CHAPTER 4 DESIGN OF GRID CONNECTED INDUCTION GENERATORS FOR CONSTANT SPEED WIND POWER GENERATION

Transcription

1 CHAPTER 4 DESIGN OF GRID CONNECTED INDUCTION GENERATORS FOR CONSTANT SPEED WIND POWER GENERATION 4.1 Introduction For constant shaft speed grid-connected wind energy conversion systems, the squirrel cage induction generator offers the most experienced and economical means of wind power generation to an existing Power Grid. This is because the generator is simple and robust and the control system is straight forward. Also electrical transients are relatively unimportant since the coupling is inherently flexible [55]. Many induction machines designed for motor operation are still being used for grid connected wind power generation. However, investigations have shown that the performance of this type of generator is far from optimum [14]. This is because the parameter values determined during the design stage were optimized for a motor rather than a grid-connected generator. Most of the available literature [56-61] considers the design optimization of the squirrel cage induction motor regarding objective functions such as material cost, motor performance and motor energy efficiency. These have not included generation characteristics. The generator schemes discussed in refs. 10, 13 and 15 which consider the design of self excited induction generators for autonomous (stand alone) wind energy applications, e.g. with the objective functions of active-material cost, capacitor cost, voltage regulator cost, voltage regulation and frequency regulation. In the following work an attempt is made to design an induction generator 65

2 exclusively for constant speed grid-connected wind energy applications with the objectives of reducing reactive power consumption and no-load losses. 4.2 Design Strategies In conventional induction motor design, primary importance is given to the start-up characteristics, followed by steady state characteristics, especially efficiency, power factor and cost. To meet the start-up requirements, the design methodology seeks to maximize the skin effect and to optimize the rotor resistance during starting. Also induction motors are generally designed for large leakage reactance, so as to have a small starting current. However, in designing a grid connected induction generator, the strategies are very different. The order of importance entirely changes because of operation with self starting (horizontal axis) wind turbines; hence the start-up characteristics may be completely ignored. Removing the importance for start-up characteristics, the design of grid connected induction generator allows the stator and rotor slot numbers, shapes and size to be optimized exclusively for minimizing the leakage inductance and resistance. Consequently it leads to good over load capacity and efficiency. In wind power plants generally, no-load losses are undesirable, since they make it more difficult to convert small wind speeds into electrical output and increase the non-rotational time of the turbine generator. However, induction machines as generators normally achieve large induced voltage and thus larger saturation states in normal generation than in motorized operation. This leads to 66

3 increase in no-load losses and poor power factor values. Therefore the generator should be designed for small no-load losses. The most desirable operating points for an induction motor are on the knee of the saturation curve. However, the operation of a capacitor Self Excited Induction Generator (SEIG) is stable when its magnetic circuit saturates and so the no-load current of the SEIG is between 70 and 75% of full-load current. Yet the grid-connected induction-generator operates in the low saturation region because operation in the saturation region reduces the relative permeability of the iron and increases the magneto motive force required to operate the generator. This leads to more reactive power consumption from the grid and poor power factor. When a standard squirrel cage induction generator is connected to the grid, it consumes reactive power and delivers real power. The excess MVAR is particularly undesirable for wind farms, connected to weak grids. To discourage the effect, a penalty is imposed for excessive MVAR draw from the grid. So the turbine owners provide capacitor banks to decrease the reactive power. However these capacitors are permeanently connected. Consequently, when there is little generation due to weak wind, the capacitor exports VAR into the grid, which encourages voltage instability. To overcome this aspect thyristor-controlled shuntcapacitors are fitted which connect the capacitors according to wind conditions. However, this increases cost and gives further power quality difficulties. So this work attempts to design the induction machine with less reactive power consumption to reduce the burden on capacitors and the need for no load losses. 67

4 4.3 Basic design Equations The Basic Design equations used in the Design of induction machine are discussed as below : Sizing equations The sizing equation for main dimensions applied for conventional induction machine is given by KVA input (output) Q = C 0 D 2 L n s Where D = Inner Stator Bore Diameter, m L = Stator Core Length, m n s = Synchronous Speed, rps C 0 = 11 B av ac K w cos 10-3 Where B av = Average Flux Density Over the Air gap, Wb/m 2 ac = Ampere Conductors per Metre, A/m K w = Winding factor = Efficiency cos = Power factor C 0 is called the output coefficient. The volume of the active parts is inversely proportional to the value of output coefficient C o. Thus an increase in the value of C o results in reduction in size and cost of machine. Thus, the value of C o should be as high as possible. The maximum value of C o is decided based on the effect of increased loadings on performance characteristic of machine. If high value of loadings is used, some performance characteristic like temperature rise, efficiency and power factor are adversely affected. 68

5 4.3.2 Stator Design Separation of D and L The operating characteristics of induction machine are influenced by the ratio L/ (where is the pole pitch) i.e., by the ratio L/D for a fixed number of poles. The longer core length, the flux per pole is increased and thus the number of conductors is reduced. This greatly reduces the cost of insulation. For good power factor L/ = 1.0 to 1.25 For good efficiency L/ = 1.5 Length of Airgap (L g ) The length of airgap is estimated based on the following factors; i. Power Factor The mmf required to send the flux through airgap is proportional to the product of flux density and the length of airgap. Even with very small densities the mmf required for airgap is much more than that for the rest of the magnetic circuits. Therefore it is the length of airgap that primarily determines the magnetizing current drawn by the machine. Hence power factor of machine with a greater gap length is smaller. ii. Over Load Capacity (OLC) The overload capacity of an induction machine is defined as the ratio of the maximum output to the rated output. Smaller the leakage reactance, greater the diameter of circle diagram and hence greater the overload capacity. The length of airgap affects the value of zigzag leakage reactance which forms a large part of total leakage reactance in the case of induction motors. 69

6 If the length of airgap is large the zigzag leakage flux is reduced resulting in a reduced value for leakage reactance. iii. Cooling If the length of airgap is large, the cylindrical surfaces of rotor and stator are separated by a large distance and hence it better facilitates cooling. iv. Noise The noise in induction machines is due to variation of reluctance of the path of the zigzag leakage flux. Thus noise can be reduced by increasing the length of airgap. Ventilating Ducts The stator is provided with radial ventilating ducts if the core length exceeds 100 to 125 mm. The width of each duct is about 8 to 10mm. Net iron length L i = 0.9 ( L 0.01) Stator Winding Design The three phase of the winding can be connected in either star or delta depending upon the starting methods employed. The squirrel cage motors are usually started by star delta starters and therefore their stators are designed for delta connections. The induction generator winding needs somewhat higher voltage ratings than motor and hence star connection is made in the induction generator. Turns per phase (T s ) Flux per pole, m = B av D L p Stator Voltage per phase E s = 4.44 f m T s K ws Where Ts = number of turns per phase in stator K ws = stator winding factor assumed as for infinitely distributed winding with full pitc 70

7 E s Stator turns per phase T s = 4.44 f m K ws Stator Conductors Stator current per phase I s = Q 3 Es Area of each conductor a s = I s s Where s = current density in stator conductors, A/mm 2. Shape of stator slots The shape of slots has an important effect upon the operating performance of the machine as well as the problems of installing the winding.semienclosed slots are usually preferred for induction motors because with their use the air gap contraction factor is small giving a small value of magnetizing current. Open slots are generally used for generators where it is desired to avoid excessive slot leakage thereby reducing the leakage reactance. Figure 4.1 Open Slots and Semi-enclosed Slots 71

8 Number of stator slots It will be better to consider the following points while selecting the number of stator slots. i. Leakage reactance The slot leakage reactance is inversely proportional to the number of slots/pole/phase, q s. With small value of leakage reactance the diameter of the circle diagram is large and hence the overload capacity increases. Thus, with larger number of slots, the machine has a higher overload capacity. ii. Ventilation With large number of slots, the thickness of the teeth becomes smaller and the teeth may become mechanically weak and they may have to be supported at the radial ventilating ducts by welding T or I sections. This obstructs the flow of air in the ducts thereby impairing the cooling. iii. Magnetizing current and iron losses With the large number of slots there may be excessive flux density in teeth giving rise to higher magnetizing current and higher iron loss. Total no. of Stator Slots S s = q s m p Stator Slot pitch yss = Gap Surface = Total no. of Stator Slots D S s Total no. of Stator Conductors = 6 T s Stator Conductors per slot,z ss = = 6 Ts S s 72

9 Area of stator slots Copper area per slot = Z ss a s Area of Stator Slots a ss = = Copper area per slot slot Space Factor High voltage machines have lower space factors owing to large thickness of insulation. The width of teeth should not be too large as it results in narrow and deep slots. The deeper slots give a large value of leakage reactance. In general the ratio of slot depth to slot width should be between 3 and 6. Length of mean turn of stator winding (Lmts) Lmts = 2L (m) Stator teeth A high value of flux density in the teeth is not desirable, as it leads to a higher iron loss and a greater magnetizing mmf. No. of poles = P Minimum tooth area per pole = Tooth area per pole = m 1.7 S s p m 2 Li Wts Minimum Width of stator tooth = (Wts) min = m 1.7 (S s /p) L i The minimum width of stator teeth is near the gap surface. A check for minimum tooth width should be applied before finally deciding the dimensions of stator slots. 73

10 Stator core The flux density in the core should not exceed about 1.5 Wb/m 2. The flux passing through the stator core is half of the flux per pole. Flux in the Stator Core = m 2 Depth of Stator core, d cs = m 2 B cs Li Outer Diameter of Stator Laminations D o = D + 2d ss + 2d cs (m) Resistance of stator winding at 75 o C = Rs = Rotor Design Main dimension x T a S s x L mts Diameter of rotor D r = D 2 L g Number of rotor slots The rotor slots for the squirrel cage machine is chosen based on the following general rules, i. The number of rotor slots should never be equal to stator slots but must either be large or smaller. ii. The difference between the number of stator and rotor slots should not be equal to p, 2p or 5p to avoid synchronous cusps. iii. The difference between the number of stator and rotor slots should not be equal to 3p for 3 phase machine in order to avoid magnetic locking. 74

11 iv. The difference between the number of stator and rotor slots should not be equal to 1, 2, (p+1), or (p+2) to avoid noise and vibrations. Number of Rotor Slots S r = S s p 2 Rotor Slot pitch y rs = D r S r Rotor bar design Current in each bar I b = 2 m k ws T s S r I s cos where k ws = Stator winding factor The performance of an induction machine is greatly influenced by the resistance of rotor. A machine designed with high rotor resistance has the advantage that it has high starting torque. However a rotor with the high resistance has the disadvantage that its I 2 R loss is greater and therefore its efficiency is lower under running conditions. The value of rotor resistance depends upon the current density used for rotor conductors. The higher the current density, lower is the current area and greater the resistance. I Area of each bar a b = b (mm 2 ) b where b = Current density in the rotor bar, A/mm 2. 75

12 Shape and size of rotor slots A semi enclosed slots are generally preferred for medium and large size machines. The rectangular shaped bars and slots are generally preferred to circular bars and slots as the higher leakage reactance of the lower part of the rectangular bars, during starting, forces most of the current through the top of the bar. This increases the rotor resistance at starting and improves the starting torque. Deep slots, however, give an increased leakage reactance and a high flux density at the root of the teeth. No insulation but a clearance of 0.15 to 0.4 mm is used between bars and rotor core. Figure 4.2 Rectangular and Circular shaped rotor bar End Rings The stator winding is a 3 phase distributed winding and thus produces a revolving field. This field may be considered as sinusoidally distributed in space as the harmonics in most cases are small and produce only secondary effects. This revolving field produces emfs of fundamental frequency in the bars. RMS value of end ring current I e = S r I b p (A) Area of each bar a b = I e e (mm 2 ) 76

13 Outer diameter of end ring D oe = D r - 2 d sr 10-3 Inner diameter of end ring D ie = D oe - 2 d e 10-3 Mean diameter of end ring D e = (D oe + D ie ) / 2 where, e = end ring current density, A/mm 2 Rotor Teeth d e = depth of end ring, mm d sr = depth of rotor slot, mm The width of rotor slot should be such that the flux density in the rotor teeth does not exceed about 1.7 Wb/m 2. The maximum flux density for rotor teeth occurs at their root as their section is minimum there. Actual Width of teeth provided = (D r 2d sr ) S r W sr Rotor Core Depth of Rotor core, d cr = m 2 B cr Li (m) Flux density in rotor teeth and core can be taken slightly higher than those in the stator teeth and core. This is because the iron losses in the rotor are very small owing to small value of frequency of rotor currents. Inner Diameter of Rotor Laminations D i = D r + 2d sr + 2d cr (m) 77

14 4.3.4 Operating Characteristics No Load Current I o The no load current of an induction motor is made up of two components as shown below: No load current I o = Magnetizing current, (I m ) + Loss Component current, (I l ) The magnetizing current is 90 o out of phase with the voltage while the loss component is in phase with the voltage. No load current I o (per phase)= 2 m I I 2 l No load power factor, cos o = I l / I o o = cos -1 (I l / I o ) Magnetizing Current I m The flux produced by stator MMF turns passes through the following parts: air gap, rotor teeth, rotor core, stator teeth and stator core. To calculate the required mmf, any closed path can be chosen provided the flux density along that path is known. If we use chose the path along a two points which are displaced 60 from the interpolar axis, B 60 is the same whether third harmonic component is present or not. And this is the reason for preferring this path for the calculating of magnetizing mmf in an induction machine. B 60 = 1.36 B av MMF for air gap AT g = 800,000 B 60 K g L g 78

15 Where, K g = Gap Expansion Factor = K gs K gd Gap Contraction factor for slots K gs = y s K cs W L Gap Contraction factor for ducts K gd = L K cd W s y s K cs and K cd are the Carter s gap co-efficient for slot and duct which depends on the ratio slot or duct width / gap length. MMF for stator teeth The flux density is uniform in the teeth when they are parallel sided but when parallel sided slots are used, the flux density along the length of teeth is not uniform. The value of mmf for teeth is found by finding flux density at a section 1/3 height of tooth from narrow end. Width of stator at 1/3 height from narrow end W ts1/3 = (D 2d ss / 3) S s W ss Flux density at 1/3 height of tooth from narrow end B ts1/3 = m (S s /p) L i W ts1/3 Calculation of mmf for stator teeth is based upon B ts60 where B ts60 = 1.36 B ts1/3 The mmf per metre at ts for stator teeth is obtained from the graph, flux density, B Wb/m versus ampere per meter, H A/m. MMF required for stator teeth, AT ts = at ts d ss 79

16 MMF for rotor teeth Width of rotor at 1/3 height from narrow end W tr1/3 = (D r 2d rs / 3) S r W rs Flux density in rotor teeth at 1/3 height of tooth from narrow end B tr1/3 = m (S r /p) L i W tr1/3 Calculation of mmf for stator teeth is based upon B ts60 Where B tr60 = 1.36 B tr1/3 The MMF per metre at tr for rotor teeth is obtained from the graph, flux density, B Wb/m versus ampere per meter, H A/m. MMF required for rotor teeth, AT tr = at tr d sr MMF for stator core Corresponding to flux density in stator core mmf per metre at cs is found from B H curves. The length of flux path through the core can be taken as 1/3 pole pitch at the mean core diameter. (D + 2 d sr + d cs ) Length of flux path through the Stator core, L cs = 3 p Mmf required for stator core, AT cs = at cs L cs. MMF for rotor core Corresponding to flux density in rotor core mmf per metre at cr is found from B H curves. The length of flux path through the core can be taken as 1/3 pole pitch at the mean core diameter. 80

17 Length of flux path through the rotor core, L cr = (D - 2 d sr - d cs ) 3 p Mmf required for rotor core, AT cr = at cr L cr. Total magnetizing MMF per pole for B 60 AT 60 = AT g + AT ts + AT tr + AT cs + AT cr Magnetizing current per phase, I m = p AT 60 kws T s Loss Component current I l The calculation of loss component of no load current involves the determination of no load loss. i. Iron loss W i The iron loss in induction motors consist of hysteresis and eddy current loss in teeth and cores, surface loss in teeth due to variation of air gap density, tooth pulsation loss due to variation of teeth density, loss due to non uniform flux distribution and loss in end plates. The iron loss in stator teeth and core is found out by calculating their respective weights. The loss per kg corresponding to the flux densities is obtained from the graph Specific iron loss, W sp W/kg versus flux density of the material, B m Wb/m 2. The frequency of flux reversal in the rotor is slip times the line frequency. In the case cage motors, the value of slip is small and, therefore, the iron loss in the rotor is negligible. Iron loss in teeth and core =W = = W sp B m Weight of teeth and core 81

18 ii. Friction and Windage loss W f The friction and windage losses are generally expressed in terms of output. It is assumed that the friction and windage losses are approximately 4% of the Output. Total No Load Losses W nl = W i + W f Loss Component current per phase, I l = W nl 3 E No load current Inl 2 I m I 2 l No load p.f = Cos o Il I nl Short Circuit Current I sc In order to find the value of short circuit (blocked rotor) current, the values of resistance and leakage reactance of the windings have to be evaluated. Short circuit current I sc (per phase) = E sc / Z 01 Short circuit power factor, cos sc = R 01 / Z 01 sc = cos -1 (R 01 / Z 01 ) Machine Parameters Stator Resistance The stator resistance per phase R s = cu T s Lmts a ( ) The value of resistivity for copper cu is 0.21 m at 75 C 82

19 Rotor Resistance The Rotor resistance per phase referred to stator R r = 4 m T s 2 kws 2 L b S r a b + 2 D e p 2 a e Stator slot leakage reactance Stator slot leakage reactance x ss = 8 f T s 2 L ( ss / (q s p)) Where, ss = Specific slot permeance for stator q s = Stator slots / pole / phase Rotor slot leakage reactance Rotor slot leakage reactance x rs = 8 f T 2 s L ( rs / (q s p)) rs = kws 2 ss S s / S r where, rs = Specific slot permeance for rotor Overhang leakage reactance Overhang leakage reactance x o = 8 f T s 2 L o ( o / (q s p)) o = o K s 2 L o y s where, o = Specific overhang permeance K s = Slot leakage factor which is obtained from the graph L o = Length of conductor in overhang. 83

20 Zigzag leakage reactance Zigzag leakage reactance x z = (5 / 6) X m m 2 1 q s q r 2 Magnetizing leakage reactance Magnetizing Reactance X m (per phase) = E s / I m Total Equivalent Resistance referred to stator R 01 = R s + R r Total Equivalent Reactance referred to stator X 01 =x ss + x rs + x o + x z Total Equivalent Impedence referred to stator Z 01 = R X o Performance Characteristics Circle Diagram It is possible to obtain graphically a considerable range of information from the circle diagram. The construction gives estimate of full load current and power factor, maximum power output, pull out torque and the full load efficiency and slip. The circle diagram is constructed from the following design data: I m = Magnetizing current per phase I l = Loss Component current per phase R 01 = Total Equivalent Resistance referred to stator X 01 =Total Equivalent Reactance referred to stator Z 01 =Total Equivalent Impedence referred to stator The procedure for drawing the circle diagram is given below: 1. Draw Oa and Ob perpendicular to each other. 2. Draw OO = I o at an angle o with Ob after choosing a suitable current scale. 84

21 3. Draw O D passing through O and parallel to Oa. 4. Draw OB = I sc at an angle sc for motor design and at an angle (90 + sc ) for generator design. 5. Join O with B 6. Construct the perpendicular bisector of O B intersecting the line O D at C. Point C is the centre of circle having radius O C. 7. Draw the circle O BD. 8. Draw BF perpendicular to O D and divide it at G in such a way that BG GF = R r R s 9. Join O to G. The line O G is known as torque line and line O B as output line. Rated Output Characteristic The diagram can be used to determine the characteristics for any current. The point A corresponding to rated output can be located as given below: If the diagram is drawn with a current scale of 1 cm = x ampere. Then, 1 cm = x E s watt per phase. Extend the line FB Cut off BS = rated output per phase. Draw a line SA parallel to output line O B cutting the circle at A. Then A is the operating point for rated output. 1. Draw AH perpendicular to Oa. 2. Join O to A. This gives the rotor current phase angle r 3. Label points J, K, and L Stator current per phase at full load I s = OA. 85

22 Stator power factor at full load cos = AH / OA. Constant Loss = 3 JH. Rotor Copper Loss at full load = 3 LK. Slip s = = Rotor copper loss Rotor Input = LK AK Efficiency = Rotor Output Stator Input = AL AH Torque = 3 AK. JH, LK and AK are measured on the power scale. The location of point M on circle for maximum torque is done by drawing a perpendicular on torque line from C. Line MN represents the maximum Output. Maximum Output = 3 MN. b a Figure 4.3 Circle Diagram of Machine Designed as Generator 86

23 b a Figure 4.4 Circle Diagram of Machine Designed as Motor Efficiency and OLC Losses: (i) Total Copper loss = W cu = cu s +cu r Stator copper loss cu s = 3 I 2 s R s Rotor bar copper loss cu r = S r I b 2 R b End ring copper loss cu er = 2 I e 2 R e Rotor copper loss cu r = cu r + cu er (ii) No load loss = W nl (iii) Total Losses W tl = Copper Loss W cu + No Load Loss W nl Efficiency: Q Efficiency, = Q + W nl Where, Q is the Output Power in watts. 87

24 Over Load Capacity (OLC) The Over Load Capacity (OLC) of induction machine is the ratio of maximum power output to the full load output. It depends on the dispersion coefficient ( ). The dispersion coefficient ( ) is defined as the ratio of magnetizing current to ideal short circuit current. Thus Dispersion coefficient ( ) = I m / I sc Maximum Power Output = 3 E s I sc I o 2 (1+ cos sc ) OLC = Maximum Power Output Full load Output = Temperature Rise The losses produced in the machine are converted into heat energy, as a result of which the various parts of the machine are heated, i.e., their temperature rises above that of the surrounding. Hence it is required to calculate the temperature rise in a machine. A material having a large value of thermal resistivity will dissipate less amount of heat i.e., the temperature rise will be larger for the dissipation of same heat. The steady temperature rise ( ) of surface is given by: s = l d c / s Where, l d = Total power loss in W c = Cooling co-efficient, C m 2 / W s = Cooling surface area, m 2 88

25 Outside cylindrical Surface area of armature S o Inside cylindrical Surface area of armature S i = D o L = D i L Cooling surface area of two ends of armature core and ventilating ducts S d = ( / 4) (D o 2 D i 2 ) (2 + n d ) C o = Cooling Coefficient of outside cylindrical Surface of armature C i = Cooling Coefficient of inside cylindrical Surface of armature C id = Cooling Coefficient for ducts Total loss dissipated / C rise = S o / c o + S i / c i + S d / c d Temperature Rise of the armature = Total loss to be dissipated Loss dissipated / C rise of temperature Q 4.4 The Optimization Problem S o / c o + S i / c i + S d / C d c Optimization of grid-connected constant speed generators aims to reduce the no-load losses and reactive power consumption, whilst also reducing the cost through design modifications. In the design, a number of physical parameters can be considered for modifications. Fortunately some may be assigned fixed values, because they have little influence either on the objective functions or on the specific constraints. The chosen independent variables are average airgap flux density (B av ), ampere conductor loading (ac), stator ( s ) and rotor bar ( b ) current densities and flux density of rotor core ( Bcs ). 89

26 4.4.1 Constraints for design of a motor Constraints imposed on motor design are (i) minimum limits on the full load efficiency, full-load power factor and the ratio of starting torque to full-load torque and (ii) maximum limits on the ratio of starting current to full-load current, stator temperature rise and the flux density between stator and rotor teeth Constraints for design of a generator The constraints applied to the motor design are applied to the generator design also, but with the following differences : (i) the constraints on starting current and torque are ignored, and (ii) an additional constraint of minimum airgap length is imposed for the generator design. 4.5 Evolutionary Programming (EP) and its implementation An optimization method is generally judged for its efficiency by the quality of the resulting solution and the number of functions evaluations required. The EPmethod should be capable of determining a near global optimal solution with minimal computation [62]. Evolutionary Programming is an optimization method simulated from the process of biological evolution. It is obvious that artificial simulation of the evolutionary process can provide a more general problem solving technique. It is based on the mechanics of natural selection mutation, competition and evolution. According to the problem each step could be modified and configured to achieve the optimum result. The process of evolution leads to the optimization of behaviour. 90

27 4.5.1 General Scheme of Evolutionary Programming The general scheme of the EP follows the sequence below and it can be represented with the block diagram shown in figure Vector representation of solution has to be done before getting into Evolutionary programming. Each representation is an individual in the evolutionary population. 2. Generation of an initial population i.e. parent population is done at random. The individuals in the initial population may or may not be a feasible solution. The optimal value found by Evolutionary Programming is not affected by the starting solution. 3. Each individual of initial population has assigned a fitness value. If any individual does not satisfy all the constraints incorporated, then a penalty is given to the objective function. 4. Evolutionary Programming in its search for highly fit individuals uses a rule for mutation, namely, combination rule. The combination rule operates on parent individuals to produce the new individuals that appear in the next generation. According to this rule, altering each parent individual with respect to Gaussian normal distribution creates the offspring individuals. 5. Each individual of offspring population has assigned a fitness value. If any individual does not satisfy all the constraints incorporated, then a penalty is given to the objective function. 6. The selection rule is used to determine the individuals that will be represented in the next generation. Each individual competes with some other individuals 91

28 in the combined population of the old generation and mutated old generation (offspring population). The competition results are valued using a probabilistic selection rule. The winners of the same number as the individuals in the old generation constitute the next generation. 7. Stopping rule is the given count of total generation or the constant minimum fitness value continuously for large number of generations. Initialization 'm' Parent individuals Offspring Creation m parents m offspring Competition & Selection Objective function evaluation Figure 4.5 General Scheme of Evolutionary Programming Features of Evolutionary Programming Evolutionary Programming is a population based search strategy. EP searches from a population of points, not a single point. The population can move over the hills and across valleys. Therefore EP can find the globally optimal point. In view of the fact that the computation for each individual in the population is independent of others, EP has inherent parallel computation ability. Therefore all the individuals in a population can be tested for satisfaction of constraints simultaneously and their fitness can be evaluated simultaneously. 92

29 It uses fitness information directly for the search direction rather than gradient information like non-linear programming. Evolutionary Programming can therefore deal with non-smooth, non-continuous and non-differentiable functions that are real life optimization problems like machine design problem. Traditional optimization methods approximate the problem by making some assumptions in order to design the mathematical model of the problem. EP doesn t need any mathematical model and hence it avoids approximations. This property makes EP so simple to apply. EP uses probabilistic transition rules, so they can search a complicated and uncertain area to find global optimum. Thus, EP offers a new tool for optimization of complex power system problems like machine design problem Implementation of Evolutionary Programming The steps followed for implementing EP are explained as follows : Initialisation The initial control variable population is X i. Here (a) X i represents the i th individual of the population (b) 1=1,2, m and is selected randomly from the sets of uniform distribution ranging over minimum and maximum, (c) m is the population size. Each individual of the population represents the set of chosen and independent variables of the design problem. So X i = [ B av ac B ] s b cs 93

30 The objective function value (f i ) of each X i is obtained by first using the standard design procedure and then the performance analysis usig circle diagrams. Such a circle diagram is a very useful nomogram to determine the performance of a motor or a generator with the help of only no-load and short-circuit test data. The subroutine used for finding the objective function is shown in figure 4.6, where a penalty is added to the objective function of the individual which does not satisfy the specified operating constraints. Then the minimum objective function value of this generation (f min ) is calculated Mutation Each X i is mutated and assigned to population) in accordance with equation (4.1). 1 X i (i th individual of the offspring X 1 i X N(0, ) (4.1) i i ( X X ) x f / f (4.2) i max min i min where N represents a Gaussian random number with zero mean and standard deviation of, which can be found from equation (4.2) and f min is the minimum value of the objective function of the parent population. X max, X min are the maximum and minimum limits of the independent variables and is the mutation scale. For each individual of the offspring population, the objective function value is calculated as explained in section Competition and Selection Then the objective function values of the parent and offspring populations are arranged in ascending order. The first m individuals are selected as the parent 94

31 population of the next generation. The penalty which is a very large value compared to the value of the objective function, is added to the objective function of the infeasible individual which does not satisfy any one of the constraints. This ensures that the corresponding solution will be considered as the worst solution and will not be to the next generation. Routine to find objective function For i=1 to m Subroutine for design of induction machine for ith individual Analyse performance characteritics using circle diagram All constraints satisfied? No Yes Add penalty to objective function Return Figure 4.6 Subroutine used in EP to evaluate objective function 95

32 Stopping rule The mutation, competition and selection procedure is repeated until the number of generation reaches its specified maximum. Generator design and the performance calculation using a circle diagram were developed using MATLAB 6.0 Figure 4.6 reveals the subroutine used in Evolutionary Programming to find the objective function value of a population at any generation. Evolutionary programming has been successfully implemented to optimize the reactive power consumption of constant speed grid-connected induction generators. Also EP has been applied to optimize the cost of induction motor to compare its performance with the generator design. 4.6 Results and Discussion Table 4.1 refer the various design specifications used for the analysis. Table 4.2 gives the optimized design results of constant speed grid-connected induction generators for the three given specifications, designed both as a generator and as a motor. Also figs.4.7 and 4.8 represent the reactive power consumption and efficiency of the generator against percentage slip for the design specification of machine-3 in table-4.1 when designed either as a generator or as a motor. Figs.4.9 and 4.10 represent the percentage no-load loss and efficiency of the generator against various power ratings when designed as either a generator or as a motor. As table 4.2 indicates for the generator design, as compared with the motor design, the air gap flux density, the length of airgap, diameter and length of core, 96

33 depth of the rotor slot are all decreased. Whereas, the ampere conductors per meter, number of turns per phase, width of rotor slot are all increased. With no considerations given to the starting characteristics for the generator design, it is observed that the rotor slot is inevitably shorter and wider than in the motor design. The wider and deeper stator slots of the generator design results in less iron area, which leads to small no-load losses. It is observed from figure 4.7 that the reactive power consumption of a grid connected constant speed induction machine designed as a generator is less than that with conventional motor design. In a similar way, from figure 4.8 the efficiency of the generator design is greater than that of the conventional motor design. The increase in efficiency is especially evident when the slip is small. This is especially beneficial for generation during small wind speeds. Figure 4.9 presents the no-load losses for various ratings of the machine designed either as a generator or as a motor. It is clear that the no-load losses of the generator design are much less than for the motor design which again increases electrical output in small wind speeds. Table 4.1 Design Specifications of the machines Machine 1 Machine 2 Machine 3 Machine -4 Machine 5 Output (KW) Rated Voltage(V) Syn. Speed(rpm) No. of Poles No. of Phases

34 Table 4.2 Optimal Design results for various ratings of Squirrel Cage Induction Machine Data Sheet Designed as Motor Machine 1 Machine 2 Machine 3 Designed Designed Designed Designed as as as as Generator Motor Generator Motor Designed as Generator Stator Design: Outer Diameter(m) Inner Diameter(m) Total length(m) No. of Slots Slot depth(mm) Upper Slot width(mm) Inner Slot width(mm) Teeth Width(mm) Slot Pitch(mm) Turns per Phase Conductor diameter(mm) Temperature rise( o C) Rotor Design: Length of Airgap(mm) Rotor diameter(m) No. of Slots Rotor slot Pitch(mm) Width of Rotor slot(mm) Depth of Rotor slot(mm) Width of Rotor Teeth(mm) Research Parameters: Average Flux Density(Tesla) Ampere conductors per m Ct. density of stator conductor(a/mm 2 ) Ct. density of Rotor bar(a/mm 2 )

35 Figure 4.7 Comparison of reactive power consumption Figure 4.8 Comparison of percentage efficiency 99

36 Figure 4.9 Power rating Vs percentage no-load losses Figure 4.10 Power rating Vs percentage full-load efficiency 100

37 4.7 Conclusion From the above discussion, it is concluded that an induction machine designed as a constant speed grid connected wind turbine generator using the above strategies, it is possible to reduce the reactive power consumption and the no-load losses with slight increase in efficiency. 101