Performance enhancement and optimization of primary frequency regulation of coal‐fired units under boundary conditions

Under the dual‐carbon goal, due to the long‐term operation of thermal power units under wide load and frequent fluctuating load after heat supply transformation, the dynamic process of subcritical units is modeled, and a frequency modulation optimization technology based on frequency signal accuracy is proposed to ensure the accuracy of the speed signal and improve the qualification rate of primary frequency modulation action. At the same time, the frequency regulation technology of steam engine side control optimization under boundary working conditions is proposed, so as to realize the sensitivity and rapidity of the digital electric hydraulic control system. The coordination optimization technology under boundary working conditions is proposed, and the primary frequency regulation performance of the unit is improved through a series of optimization adjustments. Finally, the engineering application is carried out and the optimization effect is analyzed.


| INTRODUCTION
With the advancement of the process of building a new type of power system, higher requirements have been put forward for the regulation support capability of thermal power units, and the frequency regulation boundary of the units in very deep working conditions after the flexibility transformation and heat supply transformation is restricted.][12] The primary frequency modulation response performance of thermal power units is affected by a variety of factors, such as signal acquisition, control strategy, and nonlinearity of the speed control mechanism.Pan et al. 13 analyzed 10 MW case system integrated with a 350 MW thermal power unit.Gao et al. 14 establish the mechanism model under different operating conditions and analyze the dynamic characteristics of the ultra-supercritical unit.Yang et al. 15 incorporated conventional control strategies in a subcritical unit and investigated the effects of sudden load changes on a subcritical unit.Huang et al. 16 verified the feasibility of building an ultrasupercritical unit at high steam temperature and pressure by using the lion group algorithm.Hou et al. 17 proposed a fuzzy neural network-based modeling method for ultrasupercritical units.Tontu et al. 18 to improve energy utilization.Conversion of waste heat into electrical energy to improve the performance of subcritical units to enable them to reach supercritical steam power plants.However, the above research basically focuses on the improvement of frequency modulation performance under conventional operating conditions.Deb et al. 19 propose an automated decision procedure for obtaining dynamic single optimal solutions online by adequately tracking the online Pareto optimality bounds.Babushkin et al. 20 analyzed the main modes of condenser operation for a 300 MW power unit capacity of a thermal power unit turbine and established a mathematical model through the results of the resulting analysis.Sultanov et al. 21estimated the depreciation effect of long service time on the efficiency of steam boilers and turbines in steam thermal power plants and developed a statistical data-based boundary operating condition algorithm.Buchta et al. 22 conducted a comprehensive reliability study of the power plant's 370 MW lignite-fired generating unit by analyzing the mean time between failures, the expected failure rate, and the mean time between outages.
This paper establishes an accurate dynamic model of the subcritical unit under boundary conditions, and proposes the optimization strategy of the unit's frequency modulation and the automatic control strategy of the heating unit's deep peaking process, so as to effectively improve the frequency modulation response capability of the unit under boundary conditions and meet the requirements of the grid for the support of the thermal power unit in terms of cleanness, high efficiency, and flexibility.
1.The subcritical unit is modeled based on thermodynamic knowledge, and different optimization strategies are proposed for the limit processing conditions and maximum frequency deviation.2. The simulation verification of the subcritical unit under different boundary conditions was carried out and compared with the actual operating conditions, and the results show that the established model and operation strategy can simulate the actual operating conditions and the model is established correctly.

| MODELING OF SUBCRITICAL UNITS
According to the heat flow, the energy conversion process of the subcritical unit in Figure 1 is divided into three processes: furnace (combustion and heat transfer in the furnace), pot (steam heat exchange and transfer), and steam engine (work done by the turbine).On this basis, the equilibrium equation in the energy transfer process of the subcritical unit is established. 23,24Thermal power units, embodiments of thermodynamic principles, function as electricity generation systems wherein thermal energy is methodically converted into electrical power.These units predominantly hinge on the exothermic combustion of fossil fuels within a boiler, a process engendering high-pressure steam.The ensuing steam propels turbines, intricately connected to generators, thereby transmuting mechanical energy into electrical energy through electromagnetic induction.Fossil fuels, including coal, oil, and natural gas, serve as the primary energy reservoirs, undergoing combustion to facilitate heat release.Alternatively, renewable resources, such as biomass, geothermal heat, or solar thermal energy, can be employed in the steam generation process.The Rankine cycle, a thermodynamic model, predominantly governs the operational paradigm, orchestrating the sequential phases of steam generation, expansion through turbines, and condensation.Noteworthily variations include combined-cycle configurations, amalgamating gas and steam turbines for augmented efficiency.As technological strides persist, contemporary thermal power units strive for heightened efficiency, reduced environmental ramifications, and seamless integration with emerging energy paradigms, underscoring a dynamic landscape in power generation.

| Combustion and heat transfer processes in the furnace
The combustion and heat transfer processes in the furnace can be represented as inertial links with pure time delays In Equation ( 1) τ 1 , T 1 , T 2 , k 1 can be obtained by calculation or test.According to the empirical data, there are generally: τ 1 = 2-5 s, T 1 = 5-10 s, formula (2), D Q indicates the boiler evaporation.In the normal peaking operation condition, we usually have T 2 = 5-7 s.T 2 can be determined according to the boiler's water-cooled wall and metal heat storage, relative to the rate of change of the boiler load, T 2 = ∂J/∂D.
Most of the thermal power units in the country are now using direct blow pulverizing systems, and a link describing the pulverizing system should be added before the amount of fuel: In Equation ( 3), B 0 is the amount of raw coal entering the pulverizing system, V 1 is the amount of primary air, and Q M pair is the amount of raw coal loaded into the coal mill.According to the boiler combustion test data, the time constant T M = 30-50 s.Separating the heat storage capacity of the boiler and steam piping, the heat storage capacity of the boiler can be obtained as: In Equation ( 4), C b is the thermal storage coefficient of the boiler, which can be determined by test.

| Steam heat exchange and transfer
Considering the main steam piping as a centralized parametric system, the heat storage capacity can be expressed as: where C n is the steam pipe heat storage coefficient; Q n is the amount of steam in the main steam pipe; V n is the steam pipe volume; γ n is the steam gravimetric coefficient.
The relationship between the pressure drop at the ends of a steam line and the steam flow rate through the line is given by: where k is Resistance coefficient of steam piping.

| Simplified dynamic modeling of subcritical units
Based on the static model of the subcritical unit established above, the model of the unit is simplified by considering the boiler and the main steam piping as a Simplified energy transfer process of thermal power unit.
centralized heat storage volume, 25 so that Equations ( 4) and ( 5) can be combined as: where c is the heat storage coefficient of the boiler and main steam piping.
The relationship between the pressure drop at the ends of a steam pipe and the flow rate of steam into the turbine is: In Equation ( 9), k T is the resistance coefficient of the steam piping and the main steam control valve.The corresponding system structure diagram is also simplified to the form shown in Figure 2. Subcritical unit coordination system as a typical dualinput dual-output system, the actual unit coordination control is usually set up in the distributed control system (DCS) boiler master control and steam engine master control respectively, to correspond to the actual unit control system, based on the simplified nonlinear model of the unit, the simplified model will be derived in the form of transfer function.
where M(s) is the turbine dynamic process and N(s) is the fuel dynamic process, respectively.
G s ( ) 0 in the transfer function matrix reflects the coupling relationship within the components in the whole system and is the core part of the unit crew model.The unit dynamic model applicable to the actual control system can be derived as: .
Ne are the transfer functions between fuel and main steam pressure and unit power; Ne t are the transfer functions between turbine regulator and main steam pressure and unit power.The further control system structure based on the thermal characteristics of the unit is converted into a more explicit control system structure of coordination and primary frequency modulation based on the dynamic characteristics of the unit as shown in Figure 3, which is in line with the actual application of the DCS control system of the unit.The primary frequency modulation function of the unit is composed of two parts: the unit master control instruction of the coordination side (CCS) and the digital electro-hydraulic control instruction (DEH) of the steam engine side, which are independent of each other, and the instruction adopts the superposition method to achieve the purpose of by controlling the opening degree of the steam engine regulating door, and the principle of the primary frequency modulation function is shown in Figure 4.
In principle, the primary frequency modulation function can be influenced from both the boiler side and the steam engine side.Boiler-side influence factors are mainly boiler energy storage, mainly reflected in the main steam pressure.When the main steam pressure is low, the primary frequency modulation response to load increase capacity is weakened, and when the main steam pressure is high, the primary frequency modulation response to load reduction capacity is weakened.At present, most of the units adopt slip parameter operation to ensure that the turbine regulating gate maintains a large opening while reducing the throttle of the regulating gate, and in this way improve the safety and economy in the operation process.

| Frequency modulation boosting technology for optimized control on the steam engine side
DEH control system is the main system to realize the regulating role of turbine regulator.According to the requirements related to primary frequency modulation, it can be optimized and adjusted from the following strategies: Segmented setting speed: when a frequency conversion is put into use, the frequency conversion effect of the low frequency difference section is not good, to enhance its ability to regulate the low frequency difference section, it can adopt the method of setting the speed inequality rate in segments, adjusting the speed inequality rate in a timely manner according to the magnitude of the frequency difference to improve the performance of the frequency conversion of the low frequency difference section and at the same time avoiding the overly strong action of the large frequency difference section of the one-time frequency conversion.
Correction of feedforward coefficient: The feedforward coefficients of the primary frequency modulation DEH feedforward action module are differentiated in different modes, loads and pressure segments.The operating mode, pressure and load of the unit have a direct impact on the turbine energy storage, so it is necessary to set feedforward coefficients matching different operating conditions to reduce the impact of changes in load, pressure and other operating parameters on the performance of primary frequency modulation.
The frequency modulation control strategy for optimized control on the steam engine side can be set based on the above technology.Based on the relevant requirements such as primary frequency modulation integral power in the grid assessment rules, the load compensation curve gain can be set with variable parameters from the time perspective.The specific optimization scheme is shown in Figure 5.

| Frequency modulation boosting technology with coordinated measurement optimization control
Aiming at the problems of unit primary frequency modulation inversion, insufficient frequency modulation response speed and duration, the unit primary frequency modulation performance can be improved through a series of optimization and adjustment strategies starting from the distributed control system (DCS) side.
Fast-action slow-return technology: When the primary frequency modulation action is in progress, the coal powder inside the coal mill is blown into the furnace quickly by increasing the set value of the pressure of the primary air duct, increasing the intensity of combustion in the furnace, and making full use of the leftover powder of the coal mill to accelerate the load response speed; setting the primary frequency modulation priority, shielding the AGC instruction that is inverse to the primary frequency modulation action, and preventing the effect of AGC on the primary frequency modulation.
Preventing reverse reversal: Under the premise of ensuring the safe operation of the unit, the main steam pressure is increased to limit the control loop of the unit, preventing reverse reversal of the high-pressure regulator when the unit does not reach the rated power because of the high deviation of the main steam pressure.
According to the above technology setup coordinated side pin optimization control strategy, for the problems of unit primary frequency modulation inversion, insufficient frequency modulation response speed and duration, and so forth, a series of optimization adjustments are made to improve the performance of unit primary frequency modulation.The specific optimization scheme is shown in Figure 6.

| Examples of engineering applications of frequency modulation technology
Applying the above DEH and DCS side control strategy to an engineering example, the primary frequency modulation logical structure framework is constructed based on the logical configuration of the unit.According to the AGC command step volume pre-adding and subtracting coordinated mode steam engine power master control power set value reversal will be preadding and subtracting volume cut off.Finally, increase the feedforward of the high-pressure heater extraction valve for primary frequency modulation.As effectively as possible to enhance the unit frequency modulation integral power.
The project after the second and third phases of the special test, only one frequency modulation from the monthly assessment of more than 500,000 yuan, down to less than 100,000 yuan of monthly assessment volume, the qualification rate increased by 60%, the optimization received good results.
F I G U R E 6 Primary frequency modulation optimization on distributed control system side.
T A B L E 1 Modeling of dynamic characteristics of typical subcritical unit coordinated control system under different loads.The raw data were taken to calculate the unit model parameters for different load conditions (80%Pe, 60%Pe, 40%Pe) as shown in Table 1.

G s ( )
The load and main steam pressure calculated by the model are compared with the actual unit stepdisturbance test data, and the load and pressure characteristics under fuel step-disturbance at 240 MW are shown in Figure 8, for example, which shows that the parameters of the model are basically the same as the actual test parameter curves of the unit, and the reliability of the model is also verified.The load and main steam pressure calculated by the model are compared with the actual unit step disturbance test data, and the load and pressure characteristics under fuel step disturbance at 240, 360, and 480 MW are shown in Figures 7-9.As can be seen in the figure, no matter the unit is under 240, 360, and 480 MW load, the unit load curve of the model is basically more than 99% similar to the actual test parameter curve of the unit, and the main steam pressure curve is more than 95% similar to the actual test parameter curve of the unit, which verifies the reliability of the selected model.
The improved control strategy is simulated for the unit at 50% Pe, 35% Pe, and 20% Pe under the boundary conditions of 6 r/min and −6 r/min, respectively, and compared with the actual data before improvement, and the simulation results are shown in Figures 10-12.
It can be seen that when the unit is at 50% Pe, the unit is in good condition, the frequency modulation performance is excellent, and the unit is not improved much before and after the improvement.35% Pe, the unit is in the low load stage, and at this time, no matter F I G U R E 10 Comparison before and after the of the +6 r/min and −6 r/min control policies at 50% Pe.whether the load disturbance of 6r or -6r the unit can't keep up with it well, and after the improvement of the boundary condition, it can be seen that the unit's response speed and the steady state output have been improved.20% Pe, because the unit itself has to maintain Under 20% Pe, since the unit itself has to maintain its own state, the frequency regulation ability is poor, and compared with the actual data before improvement, the strategy proposed in this paper has a better frequency regulation effect while maintaining the operation of the unit.

| CONCLUSION
Based on the background of the construction of a new type of power system, this paper puts forward the primary frequency modulation performance enhancement and optimization technology of coal-fired units under boundary working conditions.The research results of this paper substantially improve the frequency regulation capability of thermal power units under various boundary operating conditions, realizing the full operating conditions to support the frequency of the power grid, and at the same time guaranteeing the safe and stable operation of the units and the power grid.The following conclusions are obtained: 1. Based on the conventional operating condition frequency modulation model of thermal power units, an accurate frequency modulation model under subcritical operating condition is constructed by increasing the operating characteristics and boundary conditions of the research units; the load and main steam pressure calculated by the model are compared with the data of the actual unit step-disturbance test, and the similarity between the modeled unit load curves and the actual test parameter curves of the unit is more than 95% in the case of 240, 360 and 480 MW, which verifies the reliability of the model.2. Aiming at the thermal power unit operating output limit conditions, maximum frequency difference perturbation and other boundary conditions, a multi-mode, self-stabilized frequency modulation comprehensive optimization technology is proposed; the practical application of the strategy in the project shows that while taking into account the safety, it can significantly improve the primary frequency modulation capability of the unit, and there is a better enhancement of the frequency modulation capability before and after the improvement in the low load stage of 20%-50%.

3
| UNIT FREQUENCY OPTIMIZATION STRATEGIES FOR DIFFERENT BOUNDARY OPERATING CONDITIONS According to the subcritical unit model to analyze a 600 MW subcritical unit, respectively in 480, 360, 240 MW to take the fuel positive and negative F I G U R E 2 Simplified dynamic characteristic structure diagram of the unit.perturbation 14t/h step perturbation test and the regulator positive and negative perturbation 4% step perturbation test.

F
I G U R E 3 Coordination and primary frequency modulation control system based on the actual distributed control system system.F I G U R E 4 Schematic diagram of the primary frequency modulation function.F I G U R E 5 Primary frequency modulation optimization on the Digital electric hydraulic side.

F I G U R E 7
Comparison between the parameters of the identification model and the actual test parameters of the unit under 240 MW.I U R E 8 Comparison between the parameters of the identification model and the actual test parameters of the unit under 360 MW.I U R E 9 Comparison between the parameters of the identification model and the actual test parameters of the unit under 480 MW.

F
I G U R E 11 Comparison before and after the improvement of the +6 r/min and −6 r/min control policies at 35% Pe.F I G U R E 12 Comparison before and after the improvement of the +6 r/min and −6 r/min control policies at 20% Pe.
Q n the amount of steam in the main steam pipe V n the steam pipe volume γ n the steam gravimetric coefficient k Resistance coefficient of steam piping c the heat storage coefficient of the boiler and main steam piping k T the resistance coefficient of the steam piping and the main steam control valve G between fuel and main steam pressure and unit power G μ P t st , G μ Ne t the transfer functions between turbine regulator and main steam pressure and unit power