Performance Evaluation, Modeling and Simulation of Components of SHPP

CHAPTER-5PERFORMANCE EVALUATION, MODELING AND SIMULATION OF COMPONENTS OF SMALL HYDRO-POWER PLANTS5.1 INTRODUCTIONElectric power supply acts as an engine that drives an economy. Sufficient power supply is very vital for industrial development and economic growth of any nation. Utilities in many developing countries are finding it difficult to establish and maintain remote rural area electrification. The cost of delivering power up to such areas are becoming excessively large due to large investments in transmission lines for locally installed capacities and large transmission line losses. For these reasons, distributed power generation has received attention in recent years for remote and rural area electrification. Thus, suitable stand-alone SHPP using locally available water sources has become a preferred option [82].(????)Performance analysis of SHPP operation is a valuable tool for planning operations and judging the value of physical improvement by selecting proper systems parameters. Therefore, such investigations are essential and helpful in verifying the emergency and safety conditions and in selecting the best alternatives in the early phase of planning and design of small hydro power plants. To accomplish this task, the performance analysis of SHPP has been carried out in this chapter. In performance analysis first step is modeling of various components of SHPP which helps in finding out the parameters of the control equipments like generator, governor, exciter etc. and in determining the dynamic forces acting on the system which must be considered in structural analysis of the penstock and their support. Dynamic response of hydraulic, governor and electrical system associated with SHPP can be obtained by simulating such model, which provides information about the performance of the entire system. The modeling of various components of SHPP and necessary equations representing their dynamic behaviour, simulation models and respective data with results have been presented in this chapter. The run of river type SHPP has been assumed for modeling.

5.2 MODELING OF VARIOUS COMPONENTS OF SHPPMathematical models are of fundamental importance to understand any physical system. Mathematical modeling of various components of small hydro-power plant has been carried out and are derived as follows:

5.3PENSTOCK AND TURBINE MODELINGHydro-turbines transform the water potential (mainly high pressure) into mechanical shaft power, which is finally converted into electricity. The electrical power N available of every turbine used is proportional to the product of total pressure head H and volume-rate Q of the penstock, thus one may write:N = gHQ;where, is the total efficiency of the turbine (including the electrical generator), is the water density and g is the gravity acceleration. Two types of turbine models using non-linear model and travelling-wave model have been employed and are as discussed in the following sub-sections:

5.3.1 Non-Linear Model The linear model of the hydraulic turbine is inadequate for studies involving large variations in power output and frequency. The block diagram in Fig. 5.1 represents the dynamic characteristics of the turbine with a penstock, which is suitable for large-signal time domain simulation [19].(?????) The penstock is modeled assuming an incompressible fluid and a rigid conduit.

Fig 5.1Non-Linear Model of Turbine (Non-Elastic Water Column) (ENLARGE AND IMPROVE THE DIAGRAM)The mathematical equation representing the dynamic behaviour of the penstock-turbine is given as: [5.1]Mechanical power output is given by:[5.2]

where, fp is the friction loss coefficient,

At is the turbine gain constant,

Tw is the water starting time constant,

D is the diameter of the tunnel,

Qnl is the no load water flow-rate,

Pmech is the mechanical power,

5.3.2Travelling-Wave Model The modeling of the hydraulic effects using the assumption of inelastic water column isadequate for short and medium length penstocks. For long penstocks, the travel time of the pressure and flow waves, due to the elasticity of the steel in the penstocks and the compressibility of water can be significant [19](????????). The non-linear model of turbine-penstock incorporating water column travelling wave effect is shown in Fig. 5.2.

Fig. 5.2 Non-Linear Model of Turbine (Including Water Column Travelling Wave Effects)(ENLARGE AND IMPROVE THE DIAGRAM)The necessary equations characterizing dynamic behaviour of the turbine are given as: Assuming [5.3][5.4][5.5]

Mechanical power output is given by:[5.6] where, fp is the friction loss coefficient,

At is the turbine gain constant,

Tw is the water starting time constant,

D is the diameter of the tunnel,

Qnl is the no load water flow-rate,

Pmech is the mechanical power,

Zo is the hydraulic impedance of the penstock,

Te is the penstock wave travel time,

5.4GOVERNOR MODELING The Hydro electric power plant consists of various equipments. Among these the governor is considered as the backbone of the hydro electric power plant. The basic function of the governor is to maintain the turbine speed constant under all working conditions. The governor is highly helpful while considering the normal and grid failure conditions. The grid frequency is an important power quality parameter. To maintain grid discipline it is important to maintain frequency as near as 50 Hz. To meet this requirement, governors are used in hydro electric power plants.Two types of governor models using electro-hydraulic governor model and PID governor model have been employed. They are as discussed in the following sub-sections: 5.4.1Electro-Hydraulic Governor Modeling Modern speed governors for hydraulic turbines use electro-hydraulic systems. Functionally, their operation is very similar to that of mechanical-hydraulic governors. Speed sensing, permanent droop, temporary droop and their measuring and computing functions are performed electrically. Regulation of the head is desirable under run of river mode operation of hydro plants and hence, hydraulic governor [19] with head controller [20] is used to control the speed of a turbine. Its block diagram is shown in Fig. 5.3.The necessary mathematical equations representing the dynamic behavior of electro-hydraulic governing system are given as: [5.7][5.8][5.9][5.10]

Fig. 5.3 Electro-Hydraulic Governor Model) (ENLARGE AND IMPROVE THE DIAGRAM) < and[5.11]=0 and > 0 and [5.12]=0 and < 0 and [5.13]= < and > [5.14]= 0 and = >0 and [5.15]= 0 and = 0 and [5.27]=0 and < 0 and [5.28]= and [5.29]= 0 and = >0 and [5.30]= 0 and = < 0 and [5.31]The gate position is given by: [5.32]where, Wref is the reference speed,

Wr is the rotor speed,

Rp is the permanent droop

Rmax is the maximum gate-opening-rate limit,

Rmin is the minimum gate-opening-rate limit,

Gmax is the maximum gate-opening limit,

Gmin is the minimum gate-opening limit,(NOT CLEAR??////)

Kp Proportional gain of the PID governor,

Ki Integral gain of the PID governor,

Kd Derivative gain of the PID governor,

Tc is the Gate servo motor time constant of PID governor,

5.5 EXCITER MODELING Three distinctive types of excitation systems are identified on the basis of excitation power source. They are:i) Type DC Excitation Systems which utilize a direct current generator with a commutator as the source of excitation system power.ii) Type AC Excitation Systems which use an alternator and either stationary or rotating rectifiers to produce the direct current needed for the generator field.iii) Type ST Excitation Systems in which excitation power is supplied through transformers and rectifiersThe modeling of different types of exciters for alternators has been given as below:5.5.1 Type DC1A Exciter Modeling The type DC1A exciter model represents field-controlled dc commutator exciter with continuously acting voltage regulators. The exciter may be separately excited or self-excited. When it is self-excited, Ka is selected so that initially X7 is zero. Fig. 5.5 shows the block diagram of the DC1A excitation system model [19].

Fig. 5.5 Type DC1A Excitation System Model(ENLARGE AND IMPROVE THE DIAGRAM)

The necessary equations representing dynamic behaviour of DC1A excitation system are given as: [5.33] [5.34] [5.35] [5.36] [5.37] [5.38] [5.39] [5.40] [5.41] [5.42]The exciter output voltage is given by: [5.43]where, Vref is the reference voltage,

Vter is the generator terminal voltage,

Tt is the voltage time constant,

Tc is the transient gain reduction (tgr) time constant,

Te is the amplifier time constant,

Ke is the exciter gain constant,

A is the saturation constant,

Kf is the stabilizing circuit gain constant,

Tf is the stabilizing circuit time constant,

Vmax is the maximum amplifier output,

Vmin is the minimum amplifier output,

Efd is the exciter output voltage,

5.5.2 Type ST1A(????) Exciter ModelingThe type ST1A exciter model represents a potential-source controlled-rectifier system. The excitation power is supplied through a transformer from generator terminals and is regulated by a controlled rectifier. The maximum exciter voltage available from such a system is directly related to the generator terminal voltage. In this type of system, the inherent exciter time constants are very small and exciter stabilization as such is normally not required.

Fig. 5.6 shows the block diagram of the ST1A excitation system model [1].

Fig. 5.6 Type ST1A Excitation System Model

The necessary equations representing the dynamic behaviour of ST1A excitation system are as below: [5.44] if [5.45] if [5.46] [5.47] [5.48] [5.49]

The exciter output voltage, Efd is given by: [5.50] [5.51] [5.52]

where, Vter is the generator terminal voltage,

Tt is the voltage time constant,

Ka is the amplifier gain constant,

Kc is the rectifier constant depending on commutating reactance,

Ifd is the field current,

Iir is the feedback rate limit,

Vrmax is the maximum regulator output limit,

Vrmin is the minimum regulator output limit,

Efd is the exciter output voltage,

5.5.3Type AC1A Exciter ModelingThe type AC1A exciter model represents a field-controlled alternator excitation system with non-controlled rectifiers and it is applicable to brushless excitation systems. This excitation system consists of an alternator main exciter with non-controlled rectifiers. The exciter does not employ self-excitation and the voltage regulator power is taken from a source not affected by external transients. A pilot exciter supplies the exciter field. Fig. 5.7 shows the block diagram of the AC1A excitation system model [1]. Fig. 5.7 Type AC1A Excitation System Model(ENLARGE AND IMPROVE THE DIAGRAM)The necessary equations representing the dynamic behaviour of AC1A excitation system are given as: [5.53] [5.54] [5.55]

[5.56] [5.57] [5.58] [5.59] [5.60] [5.61] [5.62] [5.63] [5.64] [5.65] [5.66] The exciter output voltage is given by: [5.67]where The value of is given by: [5.68]where, Vref is the reference voltage,

Vter is the Generator terminal voltage,

Tt is the Voltage time constant,

Tc is the Transient gain reduction (tgr) time constant,

Ka is the Amplifier gain constant,

Ke is the Exciter gain constant,

Te is the Exciter time constant,

A is the Saturation constant,

Kf is the Stabilizing circuit gain constant,

Tf is the Stabilizing circuit time constant,

Kc is the Rectifier constant depending on commutating reactance,

Kd is the Ac exciter synchronous and transient reactance constant,

In is the Rectifier load current,

Fex is the Rectifier regulation depending upon the input,

Vmax is the Maximum amplifier output,

Vmin is the Minimum amplifier output,

Vrmax is the Maximum regulator output limit,

Vrmin is the Minimum regulator output limit,

Efd is the Exciter output voltage,

Kd is the Damping constant,

The expression for the function characterizing the three modes of rectifier circuit operation are: Mode - 1: [5.69]Mode - 2-: [5.70]Mode - 3: [5.71] should not be greater than 1.0 but if for some reason it is, Fex should be set to zero.5.6 SIMULATION OF COMPONENTS OF SHPPIn the previous section mathematical modeling of various components of small hydro-power plant has been carried out and simulation models and respective data inputs are shown in section.5.7SIMULATION OF PENSTOCK AND TURBINE 5.7.1Simulation of Non-Linear ModelThe simulink model shown in Fig. 5.8 is in reference to Fig. 5.1 giving non-linear model of the turbine .

Fig. 5.8 Simulink Block Diagram of Non-Linear Turbine(Non-Elastic Water Coulmn)5.7.2Simulation of Travelling-Wave Model The simulink model shown in Fig. 5.9 is in reference to Fig. 5.2 giving travelling-wave model of the turbine.

Fig. 5.9 Simulink Block Diagram of Travelling Wave Turbine Model(ENLARGE AND IMPROVE THE DIAGRAM)

Penstock and turbine data are provided in Table 5.1.Table 5.1 Penstock and Turbine data

Sr. No.DescriptionValue

1.Penstock length Lp250.0 m

2.Friction loss coefficient Fp0.0 m/(m3/sec.)2

3.Turbine rating Pt125kW

4.Rated head of turbine Hr10.0 m

5.No-load water flow rate Qnl0.00 m3/sec

6.Turbine damping constant Dt0.01

7.Penstock cross section area Ap5.0 m2

8.Acceleration due to gravity g9.8 m3/sec

9.Base head of turbine Ho15.0 m

10.Rated water flow rate of turbine Qr4.43 m3/sec

11.Rated gate position Gr0.70 p.u.

12.Penstock wave velocity a1700 m/sec

5.8SIMULATION OF GOVERNOR5.8.1Simulation of Electro-Hydraulic Governor Model Simulink model of the Electro-Hydraulic Governor is shown in Fig. 5.10 is in reference to the Electro-Hydraulic Governor model shown earlier in Fig. 5.3 of this chapter.

Fig. 5.10 Simulink Block Diagram of Electro-Hydraulic Governor(ENLARGE AND IMPROVE THE DIAGRAM)Electro-Hydraulic Governor data has been tabulated in table 5.2.Table 5.2 Electro Hydraulic Governor dataSr. No.DescriptionValue

1.Pilot valve time constant of hydraulic governor Tp0.05 sec

2.Main servo motor time constant of hydraulic governor Tg0.20 sec

3.Temporary droop of hydraulic governor Rt2.60

4.Maximum gate opening rate, Rmax0.16

5.Maximum gate opening limit, Gmax1.00 p.u.

6.Heat float transducer gain, Kt0.15

7.Servo gain, Ks4.00

8.Permanent droop Rp0.04

9.Reset time Tr10.00 sec

10.Minimum gate opening rate, Rmin-0.16

11.Minimum gate opening limit, Gmin0.00 p.u.

12.Rectifier constant depending on commutating reactance Kc0.15

5.8.2Simulation of PID Governor ModelThe Simulink model of the PID Governor is shown in Fig. 5.11 is in reference to the PID Governor model shown earlier in Fig. 5.4 of this chapter.

Fig. 5.11 Simulink Block Diagram of PID Governor(improve the diagram) PID Governor data here has been tabulated in Table 5.3.Table 5.3 PID Governor dataSr. No.Descriptionvalue

1.Proportional gain of PID governor Kp3.00

2.Derivative gain of PID governor Kd0.2

3.Gate servo motor time constant of PID governor Tc0.02 sec

4.Maximum gate opening rate, Rmax0.2

5.Maximum gate opening limit, Gmax.975 p.u.

6.Head float transducer gain, Kt0.15

7.Integral gain of PID governor Ki0.70

8.Amplifier time constant Ta0.05 sec

9.Gate servo motor time constant of PID governor Td0.02 sec

10.Minimum gate opening rate, Rmin-0.2

11.Minimum gate opening limit, Gmin0.00 p.u.

12.Rectifier constant depending on commutating reactance Kc0.15

5.9SIMULATION OF EXCITER5.9.1Simulation of Type DC1A Exciter Model The simulink model of DC1A is shown in Fig. 5.12. This is in reference to the DC1A Exciter System shown earlier in Fig. 5.5 of this chapter.Fig. 5.12 Simulation Block Diagram Of DC1A Exciter System(IMPROV ETHE DIAGRAM) DC1A Exciter data has been tabulated in Table 5.4.Table 5.4 DC1A Exciter dataSr. No.DescriptionValue

1.Voltage time constant Tt0.2

2.Amplifier time constant Ta0.01

3.Minimum amplifier output Vmin-1.70

4.Stabilizing circuit gain constant Kf0.1

5.Transient gain reduction time constant Tc0.173

6.Amplifier gain constant Ka187

7.Maximum amplifier output Vmax1.70

8.Exciter time constant Te0.01

9.Stabilizing circuit time constant Tf0.001

5.9.2Simulation of Type AC1A Exciter Model The simulink model of the AC1A Exciter System is shown in Fig. 5.13. This is in reference to the AC1A Exciter System shown earlier in Fig. 5.6 of this chapter.

Fig. 5.13 Simulation Block Diagram of AC1A Exciter SystemTable 5.5 AC1A Exciter dataSr. No.Descriptionvalue

1.Voltage time constant Tt0.00001

2.Amplifier time constant Ta0.02

3.Minimum amplifier output Vmin-15.00

4.Minimum regulator output limit Vrmin-6.60

5.Exciter time constant Te0.8

6.Stabilizing circuit time constant Tf1.0

7.Ac exciter synchronous and transient reactance constant Kd0.38

8.Transient gain reduction time constant Tc0.00001

9.Amplifier gain constant Ka200.00

10.Maximum amplifier output Vmax15.00

11.Maximum regulator output limit Vrmax7.30

12.Exciter gain constant Ke1.00

13.Stabilizing circuit gain constant Kf0.03

14.Rectifier constant depending on commutating reactance Kc0.05

5.10 SIMULATION RESULTSThe results of simulation as per data given in the previous section for two different cases have been presented and summarized through two case studies explained below: Case-1In this case, the generator has been connected to an Isolated Load with EHD Governor System. It is shown in Fig. 5.14.

Fig. 5.14 Simulation Circuit for Isolated Generator with EHD Governor SystemInitially the generator terminal voltage has been at 1000V r.m.s. and load at 1KW, 100VAR. The EHD governor and the DC1A exciter has been used for this case. The results of simulation for this case are shown in Fig. from 5.15 to 5.28.Some of the findings are:i. Fig. 5.15 shows that there is constant movement of water through penstock.ii. Mechanical energy used per unit time is shown in Fig. 5.16. It is observed that while in the initial stages from 0 to 0.3 second there is an increasing trend and later on it attains a constant value.iii. From Fig. 5.17 it is revealed that the terminal voltage increases from 0 to 0.95 during the time period of 0 to 0.07 second thereafter it becomes constant.iv. Fig. 5.18 shows that the exciter voltage becomes constant after 0.25 second.v. The current developed in the armature of the stator with respect to time is shown in Fig. 5.19.vi. From Fig. 5.20 it is observed that the field current shows an increase from 1 to 1.25 with a time period of 0.5 second. vii. Fig. 5.21 shows that the electrical power per unit remains almost constant.viii. The rotor speed at the starting has to be more in order to take up inertia forces, but, at the later stage it goes down and then it attains a constant value as shown in Fig. 5.22.ix. From Fig. 5.23 it is clear that, practical deviation of rotor speed shows reduction initially and then turns into constant value.x. Rotor-angle deviation shows a decrease in its value from 0 to 0.15 in 0.5 second as shown in Fig. 5.24.xi. Fig. 5.25 emphasis that the value of rotor mechanical angle should be . xii. Fig. 5.26 obtained in respect of load-angle shows an increase in its value from 0 to 0.5 second. Performance Evaluation, Modeling and Simulation of Components of SHPP

xiii. Fig. 5.27 and 5.28 confirm that the line voltages and the currents in conductors are at phase apart. 143

Result of Case I

Fig. 5.15 Gate Opening Vs Time Characteristics

Fig. 5.16 Mechanical Power Vs Time CharacteristicsFig. 5.17 Terminal Voltage Vs Time Characteristics

Fig. 5.18 Exciter Voltage Vs Time Characteristics

Fig. 5.19 Armature Current Vs Time Characteristics

Fig. 5.20 Field Current Vs Time Characteristics

Fig. 5.21 Electrical Power Vs Time Characteristics

Fig. 5.22 Rotor Speed Vs Time CharacteristicsFig. 5.23 Rotor Speed Deviation Vs Time Characteristics

Fig. 5.24 Rotor Angle Deviation Vs Time CharacteristicsFig. 5.25 Rotor Mechanical Angle Vs Time Characteristics

Fig. 5.26 Load Angle Vs Time Characteristics

Fig. 5.27 Line Voltage Vs Time Characteristics

Fig. 5.28 Load Current Vs Time Characteristics

Case-IIIn this case, the generator has been connected to an Isolated Load with PID Governor System. It is as shown in Fig. 5.29. Initially generator terminal voltage has been at 1000V r.m.s. and load at 1KW, 100VAR. The PID governor and the DC1A exciter has been used for this case. The values of parameters of the governor, the exciter and the hydraulic components are same as in case-I. The results for this case are shown in Fig. 5.30 to 5.43. The proposed model has been tested in order to ensure that good prediction is made to PID governor settings and variations in parameters that yeilded comparable results with EHD.Effects of PID controller gain Kp, Ki, and Kd on a modified system have been summarized in Table 5.6.

Table 5.6 Effects of Kp, Ki, and Kd on a system

Sr. No.Gain responseRise timeOvershootSettling timeS-S error

1.KpDecreasesIncreasesSmall ChangeDecreases

2.KiDecreasesIncreasesIncreasesEliminated

3.KdSmall ChangeDecreasesDecreasesSmall Change

The above mentioned correlations shown in the Table 5.6 may not be exactly accurate, because Kp, Ki, and Kd are dependent on each other and changing one of these gains can change the effect of the other two. For this reason, the Table should only be used as a reference when we determine the values for Kp, Ki, and Kd.The predictions made in the values of the PID controller parameters are in good agreement to consequence output with EHD Governor of the proposed SHPP model.

Fig. 5.29 Actual Simulation Circuit for Isolated Generator with PID Governor System(ENLARGE AND IMPROVE THE DIAGRAM)Result of Case II(ENLARGE AND IMPROVE ALL THE DIAGRAMS)

Fig. 5.30 Gate Opening Vs Time CharacteristicsFig. 5.31 Mechanical Power Vs Time Characteristics

Fig. 5.32 Terminal Voltage Vs Time Characteristics

Fig. 5.33 Exciter Voltage Vs Time Characteristics

Fig. 5.34 Armature Current Vs Time Characteristics

Fig. 5.35 Field Current Vs Time Characteristics

Fig. 5.36 Electrical Power Vs Time Characteristics

Fig. 5.37 Rotor Speed Vs Time Characteristics

Fig. 5.38 Rotor Speed Deviation Vs Time CharacteristicsFig. 5.39 Rotor Angle Deviation Vs Time CharacteristicsFig. 5.40 Rotor Mechanical-Angle Vs Time Characteristics

Fig. 5.41 Load-Angle Vs Time CharacteristicsFig. 5.42 Line Voltage Vs Time Characteristics

Fig. 5.43 Load Current Vs Time Characteristics

5.11 FINDINGSInvestigations carried out in the simulation process revealed the following observations: It is indicated from Fig. 5.30 that there is a constant movement of water through the penstock. Mechanical energy used per unit time as indicated by Fig. 5.31, shows that while in the initial stages from 0 to 0.3 second, there is an increasing trend but later on it attains a constant value. Fig. 5.32 depicts that terminal voltage increases within a range of 0 to 0.95 during the time period 0 to 0.07 second and thereafter it achieves a constant value. Fig. 5.33 shows that exciter voltage achieves a constant value after 0.25 second. The current developed in the armature of the stator attains a constant value within 0.05second which is shown in Fig. 5.34. Fig. 5.35 indicates that field current shows an increased trend from 1 to 1.25 within a time period of 0.5 sec. Fig. 5.36 shows that the value of electrical power per unit almost remains constant. The rotor speed as indicated by Fig. 5.37, is found to be more at the starting in order to take up inertia forces but, at the later stage it goes down and ultimately achieves a constant value. Practical deviation of rotor speed shows initial reduction and then turns to be a constant as shown in Fig. 5.38.Rotor-angle deviation as indicated by Fig. 5.39, shows a reduction from 0 to 0.15 in 0.5 second.Fig. 5.40 depicts that the rotor mechanical angle should be .Load angle as shown by Fig. 5.41 indicates an increase in its value from 0 to 120 within 0.5 second.Fig. 5.42 and 5.43 confirm that the line voltages and currents in conductors are at 1200 phase apart.

5.12 CONCLUSION A small hydro power plant (SHPP) model has been successfully simulated using MATLAB/ Simulink. Simulations performed on the proposed control scheme using the Simulink utility of MATLAB have demonstrated the efficacy of the proposed virtual SHPP model. Servomotor as Governor using PID Controller is found to be best suited for speed governing in SHPP. The values of proportional gain Kp and integral gain Ki of a PID Controller has significant roles to play in determining the stabilizing time. So optimization of these parameters is absolutely necessary. Increase in water starting time leads to increase in perturbations due to response of the hydro turbine to water change which is just the opposite to that required in the beginning.