. The sub-algorithm needs the operating characteristics and output characteristics of the components. 3.7.1. Oprrution costs. Operating costs for iI hybrid system constitute fuel consumption and component replacement, overhaul and maintenance costs as well as administrational costs. Sometimes costs arise from unsatisfied demand, like losses in production output. These are modelled in the cost/benefit formulation in Marrison and Seeling-Hochmuth ( 1997). Several objectives can be stated for a long life of diesel and battery components. Any operation action at time t, described by the decision variables collected in vector x(t), can cause an operation cost. The objective function for finding an optimal system operation strategy is given by: MIN
[OpCo](no,type,vT,x(T,no,type))
x,w r:lf,,.Ti (22)
where OpCo are discounted operation costs which are given by fuel consumption and other operation costs. The operation actions carried out under different operation strategies will have different effects on costs and system performance depending on the system state (indicated by state of charge, switch positions, cycling and diesel running history, weather and demand). 3.7.2. Battery degradation costs. Battery replacement costs are not easy to determine. Battery producers give a life time expectancy in terms of the number of full cycles the battery ‘survives’. This number of cycles depends on
Hybrid-PV energy systems
the battery current rate and the recommended maximum depth of discharge. However, in renewable energy systems the battery is not charging and discharging in full cycles nor with constant current regimes. Partial cycling in low states of charge wears out the battery. The amount of possible damage depends on the battery type. The energy available in a battery’s lifetime is specified through the average available energy from the battery, as calculated from averaging depth of discharges and number of corresponding cycles a battery lasts. This is put in relation with the charge provided to the battery per Ah discharge taken out of the battery during a time interval. Based on these calculation the number of battery replacements during the assumed project life can be determined and their costs can be discounted. 3.7.3. Diesel degradation costs. Diesel maintenance, overhaul and replacement costs are incurred after a certain number of hours of diesel running time. Consequently, the costs occurring during the assumed project life are detected and discounted. overall 3.7.4. S.vstem performance. The system performance of these designs is given in terms of the ratios of supplied to generated energy, and the average ratios for battery cycling and diesel loading. 3.8. Consimin t.s
83
inverter: xs E [WI) XR
The current from the DC bus is split between current going to the DC loads (&) and to the inverter ( 1 -xR). XRD
The diesel current is flowing to the battery charger (xRD) and to the transfer switch (1 -XRn;). 3.8.2. Constraints on operation. According to the objective function stated in the cost description the system will only provide energy for the lowest possible costs. Without the additional aim of demand coverage to a certain extent, the system might not be inclined to deliver any energy at all as thus no costs are incurred. Through the constraint “satisfy the demand allowing for certain tasks to be postponed or cancelled when necessary but observing the servicing of high priority tasks” the model is forced to minimise system energy prices, and is also compelled to meet the users’ demand needs with a sufficient amount of electricity. The currents of PV, wind, diesel energy production. and the battery current together with any current dumped must all add up to cover the demands as economically and efficiently as possible, taking a long-term perspective. The operational constraints can then be formulated as follows: I DCload
=
lDCsupply(
sion variables .xbat,.Ydiesel, xs, xRDand xs are:
I ACload
=
1~Cs,pp,y(26)
-ydiesel ( t,
1zdieselmax
< Pmax,diesel
I DCsupply
i”ac
(23)
The diesel current is limited to the maximum possible diesel output power divided by the system operation voltage. ~o~rn,n~t)<-~b,,
‘zbat.max(t)‘h
(24)
The battery current rate is limited to the range allowed by the battery’s state of charge limitations and operating characteristics. xs = 0 or 1
(25)
The transfer switch between inverter and diesel is either on or off (in the case of a bi-directional
(27)
E [o,l]
3.8.1. Constraints on the decision zjariables. The constraints placed on the deci-
05
i26)
E [kll
and
zACsupply
25
)
are as given in eqns ( 13)
and (15). 3.9. Genetic algorithms for design optimisation The optimisation uses genetic algorithms to solve the non-linear optimisation problem. Evolution strategies try to imitate biological evolution by creating a whole population of decision vectors through varying components randomly by processes called mutation, crossing-over and recombination. Individuals of a population, which minimise the objective function best, are chosen and some of their parameters are changed according to the above mentioned processes This is continued until no further improvement are achieved. Learning populations are such which change the mutation steps adaptively according to how good they
84
Seelinp-Hochmuth
minimise the objective function. The use of genetic algorithms instead of classical, often gradient-based. methods is recommended when a non-linear problem is encountered and the more variables in the problem are to be optimised. That is due to the fact that genetic algorithms do not require cumbersome calculations of gradients during each iteration step.
intensity of solving the constrained optimisatlon problem. From the initial 5 operation decision variables only 2 decision variables pro tune instant are left for the AC only system: _Y,,~~ (m Ibat) and ss. The constraints remaining on the decision variables are given by eqns ( 21 ) and (22).
3.10. Model,for an AC-only systm
4.
As an example, if only AC loads are considered in the system simulations (~.yRD is therefore 0), the constraint on operation (eqn (26)) can in this case be incorporated into the operation objective function as follows: I ACload
=(fre
-lbat
+
. (“ac/udc)
zdiesel
-URD)
.~f;fl,,‘(Lrd,!U,,)‘x,f(l-.~RD)‘Idiesel’(l-S~)
(28)
For x,= 1 (inverter on, diesel does not supply AC load) we obtain: XRD
. Idiesel
-k
=
&IIV )
IACload/(&c
-lbat)/(effbc
(uaciudc)) (29)
( 1 -XRD)
ldiesel
(30)
=O
if X, = 0 (inverter off, diesel can supply AC load and battery charger): ( 1 --~RD)
(31)
. zdiesel = IACload
For x,=0 it must be ensured that the current going to the inverter (eqn (14)) is zero and not wasted, since the inverter is switched off. Considering that only a charging process is possible leads to: -YRD
ldiesel
=
tzbat - Ire )heflfbc ( uac/ udi,,
C
))
(32) With zdiesel
=
zdiesel
wxRD +
zdiesel
( 1-
XRD )
RESULTS
The demand and weather profiles for which the design has been carried were entered into the algorithm. The hybrid system delivers power for a typical farming household requiring lighting, refrigeration, deep freezing, power for tools. TV, radio etc. All appliances are 220 V AC loads. A switched inverter is to be employed. The operating voltage of the DC bus is set to 36 V. PV and wind turbine life are assumed to be 20 years. The assumed diesel runtime until replacement is 20 000 hours, for overhaul 10 000 hours. Fuel costs are assumed 2R/liter. A summary of all the assumed costs, including costs for administration, installation, building, balance of system and maintenance, can be found in Marrison and Seeling-Hochmuth (1997). Figure 4 show the results of the minimisation of the energy costs in R( 1996)/kWh ( 1R =0.22 US$) over the number of iterations of the genetic algorithm. As can be seen the best individuals, marked on Fig. 6 with dots and labelled with the cost/kWh value, are constantly improved. The improved system component sizes are displayed in Fig. 5 for the best individuals taken from Fig. 4. In this specific case, the algorithm is converging towards a PV,iwind/battery system. The initial costs and life cycle costs (KC) for the recommended configuration can also be presented as pie charts. This enables to view the influence of operation and replacement costs on the overall
(3 3 )
eqns (28)-( 32) yield: zdiesel
=
( 1 -
xs)
[zACload
(&at - zre)/k.,
+
C
+
&
+
utlat
r/,c/
[zAChxd/(eff
effinv)
-zre)/(eff,c
’ (uac/udc))l
udi,, )I
(34) With Idiesel the fuel costs can be obtained. Equation (34) alleviates the computational time
11 I
II
IOI
HI
n
Ass
I?
m
-9
n
Fig. 4. Energy cost minimisation - initial genetic algorithm iterations.
Hybrid-PV
Fig. 5. Improvement
of best component during optimisation.
configurations
life cycle costs as compared to the initial purchase costs. The life cycle costs for the selected best component configurations are shown in Fig. 6. A corresponding chart with the initial costs for each component type for the best component configurations is also given (Fig. 7). The influence of the operating and replacement costs on the life cycle costs of the different components can be seen by comparing the two diagrams. In addition the algorithm provides the number of battery and diesel replacements, and the number of component overhauls necessary due to the employed operating strategy. The technical performance of the best system configurations are shown in Fig. 8 in terms of
Fig. 6. Life cycle costs for best component during optimisation.
Fig. 7. Initial costs of best component optimisation.
85
energy systems
Fig. 8. Technical
performance tions during
of best component optimisation.
configura-
overall system efficiency, average diesel loading and average state of charge. The time series of PV, wind turbine and diesel output as well as dumped energy and battery cycling are given as an extract in Fig. 9 for the recommended system configuration and the given demand.
configurations
configurations
during
Fig. 9. Time series output for an extract of 3 days: PV. wind. demand, waste in W, battery in W h and Ah for the best component configuration.
X6
G. C Seelmg-Hochmuth
The assumed length of the project life over which the costs were discounted is 20 years. During that time no replacement of the PV panels and the wind turbine was assumed. However, the battery had to be replaced 6 times. The design tool recommends a 1900 W inverter and a 2000 W battery charger. All the life cycle costs taken together over the amount of electricity supplied during the project life result in costs per unit electricity of R2.24/kW h in 1996 Rands. A flat tariff per kW h (not considering connection fees, inflation or arranged financing schemes) would amount to R4.46/kW h, when discounting revenues from selling the electricity. 5.
CONCLUSIONS
A general method has been developed to jointly determine the sizing and operation control of hybrid-PV systems. With this method the interdependency of hybrid operation strategies and system sizing can be incorporated. Operation strategies are selected by searching through possible settings for the system operation control, considering the non-linear characteristics of some components. The operation control and sizing selection method is based on genetic optimisation techniques. The algorithm is divided into a main and a sub-algorithm dealing with sizing and operation optimisation, respectively. Operation costs and system current flow descriptions depend on the operation decision settings or variables to be found. These descriptions establish the constrained optimisation model of the sizing and operation control problem. As a result an optimum system configuration is chosen by the algorithm together with a recommendation for an operation strategy and or its settings for a given site and application requirement. NOMENCLATURE
c cOrrr.,tor
costs
efff eff,,, ;luel_costs I Acs”pply I Acload I bat I batch I bat&s I \u*,max &nc I bClll.X”
Charge/discharge indicator Diesel start-up factor Vector of component costs (Rand) Efficiency of battery charger Efficiency of inverter battery charging efficiency Fuel cost measure (SA Rand) Current arriving at AC load (A) AC load current (A) Battery current (A) Charging current (A) Discharging current (A) Max bat. current at time r (A) Bat. charger DC output current (A) Max efficient bat charger o/p current
(A)
ID,
bus
I Dcsupply IDcload Id,esei IIn* Il”“mCa” Jmax I re no no* opco Pdiesel P max.dtesel P in> I,p P,“” -0’p PI’P POP ;OC SOC,,,, SOG,” sot,,,
/ ‘0 T
type type* TYPO u*, IL’ dc I x* -Xbat -Ydmcl % yri YRD
LX bus current (A j current arriving 31 DC. load ( A: DC load current 1,Z Diesel current ( 4 lnverter input current (A) Max efficient inv. n/p current (A) Max possible bat. current (A) Renewable energy current (A) Vector with numbers of devices Vector with optimal number of devices Operating cost (SA Rand) Diesel genset output power (kW) Max. diesel genset output power (kW ) lnverter input power ( \h’) lnverter output power ( W ) Bat. charger mput power (kW ) Bat. charger output power ( WI Self discharge rate State of charge (A h) Critical state of charge (A h) Minimum state of charge (A h) Maximum state of charge (A h) Time (hours) Starting time (hours) Length of time period (hours) Vector of component types (PV, wind. etc.) Optimal vector of component types Matrix with type on ist diagonal AC voltage ( v ) DC-bus voltage ( V ) Vector of decision variables Optimal decision vector Battery charge/discharge decision Diesel output decision Transfer switch position DC bus current routing (W) Diesel current routing (5%)
REFERENCES Barley, C.D.. Winn, C.B., Flowers, L., Green, H.J. ( I995 l. Optima1 Control of Remote Hybrid Power Systems. Part I: Simplified Model, In Proceedings of Windpower ‘95. Washington, DC. Bezerra, P., Hille, G., Siegler, M., Schott, T. ( 1991). Hybrid Systems for Decentral Electricity Generation: Lessons from a Brazilian-German Cooperation, In Proceedings of the World Renewable Energy Conference, Reading. Braun, H. (1993). Unit Commitment and Thermal Optimization Problem Statement, Optimization in Planning and Operation of Electric Power Systems. p. 143. Physica-Verlag, Heidelberg. Dantzig, G., Infanger, G. (1993). Approaches to Stochastic Programming with Application to Electric Power Systems, Optimization in Planning and Operation of Electrrt Heidelberg. Power Systems, Physica-Verlag, van Dijk, V.A.P., Alsema, E.A., Blok, K., Turkenberg, W.C (1991). A Simulation and Optimisation Model for Autonomous Energy Systems, In Proceedings of the World Renewable Energy Conference, Reading. FSEC Energy Short Course (1987) Photovoltaic System Design - Course Manual, Florida Solar Energy Centre, Cape Canaveral, Florida. Green, H.J., Manwell, J.F. (1995). HYBRID2 - A versatile model of the performance of hybrid power systems, In Proceedings of Windpower ‘95, AWEA conference, Washington, DC. Jansen, B., Roos, C., Terlaky, T. (1993). Interior point methodology for linear programming: duality, sensitivity analysis and computational aspects, Optimisation in Planning and Operation of Electric Power Systems, p. I1 1, Physica-Verlag, Heidelberg.
Hybrid-PV energy systems Jennings, S.U. (1994). Use of Computer Simulation in the RAPS Field, In Proceedings qf Solar ‘94 Conference. Sydney. Keiderling, S. ( 1990). Simulation und Optimierung von kombinierten Wind- und Solaranlagen tur Stromversorgung.
Berlin, VDI Verlag Lilienthal, P., Flowers, L., Rossmann, C. (1995). HOMER: The Hybrid Optimization Model for Electric Renewables, In Proceedings of Windpower ‘95, Washington, DC, March 1995. Lorenz, U. ( 1988). Elektrizitaetsversorgungsplanung fuer iaendliche Gebiete in Entwicklungslaendern-Ein Optimierungsmodell, Springer Verlag Berlin.
Marrison, C.I., Stengel, R.F. (1994). The Use of Random Search and Genetic Algorithms to Optimize Stochastic Robustness Cost Functions, Proceedings of the 1994 American Control Conference, Baltimompp. -1484- 1489. Marrison. CL. Seelina-Hochmuth. G.C. (1997). A Des&n Tool using ‘Genetip Algorithms’ to Size Hybrid Systems for Power Supply at Remote Sites, Part One: Analytic Framework. Proceedings of CASE conference on Village Electrification, New Delhi, India, in press. Morgan, T.R., (1995). SEU-ARES -A Refined Simulation Program for the Sizing and Optimization of Autonomous Hybrid Energy Systems, Proceedings qf the Annual Meeting
of the International
Solar Energ)’ Societ,y.
Harare. Morris, G.J. ( 1988). Performance evaluation of diesel and photovoltaic electricity generation applications in the Kruger National Park. NEC report, Energy Research Institute, University of Cape Town.
87
Papalexopoulos, A. ( 1993). Optimal Power Flow Packages - Requirements and Experiences, Optimization in Planning and Operation of Electric Power Systems, p. 309.
Physica-Verlag, Heidelberg. Pohlheim, H. (1995). Ein genetischer Algorithmus mit Mehrfachpopulationen zur Numerischen Optimienmg, at-Automatisierungstechnik 3 (1995), Berlin. Protogeropoulos, C.. Marshall, R.H., Brindworth, B.J. (1991). SEUIARES-A Hybrid Solar PV/Wind Simulation Program Description and Dynamic Battery Simulation Results, In Proceedings of the World Renewable Energy Conference, Reading. Sandia National Laboratories (1991). Stand-Alone Photovoltaic Systems - A Handbook of Recommended Design Practices, SAND87-7023, available from National Technical Information Service, U.S. Dept of Commerce, 5285 Port Royale Road, Springfield, VA 22161. Schuhmacher. J.. (1993 ). Universitv of Oldenbura. INSEL interactive simulation of renewable electrical energy supply systems, reference manual, renewable energy group, Dept. of Physics, PO Box 2503, D-261 11 Oldenburg. Seeling-Hochmuth, G.C. (1995). Optimisation of PV-Hybrid Energy System Design and System Operation Control using Genetic Algorithms. In Proceedings of 13’h EC PV Conjizrence, Nice. Seeling-Hochmuth, G.C., Marrison, Cl. (1997). A Design Tool using Genetic Algorithms to Size Hybrid Systems for Power Supply at Remote Sites, Part Two: Implementation, In Proceedings of CASE conference on k’illage E/ectr$cution. New Delhi. India, in press.
PII: SOO38#2X( 97)000285
Solar Energy Vol. 61, No. 2, pp. 77-87, 1997 Q 1997 Published by Elsevier ScienceLtd All rights reserved. Printed in Great Britain 0038-092X197 $17.00+0.00
A COMBINED OPTIMISATION CONCEPT FOR THE DESIGN AND OPERATION STRATEGY OF HYBRID-PV ENERGY SYSTEMS+ G. C. SEELING-HOCHMUTH* EDRC (Energy for Development Research Centre), University of Cape Town, Private Bag, Rondebosch, 7700 Cape Town, South Africa Received 17
November 1995: revised version accepted 13 January 1997 Communicated by GERARD WRIXON
Abstract-This paper presents a method to jointly determine the sizing and operation control of hybrid-PV systems. Hybrid energy systems use different energy sources such as solar and wind energy and diesel gensets. They are an economical option in areas remote from the grid. In this context the correct and cost-effective system sizing as well as efficient system operation are important. The problem becomes complicated through uncertain renewable energy supplies and load demand, non-linear characteristics of some components, and the fact that optimum operation strategies and optimum sizing of hybrid system components are interdependent. The outlined approach finds an optimum operation strategy for a hybrid system by carrying out a search through possible options for the system operation control. The search is conducted over some time period using estimated weather and demand data and long-term system component characteristics. The costing of the operating strategies is evaluated and component sizes are changed by the designed algorithm according to optimum search rules. As a result an optimum system configuration is chosen by the algorithm together with an optimum operation strategy for a given site and application requirement. 0 1997 Elsevier Science Ltd.
1.
achieved when operating ranges are better preserved. Hybrid systems are an important source of electricity not only for schools, clinics, village communities but also for farms and tourist facilities in areas remote from the grid. The design and operation control problem is non-linear due to non-linear component characteristics and the complexity of the problem. The operation control problem in the literature is called the economic power generation problem (Papalexopoulos, 1993). An optimal steady state is achieved by adjusting the available controls to minimise an objective function subject to specified operating requirements. The difficulty in solving the optimum operation control problem mostly lies in the dimension of the problem (B. Jansen et al., 1993). Control strategies which can be implemented by adjusting regulator settings and circuits or hardware configuration have been researched by Barley et al., 199.5. Both the optimum control decisions and the control operation strategies reflecting field operation are modelled in this paper. Stochastic models (Braun, 1993; Dantzig and Infanger, 1993) address uncertainties in demand, component failure and weather behaviour, but can be high in computations. A more recent methodology which can solve non-linear optimisation problems are genetic algorithms (Marrison and
INTRODUCTION
When electrifying remote areas it will be difficult and expensive to reach very remote communities solely by extending the grid. To fill this gap, a hybrid system offers an off-grid energy supply and is a combination of PV, wind, diesel and sometimes micro-hydro generators, in most cases incorporating battery storage (Fig. 1). These hybrid systems can provide power for productive uses. The cost-effective, reliable design and appropriate operation of these systerns is important. When sized and run efficiently a hybrid system is often fit for long-term autonomous operation at an acceptable price. Prolonged battery and diesel lifetimes are
%
solu -
I-
‘-I
Im
Ip’IiJcnUO DC Load
Ii AC
Dkcl
4
LOad
Fig. 1. Basic PV-hybrid system set-up. ‘Paper presented at the ISES Solar World Congress, Harare. Zimbabwe, 9-16 September 1995. $Fax: +27 2 I 650 2830; e-mail: [email protected] 77
Stengel, 1994; Pohlheim. 1995) which copy the evolutionary development of the biological world. This has been applied to the design hybrid systems in Seeling-Hochmuth ( 1995 ); ( 1997); Marrison and Seeling-Hochmuth Seeling-Hochmuth and Marrison ( 1997). and is used for the algorithm to be described in this paper. Quite a few software tools assess hybrid system performance for pre-defined system configurations (Bezerra et al., 1991, Jennings, 1994; Keiderling, 1990; Protogeropoulos ef al.. 1991; Morgan, 1995; Green and Manwell. 1995: van Dijk et al., 1991). Some of the sizing approaches for hybrid systems are paper-based and employ rule-ofthumb methods (FSEC Energy Short Course, 1987, Sandia National Laboratories, 1991). Other hybrid system sizing approaches apply software tools using a simplified and linear model (Lorenz, 1988; Lilienthal et al., 1995) or a complex model but varying the design randomly within a chosen range of component sizes (van Dijk et al., 1991). Seeling-Hochmuth (1995), describes the design of hybrid systems which considers the non-linear hybrid system description and the complex interdependence of operating strategy and sizing. Marrison and Seeling-Hochmuth (1997), formulated the appropriate cost/benefit function for the optimisation of hybrid systems which is used in this paper. The approach in this paper takes the interdependency between sizing and system operation strategy into account. The model is outlined and the developed algorithm is explained. Results are given at the end of the paper, 2. HYBRID SYSTEM DESIGN 2.1. Goals The general goals of the developed design algorithm are twofold: ( 1) sizing of PV-hybrid system components; and (2) operation control of a PV-hybrid system. A suitable system design and operation control should minimise the (1) life cycle costs system reliable guaranteeing (2) while operation. The latter objective includes satisfying demand and operating the system components such as the battery and diesel generator economically, in terms of replacement and maintenance needs.
Fig. 2. Interdependence between system operation strategy.
sizing and system
2.2. Appromh Minimising operation costs and unsatisfied demand are achieved not only by selecting an appropriate system configuration, but also by finding a suitable operation strategy and suitable settings for it, taking account of the special operational requirements (Fig. 2). The operating strategy adopted in handling the hybrid system combined with the sizing choice affects system performance as well as degradation and ageing of components. The sizing of the hybrid system is encapsulated in the so-called Main Algorithm (Fig. 3) which models the configuration and mix of system components for the initial system installation. The decision variables are the size of the capacities of diesel generator, PV, wind, battery, cables etc., and number of components, relevant installation heights or angles, and the controller settings. The system component mix is initially chosen randomly. The control settings and costs of operation strategies for a certain component mix are investigated by the imbedded subalgorithm and then passed back to the main
Fig. 3. Main and sub-algorithm.
79
Hybrid-PV energy systems
algorithm. The quality of the obtained system performance from the component mix is evaluated. After that the components are varied according to optimal search rules in the optimisation algorithm. The different system configurations are compared and optimal ones are recommended. Each main problem is associated with sub-problems which model possible system operations. The sub-algorithm is provided with the following information by the main algorithm: the system configuration, the local weather data or the renewable energy outputs, the demand, the costs for maintenance, overhaul, replacement, refuelling, and administration. The system model contains all relevant component descriptions of energy generation, conversion and distribution, and component wear. The sub-algorithm assesses the possible operating strategies with regard to life cycle costs and performance efficiency. The sub-algorithm decides which operating strategies and settings are recommendable and passes them on to the main algorithm. Different operation strategies can be envisaged. Some will always use the renewable energy sources plus the energy stored in the battery to cover demand, and switch on the diesel only if this is not possible. Or the diesel is always employed to cover demand and other energy sources are used as a back-up. In some operating strategies, the diesel, once it is switched on, is required to run for some time period. Or the diesel is only run if it has a capacity load above a certain amount. Other strategies switch on the diesel when the battery is discharged to a certain level, or only use renewable energy sources to charge the battery once it has reached a certain level of charge. Many other strategies have been researched (e.g. Barley et al., 1995). In addition to these field operating strategies, an ideal or optimum resource allocation of the available capacities can be investigated to meet the demand for electricity and vice versa, based on demand, weather and component performance estimates. Possible extension of the subproblems would be to include controllable loads to better meet supply with available demand and to allow for long-term fuel-resource, maintenance. component replacement and expansion scheduling. 2.3. output The output of the sizing and operation control algorithm is a set of component sizes for a
given application together with recommendations for system operation. The component sizes are restricted to values which reflect existing component sizes on the markets. A sensitivity analysis can be carried out to assess the impact of changes in demand, availability of renewable energies, probabilities of component failure and fuel prices. 3. HYBRID 3.1.
SYSTEM
MODEL
Introduction
The quantitative model used for describing the hybrid system contains the following elements: (1) Decision variables. Decision variables are the unknowns that are to be determined by solving the model. A specific decision is made when decision variables take on specific values. Decision variables concern component sizes, component numbers and installation settings and operating decisions: amount of battery charge or discharge current (x&, diesel output power (Xdiesel), position of switches (.~si) and routing decisions (xRi), Objective function. The objective function (2) changes value as a result of changes in the values of the decision variables. The objective function measures the desirability of the consequences of a decision. In this approach, the objective function describes a) initial equipment costs, and b) fuel and other operating costs discounted over the project planning period according to cost/benefit calculations (Marrison and Seeling-Hochmuth, 1997). (3) Constraints. The constraints restrict the range of the decision variables as a result of technological, socio-economic, legal or physical constraints on the system. The constraints in the presented approach are given by technical characteristics of battery and diesel operation and by matching demand and supply. 3.2 System component models 3.2.1. PVlwind. With weather data from the site, component output characteristics and installation details like angle and height, the energy output is calculated based on the models explained in (Schuhmacher, 1993). 3.2.2. Diesel. The diesel power output and the length of its running time is non-linearly related to fuel consumption (Morris, 1988). The
HI)
CJ L
Seelmg-Hochmuth
diesel current is the product of maximum possible nominal diesel current Idleselnaxand the diesel output decision variable .xdlese,:
at time r: fbat,max= max[O,min[l,,, ,(i ISOC,,, +(SOc‘--SOC,,,).(
ldiesel
= ~dieselmax
(1)
.ydiesel
Fuel consumption levels for different diesel sizes can be entered by the user as data points for each available diesel genset type or by scaling an entered fuel consumption curve up or down. The arising fuel consumption costs during operation are calculated as follows: fuel-costs = cost/litre . litre used = cost/litre ‘1, =lo, I
SOC(t+ l)=SOC(t)~o+Z,,,(t)~
At .r&,(t)) (3)
G is the self-discharge rate, q the charging efficiency and Z,,, the charge/discharge current. During discharge, yeis assumed to be 1. When charging, q is 0.85 to 0.65, depending on the charging current. When gassing starts at a critical state of charge SOCcrit(1,,,), q drops to 0.3 to 0.01. The battery’s state of charge is limited between maximum and minimum state of charge. The latter depend on battery type, battery current, temperature, and the battery’s age and condition. The state of charge limits produce maximum possible ranges of charge acceptance (SO&,, - SOC), discharge depth which can influence the (SOC-SOC&n), maximum possible battery current rate Zi,at,max
l-cf))iAt]]
(4)
The amount of Ibat,maxdepends on the battery’s state at each time instant. The battery’s state is described by the amount of the battery’s state of charge, by the sign of the battery current (negative sign: discharge; positive sign: charge) as well as the history of the battery. /,,,,X is given by manufacturers as around 20% of the value of nominal capacity. (’ is zero during discharge and 1 during charge. The battery current Ihat is given by decision variable _ybat times maximum possible charge or discharge current Iba,,maxat time t:
(2)
where corrfactor accounts for increases in fuel needs during start-up. Running the diesel with a low capacity factor increases fuel consumption and wear. The fuel consumption is higher than normal during a cold start of the diesel, especially under low capacity factors. Many such starting periods in a short time contribute to increased diesel wear. 3.2.3. Other energy sources. Micro-hydro generators and their performance can be modelled as well. battery model is 3.2.4. Battery. The explained in detail in Schuhmacher ( 1993). Energy losses occur when charging a battery. The battery efficiency drops further when the battery is ageing or is not operated correctly. The battery’s state of charge (SOC) is computed as follows:
SO(‘)
Ibat =vxbat
(5)
lbat,max
3.2.5. fnwrter. The inverter input current. required to satisfy the AC load current IAcioad when drawn from the inverter, is given as: I,,, =
iACload
u,,t(
ud,
e$L
1
(6)
where p*,~
i/p
rILv
= Pinv
(7)
-o/p
Manufacturers give the inverter efficiency ejj& over the inverter output power. These can be entered into the algorithm by the user or be taken from default values. The characteristic inverter curves are non-linear. If the inverter is to be sized as well, a decision variable linvmean has to be introduced which indicates the AC current regime with the most efficient operating range of the inverter. An example for possible values could be 60% of the diesel output linvmean power or maximum range of AC load current etc. 3.2.6. Batterq’ charger. The output power P o,p of the battery charger equals the input power Pi,p times the efficiency losses e& during the energy conversion: ‘O:p =
‘i/p
(8)
eflbc
where pilp
=
XRD
(9)
zdiesel uac
XRn stands for the percentage of diesel current allocated to the battery charger. (1 -xi& goes to the transfer switch between inverter, diesel and AC loads. It follows that the amount of the diesel current going to the battery charger is given by: XRD
ldiesel
= Ibc - DC
The manufacturers
udc/(uac
‘effb,
(lo)
give characteristic curves of
Hybrid-PV
battery chargers as efficiency losses efsb, versus output power. In such a curve e& depends non-linearly on the DC output power, and therefore non-linearly on the DC output current of the battery charger Z,_,. Again, the user can enter the data points of the characteristic curve or use default data points. When the operation and sizing algorithm has to choose the size of the battery charger as well, a variable I bcmeanis introduced which indicates in which current regime the maximum efficiency range for the energy conversion should lie. 3.2.7. Transfer switch. The transfer switch models the switch positions “inverter off - diesel can supply the AC loads” and “inverter on diesel does not supply the AC loads”. The switch is modelled as X,(,itch)= 1 for inverter on, and 0 for inverter off. If a parallel inverter is used, then X, E [O,l ] and both the diesel and the inverter can supply the AC load at the same time. 3.2.8. ACJDC load mix. If DC appliances are used, XR(outing) denotes the percentage of the DC bus current which is directed to the DC devices. ( 1 -xR) goes through the inverter (see Fig. 1). 3.2.9. Loads. Most common loads are 12, 24, or 36 V appliances or 220 V AC appliances. The estimated power consumption should be given in one hour to 15 minute intervals, for the length of a week, month or year. 3.3. Powerflow The system model is based of current flows through the efficiency losses. At the AC flow arriving can be described
on a description system including load the current as follows:
where zinc = ( 1 - xR >
+eff
(Ire - Ibat
‘(“acludc)‘zdiesel
.XRD)
(12)
is the current produced from the renewable energy sources. Z,, depends on the renewable component sizes chosen by the main algorithm. The demands, ZACload and IDCload,are known. The arriving current flow description at the DC-load is I,,
I DCsupply
= XR
All these variables are time-dependent. Another DC bus and multiple parallel battery and inverter devices can be included in the energy flow description. 3.4. Sizing and control setting decisions The sizing and control settings being optimised by the main algorithm concern sizes and numbers of component, installation angle and height, and controller settings. 3.5. Operation decisions The operation decision variables are collected in a vector called n whose components have to be determined by the chosen operation strategy or found in an optimisation procedure. The components of x represent routing and operation decisions:
( &cl uctc) . zdiesel . XRD)
(13)
(14)
X(t)=[XbatXdieselXSXRXRDl~t)
x = Vx(t)
for all t
(15)
The hybrid model was formulated based on the decision vector x. Within this model different operating strategies can be formulated. As an example, the operation strategy “using renewable energy sources whenever possible” is formulated as follows for an AC load only system: Routing to DC bus: x,=0, as there is no DC bus. Inverter switch position: X, = 1 (inverter on) when renewable and stored energy are enough to satisfy the demand, otherwise it is 0 (inverter off ). Battery current [%]: xbat = sign(Z,,,,). The battery current is calculated based on the rules of the operation strategy. When the diesel is employed to cover demand, the battery is charged by renewable energy and diesel. If enough renewables are there to satisfy the demand. then any oversupply of renewables is stored in the battery. I batch
= nlin[k
WGax
xs f Ik -DC
-_ (lac/effv) -
( 1 -- & )?
SOC)lAt]
( 16)
The battery is discharging if needed to supply the demand in conjunction with the renewable energy sources: I batdls
= min[O?max(&e
-
(zac/effinv)
-(SOC-SOC,i,)/At)].
(I,., - ibat
+ e%
81
energy systems
%.
(17)
Diesel output power [%]: Xdiesel=0 if enough renewable energy and energy stored in the batteries are available to cover the demand,
82
(2 d
otherwise it is the normalised power as Xdiesel
=
min[zdiesmax. +
kc
DC
beding-HochmuOl
diesel output
lacl.oad udc/(
(/,c
c%x )lil~d,esmax (18)
Where rent to battery charge
Zbc_ DC,the battery charger output curthe DC bus, charges the battery if the can accept further charge next to the from the renewable energy sources.
&-DC =min[max[(SOC,,, (zdiesmax
-
zacLoad
- SOC)IAt -Z,,,O], )
t”ac ’e.c>:“dcl
(19) Diesel routing to battery charger: if the renewable and stored energy are not enough to cover the demand, then the diesel covers the load and simultaneously charges the battery if it can accept charge
/At
-
Ire 1
udc /( uac
d&c
)l/zdiesel
( 20 )
If enough renewable and stored energy is available to cover the demand then xRD=O. Similarly, the other operating strategies are implemented. For the optimum or ideal operation strategy, the optimal vector x, denoted x*, is to be found for all instances in the time period investigated such that a minimum of the objective cost functions is achieved over that time period. 3.6. Cost function The output of minimising the objective functions are the desired decision variables for operation control settings, sizing and possibly demand management. 3.7. Initial costs The initial equipment costs are related to the size of the supply devices. The problem of minimising the initial costs is expressed as: MIN
noT TYPE. Cosf~(fype)~~,,~~, (21)
The matrix TYPE has on its diagonal a list of variables called “typei” which represent the component sizes of every component category to be optimised. Such categories are “Diesel”, “PV”, “Wind Turbine”, “Inverter”, “Battery”, “Cable”, “Converter”, “Battery Charger” etc. The optimal size can be chosen from a list of permissable sizes. TYPE is zero everywhere outside the diagonal. For example, for the com-
ponent category “PV”. the diagonal of TYPZ: can contain a value (in IQ’,)such as 40, 48. 5.1 etc. which can be changed by the optimisation process. The vector 110stands for the numbers of the component types selected for each category. The vector Costs contains costs per unir dimension prompted for the corresponding equipment types. These costs include installation, and balance of systems costs. The result of the optimisation procedure yields an optimal vector for no and !~pt (containing the diagonal values of TYPE). called type* and no*. The vectors type* and no* together indicate the optimal system configuration in Lerms of componeni sizes available on the market and the number of each component type required in the system. The minimisation of equipment costs can only be carried out in connection with the subalgorithm which deals with the operation requirements of the system. The sub-algorithm needs the operating characteristics and output characteristics of the components. 3.7.1. Oprrution costs. Operating costs for iI hybrid system constitute fuel consumption and component replacement, overhaul and maintenance costs as well as administrational costs. Sometimes costs arise from unsatisfied demand, like losses in production output. These are modelled in the cost/benefit formulation in Marrison and Seeling-Hochmuth ( 1997). Several objectives can be stated for a long life of diesel and battery components. Any operation action at time t, described by the decision variables collected in vector x(t), can cause an operation cost. The objective function for finding an optimal system operation strategy is given by: MIN
[OpCo](no,type,vT,x(T,no,type))
x,w r:lf,,.Ti (22)
where OpCo are discounted operation costs which are given by fuel consumption and other operation costs. The operation actions carried out under different operation strategies will have different effects on costs and system performance depending on the system state (indicated by state of charge, switch positions, cycling and diesel running history, weather and demand). 3.7.2. Battery degradation costs. Battery replacement costs are not easy to determine. Battery producers give a life time expectancy in terms of the number of full cycles the battery ‘survives’. This number of cycles depends on
Hybrid-PV energy systems
the battery current rate and the recommended maximum depth of discharge. However, in renewable energy systems the battery is not charging and discharging in full cycles nor with constant current regimes. Partial cycling in low states of charge wears out the battery. The amount of possible damage depends on the battery type. The energy available in a battery’s lifetime is specified through the average available energy from the battery, as calculated from averaging depth of discharges and number of corresponding cycles a battery lasts. This is put in relation with the charge provided to the battery per Ah discharge taken out of the battery during a time interval. Based on these calculation the number of battery replacements during the assumed project life can be determined and their costs can be discounted. 3.7.3. Diesel degradation costs. Diesel maintenance, overhaul and replacement costs are incurred after a certain number of hours of diesel running time. Consequently, the costs occurring during the assumed project life are detected and discounted. overall 3.7.4. S.vstem performance. The system performance of these designs is given in terms of the ratios of supplied to generated energy, and the average ratios for battery cycling and diesel loading. 3.8. Consimin t.s
83
inverter: xs E [WI) XR
The current from the DC bus is split between current going to the DC loads (&) and to the inverter ( 1 -xR). XRD
The diesel current is flowing to the battery charger (xRD) and to the transfer switch (1 -XRn;). 3.8.2. Constraints on operation. According to the objective function stated in the cost description the system will only provide energy for the lowest possible costs. Without the additional aim of demand coverage to a certain extent, the system might not be inclined to deliver any energy at all as thus no costs are incurred. Through the constraint “satisfy the demand allowing for certain tasks to be postponed or cancelled when necessary but observing the servicing of high priority tasks” the model is forced to minimise system energy prices, and is also compelled to meet the users’ demand needs with a sufficient amount of electricity. The currents of PV, wind, diesel energy production. and the battery current together with any current dumped must all add up to cover the demands as economically and efficiently as possible, taking a long-term perspective. The operational constraints can then be formulated as follows: I DCload
=
lDCsupply(
sion variables .xbat,.Ydiesel, xs, xRDand xs are:
I ACload
=
1~Cs,pp,y(26)
-ydiesel ( t,
1zdieselmax
< Pmax,diesel
I DCsupply
i”ac
(23)
The diesel current is limited to the maximum possible diesel output power divided by the system operation voltage. ~o~rn,n~t)<-~b,,
‘zbat.max(t)‘h
(24)
The battery current rate is limited to the range allowed by the battery’s state of charge limitations and operating characteristics. xs = 0 or 1
(25)
The transfer switch between inverter and diesel is either on or off (in the case of a bi-directional
(27)
E [o,l]
3.8.1. Constraints on the decision zjariables. The constraints placed on the deci-
05
i26)
E [kll
and
zACsupply
25
)
are as given in eqns ( 13)
and (15). 3.9. Genetic algorithms for design optimisation The optimisation uses genetic algorithms to solve the non-linear optimisation problem. Evolution strategies try to imitate biological evolution by creating a whole population of decision vectors through varying components randomly by processes called mutation, crossing-over and recombination. Individuals of a population, which minimise the objective function best, are chosen and some of their parameters are changed according to the above mentioned processes This is continued until no further improvement are achieved. Learning populations are such which change the mutation steps adaptively according to how good they
84
Seelinp-Hochmuth
minimise the objective function. The use of genetic algorithms instead of classical, often gradient-based. methods is recommended when a non-linear problem is encountered and the more variables in the problem are to be optimised. That is due to the fact that genetic algorithms do not require cumbersome calculations of gradients during each iteration step.
intensity of solving the constrained optimisatlon problem. From the initial 5 operation decision variables only 2 decision variables pro tune instant are left for the AC only system: _Y,,~~ (m Ibat) and ss. The constraints remaining on the decision variables are given by eqns ( 21 ) and (22).
3.10. Model,for an AC-only systm
4.
As an example, if only AC loads are considered in the system simulations (~.yRD is therefore 0), the constraint on operation (eqn (26)) can in this case be incorporated into the operation objective function as follows: I ACload
=(fre
-lbat
+
. (“ac/udc)
zdiesel
-URD)
.~f;fl,,‘(Lrd,!U,,)‘x,f(l-.~RD)‘Idiesel’(l-S~)
(28)
For x,= 1 (inverter on, diesel does not supply AC load) we obtain: XRD
. Idiesel
-k
=
&IIV )
IACload/(&c
-lbat)/(effbc
(uaciudc)) (29)
( 1 -XRD)
ldiesel
(30)
=O
if X, = 0 (inverter off, diesel can supply AC load and battery charger): ( 1 --~RD)
(31)
. zdiesel = IACload
For x,=0 it must be ensured that the current going to the inverter (eqn (14)) is zero and not wasted, since the inverter is switched off. Considering that only a charging process is possible leads to: -YRD
ldiesel
=
tzbat - Ire )heflfbc ( uac/ udi,,
C
))
(32) With zdiesel
=
zdiesel
wxRD +
zdiesel
( 1-
XRD )
RESULTS
The demand and weather profiles for which the design has been carried were entered into the algorithm. The hybrid system delivers power for a typical farming household requiring lighting, refrigeration, deep freezing, power for tools. TV, radio etc. All appliances are 220 V AC loads. A switched inverter is to be employed. The operating voltage of the DC bus is set to 36 V. PV and wind turbine life are assumed to be 20 years. The assumed diesel runtime until replacement is 20 000 hours, for overhaul 10 000 hours. Fuel costs are assumed 2R/liter. A summary of all the assumed costs, including costs for administration, installation, building, balance of system and maintenance, can be found in Marrison and Seeling-Hochmuth (1997). Figure 4 show the results of the minimisation of the energy costs in R( 1996)/kWh ( 1R =0.22 US$) over the number of iterations of the genetic algorithm. As can be seen the best individuals, marked on Fig. 6 with dots and labelled with the cost/kWh value, are constantly improved. The improved system component sizes are displayed in Fig. 5 for the best individuals taken from Fig. 4. In this specific case, the algorithm is converging towards a PV,iwind/battery system. The initial costs and life cycle costs (KC) for the recommended configuration can also be presented as pie charts. This enables to view the influence of operation and replacement costs on the overall
(3 3 )
eqns (28)-( 32) yield: zdiesel
=
( 1 -
xs)
[zACload
(&at - zre)/k.,
+
C
+
&
+
utlat
r/,c/
[zAChxd/(eff
effinv)
-zre)/(eff,c
’ (uac/udc))l
udi,, )I
(34) With Idiesel the fuel costs can be obtained. Equation (34) alleviates the computational time
11 I
II
IOI
HI
n
Ass
I?
m
-9
n
Fig. 4. Energy cost minimisation - initial genetic algorithm iterations.
Hybrid-PV
Fig. 5. Improvement
of best component during optimisation.
configurations
life cycle costs as compared to the initial purchase costs. The life cycle costs for the selected best component configurations are shown in Fig. 6. A corresponding chart with the initial costs for each component type for the best component configurations is also given (Fig. 7). The influence of the operating and replacement costs on the life cycle costs of the different components can be seen by comparing the two diagrams. In addition the algorithm provides the number of battery and diesel replacements, and the number of component overhauls necessary due to the employed operating strategy. The technical performance of the best system configurations are shown in Fig. 8 in terms of
Fig. 6. Life cycle costs for best component during optimisation.
Fig. 7. Initial costs of best component optimisation.
85
energy systems
Fig. 8. Technical
performance tions during
of best component optimisation.
configura-
overall system efficiency, average diesel loading and average state of charge. The time series of PV, wind turbine and diesel output as well as dumped energy and battery cycling are given as an extract in Fig. 9 for the recommended system configuration and the given demand.
configurations
configurations
during
Fig. 9. Time series output for an extract of 3 days: PV. wind. demand, waste in W, battery in W h and Ah for the best component configuration.
X6
G. C Seelmg-Hochmuth
The assumed length of the project life over which the costs were discounted is 20 years. During that time no replacement of the PV panels and the wind turbine was assumed. However, the battery had to be replaced 6 times. The design tool recommends a 1900 W inverter and a 2000 W battery charger. All the life cycle costs taken together over the amount of electricity supplied during the project life result in costs per unit electricity of R2.24/kW h in 1996 Rands. A flat tariff per kW h (not considering connection fees, inflation or arranged financing schemes) would amount to R4.46/kW h, when discounting revenues from selling the electricity. 5.
CONCLUSIONS
A general method has been developed to jointly determine the sizing and operation control of hybrid-PV systems. With this method the interdependency of hybrid operation strategies and system sizing can be incorporated. Operation strategies are selected by searching through possible settings for the system operation control, considering the non-linear characteristics of some components. The operation control and sizing selection method is based on genetic optimisation techniques. The algorithm is divided into a main and a sub-algorithm dealing with sizing and operation optimisation, respectively. Operation costs and system current flow descriptions depend on the operation decision settings or variables to be found. These descriptions establish the constrained optimisation model of the sizing and operation control problem. As a result an optimum system configuration is chosen by the algorithm together with a recommendation for an operation strategy and or its settings for a given site and application requirement. NOMENCLATURE
c cOrrr.,tor
costs
efff eff,,, ;luel_costs I Acs”pply I Acload I bat I batch I bat&s I \u*,max &nc I bClll.X”
Charge/discharge indicator Diesel start-up factor Vector of component costs (Rand) Efficiency of battery charger Efficiency of inverter battery charging efficiency Fuel cost measure (SA Rand) Current arriving at AC load (A) AC load current (A) Battery current (A) Charging current (A) Discharging current (A) Max bat. current at time r (A) Bat. charger DC output current (A) Max efficient bat charger o/p current
(A)
ID,
bus
I Dcsupply IDcload Id,esei IIn* Il”“mCa” Jmax I re no no* opco Pdiesel P max.dtesel P in> I,p P,“” -0’p PI’P POP ;OC SOC,,,, SOG,” sot,,,
/ ‘0 T
type type* TYPO u*, IL’ dc I x* -Xbat -Ydmcl % yri YRD
LX bus current (A j current arriving 31 DC. load ( A: DC load current 1,Z Diesel current ( 4 lnverter input current (A) Max efficient inv. n/p current (A) Max possible bat. current (A) Renewable energy current (A) Vector with numbers of devices Vector with optimal number of devices Operating cost (SA Rand) Diesel genset output power (kW) Max. diesel genset output power (kW ) lnverter input power ( \h’) lnverter output power ( W ) Bat. charger mput power (kW ) Bat. charger output power ( WI Self discharge rate State of charge (A h) Critical state of charge (A h) Minimum state of charge (A h) Maximum state of charge (A h) Time (hours) Starting time (hours) Length of time period (hours) Vector of component types (PV, wind. etc.) Optimal vector of component types Matrix with type on ist diagonal AC voltage ( v ) DC-bus voltage ( V ) Vector of decision variables Optimal decision vector Battery charge/discharge decision Diesel output decision Transfer switch position DC bus current routing (W) Diesel current routing (5%)
REFERENCES Barley, C.D.. Winn, C.B., Flowers, L., Green, H.J. ( I995 l. Optima1 Control of Remote Hybrid Power Systems. Part I: Simplified Model, In Proceedings of Windpower ‘95. Washington, DC. Bezerra, P., Hille, G., Siegler, M., Schott, T. ( 1991). Hybrid Systems for Decentral Electricity Generation: Lessons from a Brazilian-German Cooperation, In Proceedings of the World Renewable Energy Conference, Reading. Braun, H. (1993). Unit Commitment and Thermal Optimization Problem Statement, Optimization in Planning and Operation of Electric Power Systems. p. 143. Physica-Verlag, Heidelberg. Dantzig, G., Infanger, G. (1993). Approaches to Stochastic Programming with Application to Electric Power Systems, Optimization in Planning and Operation of Electrrt Heidelberg. Power Systems, Physica-Verlag, van Dijk, V.A.P., Alsema, E.A., Blok, K., Turkenberg, W.C (1991). A Simulation and Optimisation Model for Autonomous Energy Systems, In Proceedings of the World Renewable Energy Conference, Reading. FSEC Energy Short Course (1987) Photovoltaic System Design - Course Manual, Florida Solar Energy Centre, Cape Canaveral, Florida. Green, H.J., Manwell, J.F. (1995). HYBRID2 - A versatile model of the performance of hybrid power systems, In Proceedings of Windpower ‘95, AWEA conference, Washington, DC. Jansen, B., Roos, C., Terlaky, T. (1993). Interior point methodology for linear programming: duality, sensitivity analysis and computational aspects, Optimisation in Planning and Operation of Electric Power Systems, p. I1 1, Physica-Verlag, Heidelberg.
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Berlin, VDI Verlag Lilienthal, P., Flowers, L., Rossmann, C. (1995). HOMER: The Hybrid Optimization Model for Electric Renewables, In Proceedings of Windpower ‘95, Washington, DC, March 1995. Lorenz, U. ( 1988). Elektrizitaetsversorgungsplanung fuer iaendliche Gebiete in Entwicklungslaendern-Ein Optimierungsmodell, Springer Verlag Berlin.
Marrison, C.I., Stengel, R.F. (1994). The Use of Random Search and Genetic Algorithms to Optimize Stochastic Robustness Cost Functions, Proceedings of the 1994 American Control Conference, Baltimompp. -1484- 1489. Marrison. CL. Seelina-Hochmuth. G.C. (1997). A Des&n Tool using ‘Genetip Algorithms’ to Size Hybrid Systems for Power Supply at Remote Sites, Part One: Analytic Framework. Proceedings of CASE conference on Village Electrification, New Delhi, India, in press. Morgan, T.R., (1995). SEU-ARES -A Refined Simulation Program for the Sizing and Optimization of Autonomous Hybrid Energy Systems, Proceedings qf the Annual Meeting
of the International
Solar Energ)’ Societ,y.
Harare. Morris, G.J. ( 1988). Performance evaluation of diesel and photovoltaic electricity generation applications in the Kruger National Park. NEC report, Energy Research Institute, University of Cape Town.
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Papalexopoulos, A. ( 1993). Optimal Power Flow Packages - Requirements and Experiences, Optimization in Planning and Operation of Electric Power Systems, p. 309.
Physica-Verlag, Heidelberg. Pohlheim, H. (1995). Ein genetischer Algorithmus mit Mehrfachpopulationen zur Numerischen Optimienmg, at-Automatisierungstechnik 3 (1995), Berlin. Protogeropoulos, C.. Marshall, R.H., Brindworth, B.J. (1991). SEUIARES-A Hybrid Solar PV/Wind Simulation Program Description and Dynamic Battery Simulation Results, In Proceedings of the World Renewable Energy Conference, Reading. Sandia National Laboratories (1991). Stand-Alone Photovoltaic Systems - A Handbook of Recommended Design Practices, SAND87-7023, available from National Technical Information Service, U.S. Dept of Commerce, 5285 Port Royale Road, Springfield, VA 22161. Schuhmacher. J.. (1993 ). Universitv of Oldenbura. INSEL interactive simulation of renewable electrical energy supply systems, reference manual, renewable energy group, Dept. of Physics, PO Box 2503, D-261 11 Oldenburg. Seeling-Hochmuth, G.C. (1995). Optimisation of PV-Hybrid Energy System Design and System Operation Control using Genetic Algorithms. In Proceedings of 13’h EC PV Conjizrence, Nice. Seeling-Hochmuth, G.C., Marrison, Cl. (1997). A Design Tool using Genetic Algorithms to Size Hybrid Systems for Power Supply at Remote Sites, Part Two: Implementation, In Proceedings of CASE conference on k’illage E/ectr$cution. New Delhi. India, in press.