CHAPTER 2 MODELING OF POWER SYSTEM

Transcription

1 38 CHAPTER 2 MODELING OF POWER SYSTEM 2.1 INTRODUCTION In the day to day scenario, power is an essential commodity to the human beings. The demand is more in developed countries and there is increase in demand for power in the developing countries. To match the requirement, suitably, generation has to be maintained. When there is mismatch between load demand and generation, it results in variations in the frequency. When the generation in an area is more than the demand, then the frequency will be more. Similarly when the demand is more than the generation, it results in reduction in frequency. This leads to instability of power system. Control of frequency variations with load is designed using transfer function model of the system. It is reported that the transfer function model for Power System is furnished by Elgerd [29] and is utilized by most of the researchers. The primary loop in Load frequency control maintains the generation with load demand. Speed Governor Mechanism is the primary

2 39 control loop and this maintains the system frequency during mismatch of load and generation. Free Governing mode of operation has to be introduced in all generating stations. They have to contribute to the primary frequency control. That is if there is frequency augmentation by 0.1Hz, then the station load should by design and instantaneously let-down by 4 to 5%.After the subsequent 4 to 5 minutes, the unit load should progressively be got back to the preceding stage by additional control, when grid frequency stay on below the unit s frequency limit.in this chapter transfer function representation of the Thermal power and Hydro power is explained. 2.2 THERMAL POWER PLANT The components of a Thermal power plant are speed control mechanism which includes speed governor, governor controlled valves, speed control mechanism and speed changer, steam turbine and power system are modelled for doing small signal analysis. As given by Elgerd in 1983 [30], the mathematical model of Thermal power plant for single area system is shown in figure 2.1. The components of a Thermal power plant are speed control mechanism which includes Speed Governor, Governor controlled valves, Speed control Mechanism and Speed changer, Steam Turbine and power system are modelled for doing small signal analysis. As given by Elgerd in

3 [30], the mathematical model of Thermal power plant for single area system is shown in figure 2.1. Figure 2.1 Block diagram of single area system with Thermal power Transfer function of Speed control mechanism is represented as Ks 1+ST s (2.1) Transfer function of Turbo generator is represented as KTG 1+ST TG (2.2) Transfer function relating to frequency change to the change in input and output power KP 1+ST P (2.3)

4 Transfer function model of Thermal power system Single area with Thermal Power as source is designed in Simulink and the performance is analysed. Simulink representation from MATLAB is shown in Figure 2.2. Figure 2.2 Transfer function model of Thermal Power system The change in frequency ( f) and the P ref are input to Speed governor. Based on the difference between these parameters, steam input will be changed to the Turbine. Suppose if the load increases, the speed of the Synchronous generator reduces slightly and thereby frequency reduces. Then the governor of any Thermal Unit reacts to the speed variation and permits more steam to enter the Turbine. The equation of a speed governor for transfer function is given by Equation (2.4).

5 42 P = P G Re f 1 f R ( 2. 4 ) In case of high pressure of steam, the speed governor finds it difficult to operate. Hence, through several stages of hydraulic amplifier, large mechanical forces positions the gate valves of the turbine against high pressure steam. The transfer function of the hydraulic amplifier is given as Equation (2.5). 1 P H = 1 + S T H P G ( 2.5) In this research, non-reheat turbine is considered. It acts as a chief transporter for the generator and also provides the energy to the power system model. Now, the transfer function model of it can be written as Equation (2.6). 1 PTG = 1 + ST T P H ( 2.6) The output power of the turbine acts as input to the generator for feeding electrical energy to the power system. The generator with the power system in load variation is represented as Equation (2.7).

6 43 K P F ( S ) = [ P ( S ) P ( S ) ]( ) G D 1 + ST P ( 2. 7 ) K where p 1 = H z / p. u. M. W ( 2. 8 ) D Load damping factor is D and is defined as P D = f D p. um W / H z ( 2. 9 ) P D =load demand in p.u D. f. p. u. M W = Increase in load demand T P = 2 f s H * D ( ) where H = W s P R ( ) H= Inertia constant and W s = Kinetic energy at the synchronous speed W 1 s = I ( 2 π f ) 2 Rate of change of Kinetic energy is the increase in power. 2 ( )

7 44 P r = p u ( ) d dt 2W d f dt S ( W ) = ( ) s f p. u ( ) Taking P r = 1. 0 p. u Simulation Results of Thermal Power System The transfer function model of the simulink block diagram shown in figure 2.1 is built up in MATLAB simulink environment. A unit step load disturbance of 0.01p.u is applied to simulink block. The variations in the frequency are shown in figure 2.3. Figure 2.3 Response of frequency in thermal power system with no secondary controller

8 45 From the figure2.3, it is evident that speed governor brings back the change infrequency but the steady state error could not be brought to zero. A secondary controller is needed to fine tune the frequency to zero through power reference setting. 2.3 HYDRO POWER STATIONS As explained by Prabha Kundur [98], Impulse type hydraulic turbine also known as Pelton wheel is used for high heads 300 meters or more and high velocity jets of water imposed on buckets on the runner deflect the water axially about 160. In a reaction type hydraulic turbine, the pressure within the Turbine is above atmospheric and the energy supplied by the water is in both potential and kinetic form. The performance of a hydraulic turbine as explained by Prabha Kundur [98] is influenced by the characteristics of the water column feeding the turbine including the effects of water inertia, water compressibility and pipe wall elasticity in the penstock. As explained by Prabha Kundur [98], the primary speed/ load control function involves feeding back speed error to control the gate position. The IEEE Committee Report [53] has studied hydro thermal plant and developed mathematical model of the system with speed governor, hydro turbine and power system.

9 46 Block diagram of the Hydro Power system is shown in figure 2.4. As explained by Murty P.S.R. (2005) [89], the governing system of hydro turbines has to meet complex requirements because of the destabilizing effect of the inertia of water and these governors are provided with temporary droop compensation to prevent over travel of gate motion. Speed drop for a hydro unit is p.u. speed drop = N N ( ) N 1 2 R N 1 = extrapolated speed corresponding to Zero gate opening N 2 = extrapolated speed corresponding to 100% gate opening N R = Rated speed Dash pot droop mechanism is δ T S r 1 + S T r ( ) Where s is the complex frequency σ + jω

10 47 Value of the gain δ varies from 0.2 to 1.0. The rest or decay time constant T r lies between 2.5 and 25sec. Value of K lies between 0.03 to 0.06.Block diagram of hydro turbine speed governing mechanism is indicated in figure 2.4. Figure 2.4 Block diagram of hydro turbine speed governing mechanism Penstock Turbine model Considering an effective length of L mtrs., discharging water to the turbine at a velocity V m/s operating at a head of H m. Following load change, following are the p.u. changes. Change in head= H

11 48 Change in Speed= N Change in Turbine gate opening= X Change in flow= Q Change in Turbine Torque= T p.u. change in Head / p.u.change in flow= H Q = T Z = T S e s w ( ) Where T e is elastic limit of the penstock Z s is the normalised penstock impedance T w is water starting time Changes in flow and torque are represented by Equations (2.18) & (2.19). Q = a H + a N + a X ( ) T = a H + a N + a X ( ) Where a 11, a 12, a 13, a 21, a 22 and a 23 are constants. Speed change is relatively small and hence can be neglected.

12 49 T 1 X T S 0 w = X X T S 0 w ( ) For an ideal loss less turbine with valve opening X 0, the values of the constants are considered as a 1 1 = 0. 5 X o ( ) a = 1. 5 X ( ) a13 = a23 = 1.0 ( 2.2 3) At full load in p.u. x 0 = 1.0 ( 2.2 4) T 1 T S w = = X T S w G ( S ) PT ( 2.2 5) Water starting time is calculated as shown in Equation (2.26) T w = LV Hg ( 2.2 6) Here g is 6.8 m/s 2.

13 Block diagram of the Hydro Turbine System A complete block diagram representing speed governing system, turbine and penstock for dynamic studies is shown in figure 2.5. Figure 2.5 Block diagram of hydro turbine speed governing system In figure 2.5, transfer function model of speed governing system and transfer function of the change in torque of the turbine with change in gate position is represented. The Transfer function model of the hydro power System is shown in figure 2.6.

14 51 Figure 2.6 Transfer function of a hydro power system The working of Hydro Power model (HPM) is analogous to that of thermal power model. The speed governor of HPM using hydraulic amplifier mechanism is expressed as Equation (2.27). K 1 1+ st R 1 PHV = Pref ( f ) 1+ st1 1+ st2 R ( 2.2 7) As explained by Prabha Kundur [98], hydro turbines have a peculiar response due to water inertia. A change in gate position produces an initial turbine power change. For stable performance, a large transient (temporary) droop with long resetting time is required and is achieved by the provision of a rate feedback or transient gain reduction compensation. The rate feedback limits the gate movement until the water flow and power

15 52 output has time to catch up. This results in a governor, which demonstrates more droop for quick velocity variations and normal low droop for stable condition. A dashpot is used for transient droop compensation. As explained by Prabha Kundur [98], for steady business under islanding condition, best possible choice of the provisional droop R T and reset time T R is related to water starting time and mechanical starting time T M =2H where H is inertia constant. R T ( T ) = 2.3 w ( 2.2 8) 5.0 ( 1.0) 0. 5 ( 2.2 9) T = T T R w w Transfer function of Hydraulic Turbine is represented in Equation (2.30). 1 STw PHT = P ST w HV ( 2.3 0) Where T w is referred to as water starting time, it represents the time necessary for a head H 0 to increase speed of the water in the penstock from idle to the velocity U 0. Water starting time (T w ) varies with load and full load lies between 0.5sec and 4sec. The output of the Turbine acts as input to the generator. Then generator rotor starts rotating and electrical energy is produced. The relation between change of load, turbine power and change in the frequency in the power system is shown in Equation (2.31).

16 53 P P = T D K p 1+ ST p f ( ) 2.4 SIMULATION RESULTS OF HYDRO POWER SYSTEM The transfer function model of the simulink block diagram shown in figure 2.6 is developed in MATLAB simulink environment. A unit step load of 0.01p.u is applied. Variations in the frequency are shown in figure 2.7. Figure 2.7 Response of Hydro power system with no secondary controller From the above graph, it may be noted that with the increase in demand, the frequency has reduced and it immediately increased due to the

17 54 governor action. However, there is steady state error and is not reached to zero error. 2.5 TIE LINES As explained by Elgerd in 1983 [30], the power system contains many control areas and these are interconnected by tie lines to improve the stability and reliability of the system. As reported by P.S.R Murthy [89], in a flat frequency control of interconnected systems, two generating stations are connected through a transmission line known as tie line and for a load increment in station B, the K.E of the generators reduces to absorb the load increase in both the stations A & B and frequency will be less than normal at the end of governor response. Load increment is supplied partly by B and partly by A and tie line power flow changes accordingly. Under the heading (2.1), about thermal power system is explained and is considered as one control area. Similarly, hydro power system is explained under the heading (2.5) and this hydro power system is implemented as another control area Tie-Line Power Model in figure 2.8. Tie- line is a Transmission line which connects two areas as shown

18 55 Tie line(x) V 1,δ 1 AREA-1 P 0 12 V 2,δ 2 AREA-2 Figure 2.8 Tie line power model The interconnected areas operate at the same frequency f and power P 0 12flows from Area1 to Area 2.The voltage magnitude and phase angle at area1and area 2 are V 1,δ 1 and V 2,δ 2 respectively at the two ends of the Tie line and P 0 12is the power that flows from area 1 to area2 as indicated in Equation (2.32). P V V = sin( δ δ ) X ( 2.3 2) Here reactance of the transmission line is represented as X. Synchronizing coefficient of the tie line or stiffness coefficient of the line are denoted by T as shown in Equation (2.33). P = T ( δ δ ) ( 2.3 3) The tie line power changes due to variations in load angle i.e variations in speed and i.e variation in frequency and is shown in Equation (2.34).

19 56 0 2πT0 P 12 ( S ) ( F1 ( S ) F2 ( S )) S = ( 2.3 4) The block diagram of tie line power is given in figure-2.9. Area1 f 1 f 2 Figure 2.9 Tie line power Area2 2.6 HYDRO AND THERMAL POWER SYSTEM Each area has both hydro power and Thermal power stations. It is considered that each area has 1000MW power generation with 4 generators of each 210MW thermal power and 4 generators of 50MW hydro power in each area. These stations are interconnected through tie line. If there is an increase in load in one area, that area will be supplied by both the areas. The representation of both the areas is indicated in figure 2.10.

20 57 Thermal units Thermal Tie line Hydro units Hydro units Load Load Area-1 Area-2 Earth Figure 2.10 Representation of two sources two area power system Transfer function model of single source Hydro Thermal power system Model of hydro thermal system using Transfer function as defined by Elgerd and Fosha in 1970 [29] is shown in Figure In this transfer function, in one control area the grid is fed from Hydro Power system and another control area is fed from Thermal power system. The simulink block diagram of single source multi area is shown in figure 2.11.Here both the areas are fed with a disturbance of 0.01 p.u. step load. In area -1, Thermal power source is implemented. In the second area, Hydro power source is used.

21 58 Figure 2.11 Representation of single source multi area system Simulation result of multi area single source system The response of the transfer function model without secondary controller in MATLAB simulink is observed and the response of change in frequency in the area with hydro power source, area with thermal source, and tie line power are observed and shown in figure 2.12 (a), figure 2.12(b) and figure 2.12 (c) respectively.

22 59 Figure 2.12 (a) Frequency response with hydro power as source Figure 2.12 (b) Frequency response with thermal power as source

23 60 Figure 2.12 (c) Tie line power with hydro power and thermal power in multi area single source system. The response with step load in single area and with no load in other area has been observed and plotted. In area-1, thermal power with load is included. In area-2, hydro power is implemented and no load is included. Tie line response is observed. Here there is only primary control. The response has been observed and plotted in figure 2.13(a), figure 2.13(b) and figure2.13(c).

24 61 Figure 2.13 (a) Change in Frequency in Area1 with Thermal power and load in Area1 Figure 2.13 (b) Change in frequency in Area2 with hydro power and no load

25 62 Figure 2.13(c) Tie line power with load in one area 2.7 TWO AREA TWO SOURCE HYDRO THERMAL POWER SYSTEM In the two area two source system, each control area is a combination of Hydro and Thermal power. The total power generated is equal share of both Hydro and Thermal systems. The mathematical model of the two area two source system with no secondary controller and the response with step load disturbance in both the areas is shown in figure 2.14.

26 63 Figure 2.14 Two area two source transfer function model The transfer function model without secondary controller shown in figure 2.14 has been subjected to step load disturbance and frequency variations and change in tie line power response has been observed using MATLAB simulink. The variation in frequency in area1 and area2 and tie line power are shown in figure 2.15(a), figure 2.15(b) and figure 2.15(c) respectively.

27 64 Figure 2.15 (a) Two area Two source system- frequency variation in area1 Figure 2.15 (b) Two area two source system- frequency variations in area2

28 65 Figure 2.15(c) Two area Two source- Tie line power flow 2.8 RESPONSE ANALYSIS Frequency response of single source in single area are tabulated in Table 2.1 in terms of Integral Absolute error (IAE), Integral Square Error (ISE), Integral Time Average Error (ITAE), settling time in sec, and steady state error. Graphical representation is made in figure 2.16.

29 66 Table 2.1 Performance of Hydro Thermal System single source single area Description Single source Single area Type of Source Thermal power Hydro power IAE (p.u) ISE (p.u) ITAE (av.) Time in seconds Steady State error (p.u) Single area single source response in graphical representation is shown in figure Figure 2.16 Single area single source response with primary control alone

30 67 Performance of Hydro Thermal system with single source in each area and two sources- in two areas are shown in Table 2.2. Table 2.2 Performance of Hydro Thermal System single source two area and two-source two area Description of Parameters Parameters single source multi area Thermal in area 1 and Hydro in area2 Two source Two area Both Thermal & Hydro power source in each area Change in frequency IAE(p.u) ISE (p.u) ITAE(average) f f Area Area Area Area Area Area Settling Time in sec Area1 and area

31 68 It may be noted from the results that there is dip in frequency in area1 and area2.there is steady state error in both the areas. Comparative representation of the response of single source multi area is shown in figure 2.17 through bar graph. Figure 2.17 Single source and two area performance with primary control Response of two sources and two area system is indicated through bar graph in figure 2.18.

32 69 Figure 2.18 Performance of two area two source response with primary control 2.9 CONCLUSION In this chapter, model of hydro and thermal system has been designed using transfer functions and analysed in single source single area, single source two area and two-source two area systems. Here only governor control i.e primary control is applied and no secondary controller is introduced. The results show that there is dip in frequency and there is steady state error. This error can be minimized using secondary controllers, which is implemented and discussed in chapter-3.