Impact of Wind Turbine Generator FOR on the Reliability and Economics of a Remote WTG system S. Sanajaoba Singh
Eugene Fernandez
Bharathikoppaka
Electrical Engineering Department Indian Institute of Technology Roorkee, Roorkee-247667, Uttarakhand, India
[email protected]
Electrical Engineering Department Indian Institute of Technology Roorkee, Roorkee-247667, Uttarakhand, India
[email protected]
Electrical and Electronics Engineering Department, Raghu Institute of Technology, Visakhapatnam-531162, India
[email protected]
Abstract—Wind turbine based generation of power is regarded as one of the renewable energy based power generation system which has received considerable global attention very recently. This paper highlights the impact of wind turbine generator force outage rate on the reliability and economics of a remote wind-battery system. The optimal system configuration is achieved through an optimization algorithm based on genetic algorithm (GA). The cost function involves the investment, operation and maintenance cost along with cost of energy not served. System reliability is assessed using Loss of load probability (LOLP) concept through Monte Carlo simulation. Keywords—wind turbine generator; force outage rate; loss of load probability; Monte Carlo simulation
I. INTRODUCTION Increasing negative impacts of global warming and hike in the price of the conventional energy sources have encouraged many countries to explore alternative options like making use of renewable energy potential for power generation. Such renewable energy sources like wind, solar etc. are environmentally friendly and promoted nowadays by various governmental policies like providing financial support in different forms and adopting various rules for penalizing conventional based energy generation facilities that emit green house gases. Improving the performance of renewable energy based power generation system is of engineering interest and various researches and development work are being carried out. There are many available literatures concerning the modeling, optimal design and evaluation of a wind energy based power generation system. A simplified model for estimating the monthly system performance of a wind energy system is developed in [1]. In [2], optimal battery size for hybrid wind energy system is calculated through assessing the impact of battery storage capacity variation on power generation. Loss of load probability (LOLP) is used in [3] to evaluate the hybrid wind energy system. In this paper, a practical evaluation model of wind power in coordination with battery backup is presented. Genetic algorithm (GA) is used to determine the optimal size of the wind-battery system through minimizing the total system cost. GA is an optimization algorithm based on the biological
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genetic process of organisms [4].The optimal wind-battery system is evaluated at different values of the wind turbine generator (WTG) force outage rate (FOR) to assess the impact of FOR on the system reliability identified with LOLP in our case. The LOLP index is calculated using Monte Carlo simulation. LOLP is the overall probability such that the total system load exceeds the total system generation capacity. LOLP value of 0 means the system is capable of fulfilling the demand and a value of 1 indicates the demand will never be fulfilled. The load demand on the system is fulfilled when the WTG generated power is sufficient and storage battery energy is not exhausted. The excess energy is stored in the batteries, when the WTG generated power is greater than load demand. Furthermore, the impact of wind turbine generator FOR on system economics is investigated by optimizing the system at different values of wind turbine generator FOR. II. WTG SYSTEM MODELLING For calculating the wind turbine generator (WTG) power output, the measured wind speed at the anemometer height is first adjusted to the corresponding hub height using the power law profile.
V (h hub) h hub V (h anem) h anem
(1)
where h hub is the hub height (m), h anem is the anemometer height (m), V (h hub) is the wind speed at hub height of the wind turbine (m/s), V (h anem) is the wind speed at anemometer height (m/s), is the power law exponent. The power output is calculated by referring the power curve of the wind turbine as [5]: 0 PWTG (a v 3 b Prated P rated
0 v vcut in and v vcut out vcut in v vrated vrated v vcut out
(2)
The constants a and b are given by the following equations:
a
b
IV. MODELING CONVERTER
Prated v rated v 3cut in 3
A converter is required for systems consisting of both AC and DC components. An inverter converts DC power to AC power and the efficiency ( ) at which the conversion takes place is assumed constant and taken as 90% with a life time of 10 years.
vcut in v
3
rated
v 3cut in
In addition, the effect of WTG force outage rate is incorporated in the WTG power output modeling. A WTG can reside in either of the following two states: fully available and unavailable. At the start of each hour, a uniformly distributed random number (u) on the interval [0, 1] is drawn for each WTG in order to decide its operating state, based on the following procedure: 1.
If u FOR , WTG is unavailable.
2.
If
u FOR , WTG is fully available.
Finally, the sequential up down up cycles of a WTG are then combined with the hourly available wind power derived from eqn. 2 to obtain the final hourly available wind power output.
The power flow in kW through the battery is given by
P t batt P t WTG Load t /con
The schematic of a remote wind-battery system is shown in fig.1. The design problem is formulated as an optimization problem with the objective of minimizing total system cost (CTotal ) subject to various design and operational constraints. The design variables include number of wind turbine generator (WTG), number of battery unit and converter. Minimize: r (1 r0 ) m CTotal Min ni Ri Ai 0 om Ri Ai CostReliability,i m (1 r0 ) 1
P
t
WTG
P t Batt ENS t
Load t
con
0 ni N
th Load t = Load during t time unit, kW.
SOCmin SOC SOCmax
con = Converter efficiency. Battery charging operation is indicated by a positive value of eqn. (3) and a negative value indicates the discharging operation of battery. The battery state of charge (SOC) is changed by the charging and discharging operation of the battery [6] and can be calculated as
P t battery l (t ) batt SOC t 1 SOC t 1 24 Ebatt
(4)
where ηbatt is battery charging efficiency in charging mode and discharging efficiency in discharging mode, σ is the self discharge rate of battery, l(t) is the length of tth time unit and Ebatt is the energy rating of battery storage. Further, the following equation constrained the battery charging and discharging operation.
P t batt,c max P t batt P t batt,d max
(5)
where ;
maximum
battery charge power. battery discharge power.
V. FORMULATION OF OPTIMIZATION PROBLEM
Subject to:
(3)
where
P t batt,d max (SOC t SOCmin ) Ebatt ;
(6)
where i WTG, Batt , Con , CostRe liability CENS EENS
III. BATTERY MODELLING
P t batt,c max (SOCmax SOC t ) Ebatt
P t inv out ( Pt WTG P t batt )
maximum
where ni represents the number of i th component, Ri is the capacity of the i th component, Ai is the unit cost (Rs/kWh) of the i th component, r0 is the annual interest rate, m is the component life time, om is the percentage operation and maintenance cost, C ENS is the cost for energy not supplied (Rs/kWh) and EENS is the expected energy not supplied in kWh/year when system load exceeds the available generation capacity. P t WTG , P t Batt , ENS t , Load t are the WTG power, charged/discharged battery power, energy not supplied and system load demand respectively at any period t , N i is the maximum number of the i th component, SOCmin and SOCmax are the minimum and maximum state of charge (SOC) value of the storage battery.
VII. DESCRIPTION OF CASE STUDY AREA A. Location The case study area has a latitude of 29038’’21’N and longitude of 79029’’56’E with a height of 1576 meters from mean sea level (MSL) and is located at Almora district of Uttarakhand, India. B. Wind resource The hourly wind speed data is taken from [8] for the period of Jan 2002 to Dec 2002. The study area experience wind speed in the range of 2-15m/s and corresponding wind speed profile is shown in fig.2. Fig. 1 Schematic of a stand-alone WTG system with battery
VI. MONTE CARLO SIMULATION Monte Carlo method (MCS) is one of the simulation techniques which utilizes random numbers for solving problems related with uncertainty analysis, optimization, and reliability based design etc [7]. MCS technique evaluates iteratively the behavior of physical systems and mathematical model (deterministic) with the help of random numbers as inputs. The use of random numbers characterizes MCS as nondeterministic and comes under the category of stochastic methods. MCS can also be regarded as a sampling method because of random generation of inputs from probability distributions in order to simulate the process of sampling from an actual population. In the current study, load demand and generation is assumed constant during each hour simulated and each state representing load demand, generation is sampled by randomly choosing an integer uniformly distributed in [1, 8760]. A. Procedure for MCS
C. Demand profile The demand profile of the study area is shown as in fig.3 which has an energy consumption of 126 kWh/day and 23.5 kW peak. The load profile is synthetic and calculated using HOMER software from the load data given in the literature [9] D. Wind turbine Wind turbine selected is a typical 3kW, 48V DC with a capital cost of Rs. 80000 and life time of 20 years. The cut in and cut out speed are respectively 3.5 m/s and 17 m/s. The percentage operation and maintenance cost is taken at 2%. E. Battery storage Batteries rated at 6V, 360 Ah (2.16kWh) are connected in series to form battery string with each string comprising of 8 batteries and capable of producing 17 kWh of electric energy. Hence, the system DC bus voltage is fixed at 48V. The capital cost is Rs. 10000 with a life time of 5 years. The percentage operation and maintenance cost is taken at 2%.
1) Input hourly generation and load state ( X i ); i =1 to 8760, initialize sample size (S ) , P=0, E=0. 2) Randomly select X j sample with size N, where X j X i ;
j 1 3) Identify X j as X failure and X success . X failure is identified when system load level is greater than total generation while X success is identified when system load is equal to or less than total generation. 4) If X j X failure then P = P+1, E E P , P is the unbalance power. 5) Do again steps 3 to 4 till j S . 6) Evaluate LOLP P S 7) Evaluate EENS
8760 E S
8) Do again steps 2 to 7 until acceptable values of LOLP, EENS or stopping criteria are reached.
Fig. 2 Wind speed profile of the study area.
Fig.3 The study area demand profile. Fig. 4 Convergence characteristic of the GA
VIII. RESULTS AND ANALYSIS The simulation work is being carried out in MATLAB programming environment. The formulated optimization problem applicable to a remote wind-battery system is solved using genetic algorithm for a fixed value of FOR (say 0.05) of the wind turbine generator unit. The convergence characteristic of the optimization algorithm is shown in fig. 4 and optimized system configuration in depicted in table I. The convergence characteristic shows that the objective function converges to final optimum value more or less after 100 numbers of iterations. Hence 150 numbers of iteration is taken as a fair stopping criterion. The GA based optimization follows the following general steps. 1.
Create initial population randomly.
2.
Evaluate the fitness of the chromosomes.
3.
Select the parents using selection function.
4.
Apply crossover and mutation to create offspring.
5.
Go to step 2 if termination criteria is not satisfied.
The optimum wind-battery system obtained using GA is evaluated at different values of wind turbine generator FOR ranging from 0 to 0.15 to investigate the impact of FOR on the system reliability identified with LOLP reliability index. The calculation of LOLP reliability index is carried out using Monte Carlo simulation. Variation of LOLP with wind turbine generator FOR for the optimal wind-battery system is depicted in fig. 5. Careful examination of fig.5 reveals that system reliability is strongly influenced by FOR of the wind turbine generator unit as the optimal system which was having a LOLP value of zero suffers from higher values of LOLP as the force outage rate values of WTG increases.
In the present case, selection function is based on tournament selection and, simulation is carried out with mutation probability and crossover ( Pm ) 0.07 probability ( Pc ) 0.83 . TABLE I. GA OPTIMIZED SYSTEM CONFIGURATION
No. of 3kW WTG
No. of battery string each of 17 kWh
Converter (kW)
Optimized Cost (Rs.)
23
20
21
897451
Fig. 5 Variation of LOLP with wind turbine generator FOR
Furthermore, the wind turbine generator FOR impact on the system optimal cost is assessed by optimizing the system size at different values of FOR. The optimization results show a significant variation of optimized cost with WTG force outage rate as shown in fig. 6. It is quite obvious from fig.6 that the optimized cost of the system increases as the force outage rate of WTG increase. Hence, both reliability and economics of the system are greatly affected by the force outage rate of WTG unit. Consequently, the physically available or unavailable states of the WTG should be suitably incorporated while modeling the WTG unit so as to be suitably used in system sizing
REFERENCES [1]
[2]
[3]
[4]
[5]
[6]
[7] [8]
[9]
Fig.6 Variation of optimized cost with wind turbine generator FOR
IX. CONCLUSIONS This paper has developed a practical evaluation model of wind turbine generator and storage backup using battery which is suitable for used in Monte Carlo simulation. The developed models are applied for obtaining the optimal windbattery system while minimizing the total system cost through optimization by GA. The impact of wind turbine generator FOR on the optimal system reliability and cost is investigated considering a study area located in remote Almora district of Uttarakhand, India. It is found that the WTG force outage rate greatly influence the reliability and optimized cost of the system. Hence, WTG force outage rate is a detrimental system parameter while modeling wind turbine unit. The methodology and model presented in this paper should prove to be useful to system planners for accurately calculating the optimal system size. APPENDIX Values of constant used in the study.
0.2% / day , batt 75% (charging), batt 100% (discharging), SOCmax 100% 336 (Rs/kWh), ( power law exp onent ) 1/7, hhub 25m , hanem 10m
SOCmin 40% , con 90% , CENS
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