Steam turbine governor modeling and parameters testing for power system simulation

Abstract

The theoretical modeling, parameters test and model correction for a steam turbine (ST) governor are discussed. A set of ST Governor system model for power system simulation is created based on this research. A power system simulation for an actual power grid accident is conducted using this new model and the comparison between the simulation and actual data show that the results are satisfactory.

Keywords

power system simulation / ST governor system / modeling / parameters testing

Introduction

The safe and stable operation of modern electric power system relies on the developments of various kinds of simulation technology. The identification of four parameters (generator, excitation system, governor system, and load character) is the basis of electric power system simulation [1]. The successfully applied excitation system modeling result shows that the adoption of a new particular model can raise the analysis result of regional grid transportation capability by up to 4%—6% compared with the original result, indicating the necessity of building a particular model database for power system simulation [2]. The quick development of ST governing technology and application of modern control theory make modern governor system distinctly different from traditional ones. Building a governor system model that can characterize the actual system performance is important for particular grid operation and management.

Theory analysis of ST governor system modeling

The principal of ST speed governor system is shown in Fig.1. When a grid load waving leads to a system frequency variation and turbine speed changing, speed governor senses the changing and automatically turns the governor valve through the driving machine and servo machine. The steam flow and mechanical power output of ST will be changed to satisfy the requirement of load variation. The ST governor system consists of the speed governor, the servo machine, and the turbine. The analysis and modeling of these three parts should be done before the modeling of the whole governor system [3].

Control logic of ST speed governor system

In modern ST unit governor control system, the turbine, the boiler and the power grid form an interaction framework as shown in Fig. 2. The traditional ST Governor system has been greatly changed by advanced control and computer techniques, and is embedded into the whole unit control system, making the boundaries that split the governor system with other control systems vaguer. In modern ST units, governing and control are usually realized by automatic generation control (AGC), and the realization of AGC control relies on the coordinated control system (CCS) [4].

To avoid reversed regulation by AGC, frequency feedback loop is normally set in CCS to realize primal frequency regulation (PFR) and boiler fuel regulation according to speed feedback for further ST output regulation.

Most modern ST regulation systems operate in DEH+CCS mode. Commands from DEH and CCS are combined to regulate the power of unit through servo-valve control logic. A typical ST governor model is built according to this construction, as shown in Fig. 3.

Theory model of servo-mechanism

A modern servo-mechanism is usually controlled by DEH and consists of a servo-controller, a servo-valve, a servo-motor, a displacement transducer, and a check-valve [5,6]. The input signal of the servo-mechanism control loop is the required opening value of the servo-valve, while the output signal is the servo-motor position which is also the real opening valve of the servo-valve. The transfer function of a servo-mechanism is:

The servo-valve

{\displaystyle \frac{Q(s)}{i(s)}}={\displaystyle \frac{k}{s^{\mathrm{2}}/{\omega }_{\mathrm{n}}^{\mathrm{2}}+\mathrm{2}\varsigma s/{\omega }_{\mathrm{n}}+\mathrm{1}}};

The servo-motor

X(s)={\displaystyle \frac{x_{\mathrm{cy}}}{Q}}={\displaystyle \frac{\mathrm{1}}{T_{\mathrm{cy}}s}};

The PI regulator

\mathrm{PI}(s)=P+{\displaystyle \frac{\mathrm{1}}{s}};

The whole servo-mechanism

{\displaystyle \frac{x_{\mathrm{cy}}(s)}{x_{\mathrm{re}}(s)}}={\displaystyle \frac{Ps+I}{T_{\mathrm{sv}}{T}_{\mathrm{cy}}{s}^{\mathrm{3}}+T_{\mathrm{cy}}{s}^{\mathrm{2}}+Ps+I}};

here, Q(s) is the transfer function, a 2–order transfer function is like Q(s)=k/(t₂s²+t₁s+t₀), where k is transfer gain; t₂, t₁ and t₀ are time constants. Q is inlet oil flow in servo-motor through servo-valve. i(s) is electric current of servo-valve. k is static gain of servo-valve. ς is damp rate. ω_n is angular frequency of servo-valve, ω_n=2πf, where f is system frequency. X is dimensionless expression for servo-motor, X=x_cy/Q; x is servo-motor stroke. PI is PI regulator transfer character. P is proportional coefficient. I is integral coefficient. T is time constant. x_re is difference between setting and real valve opening position. The subscript cy is servo motor and sv is servo valve.

The mathematical model of the servo-mechanism is a high order one which can be first order-reduced and then used to calculate the frequency character curve of the servo-mechanism. Within a 15 Hz frequency variation span, the first-order simplified model can be obtained according to the calculated character curve, as shown in Fig. 4.

Theory model of prime-mover

Presently, the main ST generator units of the Chinese power grid are 1 ST and 1 boiler units with reheaters. So the modeling work of prime-mover is based on this unit type [7]. The ST prime-mover consists of stage group model of through-flow parts and middle cubage model of reheaters. The first model describes the dynamic flow characteristics of the cascade path, and the last model describes the dynamic pressure and flow characters of middle cubage. The whole transfer function model of ST unit prime-mover can be obtained based on these two models, whose input signal is servo-valve opening value and output signal is ST mechanical power, shown as Fig. 5. The model can be simplified by ignoring the affection of exhaust steam pressure to stage group flow. The simplified model includes 6 parameters: power proportions of HP, IP, and LP cylinder (F_HP , F_IP and F_LP), time constant of steam cubage, reheater and cross tube (T_CH, T_RH, and T_CO).

Theory model of whole ST governor system

On the basis of control logic, servo-mechanism model, prime-mover model, and transferring and coupling relationship of each part, the typical ST governor system theory model can be set up as shown in Fig. 6.

Sensitivity analysis of the parameters in ST governor system

A numerical simulation method is used to analyze the sensitivity of each parameter in the model Fig. 6. The simulation result shows that in ordinary scope, governor droop constant (K₁) is the most sensitive parameter to model output. The value of K₁ directly affects the final stable power output i.e. the governing ability of the whole governor system. Power proportions of HP cylinder (F_HP) and time constant of the reheater (T_RH) mainly affect the dynamic responding course of the system. The key parameters of the governor system model such as governor droop constant (K₁), time constant of the servo-mechanism (T₃), time constant of the steam cubage and the reheater (T_CH, and T_RH), and power proportions of HP cylinder (F_HP) can be found through this sensitivity analysis. Figure 7 shows the analyzing result of K₁.

ST governor system test and model parameter identification

ST governor system test

Four units of different type and capacity were selected for the governor test, in order to find out the dynamic characters of governor system under different operation mode (power load and control mode). The test data were used to correct the theory model of ST governor model and identify the key parameters. The test units are listed in Table 1.

Test result and theory model correction

The result of the analysis of test data shows that the real ST governor system is different from the theory model in two ways. For unit A and C, droop constant (K₁) can remain stable within a certain power scope. Although K₁ is a little smaller than the design value, yet when the unit power output is elevated and goes beyond this scope, it increases rapidly and the governing capability gradually becomes weak. For unit B and D, the governing capability behaves quite uncertainly and it is hard to get a stable droop constant K₁ from the test data.

The reasons for these differences are as follows. First, for modern ST governor system, both the control logic and the servo-mechanism can operate with high precision, so the nonlinearity of the governing capability is mainly caused by the prime-mover. Traditional ideal prime-mover model ignores the influence of steam parameters such as flow, pressure, and pressure difference of the governing valve, considering that the unit ability of energy supply is infinite, i.e., the relationship between the power output and the governing valve opening value is linear. However, during a real governing process, the realization of power governing is dependent on the energy storage of the prime-mover which is finite. The governing valve position variation will also cause the variation of steam parameters, thus causing the difference between the real and ideal governor model, which leads to the weakening of system governing capability.

Second, most ST units (125 MW and up) have 4 or 6 HP governing valves. There are two valve control modes: synchronous and sequential. For synchronous mode, all valves are synchronously governed by the steam distributing gear as a single valve, and the steam flow is equally distributed to each valve which has a uniform control character with others. In this mode, the steam flow is highly nonlinear with the valve opening value. That means under a certain governing valve opening value, the main steam pressure has a great influence on the steam flow. That is why from the test result of unit B and D, it is hard to get a stable droop constant K₁. For sequential mode, HP governing valves are sequentially governed according to a certain order. This control mode is designed to operate the units economically. During a power output scope of 10%—90%, the steam flow is linear with the valve opening valve. When the power output is greater than 90%, the throttling ability of the governing stage is obviously depressed. So the control mode of HP governing valve has a great influence on the governor system.

Considering the test phenomenon that unit energy supply ability varies rapidly during governor system working procedure, a “ST governor system cooperation curve” is brought forward to collaborate the multi-condition and multi-factor, to describe the dynamic property of ST unit, and to correct the theory model of ST governor system, as shown in Fig. 8.

Parameter confirming of ST governor system model

The following steps were adopted for parameter confirmation of corrected ST governor system model. First, set the parameters such as dead band, droop constant, and PID control parameters by control logic. Next, identify the time constant of the servo-mechanism and the reheater from the test result using identification software. Figure 9 shows the identification result of the reheater time constant.

After that, measure the power proportions of HP cylinder (F_HP) by test. And finally, select typical data for such parameters which will not influence the precision of the model [8] through sensitivity analysis.

Power grid accident restoration based on test corrected model

A frequency restoration of a power grid accident was made based on the test corrected ST governor system model and a real grid frequency drop accident. The accuracy of the model can be clarified by comparing the simulation result with measured frequency data of the accident.

The power system simulation software NETMAC was used for restoration. The corrected ST governor system model was added in NETMAC as a user-defined model. Restoration result (Fig. 10) shows that compared with the other two theoretical models, the user-defined model simulation curve is a better approach to measuring the frequency curve, indicating that the governor model is accurate and can be used in power grid stability analysis.

Conclusions

The theory model of ST governor system model is thoroughly analyzed. A series of test was conducted for theory model correction. Two conclusions can be reached from the tests:

1) HP governing valve control mode is a key factor to governing the ability of ST governor system.

2) The supply ability of ST unit varies rapidly in the system governing procedure, and a “ST governor system cooperation curve” is brought forward to collaborate multi-condition and multi-factor and describe dynamic property of ST unit.

A set of modeling and test correction method for ST governor system research is established, which is verified to be effective using a power grid accident restoration based on the corrected model.

References

[1] Gao Hong, Zhang Jianwen, Wu Fang. Application of system identification theory in electric power system. Shanxi Electric Power, 2001, (5): 51-52 (in Chinese)

[2] He Renmu. The study of generator excitation system modeling and parameters estimation. Power System Technology, 2007, 31(14): 62-67

[3] Li Peizhi, Lian Hongwei. Power Plant Steam Turbine DEH System. Beijing: Electric Power Publishing of China, 2005

[4] Wang Li. Application of automatic generation control system in 300 MW coal-fired power unit. Journal of North China Electric Power University, 2002, 29(1): 109-111

[5] de Mello F P. Dynamic models for fossil fueled steam units in power system studies. IEEE Transaction on Power Systems, 1991, 6(2): 753-761

[6] Pereira L, Undrill J, Kosterev D, . a new thermal governor modeling approach in the WECC. IEEE Transactions on Power Systems, 2003, 18(2): 819-829

[7] Borghettia A, Migliavaccab G, Nuccia C A, . Black-start-up simulation of a repowered thermoelectric unit. Control Engineering Practice, 2001, 9(7): 791-803

[8] Cheres E. Basic Turbine Values from Data of Fault Events. IEEE, 2004

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Higher Education Press and Springer-Verlag Berlin Heidelberg