energy storage system

Electrical Power and Energy Systems 43 (2012) 262–279

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GA based frequency controller for solar thermal–diesel–wind hybrid energy generation/energy storage system Dulal Ch. Das ⇑, A.K. Roy, N. Sinha Electrical Engineering Department, NIT Silchar, Assam, India

a r t i c l e

i n f o

Article history: Received 19 July 2011 Received in revised form 11 May 2012 Accepted 14 May 2012 Available online 23 June 2012 Keywords: Genetic algorithm Aqua electrolyzer Fuel cell Diesel engine generator Battery energy storage system Wind turbine generator

a b s t r a c t Wind, Solar photovoltaic and solar thermal power systems are emerging renewable energy technologies and can be developed as viable options for electricity generation in future. In this paper, autonomous hybrid generation systems consisting of wind turbine generators (WTGs), solar thermal power system (STPS), solar photovoltaic (PV), diesel engine generators (DEGs), fuel cells (FCs), battery energy storage system (BESS), flywheel (FW), ultra capacitors (UCs) and aqua electrolyzer (AE) have been considered for simulation studies. The power system frequency deviates for sudden changes in load or generation or the both. The comparative performance of the controllers installed to alleviate this frequency deviation for different hybrid systems, is carried out using time domain simulation. In practice, controllers (PI or PID) are tuned manually which is difficult and time consuming. The computational intelligence has opened paths to a new generation of advanced process control. Here, GA is used for optimization of controllers’ gains of the proposed hybrid systems. The simulation results demonstrate the effectiveness of the GA based controllers in terms of reduced settling time, overshoot and oscillations. The results are compared with conventional controllers. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction In recent years the increasing concerns about the limited fossil fuel resources led to the awareness that the amount of energy import should be decreased so as to become less dependent of oil exporting countries. Further, the impact of fossil fuel on the environment, especially the global warming and the harmful effects of carbon emissions have created a new demand for clean and sustainable energy sources. Wind, sea, solar, biomass, geothermal powers are sustainable energy sources. Among these, wind and solar have the potential to make significant contribution and hence assume great importance. Fuel cell (FC) also has the potential [1] to be considered as one of the green power sources of the future. Off-grid electricity can be generated by single source system such as using solar photovoltaic panels, wind turbine generators, micro-hydro plants, or fuel-powered combustion engine generator sets, or by combining two or more of these electricity generating sources in a so called hybrid system. The systems often include

Abbreviations: GA, genetic algorithm; AE, aqua electrolyzer; DEG, diesel engine generator; WTG, wind turbine generators; FC, fuel cells; FW, flywheel; BESS, battery energy storage system; PS, power system; PV, solar photovoltaic; STPS, solar thermal power system. ⇑ Corresponding author. Tel.: +91 9435172774; fax: +91 3842 233797. E-mail addresses: [email protected] (D.Ch. Das), anjan_kumarroy@ rediffmail.com (A.K. Roy), [email protected] (N. Sinha). 0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2012.05.025

energy storage in the form of batteries. A hybrid system can supply power AC or DC or both [2]. Component or system control or both is used to regulate the overall system operation. Various optimization approaches, such as, genetic algorithm, particle swam optimization, artificial neural network, are applied to optimize the gains of the controllers used in automatic generation control. These techniques have not yet been reported to apply in the field of hybrid energy systems for optimization of controller gains. In [3,4] hybrid system studies proportional plus integral (PI) controller is used to regulate the output powers from distributed generation system to achieve power balance condition due to sudden variations in generation and load. The gain values of PI controller are chosen by trial and error method. In [5] the conventional PI controller has traditionally been tuned by the method described in Ziegler and Nichols. The controller gains once tuned for a given operating point are only suitable for limited operating point changes. Therefore, the use of the conventional PI controller does not meet the requirements of the robust performance [5]. Moreover, when the number of parameters to be optimized is large, conventional technique for optimization is certainly not preferred one. In this article, the genetic PI, PID controllers are tuned using GA technique. The GA is finding widespread applications in systems optimizations. As an intelligent control technology the GA can give robust adaptive response with nonlinearity, parameter variation and load disturbance effect [6–8]. Basics of genetic algorithm are

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Nomenclature

Df Ksys

system frequency deviation frequency characteristic constant of hybrid power system GSYS(s) transfer function of hybrid power system PDEG output power of diesel generators GDEG(S) transfer function of diesel generator gain of diesel generator KDEG TDEG time constant of diesel generator PFC output power of fuel-cell generators KFC gain of fuel cell time constant of fuel cell TFC GFC(S) transfer function of fuel-cell generators PBESS power of battery energy storage system PSTPS output power to solar thermal power system GSTPS (S) transfer function of solar thermal power system Ts time constant of solar collector(s) TT charging time constant of the thermal turbine gain of the solar collector KS KT gain of the thermal turbine GBESS(S) transfer function of battery energy storage system KBESS gain of battery energy storage system time constant of battery energy storage system TBESS GUC (S) transfer function of ultra capacitors

illustrated in [9]. The results of applying the genetic PI, PID controllers to the hybrid-power system are compared to those obtained by the application of a conventional PI, PID controllers respectively. Simulated results show that the GA based controllers provide improved dynamic performance than fixed gain conventional controllers. The genetic controllers also show better transient performance for load disturbances. 2. Proposed hybrid system The general block diagram of the proposed hybrid system is shown in Fig. 1. Table 1 shows the parameters [3] of the proposed hybrid system. The system consists of wind turbine generators, diesel generator, fuel cell, aqua electrolyzer, solar thermal and battery energy storage system. The power supplied to the load is the sum of output powers from wind turbine generators, diesel generator, fuel cell and battery energy storage system. The aqua electrolyzer is used to absorb the fluctuations of wind turbine generator and produce the hydrogen gas which is used as input to fuel cell generator. The mathematical models with first order transfer func-

Φ

TUC GAE(S) PAE KAE TAE PS PL DPe M D PWTG GWTG(S) KWTG TWTG PPV GPV(S) TPV GFW(S) PFW TFW

time constant of ultra capacitors transfer function of aqua electrolyzers aqua electrolyzers power gain of the aqua electrolyzer time constant of the aqua elctrolyzer total power generation to the system Average power absorbed by loads. error in power supply and demand inertia constant of the hybrid power system damping constant of the hybrid power system power output of wind generator transfer function of wind generator gain of wind generator time constant of wind generator output power of solar photovoltaic system transfer function of solar photovoltaic time constant of solar photovoltaic transfer function of flywheel power of flywheel time constant of flywheel

tions for wind turbine system, fuel cell, aqua electrolyzer, PV system, diesel engine generator are shown in this section [10]. 2.1. Wind turbine model The output of wind turbine generator depends on the wind speed at that instant. The characteristic of wind turbine generator is illustrated in [3]. The wind turbine system contains several nonlinearities. When a wind turbine uses its pitch controller to counteract utility grid frequency oscillations, its output power varies between maximum, or rated power, and zero power. Hence, the pitch angle setpoint is nonlinearly limited by these boundaries. The pitch system, which turns the pitch angle according to wind speed, introduces a nonlinearity. The wind turbine can be simplified to a first order system. The transfer function of the WTG is represented by a first-order lag [10] as

GWTGðSÞ ¼

K WTG sT WTG þ 1

ð1Þ

Fig. 2a illustrates the wind farm model; it produces randomly variable wind power. Random output fluctuation is derived from white noise block with a low pass filter [11]. This model has been included in study case2. 2.2. Solar thermal power system Recently, trough solar power and solar power tower are two solar thermal power systems (STPS) that are being explored and

Table 1 Parameters of proposed hybrid system. Gains

Fig. 1. Block diagram of hybrid system.

KWTG = 1.0 KAE = 1/500 KDEG = 1/300 KFC = 1/100 KBESS = 1/300

Time constants (s) KUC = 7/10 KFW = 1/100 KPV = 1 KS = 1.8 KT = 1

TWTG = 1.5 TAE = 0.5 TDEG = 2 TFC = 4 TBESS = 0.1

TUC = 0.9 TFC = 0.1 TPV = 1.8 TS = 1.8 TT = 0.3

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1

1800 s + 1 _ Band limited white noise

+

+

_ x

+

_

+ +

X %

Output

300s 300 s + 1

Initial load

gain

sqrt

Fig. 2a. Wind firm model.

researched all over the world. They can be hybridized with wind, fossil fuel, etc. Trough solar power plant consists of large fields of parabolic trough collectors with the bending of single-direction. Each collector has a linear parabolic-shaped reflector that focuses the sunlight onto a linear receiver located at the focus of the parabola to heat working fluid (oil or water) in the pipes into some certain temperature (393 °C) [12]. Then, the steam is created by the heat transfer equipment and drive the steam turbine to generate electricity. Solar power tower use high-temperature heat from concentrated solar radiation by focusing the radiation on a tower-mounted heat exchanger (receiver). The system consists of large numbers of sun-tracking mirrors called heliostats to reflect the incident sunlight onto the receiver. The heat transfer fluids (water or other fluids) heated by solar thermal energy in the receiver heats water to generate high temperature steam (up to 560 °C) to drive the turbine to generate electricity. Currently, the total efficiency of the solar power tower that has been built is about 13%, and the efficiency of the sunlight collection and heat absorption is approximately 70%, as in [13]. The changing weather and the alternation of the day and night, demands heat storage technology to supply energy continuously like fossil boiler. In heat storage technology the heat energy collected by collector heats the working fluid in receiver, and thus thermal energy in the receiver is passed to the thermal storage medium in the thermal storage container. There are three main thermal storage medium, molten salt, high temperature oil and water. Because of the storage, power output from the turbine generator remains constant through fluctuations in solar intensity and until all of the energy stored in the hot tank is depleted. Energy storage are very important for the success of solar power tower technology, and molten salt is believed to be the key to cost effective energy storage [14].

Fig. 2c. Variable load model.

These plants are best suited for utility-scale applications in the 30–400 MW range [15]. At present, in Italy, Spain, Japan, France, and the United States experimental facilities are built to prove that solar power towers can produce electricity and to prove and improve on the individual system components The list of the solar thermal power stations include the 354 MW Solar Energy Generating Systems power installation in the USA, Solnova Solar Power Station (Spain, 150 MW), Andasol solar power station (Spain, 100 MW), Nevada Solar One (USA, 64 MW), PS20 solar power tower (Spain, 20 MW), and the PS10 solar power tower (Spain, 11 MW). The 968 MW Blythe Solar Power Project, located in California’s Mojave Desert, is the world’s largest solar thermal power plant project currently under construction [16]. The solar thermal power industry is growing rapidly, with about 1.17 GW of concentrating solar power (CSP) plants online as of 2011 [17] 582 MW of them are located in Spain, and the United States has 507 MW of capacity. About 17.54 GW of CSP projects are under development worldwide, and the United States leads with about 8.67 GW. Spain ranks second with 4.46 GW in development, followed by China with 2.5 GW [17]. In this paper, we consider the transfer function for the solar thermal power model as

GSTPS ðSÞ ¼

KS KT  Tss þ 1 TT s þ 1

ð2Þ

Fig. 2b illustrates the solar thermal power system model; it produces randomly variable solar thermal power. Random output fluctuation is derived from white noise block with a low pass filter. This model has been included in study case2.

Fig. 2b. Variable solar thermal power model.

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the solar radiation, and Ta is ambient temperature in degree Celsius. The value of PPV depends on Ta and U because g and S are constant. For low frequency domain analysis it is represented by a first order lag transfer function model given as [10]

Start

Create initial population

GPV ðSÞ ¼

K PV T PV s þ 1

ð4Þ

2.4. Diesel generator Generation=1

Diesel engine produces the torque, driving the synchronous machine generating the electrical power output. Because of sudden changes in load demands by the consumers, it is important that the diesel prime mover has a fast dynamic response and good capabilities of disturbance rejection. A diesel generator is a nonlinear system because of presence of a nonlinear, time-varying dead time between the injection and production of the mechanical torque. Engine model gives the description of the fuel consumption rate as a function of speed and mechanical power at the output of the engine. The transfer function describes relation between fuel consumption and engine mechanical power [21]. In this paper, diesel generator is modeled by a simple first order transfer function given by [10]

Evaluate fitness value

Perform Selection Crossover and Mutation process

GDEG ðSÞ ¼

K DEG T DEG s þ 1

ð5Þ

No Generation=Gen eration+1

Generation> max. Generation

2.5. Aqua electrolyzer Aqua electrolyzers are used to absorb the rapidly fluctuating output power from wind turbine generators and solar thermal power system and generate hydrogen. The generated hydrogen is stored in the hydrogen tank and used as fuel for fuel. The decomposition of water into hydrogen and oxygen can be achieved by passing the electric current between the two electrodes separated by aqueous electrolyte. The transfer function model of aqua electrolyzer can be expressed by [10]

Yes Repalce with new parameter

GAE ðSÞ ¼

End

K AE T AE s þ 1

ð6Þ

Since a typical AE consists of several power converters, time constant of the AE is very small [10].

Fig. 3. Flowchart of GA algorithm.

2.6. Fuel cell 2.3. Photovoltaic power system PV power supplied to the utility grid is gaining more and more visibility, while the world’s energy demand is steadily increasing. With reduction in the system cost (PV modules, dc/ac inverters, cables, fittings and manpower), the PV technology has the potential to become one of the main renewable energy sources for the future electricity supply [18]. The characteristic of PV system is illustrated in [19]. Large PV system generates dc voltage that is converted into ac using dc–ac converter. For extracting maximum power, under a given irradiance and cell-surface temperature, a PV array should operate near at the peak point of the VP curve. Various maximum power point tracker (MPPT) techniques have been discussed in [20]. Power output (in Watts) of a PV array which varies with irradiance and cell-surface temperature, of a PV system is given by [10]

PPV ¼ gSUf1  0:005ðT a þ 25Þg

ð3Þ

where g is the conversion efficiency of the PV array (9% to 12%), S (=4084 m2) is the measured area of the PV array, U (kW/m2) is

Fuel cell generates power through the electrochemical reaction between hydrogen and oxygen. Fuel cell offer alternatives to conventional generators, such as diesel generators, that would allow power to be produced without noise or on-site pollutants. A typical fuel cell produces a small dc voltage that is converted into ac using dc–ac converter. To create enough voltage, the cells are layered and combined in series and parallel circuits to form a fuel-cell stack. Fuel-cell developers claim a higher efficiency than traditional combustion technologies. The only drawback, as fuel-cell proponents

Table 2 Parameters of GA. Parameter

Value

Selection method Population size Crossover probability Mutation probability Maximum no of generation Time limit

Roulette 20 0.8 0.01 100 400 s

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Table 3 Simulation conditions for each case. Case

Subsystems

Simulation time (s)

Operating conditions

1.

WTG, STPS, AE, FC, DEG, BESS and Load

120

2. 3.

WTG, STPS, AE, FC, DEG, BESS and Load WTG, AE, FC, DEG,BESS, FW, PV and Load

400 120

4.

WTG, PV, AE,FC, DEG, BESS, UC and Load

120

PWTG = 0.5 p.u at 0 < t < 40 s =0.4 p.u at t > 40 s PSTP = 0.36 p.u at 0 < t < 40 s =0.18 p.u at t > 40 s PL = 1 p.u at 0 < t < 40 s =1.1 p.u at t > 80 s Randomly variable WTG, STPS and load (Figs. 2a, 2b and 2c PWTG = 0.5 p.u at 0 < t < 40 s =0.4 p.u at t > 40 s PSPV = 0.2 p.u at 0 < t < 40 s =0.1 p.u at t > 40 s PL = 1 p.u at 0 < t < 40 s =1.3 p.u at t > 80 s PWTG = 0.5 p.u at 0 < t < 40 s =0.4 p.u at t > 40 s PSPV = 0.2 p.u at 0 < t < 40 s =0.1 p.u at t > 40 s PL = 1 p.u at0 < t < 40 s =1.3 p.u at t > 80 s

0

PID GA

-1

PID

-2

PI GA (dotted line) PI

Frequency deviation (Hz)

-3 0

1

2

3

4

5

6

7

8

At t=40s wind power changes from .5 p.u to .4 p.u and solar thermal power changes from .36 p.u to .18p.u

0.4 0.2 0 -0.2 -0.4

Load demand at t=80s increased by 10% 0

20

40

60

80

100

120

Time (s) PID GA

0 -0.1

PI GA (dotted line)

-0.2 -0.3

PID

PI 80

80.5

81

81.5

82

82.5

83

83.5

84

84.5

85

Fig. 4a. Frequency deviation.

concede, is that hydrogen is still more expensive than other energy sources such as coal, oil and natural gas. Fuel cell generator is a higher order model and has non linearity. For low frequency domain analysis it is represented by a first order lag transfer function model given as [10]

K FC GFC ðSÞ ¼ T FC s þ 1

ð7Þ

2.7. Load model To examine effects of loading power demand variation a variable load model is developed as shown in Fig. 2c. The random

fluctuation is generated from white noise block, using low-pass and high-pass filters respectively [11]. This model has been included in study case2. 2.8. Battery energy storage system The short time power fluctuation from wind, solar or solar thermal causes large problems for power systems operation. A possible solution is storage of wind energy. Due to very good technical characteristics (large energy density, fast access time) the battery energy storage system has been an effective energy storage technology to store large amount of wind energy [22]. They can supply the system with a large amount of the power in a short

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1.2

PS (p.u)

1 Load demand at t=80s increased by 10%

0.8

At t=40s wind power changes from .5 p.u to .4 p.u and solar thermal power changes from .36 p.u to .18p.u

0.6

Error in supply and demand (p.u)

0.4 0.2

0

20

40

60

80

100

120

100

120

0.2 Load demand at t=80s increased by 10% 0 -0.2 At t=40s wind power changes from .5 p.u to .4 p.u and solar thermal power changes from .36 p.u to .18p.u

-0.4 -0.6 0

20

40

60

80

Time (s) Fig. 4b. Total power generation, error between supply and demand.

PAE (p.u)

x 10 0 -5

(p.u) DEG

P (p.u)

PI GA

PI

PID 0

20

40

60

80

100

PI

0.4

120

PID

0.3 0.2

PI

PI GA

0.1 0

BESS

PID GA

-10 -15

P

-3

0

20

40

60

80

100

120

100

120

0.4

PID (broken line)

0.3

PI GA (dotted line)

PID GA (solid line)

0.2

PI

0.1 0

P

FC

(p.u)

0

20

0.3

40

60

80

PI

0.2

PI

0.1

PI

PID

0

0

20

40

60

80

100

120

Time (s) Fig. 4c. Power outputs of DEG, BESS, FC and input power to AE.

time, or large amount of energy for a longer period. The battery energy storage system (BESS) consists of a battery bank and a power converter [23] that interfaces the battery bank to the autonomous utility grid. A higher power capacity can be achieved by connecting more modules. The transfer function model of battery energy storage system expressed by first order as [10]

GBESS ¼

K BESS T BESS s þ 1

ð8Þ

2.9. Ultra capacitor Ultra capacitor or super capacitor also called double layer capacitor, is an emerging device for energy storage. It stores charge in a double layer formed on a large surface area of micro-porous material such as activated carbon [24]. It has specific energy in the range of 1–10 W h/Kg and high specific power in the range of 1000–5000 W/Kg. The charge/discharge efficiency (85–98%) and rate of discharge (0.3–30 s) very high. It offers large capacitances

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Power (p.u)

1.2 1 Load demand

0.8

Wind power

0.6 0.4 0.2 0

Sola thermal power 0

20

60

40

80

120

100

Time (s) Fig. 4d. Output power of WTG, STPS and load demand.

Table 4 Gains of PI/PID controllers. Gains

Conventional values

GA Values Initial values

Case

Case1

Case2

PI controllers KpAE KiAE KpFC KiFC KpDG KiDG KpBESS KiBESS

37.765 78.728 42.32 31.22 0.924 12.12 68.3613 51.8013

4.523 7.632 13.4087 3.22 18.2187 51.1674 25.245 22.89

0.72973 0.59154 0.51306 1.42127 0.07901 2.72918 0.27692 0.49676

PID controller KpAE KiAE KdAE KpFC KiFC KdFC KpDG KiDG KdDG KpBESS KiBESS KdBESS

38.25 13.32 3.23 26.4087 1.22 48.33 13.2187 33.2187 52.4187 12.45 15.89 8.4187

3.25 1.32 3.23 26.4087 2.3063 25.2087 23.2187 33.1674 22.4187 12.45 15.89 4.33

0.97616 0.89971 0.1819 0.1880 0.40789 0.76931 1.49502 1.91876 1.45962 2.98137 1.1906 1.37537

in the order of thousands of farads but at a low voltage of about 2.5 V [25]. The combination of ultra capacitors and batteries can take the advantage of each kind of device to yield a power source of high power capability and longer run time. Neglecting all the non-linearities, the transfer function of ultra capacitor is given by first order lag:

K UC GUC ðSÞ ¼ T CU s þ 1

Final values

Case1

Case2

Case1

Case2

82.75 53.50 19.3669 64.892 1.799 27.336 60.112 23.839

43.13781 95.61633 49.1506 64.8009 1.10444 12.16335 80.98984 81.40701

9.29387 14.6409 14.86331 7.9815 23.16815 77.22128 49.1466 56.2557

8.78383 7.49308 8.21164 3.9685 11.7998 4.65816 5.50992 8.2296 11.7168 4.5548 10.673 4.1531

51.5119 30.5922 5.5998 44.06883 13.82331 69.06256 32.86629 62.9723 93.25501 .30806 96.3875 17.4479

5.3743 29.0454 4.12819 26.94917 1.22521 39.79462 36.87804 58.7816 48.85845 47.9564 35.4999 13.0584

rotation [28]. When the machine works as generator, the electrical energy is delivered to the load. The rotor of a flywheel made of composite materials instead of steel because of the composite’s

Best: 0.076383 Mean: 0.076491

10

Best fitness Mean fitness

9

ð9Þ

8

The few day power variation can be balanced by hydrogen based energy storage, while the short time turbulent power pulsation produced by wind turbine generator or solar thermal power system can be balanced by flywheel energy storage drive [26]. It is more suitable for repetitively absorbing and releasing electric energy for a short period of time than a battery energy storage system [27]. The flywheel energy storage is rediscovered nowadays for wide range of powers due to its advantages over the other energy storage systems: reliability, long-life, cost, fast response [26]. Flywheel energy storage systems operate by storing energy mechanically in a rotating flywheel. The generating motor is used to rotate the flywheel and to generate electricity from flywheel

Fitness value

7

2.10. Flywheel energy storage system

6 PI

5 4 3

Best fitness

2

Mean fitness

1 0

10

20

30

40

50

60

70

80

90

100

Generation Fig. 4e. Plot of fitness function value versus generation of PI controller.

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D.Ch. Das et al. / Electrical Power and Energy Systems 43 (2012) 262–279 Table 5 Gains of PI/PID controllers. Gains

Conventional values

GA values

Case

Case3

Case4

Case3

Case4

Case3

Case4

PI controllers KpAE KiAE KpFC KiFC KpDG KiDG KpBESS KiBESS KpFW KiFW KpUC KiUC

128.458 165.030 346.161 125.781 438.806 249.846 883.791 222.807 212.577 20.804  

454.99 165.03 756.594 890.493 18.806 149.846 143.394 78.134

6.139 6.04287 0.79194 12.5062 13.6039 6.1856 15.290 6.27937 12.9208 14.1064  –

0.82912 6.0699 60.6407 21.1007 101.603 36.9765 45.3288 59.7032

199.724 14.2427 1093.392 235.783 761.7839 307.2137 1233.473 299.7437 275.9768 87.8673

1151.078 200.1604 1459.82157 2475.596 33.633 179.718 179.72 113.031   223.53 402.184

PID controller KpAE KiAE KdAE KpFC KiFC KdFC KpDG KiDG KdDG KpBESS KiBESS KdBESS KpFW KiFW KdFW KpUC KiUC KdUC

127.354 124.337 111.232 121.383 72.514 227.43 132.383 102.332 261.321 42.163 29.343 34.312 73.263 53.343 21.982 – – –

93.234 79.234 80.234 189.234 60.836 115.236 187.072 129.524 215.437 92.543 61.301 21.592 – – – 23.05 35.259 37.27

Initial values

45.95 120.84

1 2 Ix 2

ð10Þ

where I is the moment of inertia and x is the angular velocity. The moment of inertia is the integral of the square of the distance ‘x’ from the axis of rotation to the differential mass ‘dmx’.

Best: 0.073716 Mean: 0.073822

10

Best fitness Mean fitness

9 8

Fitness value

7 6 5 PID

4 3

26.3288 59.7032

0.74396 1.6877 0.90822 0.61832 0.59072 0.27792 0.66389 1.7228 0.31928 1.4110 0.39014 1.26201 0.18747 0.01812 0.77666 – – –

ability to withstand the rotating forces exerted on the flywheel. In order to store energy the flywheel is placed in a sealed container which is then placed in a vacuum to reduce air resistance. The amount of energy stored by flywheel may be given by

E¼

Final values

0.86331 1.7363 0.46776 0.74395 0.6490 0.30614 1.23508 1.676 1.9795 0.62173 1.09345 1.54876  – – 1.07492 0.57599 1.13049

I¼

Z

X 2 dmx

116.36 83.9926 90.0618 292.9134 74.1479 224.6159 340.888 182.8237 331.591 148.2045 81.8494 23.0866  – – 27.33 55.357 64.025

ð11Þ

The solution for a cylindrical flywheel of mass ‘m’ and radius ‘r’ is

I ¼ m  r 2 and E ¼

1 m  r 2  x2 2

ð12Þ

The amount of energy stored varies linearly with the moment of inertia of the flywheel and the square of its angular velocity. Flywheels can be designed for low-speed or high-speed operation. A low-speed flywheel has the advantages of lower cost and the use of proven technologies when compared to a high-speed flywheel system. The main disadvantages are less stored energy per volume, higher losses, and increased volume and mass [29]. Since the energy stored is proportional to the square of angular velocity, increasing the angular speed increases stored energy more effectively than increasing mass. But increasing angular speeds results in increased frictional losses and hence thermal problems. With the help of magnetic bearing technology, the frictional losses due to bearings can be overcome, but at the expense of reliability. The transfer function of flywheel energy storage system can be expressed as first order lag [10]

GFW ðSÞ ¼

Mean fitness

32.4048 7.48314 73.4854 301.32 6.4479 327.0205 435.38163 235.8074 415.6806 80.3064 50.289 41.0712 36.468 87.343 172.119 – – –

K FW T FW s þ 1

ð13Þ

2

2.11. Power and frequency deviations

Best fitness

1 0 10

20

30

40

50

60

70

80

90

100

Generation Fig. 4f. Plot of fitness function value versus generation of PID controller.

In order to provide good quality of supply to the consumers it is very important maintain the scheduled frequency under varying demand and supply conditions. Frequency can be maintained at desired level by maintaining the active power balance between

D.Ch. Das et al. / Electrical Power and Energy Systems 43 (2012) 262–279

Load demand (p.u)

270

1.01 1.005 1 0.995 0.99 0

50

100

150

200

250

300

350

400

0

50

100

150

200

250

300

350

400

0

50

100

150

200

250

300

350

400

PWTG (p.u)

P

STPS

(p.u)

0.2

0.18

0.16

0.36 0.34 0.32 0.3 0.28

Time (s) Fig. 5a. Load demand, output power of STPS and WTG under. Randomly varying conditions.

Gsys ðsÞ ¼

Frequency deviation

2.12. Genetic algorithm

PID GA

-1

PI

-2

PID

-3 -4 0

1

2

3

50

100

150

4

5

6

7

8

200

250

300

350

400

0 -1 -2

0

Time (s) Fig. 5b. Frequency deviation.

the generation and demand. A hybrid system with wind/solar/solar thermal as one of the generating unit requires special control strategies because of highly fluctuating nature of wind. The strategies to be adopted to alleviate mismatch between generation and demand can either be by controlling the fuel to diesel electric power-generating unit or by rescheduling. The conventional approach normally uses a PI or PID controller. The use of GA based frequency control is more efficient method. In this paper power control strategy is obtained by difference between the power demand reference PL and total power generation PS.

DP e ¼ P S  P L

ð14Þ

Because system frequency is changed with net power variation, the system frequency variation Df is calculated by [10]

Df ¼

ð16Þ

PI GA

0

1

Df 1 1 ¼ ¼ DPe K sys ð1 þ sT sys Þ Ms þ D

DPe K sys þ D

ð15Þ

Since an inherent time delay exists between system frequency variation and power deviation, the transfer function for system frequency variation to per unit power deviation can be expressed by [10]

The GA is an optimization technique inspired by the principles of Darwinian Theory of natural selection, a biological process in which stronger individual is likely to be the winners in a competing environment. It was first proposed by Holland in 1975 [9]. Since then it has been useful in solving a wide variety of optimization problem including problems in which the objective function is discontinuous, non-differentiable, stochastic, highly nonlinear, or highly complex problems [30]. Fig. 3 presents an illustrative flowchart of the GA algorithm implementation. The algorithm begins by creating a random initial population. Then it creates a sequence of new generations. At each step, the algorithm uses the individuals in the current generation to create the next generation. In order to create new generation, the algorithm computes the fitness value each member of the current population. Selects parents based on their fitness. Highly fit individuals have a higher probability of being selected and producing children for next generation. The selected individuals are then improved through application of three basic operators i.e., Selection, Crossover and Mutation. The algorithm is repeated for many generations and stops when one of the stopping criteria is met. The steps of the genetic PID controllers are summarized as follows: Step 1: Create a population of initial solution of parameters (Kp, Ki, Kd). Each parameter in the problem is called as a gene. A Chromosome consists of the genes and thus each chromosome represents a solution to the problem. Step 2: Evaluation of objective function. In the present problem, Integral Square of the frequency deviation is to be minimized. For each chromosome, the MATLAB model is simulated and J is computed. Step 3: Evaluation of fitness function. The degree of fitness of a solution is qualified by assigning a value to it. This is done by defining a proper fitness function to the problem. Since GA is used for minimization problems, the objective function is the fitness function.

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1.004

PI with gains optimized under varying wind, solar thermal and load (broken line) 1.002

1

PI GA with gains optimized under varying wind, solar thermal and load (solid line)

0.998

P (p.u)

200 2

205

210

215

220

225

230

235

240

245

250

S

1 0 0

50

100

150

200

250

300

350

400

Time (s) PID with gains optimized under varying wind, solar thermal and load (dotted line)

1.004 1.002 1

PID GA with gains optimized under varying wind, solar thermal and load (solid line)

0.998 0.996 200

205

210

215

220

225

230

235

240

245

250

Fig. 5c. Total power generation.

-3

PAE (p.u)

x 10 0 -10 -20

PID 0

50

100

P

DEG

(p.u)

0.5

PID GA (solid line)

(p.u) BESS

P

PID

250

300

350

400

PI (dotted line)

PI GA 0

50

100

150

200

250

300

350

400

250

300

350

400

250

300

350

400

PI GA

0.1 0.08 0.06

PID GA 0

(p.u)

200

0.4

0.04

FC

150

0.45

0.35

P

PID GA, PI GA, PI

50

PI

PID 100

150

200

0.04 0.02

PID GA

PID

PI

PI GA

0 0

50

100

150

200

Time (s) Fig. 5d. Output power of DEG, BESS, FC and input power of AE.

Step 4: Generation of offspring: Offspring is a new chromosome obtained through the steps of selection, crossover and mutation. After fitness of each chromosome is computed, parent solutions are selected for reproduction. It emulates the survival

of the fittest mechanism in nature. Following the selection of parent population, crossover and mutation are performed to generate offspring population. The crossover and mutation are performed based on the probability of crossover and mutation.

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Step 5: Replace the current population with the new population. Step 6: Terminate the program if termination criterion is reached; else go to step2.

Best: 0.056832 Mean: 0.057107

10

Best fitness Mean fitness

9 8

J¼

Z

a

ðDf Þ2 dt

7

Fitness value

In PID controller design methods, the most common objective function are integrated absolute error (IAE), the integrated of time weight square error (ITSE) and integrated of squared error (ISE), etc. These three integral performance criteria have their own advantages and disadvantages. In this paper, integral of the square of frequency deviation is chosen as the objective function.

PID

6 5 4

Mean fitness

3

ð17Þ

0

2

Minimize J

Best fitness

1

Subject to K min  K p  K max p p

ð18Þ

0

10

20

30

40

50

60

70

80

90

100

Generation

ð19Þ

 K d  K max K min d d

ð20Þ

Typical range selected for each of Kp, Ki, Kd is [2000 to 2000]. The minimization of the objective function or the fitness function is implemented to determine the optimal parameters of PID controllers. The gains of PI controllers are optimized in the similar manner. Genetic algorithm (GA) is a computationally simple and powerful algorithm and has been employed successfully in the field of sociology, science and technology. However, it has some limitations. GA may require long processing time to get a near-optimum solution. Moreover, there is a degradation in efficiency when applied to highly epistatic objective functions (i.e., where the parameters being optimized are highly correlated), the crossover and mutation operations cannot ensure better fitness of offspring because chromosomes in the population have similar structure and their average fitness are high toward the end of the evolutionary process [31–33]. However, the scope of the present work is to compare the competence of GA with conventional one. This has been performed using GA Toolbox in MATLAB/SIMULINK considering the following parameters as shown in Table 2. 3. Simulation results and analysis In this section, dynamic performances of the proposed hybrid generation systems are analyzed using time-domain simulation. The responses of different combinations under various operating points and disturbance conditions are presented with optimum gain settings of conventional and GA based PI and PID controllers respectively. In the conventional optimization approach, a sequential optimization method is used where one parameter is optimized at a time using ISE criterion keeping the other parameters fixed. Then this operation repeats for every other parameters intern to complete one iteration of optimization. The following four cases, as shown in Table 3 are considered for case studies. 3.1. Time-domain analysis:case1 In this case, during 0 < t 6 40 s, the average wind power and solar thermal power is kept 0.5 p.u and 0.36 p.u respectively. Load demand is 1 p.u during 0 < t 6 80 s. After 40 s wind power and solar thermal power is suddenly decreased to 0.36 p.u and 0.18 p.u respectively. At t = 80 s load is suddenly increased from 1 p.u to 1.1 p.u. The deviation in generation and load is automatically ad-

Fig. 5e. Plot of fitness function value versus generation of PID.

Best: 0.09982 Mean: 0.10009 10 Best fitness Mean fitness

9 8 7

Fitness value

 K i  K max K min i i

6 5 PI

4 3

Mean fitness

2

Best fitness

1 0

10

20

30

40

50

60

70

80

90

100

Generation Fig. 5f. Plot of fitness function value versus generation of PI.

justed by fuel cell, battery energy storage device and diesel generator through the controllers since the wind and solar thermal generator generate constant power. The power generation in this case can be expressed by

PS ¼ P DEG þ PWTG þ PSTPS þ P FC  P AE  PBESS

ð21Þ

The power system frequency fluctuates due to these sudden changes in power generation by wind and solar thermal and load demand. This deviation in frequency is controlled by the controllers (PI/PID) and the outputs of system components are automatically adjusted to corresponding values such that the error in supply demand and the deviation in frequency are minimum. Fig. 4d shows the step changes in wind, solar thermal power and load demand. When wind power decreased from 0.5 p.u to 0.4 p.u, solar thermal power reduced from 0.36 p.u to 0.18 p.u after 40 s, and the load increased from 1 p.u to 1.1 p.u suddenly at 40 s, the power outputs of the fuel cell, battery energy storage, and diesel generators are increased to different values for different controllers. Thus, the mismatch in generation and demand is alleviated. Finally the frequency settles to a steady state value. The gain values of the

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6

-3

x 10

PI-GA with gains optimized using step change in wind, solar thermal and load

4 X: 86.69 Y: 0.003928

2

X: 86.53 Y: 0.002428

0

Frequency deviation (Hz)

-2 -4

PI-GA with gains optimized undervarying wind, solar thermal and load

80 5

85

90

95

50

100

150

100

105

110

115

120

200

250

300

350

400

0 -5 10

0 -3 x 10

Time (s) PID-GA with gains optimized under varying wind, solar thermal and load

X: 89.27 Y: 0.006324

PID-GA with gains optimized using step change in wind, solar thermal and load

5 X: 89.12 Y: 0.004954

0

-5 80

85

90

95

100

105

110

115

120

Fig. 5g. Frequency deviation.

0.4 PI GA

0.2 0 -0.2 -0.4

PID GA

-0.6

Frequency deviation (Hz)

-0.8 -1 -1.2 0

1

0.5

1.5

1

2

2.5

3

80

100

120

0 -1 -2 0

20

40

60

Time (s) PI GA(dotted line)

0 PID

PID GA (solid line)

-0.5

PI

PID

PI GA PI

-1

0

PID GA

0.5

1

1.5

2

2.5

Fig. 6a. Frequency deviation.

controllers obtained through conventional and GA technique and are given in Tables 4 and 5. The power outputs of the fuel cell, battery energy storage, diesel generators and input power to AE are presented in Fig. 4c. During 4–8 s, AE, which uses GA based PID or PID controller, absorbs some power as generation is higher than

load demand. Input to this AE for the remaining period is zero. Fig. 4a shows the frequency deviation of the hybrid power system. It may be observed that that the response of PID controller is the best amongst PI and PID controllers considered for study in terms of peak transient deviation and settling time. Further, it is observed

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2 1.5 1 0.5

PS (p.u)

0

0

20

40

60

80

100

120

Time (s) 1.4

PID GA (solid line) PID (broken line line)

1.3 1.2

PI PI GA

1.1 1 79.9

80

80.1

80.2

80.3

80.4

80.5

80.6

80.7

80.8

80.9

Fig. 6b. Total power generation.

P

BESS

(p.u)

0.4 0.3

PI

PID (broken line) 0.2

PI GA

PID GA (solid line)

0.1 0

PAE (p.u)

0

20

x 10

0

PI GA

-4

(p.u)

80

100

120

60

80

100

120

100

120

PID, PI

PID GA 0

DEG

60

-2

-6

P

40

-3

20

40

0.5 0.4 0.3 0.2 0.1

PI

PID GA

PI GA PID (broken line) 0

20

40

60

80

PI

PID

PID GA

PI GA

0.2

P

FW

(p.u)

0.4

0

P

FC

(p.u)

0

20

40

60

80

100

120

PI GA 0.2

PI

0.1

PID

PID GA

0 0

20

40

60

80

100

120

Time (s) Fig. 6c. Output power of BESS, DEG, FW, FC and input power of AE.

that the performance of all the GA optimized controllers is better than their respective counterparts optimized using conventional method. Fig. 4b represents total power generation and error in

supply demand. The plots of fitness function value versus generation for PI and PID are shown in Figs. 4e and 4f respectively. In all the cases PID represents conventional PID.

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1.2

X: 81 Y: 1.3

Load demand

Power (p.u)

1 0.8 X: 39.96 Y: 0.5

0.6

Wind

X: 77.28 Y: 0.4002

0.4 X: 39.96 Y: 0.2

0

0

20

Solar

X: 47.67 Y: 0.1014

0.2

40

60

80

100

120

Time (s) Fig. 6d. Load demand, output power of WTG and PV.

Best: 0.2703 Mean: 0.27141

10

8

8

7

7

6 5

Mean fitness

4

PID

3

6 5

PI

4

Mean fitness

3

Best fitness

2

2

1 0

Best fitness Mean fitness

9

Fitness value

Fitness value

9

Best: 0.27895 Mean: 0.27963

10

Best fitness Mean fitness

Best fitness

1 10

20

30

40

50

60

70

80

90

100

Generation

10

20

30

40

50

60

70

80

90

100

Generation

Fig. 6e. Plot of fitness value versus generation of PID controller.

Fig. 6f. Plot of fitness value versus generation of PI controller.

3.2. Time-domain analysis: case2 In this study, simulation time considered is 400 s. In order to examine the effects of practically variable wind, solar thermal and load power on dynamic performance of the hybrid system, randomly variable wind, solar thermal power and load model are considered. These models are shown in Figs. 2a, 2b and 2c respectively. The net power generation in this case also may be expressed by

PS ¼ PDEG þ PWTG þ PSTPS þ PFC  PAE  PBESS

0

ð22Þ

Fig. 5a shows the load demand, output power of solar thermal system and output power of wind generators under randomly varying conditions. In order to eliminate the mismatch between generation and load demand, the output power of the battery energy storage system, diesel generators and the fuel cells are altered by installing controllers. The power outputs of these generating systems are changed to different values for different controllers. This in turn alleviates the frequency fluctuation of system. The output powers and input power to the AE are presented in Fig. 5d. It is observed that AE, which uses PID controller, absorbs a small amount of power as generation is higher than load demand. Input power to AE, which uses any of the other controllers, remains zero. The plots of fitness function value versus generation for PID and PI are shown in Figs. 5e and 5f respectively. Figs. 5b, and 5c shows the frequency deviation, and total power generation for conventionally optimization

technique as well as GA optimization technique. It is observed that the performance of all the GA optimized controllers is better than their respective counterparts optimized conventional method. However, the GA based PID controller out-performed the conventionally optimized PI, and PID and the GA optimized PI controllers. The gain values of the controllers obtained through conventional and GA technique and are presented in Table 4. The initial and final values of GA optimized parameters are also presented in this table. Further, in order to examine the robustness of the GA optimized controllers, their performance with their gains optimized using step change load, wind power, solar thermal power are compared with the controllers with their gains optimized under varying load, wind and solar thermal power. Comparative performance of these controllers may be observed from the responses of frequency deviation as shown in Fig. 5g. It may be observed that there is a negligible frequency and power difference between the two. This shows the robustness of the controllers.

3.3. Time-domain analysis: case3 In this case, the hybrid system comprises of wind turbine generator, solar photovoltaic, aqua electrolyzer, diesel engine generator, battery energy storage system and flywheel energy storage system. The combination of photovoltaic power system, wind generator, diesel engine and energy storage systems increases the

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1 PI (broken line)

0.5 PID GA(solid line)

0 PID

-0.5

Frequency deviation (Hz)

PI GA (dotted line)

-1 0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 -0.2 -0.4 0

20

40

60

80

100

120

Time (s) 0.2 PI GA (dotted line)

PID GA(solid line)

0 -0.2

PID PI (broken line)

-0.4

80

80.5

81

81.5

82

82.5

Fig. 7a. Frequency deviation.

2 1.5 1

0

S

P (p.u)

0.5 0

20

40

60

80

Time (s)

1.5

100

120

PI PI GA PID PID GA

1.4

3.4. P. Time-domain analysis: case4

1.3 1.2 1.1 1 80

80.2

80.4

80.6

80.8

81

Fig. 7b. Total power generation.

In this case the hybrid system considered is same as case3 except that flywheel is replaced by ultra-capacitor. In order to examine the fact that ultra capacitor delivers high power within a short duration of time during peak load demand it is incorporated in hybrid system. The net power generation in this case may be expressed as

PS ¼ P DEG þ PWTG þ PPV þ PFC  PAE  PBESS  PFW

reliability [34]. The flywheel energy storage system is incorporated because it is capable of mitigating the short time power fluctuation due to intermittent generation of wind generator and PV system. The net power generation in this case may be expressed as

PS ¼ PDEG þ P WTG þ PPV þ PFC  PAE  PBESS  PFW

the power outputs of the fuel cell, battery energy storage system, flywheel, diesel generators and input power to AE are also increased to different values for different controllers respectively. This in turn, alleviates the mismatch in generation and demand. Finally the frequency settles to a steady state value. Figs. 6a and 6b, represents respectively, the frequency deviation of system and total generation. The plots of fitness function value versus generation for PID and PI are shown in Figs. 6e and 6f respectively. The power outputs of the fuel cell, battery energy storage system, flywheel, diesel generators and input power to AE are shown in Fig. 6c.

ð23Þ

The power system frequency fluctuates due to these sudden changes in power generation by wind and solar photovoltaic and load demand. This deviation in frequency is controlled by the controllers (PI/PID) and the outputs of system components are automatically adjusted to corresponding values such that the error in supply demand and the deviation in frequency are minimum. Fig. 6d shows the step changes, solar photo voltaic, wind power and load. When wind power decreased from 0.5 p.u to 0.4 p.u at 40 s, solar photo voltaic power reduced from 0.2 p.u to 0.1 p.u at 40 s and the load increased from 1 p.u to 1.8 p.u suddenly at 80 s,

ð24Þ

The power system frequency fluctuates due to these sudden changes in power generation by wind and solar photovoltaic and load demand. This deviation in frequency is controlled by the controllers (PI/PID) and the outputs of system components are automatically adjusted to corresponding values such that the error in supply demand and the deviation in frequency are minimum. Simulation results are shown in Figs. 7a–7f. Fig. 7d shows the step changes in solar photo voltaic, wind power and load. When wind power decreased from 0.5 p.u to 0.4 p.u at 40 s, solar photo voltaic power reduced from 0.2 p.u to 0.1 p.u at 40 s and the load increased from 1 p.u to 1.3 p.u suddenly at 80 s, the power outputs of the fuel cell, battery energy storage system, ultra capacitor, and diesel generators are increased to different values for different controllers respectively. This in turn, alleviates the mismatch in generation and demand. Finally the frequency settles to a steady state value. Figs. 7a, and 7b, represents respectively, the frequency deviation of system, total generation. The plots of fitness function value

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(p.u)

1

PID GA (solid line)

PI GA (dotted line)

P

UC

0.5

PI (broken line) 0

0

20 x 10

40

PID

60

80

100

120

60

80

100

120

-4

(p.u)

0

PI (solid line) PID GA, PID

P

AE

-10

PI GA -20 0

20

40

0.06

(p.u)

PID 0.04

BESS

PI (dotted line) 0.02

P

PID GA

0

PI GA(solid line) 0

20

40

(p.u)

0.1

60

PI (broken line)

80

100

120

PID PID GA

0.05

P

FC

PI GA (solid line)

0

(p.u)

0

40

60

80

PID

PI (broken line)

0.1

P

DEG

0.2

20

100

120

100

120

PID GA

PI GA (dotted line)

0 0

20

40

60

80

Time (s) Fig. 7c. Output power of UC, BESS, FC, DEG and input power of AE.

1.4 X: 81 Y: 1.3

1.2 Load demand

Power (p.u)

1 0.8 X: 11.2 Y: 0.4993

0.6

X: 45.98 Y: 0.4021

Wind

0.4 X: 10.39 Y: 0.1994

Solar photovoltaic

0.2

X: 96.91 Y: 0.1

0 0

20

40

60

80

100

120

Time (s) Fig. 7d. Load demand, output power of WTG and PV.

versus generation for PID and PI are shown in Figs. 7e and 7f respectively. The power outputs of the fuel cell, battery energy storage system, ultra capacitor, diesel generators and input power to AE are shown in Fig. 7c.

4. Conclusion The autonomous hybrid generation/energy storage system requires an automatic generation control system to eliminate the

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method. However, in all cases, the GA based PID controller out-performed the conventionally optimized PI, and PID and the GA optimized PI controllers. It can be concluded from the simulation results that GA-based optimization technique is much better to enable automatic generation control.

Best: 0.08786 Mean: 0.088605

10

Best fitness Mean fitness

9 8

Fitness value

7 6

Acknowledgement

5

PID

4

Authors wish to thank Electrical Engineering Department, NIT Silchar, for providing the necessary facilities for completing this work.

Best fitness

3 2

Best fitness

References

1 0

10

20

30

40

50

60

70

80

90

100

Generation Fig. 7e. Plot of fitness value versus generation of PID controller.

Best: 0.25855 Mean: 0.25922 10 Best fitness Mean fitness

9 8

Fitness value

7 6 5 4

PI

3

Best fitness

2

Best fitness

1 0

10

20

30

40

50

60

70

80

90

100

Generation Fig. 7f. Plot of fitness value versus generation of PI Controller.

mismatch in supply and demand under varying condition of load and generation. This paper presents models of an autonomous hybrid generation/energy storage system. The studied hybrid system consists of wind turbine generators, diesel generators, aqua electrolyzers, solar thermal power system, photovoltaic, battery energy storage system, flywheel, ultra-capacitors and fuel cells. The generated hydrogen from the aqua electrolyzer is used as fuel for the fuel cell. The models for wind power, solar thermal and load are also properly selected to simulate the important performance of the studied hybrid system. In order to reduce the frequency deviation i.e., eliminate the mismatch in supply and demand under varying condition of load and generation, the output power from the sources is regulated using controllers (PI/PID). The gains of controllers are designed by using conventional method and GA. Performance of each controller is examined from the dynamic behaviour in time-domain simulations of the system in isolated mode of operation. It has been observed that the response of PID controller is the best amongst PI and PID controllers considered for study in terms of peak transient deviation and settling time. Further, it is observed that the performance of all the GA optimized controllers is better than their respective counterparts optimized using conventional

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