Amir Emadi

Esmaeil Barati

Hamed Fotoohabadi

Fossil-Fired Generation Unit Model for Dynamic Analysis

Keywords: Power system dynamic analysis, Power system modeling, Fossil fired steam unit, Power system simulations I

In this paper, a new linear model of the fossilfired steam unit is presented. Classic models have been used in power system dynamic analyses for decades. The effect of the main steam pressure is usually ignored in classic models or a more complex model of boilers is adopted. Furthermore, the variation of the turbine enthalpy drop is not considered, which could result in great variations during transient periods. The effect of the main steam pressure and turbine enthalpy drop is considered in the new linear model, which can improve the accuracy of classic models. To compare the performance of the proposed model with the classic one, test data of a 600 MW coal-fired generation unit is adopted. The time domain simulation is performed using PSCAD/EMTDC software.

INTRODUCTION

One of the main factors on power system dynamic behavior is the power response of generation unit [START_REF] Gao | Analysis of power system frequency responses with hydro turbines incorporating load shedding[END_REF]. To provide a suitable mathematical model of generation unit, many studies have been done by researchers. Complex models provided by manufactures for the plant's design are accurate enough [START_REF] Bize | Frequency control considerations for modern steam and combustion turbines[END_REF], [START_REF] Mehrtash | Fast stochastic security-constrained unit commitment using point estimation method[END_REF]. However, they require huge computational resources and consist of many timeconsuming processes which may result in a not suitable model for many power system simulations, especially for large power grids [START_REF] Wu | Analysis of effects on primary frequency control and power grid stability of different control logic[END_REF].

Classic models have been presented for steam turbine units where the steam chests are the only dynamic components in the linear model of the steam turbine. However, the effects of the main steam pressure are ignored in these models. Moreover, linearizing mechanical power versus flow characteristic is often assumed which seems not valid during transient periods [START_REF] Ghannadi | Determining inactive constraints in stochastic securityconstrained unit commitment using cumulants[END_REF], [START_REF] Gao | A new framework for power system identification based on an improved genetic algorithm[END_REF].

In this paper, a new model of steam turbine unit is presented. This model is more accurate than classic ones and it's not too complex which makes it suitable for large power system analyses.

II. TURBINE MODEL

The mass flow rate of the turbine is often limited by the pressure drop [START_REF] Mehrtash | Considering Multiple Uncertainties in Stochastic Security-Constrained Unit Commitment Using Point Estimation Method[END_REF]. The mass flow rate and the pressure drop can be related by Flugel equation, which is widely used for thermal dynamic analyses in steam turbine under non-design conditions. This relationship can be shown as follows:

It should be noted that the inlet temperature variation has been ignored. In this equation, 𝑝 is usually much smaller than "1" in a generation turbine [START_REF] Vahidi | Determining parameters of turbine's model using heat balance data of steam power unit for educational purposes[END_REF]. By defining:

The relative variation of flow rate is equal to the relative variation of turbine inlet pressure as follows:

This equation is consistent with the classic model, where the output power or torque of the turbine is only proportional to the steam mass flow rate. However, in the large power reheat turbine unit, the effect of enthalpy drop should be considered for HP turbine during the transient period [START_REF] Zakernejad | A New Approach for Probabilistic Evaluation of Transient Recovery Voltage Across Circuit Breakers in TCSC Compensated Transmission Lines[END_REF].

The turbine power can be shown as a product of mass flow rate, enthalpy drop and efficiency:

The enthalpy drop is a function of the inlet and outlet pressure of the turbine as: By expanding the variation of enthalpy drop which can be described as And changing it into a relative variation form, the following equation can be obtained:

If we ignore the variation of the efficiency, the variation of turbine power can be shown as:

Finally, by ignoring the second order items and using former equations, the variation of turbine power can be obtained as follows:

For small power turbine unit, the reheater volume is very small and the time constant is short. This makes the outlet pressure can vary fast enough relative to the variation of inlet pressure. So, for dynamic analyses on small turbine units, the assumption of constant enthalpy drop can be reasonable [START_REF] Kouhanjani | Comparison of VSC and Z-source converter: power system application approach[END_REF].

The time constant of IP steam volume, 𝑇 𝑅 , is about four to ten times larger than the HP steam volume time constant, 𝑇 𝐻 , in a large steam turbine.

The IP time constant in modern steam turbine unit is about 10 to 14s, which is long enough to a dynamic analysis. The output power of a whole turbine unit can be shown as:

Where By considering a new dynamic item

The HP turbine power fraction, 𝐾 𝐻 can be replaced by inlet pressure coefficient, 𝐷 𝐻 . The value of 𝐶 𝐻 can be calculated based on the design parameters or steady states data. For modern steam turbine, 𝐶 𝐻 is about 0.1 to 0.6, while the original HP power friction, 𝐾 𝐻 , is about 0.3 to 0.4. Therefore, the enthalpy drop variation can affect the dynamic output of the whole generation unit during transient periods.

III. SIMULATION RESULTS

The classic turbine-boiler unit and the new improved one are shown in Fig. 1 and Fig. 2, respectively. To compare these two models and for the purpose of this paper, a proper excitation signal is required. A little change in system frequency would be well enough for comparing these two models to actual experimental data obtained from testing on a 600 MW coal-fired power generation unit. The reference frequency was raised from 50 Hz to 50.18 Hz at 1.5 s and then reduced back to 50 Hz at 77 s. These frequency changes are shown in Fig. 3.

The power fractions of HP, IP and LP turbines can be calculated based on the test data which are shown in Table I. By simulating each system model based on the identified parameters, different responses to the excitation test signal are shown in Fig. 456. The variation of pressures in the reheater and crossover pipes are shown in Fig. 4 and Fig. 5, respectively. The output power variations are shown in Fig. 6. It can be seen from the simulation results that the classic model, has relatively high pressure upstream of the turbine. However, this model shows a lower output power compared to the new presented model and actual test data.

According to Fig. 456and by considering the test data, it can be seen that the system behavior and the output power predicted by the proposed model are more accurate than the classic model.

  1 and 𝑝 2 are turbine inlet and outlet pressures, respectively. The mass flow rate entered the turbine cylinder is shown by 𝑔 and 𝑔 0 presents the steady state value. The term (

Table

Fig. 1

 1 Fig. 1Fig. 2

Fig. 2

 2 Fig. 1Fig. 2

Fig. 3

 3 Fig. 3

Fig. 4

 4 Fig. 4

Fig. 5

 5 Fig. 5

Fig. 6 REFRENCES

 6 Fig. 6