Introduction
In recent years, an increasing number of nuclear plants have joined into the power system in China. By October 2010, thirty four nuclear units had been authorized by the Chinese government and 25 nuclear power reactors were under construction. The total installed capacity was approximately 36.9 GW. China has become a country whose number of nuclear plants under construction ranges the first in the world. Nuclear power plants convert the energy released from the nucleus of atom viaβnuclear fissionβthat takes place in aβnuclear reactor. The heat released by the cooling system from the reactor core is used to generate steam which drives aβsteam turbine that isβconnected to aβgeneratorβto produceβelectricity. For security reasons, nuclear power plants are generally for base-load operation and do not participate in leak and frequency regulation of power system, which will reduce the ability of defending load disturbance in the power system.
The 2011βFukushima Daiichi nuclear disaster in Japan hadβprompted a reconsideration ofβnuclear energy policyβin many countries. To ensure the safety of the power grid, the nuclear units in the power system should be restricted to a limited range. When the power system suffers from a serious interrupt, the units should turn to frequency control to maintain the stability of the system. The variation of system frequency must be controlled in an allowable range under any disturbance. System frequency is generally regulated by primary and second primary control. Primary frequency control (PFC) regulates frequency in dynamic progress, and second frequency control (SFC) regulates frequency to nominal value by adjusting the loads of units or plants participating in frequency regulation power system [
1]. Frequency regulation of conventional thermal and hydro units should be fully utilized to prevent power plants from load disturbance and overspeed.
Some researches show that overspeed protection controller (OPC) which is to close the steam valves to avoid accelerating further when turbine speed exceeds specified limits (typically 103% to 110% of the rated speed) is very significant in modern large thermal units to protect the turbine from destructive overspeed. Younkins et al. [
2] and Kundur et al. [
3] discussed the overspeed control behavior during system disturbances on the units with electric-hydraulic control (EHC) or mechanical-hydraulic control (MHC). Kundur et al. [
3] also investigated the instability of the island system due to overspeed control. Frequent actions of the OPC will cause great crash on turbine shafting and power system, and may even cause large area load rejection and frequency oscillation. Gao and Dai [
4] studied the impact of the OPC on the stability of an islanded system and introduced an incident which caused the 110 kV circuit to form an island on February 24, 2004 when a 220 kV transformer failed in Puji transformer substation. A rise of frequency to 105.4% of the nominal frequency triggered the OPC of the two thermal units. The frequency dropped rapidly below nominal frequency due to decline of the generation and the reopen of valves. The valves opened and closed repeatedly for 15 minutes until all the loads were tripped.
To avoid a collapse of the whole system and estimate the limitation of nuclear units, the critical action of the OPC is proposed, in this paper, as the constraint of safe operation for the units. Focusing on the ability of participating in frequency regulation of the thermal units, the capacity limitation of the nuclear units in the grid is studied. Mathematic models for system simulation are established to analyze the dynamic response of power system with different capacities of nuclear units. This study can help to estimate the capacity limitation of the nuclear units in the grid on the premise of safe operation of the power system.
Power system model with nuclear units
As mentioned above, the state of the critical action of the OPC is proposed to determine the stability and safety of the power system containing nuclear units when load disturbance occurs. Since the OPC causes the instability of the power system, the turbine speed should be lower than the specified limits set by the OPC when the thermal units participate in frequency regulation to prevent the trigger of the OPC and frequency oscillation.
Some simulations of dynamic response when load disturbance occurs have been conducted in this paper. Figure 1 is the block diagram of a power system containing nuclear units. The nuclear units are regarded as static power sources due to the base-load operation and not participating in frequency regulation of power system. The conventional thermal plants are commonly categorized in two types: reheat turbine units and condensing turbine units. Most large capacity units are reheat turbine ones. The detailed models for the simulation based on Refs. [
5] and [
6] are illustrated in Figs. 2 and 3. The SFC mainly regulates slow quality of load disturbance while the PFC regulates fast frequency in dynamic progress. The models in Figs. 2 and 3 are simplified by assuming that the SFC is out of service.
In these models, T1 is the time constant of Oil Servo-motor; T2 is the time constant of dump valve; TH is the volume time constant of HP cylinder space; TRH is the time constant of reheat space; FHP, FIP, FLP is the proportion of HP, IP and LP cylinder power output in the unit output. M is the weighted mean value of the rotor time constant of all the paralleling generating units, called generating unit equivalent inertia time constant; D is the self-balancing coefficient.
A certain grid in China, approximately 10.955 GW total installed capacities, is studied in this paper. The parameters are valued according to actual test. The capacity of the units participating in frequency regulation is 4160 MW, and the dead band is 5 r/min. The OPC logic is set to quickly dump the actuator fluid of the governor valves and the interceptor valve when the turbine speed exceeds 103% of the rated speed.
Simulation results
Capacity limitation of nuclear units under different load disturbances
Most of the large capacity units are reheat turbine units. Assuming that the grid is dominated by the reheat turbine units and the maximum load disturbance is 20%, certain cases with different proportion of nuclear units in the present grid, varying from 20%, 40%, 47% to 60%, are studied in the simulation for stability analysis of the power system. The dynamic responses in each case are demonstrated in Figs. 4 and 5.
It can be seen that with the increase of nuclear units, the dynamic response speed of the power grid decreases significantly. The oscillation of frequency response as well as stability time increases when the proportion of nuclear units in the grid increases. In addition, the overshoot value is larger, which increases the possibility of the overspeed of the power system. The eigenvalues of dynamic response under load disturbance are listed in Table 1.
As shown in Table 1, the extremum of grid frequency is lower than 51.5 Hz when the proportion of unclear units is less than 47%, which means that the turbine speed cannot exceed the specified limits set by the OPC. The stability of the grid and balance of power and frequency are ensured by the normal digital electro-hydraulic (DEH) system. If 47% of the nuclear units joins in the grid, the frequency extremum would reach 51.5 Hz when 20% load is cut down, which would trigger the OPC and become a threat to the safe operation of the turbine plants. Once the proportion of the nuclear units exceeds 47%, to reach the balance of power and frequency, the OPC block may repeatedly close and open the valves, which would cause great crash to the turbine equipment such as turbine blades, pressure oil system, superheater and so on [
4]. The alternately closing and opening of valves would even result in an accident or a collapse of the power system. It should be noticed that in Fig. 5, there are two turning points in power response curve when the proportion of nuclear units is 60% as a result of the actions of the OPC.
From the discussions above, the conclusion can be drawn that the capacity limitation of the nuclear units in the power system is 47% under 20% load disturbance. For the grid mentioned in this paper, the allowable nuclear capacity is approximately 1955 MW.
Using the same method, this paper completes simulations of different load disturbances, ranging from 15%, 18%, 23% to 25%, and calculates the maximum allowable capacity of the nuclear units. The detailed results are given in Table 2.
To ensure the steady operation of the grid, certain capacities for frequency regulation should be maintained to defend the maximum load disturbance. It can be seen in Table 2 that as the load disturbance increases, the allowable capacity of the nuclear units decreases. The relationship between the capacity of the nuclear units in the grid and the load disturbance is almost proportional. Analysis of statistic data of load demand helps to estimate the maximum load disturbance, and the allowable capacity of the nuclear units in the grid can be calculated by the proposed simulation method on the premise of steady and safe operation.
Impact of condensing turbine units on the power system
Conventional power plants also include condensing turbine units. Condensing units have no reheat space, so its dynamic response is faster than reheat ones. This paper discusses the impact of frequency regulation with condensing turbine units on the grid. The detailed model for condensing units is presented in Fig. 3.
As for the grid, it is assumed that the proportion of condensing turbine units reaches 10%, approximately 416 MW. The simulation results when 20% of the load disturbance occurs are displayed in Figs. 6 and 7.
The simulation results prove that the condensing units are favorable in improving the stability of the grid. When the condensing turbine units join in frequency regulation, the dynamic characteristic improves, the overshoot value decreases, the response speed fastens, and the system reaches the steady state.
Figure 6 shows that, when the proportion of nuclear units in the grid is less than 61%, the power system can maintain the stability of frequency through the PFC function. The OPC is not triggered when 20% of the load disturbance is cut down. The extremum and steady value in dynamic response increase with the increase of the capacity of the nuclear units. When the capacity of the nuclear units exceeds 61%, the turbine units in the power system may suffer from overspeed or repeating actions of the OPC valves. From the discussion above, the conclusion can be drawn that for the grid with 10% of condensing turbine units, the allowable capacity of joined nuclear units is 61%, approximately 2530 MW.
The capacity limitation of the nuclear units in the grid under disturbance is listed in Table 3 and graphed in Fig. 8. It is seen clearly that condensing turbine units allow the grid to accept much more nuclear units by improving the ability of maintaining system frequency.
Impact of capacity limitation of the nuclear units on grid considering SFC
The simulations above only take the PFC into consideration but neglect the influence of the SFC. The SFC can regulate the frequency to nominal value by adjusting the loads of the units according to frequency and power deviation. This paper studies the impact of the SFC on frequency regulation and its influence on the allowable capacity of the nuclear units. The mathematic model for the simulation is depicted in Fig. 9 according to Ref. [
7].
The dynamic response curves of the reheat thermal units with the consideration of the SFC are exhibited in Figs. 10 and 11.
It is revealed that the SFC can eliminate frequency deviation by adjusting the power in the grid and keeping a balance between power and load. System frequency returns to an acceptable range of approximately±0.1 Hz. Figure 11 shows that the power and load of the grid reach a balance after frequency regulation. The progress time is much longer than that when the SFC is neglected, which indicates that the SFC regulates the slow quantity of the load. However, extremum of frequency has the same value as that when only the PFC works. The SFC has little effect on the dynamic overspeed of the reheat turbine units and cannot improve the ability to defend load disturbance to a great extent. In this case, the allowable capacity of the nuclear units in the grid is not improved.
For the grid with a 10% of condensing turbine units, the dynamic response curves after taking the SFC into consideration are shown in Figs. 12 and 13.
Different from cases with all reheat thermal units, the SFC can reduce the overshoot of the grid frequency with certain condensing turbine units. The frequency extremum in dynamic progress is lower than that when the SFC does not work. Therefore, the allowable capacity of the nuclear units in the grid is improved to 64%, approximately 2660 MW.
The relationship between load disturbance and capacity limitation of the nuclear units in different styles of frequency regulation is listed in Table 4 and shown in Fig. 14.
From Fig. 14, it can be observed that the analysis of the dynamic response can be used to estimate the capacity of the nuclear units in the grid. Both the condensing turbine units and the SFC can improve the ability for defending disturbance and accident to a certain extent. Also, the allowable capacity of the nuclear units in the grid increases after considering the condensing turbine and the SFC.
Conclusions
This paper focuses on the dynamic behavior of the grid with nuclear units under load disturbance and proposes the OPC critical action as a constraint of safe operation when estimating the allowable capacity of nuclear in the grid. Dynamic simulations are performed to analyze the ability of frequency regulation. The main conclusions drawn from this study are summarized as follows:
1) To ensure the security of the power system, the OPC cannot be frequently triggered when disturbance occurs. The capacity limitation can be estimated by comparing the frequency overshoot and limitative speed in dynamic process.
2) Condensing turbine units have faster response speed and lower overshoot in dynamic process than reheat turbine units due to the lack of reheat space. They help to improve both the stability and allowable capacity of the nuclear units in the power system.
3) The SFC has little effect on the dynamic overspeed of reheat turbine units, but to a certain extent, it can improve the ability to defend load disturbance and the allowable capacity of the nuclear units in the grid with condensing turbine units.
Higher Education Press and Springer-Verlag Berlin Heidelberg
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