Tuning of Power System Parameters for Dynamical Response Study

1. Introduction In power system analysis and calculations, the accuracy of power system component models directly affects the correctness of analysis and calculation results. In other hand, the parameter precision of power system models also affects the quality of power system analysis and calculations. Particularly, the dynamical models of power system require the parameters more accurate than the static models. The modern power system industries request not only the qualitative solutions but also the quantitative solutions for an analysis case. For instance, the operators want the exact values of the current, voltage or frequency at a special moment after a disturbance so as to determine the relays or control devices settings. According to the experiences in practices, the erroneous of parameters can severely impact the quality of analysis solutions. Once the model of a actual power system is established, the verification and validation process of system model parameters are indispensable before conduct case analysis. Generally, the parameters of system models are obtained from manufacture data, measured data and estimated data. These data may bring different types of errors on the parameters, such as: the manufacture data may not be suitable to the complexities of models or the simplified models; the measured data are subject to errors of metering system; and the estimated data may not be accurate. In this presentation, a technology to tune up power system model parameters will be illustrated, specially, about the tuning dynamical model parameters using site test record data. 2. Verification and Validation of Power System Model Parameters Power system models generally are classified as static-state models, like transmission line, transformer and static load model, sand dynamical models, like generator, turbine/governor, exciter/AVR and motor models. The parameters of static-state models, like transmission line and transformer impedances, can be easily verified and validated by comparing load flow analysis results against measured voltage, current and power data at any time moment. But it is not so simple for the verification and validation of dynamical model parameters, like governor and exciter transfer function time constants and gains. First, these parameters do not have apparent one to one relationships with the measurable data. Second, the response of a model to be matched with measured data is not only a single point instead of a whole process corresponding to a system event such as a load shed or a bus faulted. The shape and character of a response curve for a dynamical model during an event reflect merely the group effects of the model parameters. So it is difficult to quantitatively determine the individual parameter in a model according to a response curve. However, under some conditions may a parameter dominate certain character of the response curve, such as oscillation frequency, overshooting magnitude, raising and falling rates. This characteristic of a dynamical model can be utilized to tune the parameters of the power system dynamical models in accordance with the measured responses of frequency, voltage and so on. The next

section will investigate the relationship between a parameter of a mode and the model response process for some typical transfer function models. 3. Tuning of Power System Dynamical Model Parameters A power system dynamical device usually consists of different types of elements. These elements can be mathematically presented by some typical dynamical components or transfer functions. The following describes a number of typical dynamical components in power system dynamical models, and illustrates how the responses of these components are affected by varying their parameters. Also, a simplified model of a single generator power system is investigated in this section. Inertial Components: Its transfer function is shown as Figure 3.1. The inertial component is usually used to model the regulator amplifier, governor relay, or electric/hydraulic converter. Figure 3.1 and 3.2 display the responses of this component when applying a step input with different time constant and gain values. As can be seen from Figure 3.1, the raising rate of response will increase with reducing time constant value. But the settle down value of response would not be affected by varying time constant value. When increasing gain value, as shown in Figure 3.2, both the raising rate and settle down value of response will be increased.

Figure 3.1 Inertial Component Responses for Changing

Time Constant

Figure 3.2 Inertial Component Responses for

Changing Gain Integrate Components: Its transfer function is shown as Figure 3.3. The governor pilot servo is an example of integrate component. Figure 3.3 displays the responses of this component when applying a step input with different time constant value. As can be seen from Figure 3.3, the raising rate and output value of response will increase with reducing time constant value.

Figure 3.3 Integrator Component Responses for

Changing Time Constant Inertial-differential Components: Its transfer function is shown as Figure 3.4. The inertial-differential component can be used to model the regulator feedback stabilizer, or governor buffer. Figure 3.4 and 3.5 display the responses of this component when applying a step input with different time constant and gain values. As can be seen from

Figure 3.4, when increasing time constant value, the raising rate and overshooting magnitude of response will increase, but the falling rate during the decay segment will be decreased, thus, the settle down time of response would last longer. When increasing gain value, as shown in Figure 3.5, the raising rate and overshooting magnitude of response also will increase, but the falling rate would not be changed.

Figure 3.4 Inertial-Differential Component Responses for

Changing Time Constant

Figure 3.5 Inertial-Differential Component Responses for

Changing Gain

Single Generator Power System Model: Figure 3.6 shows a simplified model of a single generator power system. The block Ks and Kd are defined as system synchronizing

coefficient and system damping coefficient, respectively. These two coefficients represent the equivalent effects of generator, AVR, governor, loads and other system components. Figures from 3.7 to 3.12 display the power angle and speed responses of the power system model when a load shed is applied with different model parameters. As can be seen from Figure 3.7 and 3.8, when increasing damping coefficient Kd, the oscillation magnitudes of power angle and speed responses will be reduced, but the oscillation frequency of them is not changed. When increasing synchronizing coefficient Ks, as shown in Figure 3.9 and 3.10, the oscillation magnitudes of power angle and speed responses will be reduced and the oscillation frequency of them will be increased. Also, it is found that the initial power angle becomes smaller with increasing Ks. When reducing generator inertial coefficient H, as shown in Figure 3.11 and 3.12, the raising rate, overshooting magnitude and oscillation frequency of speed response will be increased, but settle down time becomes shorter. For the power angle response, its falling rate, and oscillation frequency will be increased, but its undershooting magnitude will be decreased and settle down time also becomes shorter.

Figure 3.6 Simplified Single Generator Power System Model

Figure 3.7 Generator Speed Responses for Changing

Damping Coefficient

Figure 3.8 Generator Power Angle Responses for Changing

Damping Coefficient

Figure 3.9 Generator Speed Responses for Changing

Synchronizing Coefficient

Figure 3.10 Generator Power Angle Responses for Changing

Synchronizing Coefficient

Figure 3.11 Generator Speed Responses for Changing

Inertial Coefficient

Figure 3.12 Generator Power Angle Responses for Changing

Inertial Coefficient 4. Examples of Tuning Power System Dynamical Model Parameters In this section, some examples are presented to illustrate how to tune the parameters of power system dynamical models utilizing the site test or system incidence recording data, so as to make the responses of dynamical model match the real recording data. 4.1 Generator Start-up Case This is a real test case. The test system, as shown in Figure 4.1, is a Hydro Generation Station as the backup power system of a Nuclear Power Plant. The test process includes:

first start a generator unit, at the same time flash the generator field winding, when generator terminal voltage reaches approximately 70% to 90% of rated output voltage, then a voltage relay trips the appropriate circuit breakers and connect the emergency load from the nuclear generation plant to the generator. The generator AVR and governor models are shown as Figure 4.2 and 4.3. The typical parameters of the models are listed in Table 4.1 and 4.2. When using the typical parameters in simulation study, as can be seen from Figures 4.4, 4.6, 4.8 and 4.10, the responses of generator speed, voltage, power and field voltage do not match the site test results. By investigating the response curves, obviously, some transfer function time constants and gains of both AVR and governor models and the generator damping and inertial coefficients need to be tuned up properly. A set of modified model parameters are listed in Table 4.1 and 4.2. The responses of the system corresponding to the parameter modifications show a very good match to the site test results as displayed in Figures 4.5, 4.7, 4.9 and 4.11. In this project study, it is discovered that the response of the motor start simulation will not correctly express the real situation if the formula coefficients of motor load model are not presented properly. The formula coefficients of motor load model usually can be obtained by using curve fitting technology based on the load torque curve. In most cases, the manufacturers only provide the load torque curves under the speed range from 0 to 100%. It is no problem to simulate the motor start if the system frequency within this speed range. Otherwise, the simulation results will not truly reflect the actual situations. In this test case, the generator speed ever overshoots to 120% of rated speed at a period of time. Figure 4.13 shows the response of a motor electrical power during start up have big discrepancy against the site test result when using the load model with the speed range from 0 to 100%. When remodeling the load torque curve covered the speed range to 120% as given in Figure 4.12, the response of the motor electrical power corresponding to the modified load model shows a very good match to site test results as shown in Figure 4.14.

KGEN 2 KGEN 1

W/OMod#2

4kV B1TS

600V LC 3X4 600V LC 3X8

4kV 3TC

TX-3X5

HPIP-3A600 HP

LPIP-3A400 HP

RBSP-3A250 HP

LPSWP-3A600 HP

TX-3X8

MCC 3XS1

3EPTC13

3PTC3

3TC/D/E-3B1T

3TC-3B1T

3TD/E-3B1T

3TC-3B2T

NO

B1TS-3B1T

3X5 Test 13X8 Test 1 3X8 Test 23X4 Test 23X4 Test 1

TX-3X4

13.2kV Keo#113.2kV Keo#2

U3 4kV bus13

CT4

Underground

NO

4kV B2TS

4kV 3TE4kV 3TD

600V LC 3X10600V LC 3X6600V LC 3X5 600V LC 3X9

TX-3X9 TX-3X6 TX-3X10

MCC 3XS2

LPIP-3B400 HP

RBSP-3B250 HP

LPSWP-3B600 HP

HPIP-3B600 HP

3EPTE123PTE3

MCC 3XS3

3PTD3 3EPTD13

3TD-3B1T

3TE-3B1T

3TC/D/E-3B2T

3TD-3B2T

3TE-3B2T

3TD/E-3B2T

NO

B2TS-3B2T

3X5 Test 23X6 Test 1 3X6 Test 23X9 Test 1 3X9 Test 2

EFDWP-3A600 HP

EFDWP-3B600 HP

HPIP-3C600 HP

Figure 4.1 Test System for Generator Start-up

Figure 4.2 Exciter/AVR Model Diagram of Hydraulic Generator

Parameter Typical Tuned RC 0.0 0.0 XC 0.03 0.03 TR 0.0 0.0 TC 0.0 0.0 TBB 0.0 0.0 KA 100 70 TA 0.02 0.02 KF 0.5 0.12 TF 0.5 0.8 KC 0.1 0.1

VVLR 1.07 1.07 KVL 120.0 120.0 TVL 0.05 0.05 KVF 1.0 1.0 TH 0.05 0.05

VImax 0.17 0.17 VImin -0.17 -0.17 VRmax 3.66 3.66 VRmin 0.0 0.0 Vdc 125 125 Rf 0.15 0.06

VHZ 0.74 0.74 TD 2.5 2.5 Vfb 87.5 87.5 Ifb 585 585

Vref 1.025 1.025 Table 4.1 Typical and Tuned Parameters of Exciter Model

Figure 4.3 Governor Model Diagram of Hydraulic Generator

Parameter TP Q GC TG RP RT TR H D Typical 0.04 1 2.5 1 0.02 0.4 5.5 7 2 Tuned 0.04 1 2.5 1.41 0.02 0.4 7.5 4.94 1.1

Table 4.2 Typical and Tuned Parameters of Governor Model

Figure 4.4 Comparison between Simulated Generator Speed Response

(Using Typical Parameters) and Site Measured Speed

Figure 4.5 Comparison between Simulated Generator Speed Response

(Using Tuned Parameters) and Site Measured Speed

Figure 4.6 Comparison between Simulated Generator Voltage Response

(Using Typical Parameters) and Site Measured Voltage

Figure 4.7 Comparison between Simulated Generator Voltage Response

(Using Tuned Parameters) and Site Measured Voltage

Figure 4.8 Comparison between Simulated Generator Electrical Power Response

(Using Typical Parameters) and Site Measured Electrical Power

Figure 4.9 Comparison between Simulated Generator Electrical Power Response

(Using Tuned Parameters) and Site Measured Electrical Power

Figure 4.10 Comparison between Simulated Generator Field Voltage Response

(Using Typical Parameters) and Site Measured Field Voltage

Figure 4.11 Comparison between Simulated Generator Field Voltage Response

(Using Tuned Parameters) and Site Measured Field Voltage

Figure 4.12 Induction Motor Load Torque Curve Fitting

Figure 4.13 Comparison between Simulated Induction Motor Electrical Power

Response (Using Typical Parameters) and Site Measured Electrical Power

Figure 4.14 Comparison between Simulated Induction Motor Electrical Power

Response (Using Tuned Parameters) and Site Measured Electrical Power

4.2 Diesel Generator Load Acceptance Test Case This is a real test case about a diesel generator starting an induction motor. The test system and the exciter and governor models of the diesel generator are shown in Figure 4.15, 4.16 and 4.17. The Figure 4.18 and 4.20 display the responses of a bus frequency and voltage when using the typical parameters as listed in Table 4.3 and 4.4 for the exciter and governor models. It is found from the response curves that the simulation system has less damping torque and too much inertial moment. Through the tuning of system model parameters, the responses of the bus frequency and voltage using the modified parameters as listed in Table 4.3 and 4.4 show a perfect match to the site test results as displayed in Figure 4.19 and 4.21.

2ELXA 0.6 kV 2ELXC 0.6 kV

1500 kVA

TX-2ELXC

1500 kVA

TX-2ELXE

1500 kVA

NO NO NO NONO NO NO NO NO

2*EPE538 2*EPE537 2*EPE536

NO

NONO

MCC-2EMXE MCC-2EMXA2 MCC-2EMXA MCC-2EMXC

DG-2A

4000 kW

MCC-BPH2A

FPCP-2A200 HP

NSWP-2A

1000 HP

AFWP-2A500 HP

CCHRGP-2A600 HP

SIP-2A400 HP

RHRP-2A400 HP

CSP-2A400 HP

CCP-2A2200 HP

CCP-2A1200 HP

2*EPC6A

2ETAGenlos42.3 kVA

2ETAXlos0.031 MVA

TX-2ELXA

2ETA 4.16 kV

Figure 4.15 Test System for Diesel Generator Load Shed

Figure 4.16 Exciter Model Diagram of Diesel Generator

Parameter Typical Tuned KA 156 240 KC 0.001 0.001 KE 0.08 0.08 KF 0.1 0.27 KI 9 9 KP 0.08 0.08 TA 0.05 0.05 TE 1.0 4 TF 3.0 3.0 TR 0.005 0.005

Vrmax 17.5 17.5 Vrmin -15.5 -15.5

Table 4.3 Typical and Tuned Parameters of Exciter Model

Figure 4.17 Governor Model Diagram of Diesel Generator

Parameter Typical Tuned Droop 5.0 5.0

ThetaMax 60.0 60.0 ThetaMin 4.0 4.0

Alpha 0.04 0.027 Beta 0.02 0.0192 Rho 0.1 0.3 K1 128 119 Tau 0.1 0.09 T1 0.15 0.151 T2 0.12 0.12 H 1.9 1.69 D 4.0 7.0

Table 4.4 Typical and Tuned Parameters of Governor Model

Figure 4.18 Comparison between Simulated Generator Frequency Response

(Using Typical Parameters) and Site Measured Frequency

Figure 4.19 Comparison between Simulated Generator Frequency Response

(Using Tuned Parameters) and Site Measured Frequency

Figure 4.20 Comparison between Simulated Generator Voltage Response

(Using Typical Parameters) and Site Measured Voltage

Figure 4.21 Comparison between Simulated Generator Voltage Response

(Using Tuned Parameters) and Site Measured Voltage

4.3 Network Short-Circuit Fault Test Case This test case is to simulate a system response when a short-circuit fault occurred on a bus. The test system is shown in Figure 4.22. The simulation events include: short-circuit fault occurs at MCC feeder Bus3, voltage relay trips some load at Bus-A and Bus-B when voltage drops to 50% during the fault, in 0.38 seconds the circuit breaker 52GH is tripped to disconnect fault point, in 0.8 seconds the circuit breaker 52B4 is tripped to disconnect the tie link to utility. The actual measured current and voltage of generator G4 and current at branch 52B4 are displayed in Figure 4.23. The simulation responses of the system current and voltage for using typical generator parameters listed in Table 4.5 and using tuned parameters listed in Table 4.5 are shown as Figure 4.24 and 4.25,

respectively. As can be seen from Figure 4.25, the response of the system current and voltage using tuned parameters are very close to the actual measured data.

Bus4

Bus-BBus2

Bus1

T3

12.5 MVA

pump273.936 kW

pump3937 kW

pump483.175 kW

CB4

52B4

52GH

LUMP15.848 MVA

LUMP210.75 MVA

pump5

345 kW

LUMP34.458 MVA

CB5

CB6

LUMP410.75 MVA

3.3 kV

3.3 kV3.3 kV

65 kV

3.3 kV

Bus-A

Bus3

3.3 kV

Power Grid

pump173.936 kW

G415.111 MW

Figure 4.22 Test System for Short-Circuit Fault

Parameter Typical Tuned Xd 1.48 0.75 Xq 1.48 0.74 Xd’ 0.215 0.15 Xq’ 0.45 0.16 Xd” 0.136 0.12 Xq” 0.136 0.13 Td0’ 7.05 7.05 Tq0’ 1.0 1.0 Td0” 0.042 0.042 Tq0” 0.18 0.18

H 5.4 8 D 5 1

Table 4.5 Typical and Tuned Parameters of Generator

Figure 4.23 Site Voltage and Current Recordings During Short-Circuit Fault

Figure 4.24 Simulated Generator Voltage and Current Responses

(Using Typical Parameters)

Figure 4.25 Simulated Generator Voltage and Current Responses

(Using Tuned Parameters)