Economical and Reliable Design of a Hybrid Energy System in a Smart Grid Network

Abstract

In this chapter, we introduce a hybrid wind turbine, photovoltaic, and fuel cell energy system intending to minimize the overall cost to increase the designed hybrid system’s efficiency. In our study, the associated costs in the objective function consist of initial investment costs, operational and maintenance costs, and the cost related to loss of load. To find the optimal solution with the nonlinear mixed-integer function, we utilized particle swarm optimization algorithm, and also we implemented an approximate reliability model to assess the reliability. The findings show that the overall cost of the designed hybrid system is optimized with the present value of the loss of energy expectation and total cost for 20 years, $0.13 (*10⁻⁶) and $2.59 (*10⁻⁶), respectively, which are noticeable, with respect to satisfactory ranges of reliability indexes.

Appendix

1.1 Nomenclature

A:

Wind speed’s coefficient

A_inv:

Probability of inverter availability

A_PV:

Probability of PV array availability

A_WT:

Probability of WT availability

C:

Cost function

C_loss:

Average cost of loss because of unmet load ($/kWh)

C_max:

Cost function, maximum value

C_min:

Cost function, minimum value

C_total:

Total cost

CC_i:

Equipment cost of initial investment i ($/unit)

CD(mt):

Demand cost in month m and time t ($/kWh)

CP(t):

Power purchase cost at time t ($/kWh)

D :

Vector description, P-R

D(t):

Load demand at time t (kW)

E :

Emission function

E_HST(t):

Stored energy of HST at time t (kW)

E _max :

Emission function, maximum value

E _min :

Emission function, minimum value

E _total :

Total emission (kg)

EC :

Emission cost ($/kWh)

EENS :

Expectation without energy

ELF :

Equivalent loss factor

ELF _max :

Equivalent load failure, maximum value

Er :

Emission rate (kg/kWh)

f _HGPS :

Probability function for WT and PV

f _system :

Probability function for WT, PV, and inverter

G(t) :

Incident solar irradiation to panel surface (W/m²)

h :

Height of WT (m)

h _ref :

Height of reference (m)

HHV _H2 :

Higher heating value for hydrogen (39.7 kWh/kg)

I :

Equipment index

K :

Constant

L :

Useful lifetime of project

LOE(t) :

Loss of energy at time t

LOL(t) :

Loss of load at time t

LOEE :

Loss of energy expectation

LOLE :

Loss of load expectation

m :

Counter

m_HST(t):

Hydrogen stored mass in HST at time t (kg)

MC _i :

Maintenance and operation cost of equipment i ($/kWh)

n :

Counter

N :

Number of times for the loss of load

N _i :

Number of equipment i in HGPS (kW or kg)

N _PV :

Total number of PV

N _var :

Number of problem dimension

N _WT :

Number of WT

${n}_{PV}^{fail}$ :

Failure number of PV

${n}_{WT}^{fail}$ :

Failure number of WT

NPC _i :

Net present cost for the equipment i ($/kWh)

NPC _loss :

Net present cost for the unmet load ($/kWh)

P _el-HST :

Electrolyzer’s output power (kW)

P _furl :

WT’s output power at cutout wind speed (kW)

P _FC-inv :

Fuel cell’s output power (kW)

P _HGPS-el :

Input power for the electrolyzer (kW)

P _HGPS-inv :

Renewable resources injected power to inverter (kW)

${P}_{HGPS}\left({n}_{WT}^{fail},{n}_{PV}^{fail}\right)$ :

Renewable power resources injected to DC bus

P _HGPS (t) :

Produced power by HGPS at time t (kW)

P _HST-FC (t) :

Power of HST injected to fuel cell (kW)

P _inv-load :

Injected power to the load (kW)

P _load (t) :

Load demand at time t (kW)

P _network,max :

Electrical network’s maximum power (kW)

Pnetwork,max(mt) :

Electrical network’s maximum power in month m, time t (kW)

P _network (t) :

Electrical network’s purchase power at time t (kW)

P_PV PV :

Array’s output power (kW)

P_PV,rated PV :

Array’s nominal power (kW)

P _s :

Probability of state s occurrence

P _WT :

WT’s output power (kW)

P _WT,max :

WT’s maximum output power (kW)

P _d :

Demand price ($/kWh)

Pr(t) :

Electrical network’s power price at time t ($/kWh)

PWA :

Interest rate

Q _s :

Loss load (kWh)

R :

Same dimension vector as P

round :

Function of rounding

RC _i :

Replacement cost for the equipment i ($/unit)

s :

All possible states

T :

Time index

T _s :

Duration of loss of load at state s

v _W :

Wind speed (m/s)

v _{cut in} :

Cut-in wind speed for WT (m/s)

v _{cut out} :

Cutout wind speed for WT (m/s)

v _rated :

Wind speed rate (m/s)

${v}_W^h$ :

Wind speed height h (m/s)

${v}_W^{ref}$ :

Reference height of wind speed (m/s)

β :

A number greater than 1

Δt :

Simulation Time (1 day)

η _el :

Efficiency of electrolyzer

η _FC :

Efficiency of FC

η _HST :

Storage system’s efficiency

η _inv :

Efficiency of inverter

η _PV,conv :

Efficiency of converter DC/DC

θ :

Add an angle value to x

θ _PV :

Incident solar irradiation angle (rad)