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EN 618

Assignment 1

Submitted by: Arun P

Roll No.: 04417001

Title of the paper: Multiobjective optimal unit sizing of hybrid power generation systems

utilizing photovoltaic and wind energy

Authors: Ryohei Yokoyama, Koichi Ito, Yoshiro Yuasa

Journal: Journal of Solar Energy Engineering (Vol.116, November 1994)

Objective

The paper proposes a methodology for optimal system sizing of hybrid energy systems

involving photovoltaic and wind generators. An optimisation problem has been

formulated and solved to obtain the combinations of the system components subject to

optimum annual cost and energy consumption.

Decision context

Hybrid energy systems integrate different energy conversion devices which may

include conventional and renewable resources. The optimum design of such systems is

important because of the following factors:

(i) high capital cost and relatively low conversion efficiencies of the renewable energy

components in such systems

(ii) variability of the renewable resource with the weather conditions requires storage

systems to ensure a continuous energy supply

The designer is required to select the optimum component ratings for a given location and

specified load conditions such that the desired objective is satisfied subject to the limiting

constraints involved.



The schematic of the hybrid system is given in Figure 1.

Figure 1. System configuration

Variables

(1) Photovoltaic system model

APA surface area of photovoltaic array (m2)

EPA photovoltaic array electric power (kW)Hk solar radiation on inclined array surface (kW/m

2)

T air temperature (0C)

ηPA photovoltaic array efficiency

(2) Wind generator system model

a,b non dimensional coefficients for performance characteristics of windturbine generators

EWG wind turbine electric power (kW)

NWG number of wind turbine generators

V wind speed (m/s)Vc cut in wind speed (m/s)

Vf furling wind speed (m/s)

Vr rated wind speed (m/s)WBT storage level of battery (kWh)

(3) Economic optimisation

C capital (unit) cost of device (dollar/unit, e.g. dollars/m2)

Cc annual capital cost (dollars/year)

Co annual operational cost (dollars/year)J combined objective function

J1 first objective function (annual total cost, dollars/year)

J2 second objective function (annual energy consumption, kWh/year)R capital recovery factor



w weight for objective functionμ ratio of period of demand side management to annual operational periodφ unit cost of electricity (dollars/kWh)

System modeling

The individual component models are developed to study the performance of the overall

system.

Photovoltaic system

The power output from the photovoltaic array is a modeled as a function of the air

temperature (ToC) and solar radiation on inclined array surface (kW/m

2)

The total array output is given as

PAPAu

PA Ak E k E )()( = (1)

where

PAk PAu

k H k T f k E η )())(()( = (2)

gives the power output from the unit area of the device.

Wind turbine generator

The power output from the wind turbines are modeled as given below.

It is assumed that multiple wind turbine generators of identical capacity are installed

The total power output from N wind turbines given by,

WGWGu

WG N k E k E )()( = (3)

where

the power output from individual turbine is given by

⎪⎪

⎩

⎪⎪

⎨

⎧

≤

<≤

<≤−

<

=

))((0

))((

))(()/)((

))((0

)(

33

k V V

V k V V E

V k V Vc E bV k aV

V k V

k E

f

f r

u

WG

r

u

WGr

c

WGu (4)



Battery storage

The battery storage equations are obtained taking the power conversion efficiencies in

charging and discharging. Storage at any time step is related to that at the previous time

step and the charging/discharging process as

)/)()(()()1( out

BT

out

BT

in

BT

in

BT BT BT k E k E t k W k W η η −Δ+=+ (5)

this is subject to the limits of the minimum and maximum storage levels and the

allowable limits of power in charging/discharging

Receiving device

The power of the receiving device is limited by the following constraints:

The energy purchased from the grid should not exceed the rating of the receiving device

and the contract demand

EPbuy E k E ≤)(

buybuy E k E ≤)( (6)

Further the amount of reverse power (which is sold to the grid) can not exceed the rating

of the receiving device

EPsell E k E ≤)( (7)

Energy balance

Energy balance and supply demand relationships for the overall system based on the

system configuration so that the demand is met at all times is given by

)()()( k E k E k E PW RT WGPA =+ η

)()()()( k E k E k E k E disp

in

BT

d

PW PW ++= (8)

)()()()())()()(( k E k E k E k E k E k E k E d

sellPT buyTS IV disp

out

BT

d

PW +=++++ η η

The model equations are algebraic relations which essentially give an input- output

relation for the components and provide the limits of its operating levels.



System optimisation

The optimum system configuration (photovoltaic array area, number of wind generators,

capacity of storage battery, capacity of receiving device) which minimizes the total

annual cost and annual energy consumption is determined.

For the system, the annual total cost includes the sum total of the capital cost and the

annual operation and maintenance costs.

oc C C J +=1 (9)

The annual energy consumption is given by

∑ Δ=k

buy t k E J )(2 (10)

The optimization problem is solved as a multiobjective problem with objectives with

mutual conflict. To obtain the set of Pareto optimal solutions under these conditions, a

weighting method of solution is adopted with different values for the weight with the

combined objective function given as:

21)1( wJ J w J +−= (11)

Solution procedure

A hierarchical optimization procedure is follwed to determine the device capacities and

operational strategies. At the upper level, the optimal unit sizing problem is solved to

minimize the value of J (as a non linear programming (NLP) using sequential

programming method) (equation (9)) subject to the constraints that the maximum value of

energy deficit should be zero. Scenarios with demand side management are also

considered which effectively brings down the total demand to be satisfied. To assess the

operational strategy for individual configurations, a simulation based method is utilized

using the system performance equations and the overall energy balance (equations 1-8).

The solution procedure is given in Figure 2.



Figure 2. Solution procedure

Validation

The paper has discussed a sizing methodology with the use of separate models for the

individual components. The validation of the individual models based on

measured/experimental data is not presented but specific references have been cited.

A numerical study is illustrated to show the validity and effectiveness of the optimal

sizing method using the input data for a location specified by the authors (350 N, 135

0E)

with known hourly load distribution for representative days.

Parametric variation

The effect on system sizing with changes in the following have been considered

(i) weight for objective function

(ii) effect of sale of electricity to the grid (system A and B)

Start: Initial values of system capacities, contract

demand

Whether combinedobjective function is

minimized?

Change thevalues of system

capacities,

contractdemand

System

simulation

based oncomponent

characteristicsand energy

balance

Demand

Receive

purchase power fro

grid

Solar insolation

Ambient

temperature

Wind s eed

Optimal values of systemcapacities, contractdemand

Yes No

Optimal unit sizing by

Non linear programming

Operational planning bysimulation



(iii) effect of demand side management

Conclusions

• An approach for multiobjective unit sizing for grid connected hybrid photovoltaic-wind energy system is presented.

• The trade-off relations between cost and energy savings is illustrated by generating a

set of a Pareto optimal solutions.

• Demand side management has an overall positive effect in terms of reduced ratings of

renewable energy based generators and contract demand when the objective function

gives weight to energy savings/environmental protection.

Comments

• The effect of demand side management has been taken in the model based on the

overall duration when it is exercised. It would be of interest if the illustration had

mentioned and described the specific measures in the context of grid connected

hybrid systems. Further the effect on the time of the day when demand side

management is applied and whether that has a significant effect on the system

performance should have been discussed.

• The assumption of the number of wind turbines to be a continuous variable may not

be applicable in practical system planning.

• The objective function being an economic parameter, it would be useful to consider

the sensitivity with respect to the various cost parameters.

• It should be noted that weighting approach can not generate the entire Pareto set for

non-convex problems. It would be of interest to the reader if the motivation for the

choice of weighting method had been presented.

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