Analysis and Optimization of Dynamic Characteristics of Primary Frequency Regulation Under Deep Peak Shaving Conditions for Industrial Steam Extraction Heating Thermal Power Units

Abstract

This study investigates the primary frequency regulation dynamic characteristics of industrial steam extraction turbine units under deep peak regulation conditions. A high-fidelity integrated dynamic model was established, incorporating the governor system, steam turbine with extraction modules, and interconnected pipeline dynamics. Through comparative simulations and experimental validation, the model demonstrates high accuracy in replicating real-unit responses to frequency disturbances. For the power grid system in this study, the frequency disturbance mainly comes from three aspects: first, the power imbalance formed by the random mutation of the load side and the intermittence of new energy power generation; second, transformation of the energy structure directly reduces the available frequency modulation resources; third, the system-equivalent inertia collapse effect caused by the integration of high permeability new energy; the rotational inertia provided by the traditional synchronous unit is significantly reduced. In the cogeneration unit and its control system in Guangxi involved in this article, key findings reveal that increased peak regulation depth (30~50% rated power) exacerbates nonlinear fluctuations. This is due to boiler combustion stability thresholds and steam pressure variations. Key parameters—dead band, power limit, and droop coefficient—have coupled effects on performance. Specifically, too much dead band (>0.10 Hz) reduces sensitivity; likewise, too high a power limit (>4.44%) leads to overshoot and slow recovery. The robustness of parameter configurations is further validated under source-load random-intermittent coupling disturbances, highlighting enhanced anti-interference capability. By constructing a coordinated control model of primary frequency modulation, the regulation strategy of boiler and steam turbine linkage is studied, and the optimization interval of frequency modulation dead zone, adjustment coefficient, and frequency modulation limit parameters are quantified. Based on the sensitivity theory, the dynamic influence mechanism of the key control parameters in the main module is analyzed, and the degree of influence of each parameter on the frequency modulation performance is clarified. This research provides theoretical guidance for optimizing frequency regulation strategies in coal-fired units integrated with renewable energy systems.

1. Introduction

With the large-scale integration of new energy and the continuous expansion of load peak-valley difference in power systems, the deep peak-shaving operation of thermal power units has become an important technical means to ensure the flexibility and frequency stability of the power grid [1] and the nonlinear effect of low load [2]. The influence of multiple factors, such as frequency modulation parameter settings, and so on. It is easy to cause power overshoots, regulation delays, and even instability, which seriously threatens the safe operation of the power grid [3]. Therefore, it is of great theoretical value and engineering significance to reveal the dynamic response mechanism of frequency modulation [4] of industrial steam extraction thermal power units, under the condition of deep peak regulation, and optimize the configuration [5] of key frequency modulation parameters, so as to improve the frequency stability of the power system [6].

At present, scholars’ research in the field of heating-unit modeling always takes the thermoelectric decoupling technology route as the core breakthrough direction. The research mainly focuses on the iteration of mechanism modeling methods for system dynamic response and the technological breakthroughs for enhancing system flexibility to improve energy utilization elasticity. The change in the extraction flow rate will significantly change the power distribution [5] of the steam turbine. However, the existing models mostly adopt the linearization hypothesis [6], which makes it difficult to accurately describe the nonlinear characteristics of boiler combustion stability criticality and steam pressure fluctuation under low loads.

In addition, in view of the deep peak-shaving (such as 30~50% rated load) scenario, the existing research lacks quantitative analysis of the synergistic effect of frequency modulation dead zones [7], amplitude limiting [8], and adjustment coefficients [9], which leads to the dependence of the parameter setting on experience, as well as it being difficult to balance the adjustment sensitivity and system stability [10].

For the modeling of the dynamic characteristics of frequency regulation, reference [11] established an integrated simulation system for condensation and heating conditions based on the Matlab (2024a) platform. For the first time, they quantified the influence of the steam extraction flow rate on the frequency regulation transfer function and found that the frequency regulation lag time of the unit increased by 40% under the heating condition. Aiming at frequency regulation assisted by thermal network energy storage, reference [12] proposes a coordinated control scheme based on thermal energy storage. By utilizing the feedforward signal of the district heating quick-closing valve opening to decompose the rapidly varying components of the load command, the unit’s load change rate is increased to 3% Pe/min, while the turbine inlet pressure fluctuation is reduced by 35%. Reference [13] integrated an electric boiler and a heat storage tank in a 330 MW unit. Through thermoelectric decoupling, the lower limit of the peak shaving load was reduced to 28% of the rated power. Aiming at the inaccuracies in the primary frequency regulation model of conventional thermal power units under deep peaking conditions, reference [6] proposes a variable parameter-modeling and identification method. By deriving the nonlinear relationship between parameters and main steam pressure and achieving parameter order reduction, the new model—validated at Luoyang Power Plant in Henan—stably characterizes frequency regulation dynamics across different loads with consistent accuracy.

Scholars’ research on the dynamic characteristics of frequency regulation in heating units under deep peak-shaving conditions also focuses on thermo-electric decoupling technology and multi-energy collaborative optimization. In recent years, with the increasing integration of renewable energy into the grid, the rapid frequency regulation capability of heating units has become crucial for maintaining grid frequency stability. Regarding the application of thermo-electric decoupling technologies to frequency regulation, reference [14] proposed a thermo-electric decoupling system based on absorption heat pumps, which enhances the peak shaving capacity by recovering waste heat from circulating water. The study demonstrated that the thermal storage response time could be reduced to under two minutes, significantly improving the frequency regulation dynamics of the unit under low-load conditions. Through Aspen Plus modeling and analysis, reference [15] found that the coupled system could increase the peak shaving depth to 21.85%, and the electro-thermal control strategy improved the load response rate by over 30%. For multi-energy collaborative optimization, reference [16] proposed a distributionally robust optimization model for a combined wind–solar–storage–heat system. By dynamically categorizing peak shaving modes (conventional peak shaving, deep peak shaving, and energy storage peak shaving), the study quantified the optimal frequency regulation economics of heating units at 54% rated load. Further exploring the frequency regulation benefits of combined operation between electric-driven heat pumps (P2H) and heating units, reference [17] proposed a configuration optimization method based on the static payback time (SPT), verifying that P2H equipment could increase the frequency regulation response speed to 3% Pe/min.

The limitations of the current modeling method need to be broken through. Firstly, the existing research has not fully considered the coupling effect of boiler combustion stability and heating network delay effect in deep peak shaving conditions, resulting in the contradiction between the tracking accuracy of frequency modulation power and the robustness of heating parameters has not been fundamentally improved. Secondly, the current model mostly adopts the discrete steady-state operating point modeling method, which fails to construct a dynamic model with continuous adjustable load characteristics under all operating conditions, and it is difficult to support frequency modulation control under wide operating conditions.

Under the deep peak-shaving condition, the heating unit needs to deal with the rapid fluctuations and strong coupling characteristics of both electricity and heat loads simultaneously. Due to its simplified assumptions, it is difficult to accurately characterize the nonlinear dynamic behavior of the traditional dynamic model, resulting in insufficient simulation accuracy. This paper studies the construction and improvement of dynamic models for heating units, establishes a speed regulation system model, introduces a heating-power feedback mechanism and a closed-loop control strategy for butterfly valve steam extraction, and investigates the model of a series combined single reheat steam turbine. Then, it analyzes the frequency regulation response characteristics of the unit under different peak-shaving depths and quantifies the influence degree of key control parameters on the dynamic process.

In view of the above problems, this paper takes the industrial extraction thermal power unit as the research object; constructs a refined dynamic model covering the speed control system, the single-series reheating steam turbine, and the extraction module of the medium- and low-pressure connected pipeline; focuses on the dynamic characteristics of primary frequency regulation under the condition of deep peak regulation; and conducts targeted discussions on the following aspects:

(1)

The simulation accuracy of the model in a wide load range is verified by comparing the step disturbance test data of the actual unit.

(2)

The influence mechanism of the change in peak shaving depth on the nonlinear fluctuation of the frequency modulation process is analyzed, and the coupling law between the sudden change in the heating extraction amount and the frequency disturbance is revealed.

(3)

The influence path of frequency modulation dead zone, limiting, and adjustment coefficient on dynamic response characteristics is systematically explored, and the parameter optimization interval, considering both adjustment speed and stability, is proposed.

(4)

Combined with the source-load bilateral random-intermittent coupling disturbance scenario, the improvement effect of parameter configuration on the anti-interference ability of the system is evaluated, which provides theoretical support for the design of a frequency modulation control strategy for industrial extraction units.

2. Basic Model of Industrial Extraction Thermal Power Unit

The basic architecture of a thermal power plant for heating is shown in Figure 1.

The core of this heating-supply unit consists of three key subsystems: a PID-based dynamic model of the speed control system, a tandem single-reheat steam turbine model integrated with a heating module, and a steam extraction heating model for the intermediate-low pressure crossover pipeline equipped with a butterfly valve. During system operation, the governor receives speed and load setpoints to establish closed-loop control. Based on these inputs, the governor generates a valve-opening command, which is actuated by the servo mechanism to adjust the turbine control valve position. The valve opening position and main steam pressure collectively determine the main steam flow rate—a parameter that directly governs the energy input to the turbine. The steam turbine converts thermal energy from steam into mechanical power while simultaneously outputting shaft speed and heating steam flow. The mechanical power is transferred via a coupling to the generator, where electromagnetic power is generated through electromagnetic conversion. The system continuously monitors the generator’s electromagnetic power output and rotational speed signals, feeding them back to the governor to form a complete closed-loop regulation circuit.

In actual industrial production, the inertial time constant of the spool valve differs by more than 100 s from that of the hydraulic actuator by an order of magnitude. Therefore, when building the transfer function model, the influence of the spool valve time constant on the actuator can be ignored. The mathematical model of the speed control system and its extraction module is as follows:

$$\left\{\begin{array}{c}{L}_D(t)=L_Z(t)+T_D{\displaystyle \frac{d{L}_h(t)}{dt}}+L_h(t)\\ T_h{\displaystyle \frac{d{L}_z(t)}{dt}}-L_h(t)=0\\ k_{GV}{P}_{GV}-k_p{p}_m=V_m{\displaystyle \frac{d{\rho }_g}{dt}}\\ T_e{\displaystyle \frac{dB}{dt}}+B=M_{IP}-M_e\\ T_{dv}{\displaystyle \frac{d{M}_e}{dt}}+M_e=K_{es}·B\\ Q={\displaystyle \frac{{\epsilon }^{-s{T}_{FUEL}}}{1+s{T}_{FL}}}{B}_r\\ m_W={\displaystyle \frac{1}{1+s{T}_{WF}}}Q\end{array}\right.$$

(1)

In the formula, $L_D$ is the control of the displacement of the slide valve; $L_Z$ is the oil motor displacement; $L_h$ is the displacement of the slide valve; $T_D$ is the inertia time constant of the slide valve; $T_h$ is the inertia time constant of the oil motor; $k_{GV}$ is the static magnification of the adjustable door, $P_{GV}$ is openness of the governing valve; $k_p$ is the internal pressure static magnification of the system, $p_m$ is the internal pressure of the system, $V_m$ is the internal volume of the system; ${\rho }_g$ is gas density; $T_e$ is the time constant of the heating extraction volume; $B$ is the heating extraction volume output, $M_{IP}$ is the medium-pressure cylinder outlet steam flow; $M_e$ is the steam extraction heating flow; $M_{LP}$ is the low-pressure cylinder intake flow; $K_{es}$ is the pressure-unequal coefficient; $Q$ is the fuel combustion power; $T_{FL}$ and $T_{FUEL}$ are the combustion response time constant and the combustion lag time constant; $m_W$ is the absorption power of the water wall; $T_{WF}$ is the heat absorption time constant.

A more detailed explanation, the linearization, and the parameter threshold setting are described below.

This model features multi-mode switching capabilities, including regulating stage pressure control, DEH open-loop control, and load control. However, in this paper, considering the specific operational conditions, heating units must respond in real-time to thermal user demands and grid load fluctuations, dynamically adjust output parameters, and participate in deep peak-shaving operations; the load control mode offers significant technical advantages. The primary rationale for this decision is that the massive heat storage characteristics inherent in the heating network enable the rapid adjustment of the power generation load through quick-closing valve-opening adjustments. This feature creates a synergistic effect with the rapid response mechanism of the load control mode.

The actuator is mainly composed of an electronic–hydraulic converter and the oil motor. The signal received by the module is the gate-opening instruction $P_{CV}$, and the output signal is the gate-opening signal $P_{GV}$. The actuator usually adopts the spool valve oil motor in actual production, so the opening command of the regulating valve is characterized by the displacement of the control spool valve $L_D$, and the opening signal of the regulating valve is characterized by the displacement of the oil motor $L_Z$.

$$L_D(t)=L_Z(t)+T_D{\displaystyle \frac{d{L}_h(t)}{dt}}+L_h(t)$$

(2)

$$T_h{\displaystyle \frac{d{L}_z(t)}{dt}}-L_h(t)=0$$

(3)

In actual industrial production, the difference between the inertial time constant of the slide valve and the inertial time constant of the oil motor is more than 102 s. Therefore, when building the transfer function model, the influence of the time constant of the slide valve on the actuator can be ignored. The transfer function can be obtained after the above two equations are transformed into

$${\displaystyle \frac{L_Z(t)}{L_D(t)}}={\displaystyle \frac{1}{T_{h}s+1}}$$

(4)

According to reference [18], considering the characteristics of frequency regulation and power regulation, the governor model and actuator model are established and shown in Figure 2.

In Figure 2: $\mathsf{∆}\omega$ is the deviation between the speed reference value and speed (${\omega }_{ref}-\omega$); T1 is the inertia time constant of the frequency measurement link; $K$ is the speed deviation magnification (adjustment coefficient); $K_2$ is the feedforward coefficient of load control; $K_P$, $K_I$, and $K_D$ are PID proportional, differential, and integral link multiples; $P_{CV}$ is the opening instruction signal of the adjusting door.

During steam turbine operation, the principle of mass conservation dictates that the difference between the gas mass flow rate entering and leaving the system per unit time equals the product of the system’s internal volume and the rate of density change in the gas, as mathematically expressed in Equation (5):

$$q_{in}-q_{out}=V_m{\displaystyle \frac{d{\rho }_g}{dt}}$$

(5)

In the formula, $q_{in}$ represents the gas flow into the system; $q_{out}$ to leave the gas flow of the system; $V_m$ for the internal volume of the system; and ${\rho }_g$ for gas density.

According to the valve-opening and gas flow characteristics, the gas flow into the system and the valve opening can be equated to the following relationships:

$$q_{in}=k_{GV}{P}_{GV}$$

(6)

In the formula, $k_{GV}$ is the static magnification of the regulating valve, and $P_{GV}$ is the opening of the regulating valve.

At the same time, the gas flow rate leaving the system and the internal pressure of the system can also be equivalent to the following relationship.

$$q_{out}=k_p{p}_m$$

(7)

In the formula, $k_p$ is the static magnification of the internal pressure of the system, and $p_m$ is the internal pressure of the systems.

Substituting (7) and (6) into Equation (5), we can obtain the following:

$$k_{GV}{P}_{GV}-k_p{p}_m=V_m{\displaystyle \frac{d{\rho }_g}{dt}}$$

(8)

Based on the law of mass conservation in the process of gas flow, the state of gas changes according to the changing process, and the following formula is obtained:

$$k_{GV}{P}_{GV}-k_p{p}_m=V_m{\displaystyle \frac{d{\rho }_g}{dt}}·{\displaystyle \frac{{\rho }_g}{N{p}_m}}$$

(9)

In the formula, N is the state index of the polytropic process.

About this nonlinear system, it can be approximately equivalent to a linear system near the equilibrium point, with its mathematical foundation lying in the multivariate Taylor expansion principle. Specifically, at the system’s equilibrium point, the nonlinear state equation is expanded, retaining the first-order partial derivative terms with respect to state deviations and control deviations (i.e., the Jacobian matrix), while deliberately neglecting second-order and higher nonlinear terms (which are negligible higher-order infinitesimals within a sufficiently small neighborhood). This transforms the original nonlinear equation into a linear time-invariant state equation concerning deviation quantities, achieving local linearization approximation in the neighborhood of the equilibrium point. Assuming that the equilibrium points of the key parameters in Equation (9) are ${\rho }_{g0}$, ${P_{GV}}_0$, and $p_{m0}$, the equation can be obtained.

$$k_{GV}(\Delta P_{GV}+P_{GV0})-k_p(\Delta p_m+p_{m0})=V_m{\displaystyle \frac{d{\rho }_g}{dt}}·{\displaystyle \frac{(\Delta {\rho }_g+{\rho }_{g0})}{N(\Delta p_m+p_{m0})}}$$

(10)

In the formula, $\Delta P_{GV}$ is a small increment at the balance point of the valve opening; $\Delta p_m$ is a small increment at the pressure equilibrium point in the system; $\Delta {\rho }_g$ is the small increment at the equilibrium point of gas density.

Since the small increment $\Delta {\rho }_g$ and the value $\Delta p_m$ of the relative equilibrium point can be neglected, Equation (10) can be further simplified to

$$k_{GV}\Delta P_{GV}-k_p\Delta p_m=V_m{\displaystyle \frac{d{\rho }_g}{dt}}·{\displaystyle \frac{{\rho }_{g0}}{N{p}_{m0}}}$$

(11)

Furthermore, the transfer function of the gas volume of the system can be obtained by the Laplace transform of Equation (11).

$${\displaystyle \frac{S_{pm}(s)}{S_{PGV}(s)}}={\displaystyle \frac{1}{1+\frac{V_m{\rho }_{g0}}{N}s}}={\displaystyle \frac{1}{1+Ts}}$$

(12)

In the formula, T is the system volume time constant.

Due to the similar dynamic characteristics of steam volume, reheater volume, and cross tube volume, the transfer function of steam volume, reheater volume, and cross tube volume can be obtained according to Equation (10). In view of the working characteristics of the heating-extraction module in actual industrial production (that is, the extracted heating steam will no longer return to the unit system), it is necessary to consider the heating power missing in the power feedback of the speed control system separately. According to the control block diagram of the steam turbine model and the structure diagram of the steam turbine model considering the heating-extraction module [18], the control block diagram of the series combined single reheats steam turbine model considering the heating-extraction module is shown in Figure 3.

In Figure 3, $\Delta M$ is the steam flow in the system because of the heat extraction. According to the characteristics, the parameters of the model in this study are mainly per unit value, and $\Delta M$ is numerically equal to the heating-power consumption $P_{es}$ corresponding to the heating steam. $P_M$ is the turbine output mechanical power; $F_{HP}$, $F_{IP}$, and $F_{LP}$ are the distribution coefficients of the high-, medium-, and low-pressure cylinders of the steam turbine, $F_{HP}+F_{IP}+F_{LP}=1$; $T_{ch}$ is the steam volume time constant; $T_{RH}$ is the reheater time constant; $T_{CO}$ is the cross-tube time constant; $\lambda$ is the natural overregulation coefficient of high-pressure cylinder power [18].

During the dynamic process, the output proportion of the steam turbine’s high-pressure cylinder will be greater than during steady-state operation. This phenomenon is described using the natural over-regulation coefficient of the high-pressure cylinder power, denoted as coefficient “$\lambda$”, located between the high-pressure cylinder and the intermediate-pressure cylinder. The input signal is the difference between the per-unit values of the governing stage pressure and the high-pressure cylinder exhaust pressure, while the output signal is the over-regulation increment of the high-pressure cylinder power.

The natural power overshooting coefficient of high-pressure cylinder power is an important parameter in the analysis of the dynamic characteristics of a steam turbine. It is used to describe the instantaneous overshoot phenomenon of high-pressure cylinder power when the load changes suddenly. The calculation method of the natural power overshooting coefficient of high-pressure cylinder power is as follows:

$$\lambda ={\displaystyle \frac{{\epsilon }^2}{1-{\epsilon }^2}}+{\displaystyle \frac{k-1}{k}}·{\displaystyle \frac{{\epsilon }^{\frac{k-1}{k}}}{1-{\epsilon }^{\frac{k-1}{k}}}}$$

(13)

$$\epsilon ={\displaystyle \frac{p_2}{p_1}}$$

(14)

In the formula, $\epsilon$ is the ratio of the outlet pressure of the high-pressure cylinder to the inlet pressure; $p_2$ is the outlet pressure of the high-pressure cylinder; $p_1$ is the inlet pressure of the high-pressure cylinder; k is the natural power overshooting calculation coefficient, usually taken as 1.3.

According to the gas volume transfer function described above, it can be known that the extraction volume of the heating-extraction module meets

$$M_{IP}-M_e=M_{LP}$$

(15)

$$T_e{\displaystyle \frac{dB}{dt}}+B=M_{IP}-M_e$$

(16)

where $T_e$ is the time constant of heating extraction volume; $B$ is the heating extraction volume output, $M_{IP}$ is the outlet steam flow of the medium-pressure cylinder; $M_e$ is the steam extraction heating flow; $M_{LP}$ is the intake flow of the low-pressure cylinder.

According to the working principle of the extraction module, the gas entering the butterfly valve will be affected by the unequal rate of pressure.

$$C=K_{es}·B$$

(17)

In the formula, $C$ is the heating steam extraction volume output affected by the pressure unequal rate; $K_{es}$ is the pressure-unequal coefficient.

According to the derivation of the transfer function of the oil motor, it can be concluded that the butterfly valve oil motor satisfies

$$T_{dv}{\displaystyle \frac{d{M}_e}{dt}}+M_e=C$$

(18)

In the formula, $T_{dv}$ is the time constant of the butterfly valve oil motor.

The Equations (13)–(16) are sorted out, and the Laplace transform can be obtained.

$$M_e(s)={\displaystyle \frac{K_{es}·B(s)}{1+s{T}_{dv}}}$$

(19)

$$B(s)={\displaystyle \frac{M_{IP}(s)-M_e(s)}{1+s{T}_e}}$$

(20)

The closed-loop transfer function can be obtained by combining (19) and (20).

$${\displaystyle \frac{M_e(s)}{M_{IP}(s)}}={\displaystyle \frac{K_{es}}{(1+s{T}_{dv})(1+s{T}_e)+K_{es}}}$$

(21)

Based on the transfer function derivation of the above heating extraction link, combined with the working characteristics of the heating-extraction module, the control block diagram of the medium- and low-pressure connected-pipeline extraction-heating module with a butterfly valve can be obtained as shown in Figure 4.

The basic working process of the module is shown in the figure: after the steam flow $M_{IP}$ at the outlet of the medium-pressure cylinder enters the system, subtract the steam extraction heating flow $M_e$, and the difference is processed via the extraction volume module to generate an output signal related to the time constant $T_e$. The signal is converted into a pressure deviation signal through the pressure unequal rate module $K_{es}$, and then adjusted by the PI controller according to the proportional gain and the integral gain to generate a control signal. The control signal passes through the butterfly valve oil motor module, and its dynamic characteristics are determined by the time constant $T_{dv}$. The intake flow $M_{LP}$ of the low-pressure cylinder is obtained by subtracting the extraction flow $M_e$ from the medium-pressure cylinder flow $M_{IP}$. The whole system maintains the stability of the steam extraction pressure through closed-loop control to ensure the balance of heating and power generation.

The most critical module in a two-stage bypass system is the bypass control system. Functioning as the actuator control unit, this subsystem primarily regulates the opening parameters of the high-pressure and low-pressure bypass valves while performing closed-loop control of the attemperator water mass flow based on thermodynamic equilibrium equations. By continuously monitoring key process variables such as main steam pressure, the subsystem utilizes PID control to adjust both the pressure-reducing valve opening coefficient and attemperator water injection flow. This ensures compliance with the rate-of-pressure-change constraints.

Based on the above analysis and preceding studies on actuating mechanisms. By integrating the heating-extraction module, the two-stage bypass system, and the medium-pressure regulating valve actuator, the steam turbine module of the heating unit can be transformed as shown in Figure 5.

3. Simulation Analysis of Primary Frequency Regulation of Industrial Steam Extraction Thermal Power Unit Under Deep Peak Regulation Condition

As an example of a deep peak-shaving heating unit, this study focuses on the simulation modeling of an N300-16.7/38/538-9 steam turbine and its governing system in a Guangxi-based cogeneration unit. The turbine is configured as follows: one high-pressure main steam valve and one combined intermediate-pressure steam valve are installed on each side. The oil servo cylinders for the high-pressure control valves, the right-side high-pressure main steam valve, and the intermediate-pressure control valves employ continuous hydraulic actuators, enabling precise valve-opening control. The key technical parameters of the unit are as follows: rated power output of 300 MW, with a maximum continuous output reaching 312 MW. The matched generator model is QFSN-303-2-20D, with rated parameters including a frequency of 50 Hz, rotational speed of 3000 r/min, active power of 300 MW, and a voltage level of 22 kV. The governing system utilizes the XDPS-400+ distributed control system, which features multivariable coordinated control, rapid load response, and operational parameter optimization, meeting the requirements for power system stability calculation and analysis. The reference value of the output mechanical power per unit is set to the rated power of 300 MW, and the frequency reference value is set to 50 HZ.

The main control parameters of the cogeneration unit are listed in

Table 1. Model parameters of steam turbine and speed control system.

Parameter	Numerical Value	Parameter	Numerical Value
Steam volume time constant	0.22	Output upper limit of the amplification stage	10.0
High-pressure cylinder power proportional coefficient	0.3005	Output lower limit of the amplification stage	−10.0
Proportional coefficient of intermediate pressure cylinder power	0.2801	Over-speed opening coefficient	0.1619
Low-pressure cylinder power proportional coefficient	0.4194	Oil engine opening time constant	−0.2394
Reheater time constant	10.0	Oil engine opening time constant	6.744
Cross tube time constant	2.30	Closing-time constant of the hydraulic actuator	4.521
PID of the governor model	0.1, 0.06667, 0	Time constant of the stroke feedback loop for the hydraulic engine	0.02
Natural overshoot coefficient of high-pressure cylinder power	0.6006	Dead zone of rotational speed deviation	0.0013

; they come from the measured parameters of a cogeneration unit and its control system in Guangxi.

3.1. Model Verification

(1)

The response of the pumping module under different signals

According to the actual unit, at t = 100 s, the frequency modulation reference was stepped from 3000 r/min to 3011 r/min. At the input end of the speed control system module model and the speed deviation, an up/down step disturbance with a per-unit value of $\Delta \omega =0.0036$ is set. At the same time, the frequency modulation dead zone parameter is set to 0.033 Hz, the adjustment coefficient is 4.5%, and the frequency-modulation-limiting parameter is 4.44%. Comparing the simulation results of the whole process of the primary frequency modulation of the unit model with the measured data, the results are shown in Figure 6.

According to the information in the diagram, it can be seen that the dynamic process, overshoot, and adjustment time of the primary frequency modulation in the simulation results are in line with the actual situation, and the error is within the allowable range compared with the measured data of the primary frequency modulation of the unit.

(2)

The response of the pumping module under different butterfly valve control parameters

At t = 300 s, the pumping action was carried out. The time constant ${\mathrm{T}}_{d\mathrm{v}}$ of the butterfly valve oil motor is changed to test the output characteristics of the pumping module under different time constants, as shown in Figure 7a.

At t = 300 s, the pumping action was carried out. The butterfly valve PID proportional coefficient ${\mathrm{K}}_{\mathrm{P}d\mathrm{v}}$ is changed to test the output characteristics of the pumping module under different control parameters, as shown in Figure 7b.

The following can be seen from Figure 7:

(1)

The medium- and low-pressure connected-pipeline steam extraction-heating module with the butterfly valve shows a good follow-up performance in terms of dynamic response characteristics. Its output response can accurately track the change in input instructions, the steady-state error is controlled within the allowable range, and the control parameters in the module are reasonable.

(2)

As the time constant ${\mathrm{T}}_{d\mathrm{v}}$ of the butterfly valve oil motor increases, the overshoot and adjustment time of the dynamic process of the module output increase significantly. To optimize the control performance of the module, it is recommended to take the value between ${0.5 \mathrm{T}}_{d\mathrm{v}}$ and ${\mathrm{T}}_{d\mathrm{v}}$.

(3)

With the increase in the butterfly valve PID proportional coefficient ${\mathrm{K}}_{\mathrm{P}d\mathrm{v}}$, the overshoot of the output will gradually increase. In order to optimize the control performance of the module, it is recommended to take the value between 0.5 ${\mathrm{K}}_{\mathrm{P}d\mathrm{v}}$ and ${\mathrm{K}}_{\mathrm{P}d\mathrm{v}}$.

3.2. Simulation of Deep Peak Shaving Condition

Set the frequency modulation dead zone parameter to 0.033 Hz, the adjustment coefficient to 4.5%, and the frequency modulation limit parameter to 4.44%. An upward/downward step speed disturbance was applied to the speed control system, and the peaking depth of the unit was specified to reach 0.40 (p.u.), 0.35 (p.u.), 0.30 (p.u.), 0.25 (p.u.), and 0.20 (p.u.) of the rated power. The output result was shown in Figure 8a:

According to the figure, it can be known that under the given conditions of dead zone parameters, adjustment coefficient, and frequency-modulation-limiting parameters, when the peak-shaving depth reaches the maximum, it is 0.20 (p.u.). The main reason is that when the peak-shaving depth of the heating unit is large, there is a nonlinear link between the unit and the boiler, which touches the stable combustion critically when the load is low. According to the results, it can be concluded that the simulation model can meet the requirements of the simulation analysis of the dynamic process of primary frequency regulation in deep peaking conditions (30~50% rated conditions).

Keeping the initial conditions unchanged, a downward-step disturbance in speed was applied to the governing system. The peak-shaving depth of the unit was set to 0.40 p.u., 0.35 p.u., 0.30 p.u., 0.25 p.u., and 0.20 p.u. of the rated power. By recording the output power of the steam turbine, the entire dynamic response process of primary frequency regulation, corresponding to each peak-shaving depth setting value in Figure 7b, can be obtained. According to the information in the figure, it can be concluded that, similar to Figure 7a, when the peak-shaving depth reaches the maximum value of 0.20 p.u., the entire curve of the primary frequency regulation process exhibits more pronounced fluctuations compared to curves with smaller peak-shaving depths.

3.3. The Influence of Frequency Disturbance Amplitude and Direction on Frequency Modulation

Set the frequency modulation dead zone parameter to 0.033 Hz, the adjustment coefficient to 4.5%, and the frequency modulation limit parameter to 4.44%. When the deep peak-shaving heating unit was operated at the rated working condition of 0.3 (p.u.), an up/down step speed disturbance was applied to the speed control system. Furthermore, the frequency disturbance was set to be 0.0013 (p.u.), 0.0026 (p.u.), 0.0033 (p.u.), and 0.0040 (p.u.), and the results are shown in Figure 9.

In the diagram, when the frequency disturbance increases, the frequency modulation pressure of the system shows a gradual increase. When the frequency disturbance was 0.0040 (p.u.), the frequency modulation pressure of the unit was the largest. It can be clearly seen that the output power of the turbine is in the process of frequency modulation. The overshoot increases significantly, the adjustment time was prolonged, and the stability of the frequency modulation process is reduced.

3.4. The Influence of Heating Mode on Frequency Modulation Process

If the unit was in the process of normal extraction heating, there was a frequency fluctuation for primary frequency modulation. The results are shown in Figure 10:

In the diagram, in the case of the upward step of the frequency disturbance, the settling time of the three cases was about 50 s. When the pumping power decreases, the maximum overshoot of the system is about 13%. When the steady-state primary frequency modulation and the extraction power increase, the overshoot is about 1%. In the case of the downward step of the frequency disturbance, the settling time of the three cases was about 50 s. When the pumping power increases, the maximum overshoot of the system is about 14%. When the steady-state primary frequency modulation and the extraction power decrease, the overshoot is about 1%. The following are the four cases: The first two are for the frequency step: (1) The steam extraction quantity increases: the power of the power generation will be further reduced, but the peak depth is too large, and a low-load instability phenomenon may appear. (2) The extraction amount was reduced: the frequency modulation power deviation was compensated, and the stability of the overshoot was reduced. The other two are for the step at frequency: (1) increase in the extraction amount: the deviation of the frequency modulation power was compensated, but the overshoot was large and faces low-load instability; (2) The extraction amount was reduced: the output power was also increased and the action process was stable, there was no overshoot phenomenon, and it was not affected by the peak depth.

Based on the above analysis, during the primary frequency regulation process of the deep peak-shaving heating unit, if the heating extraction power undergoes a sudden change, there will be four situations, namely, increasing/decreasing the extraction volume when there is a step disturbance at the upper frequency and increasing/decreasing the extraction volume when there is a step disturbance at the lower frequency. Among them, increasing the extraction volume during step disturbances at lower frequencies will greatly increase the stability risk of the unit model. The other three situations partially have stability risk issues of the unit, but the risks can be reduced by methods such as sharing the extraction pressure and slowing down the sudden change process of extraction.

After qualitatively analyzing the relationship between steam extraction and frequency regulation, two typical situations that may threaten the stable operation of the unit were selected for analysis. The two situations are as follows: increasing the steam extraction volume when the unit is disturbed by an upward step in the frequency direction; when the unit is subjected to step disturbances at a certain frequency, increase the extraction volume. When the deep peak-shaving heating unit operates at the rated condition of 0.3 (p.u.) and the simulation time t = 100 s, an upward step disturbance is applied to the speed regulation system, and the heating extraction power is set to 0.05 (p.u.) at the same time. By constantly changing the frequency disturbance that the unit is subjected to, the power output of the steam turbine is analyzed, and the results are shown in Figure 10. According to the information in the figure, it can be concluded that when the system is subject to frequency disturbance, the unit is in the deep-peak shaving and steam extraction heating condition. As the disturbance continuously increases, due to the regulating nature of primary frequency regulation, the steady-state value of the unit’s output power after regulation will continuously decrease. When the frequency disturbance is 0.0013 (p.u.), the corresponding output power is 0.238 (p.u.) The corresponding output power is 0.195 (p.u.) when the frequency disturbance is 0.0040 (p.u.). It can be concluded that in this case, if the frequency disturbance value is further increased, it will endanger the stability of the unit. Under this premise, the frequency disturbance needs to be limited to within 0.0040 (p.u.).

When the deep peak-shaving heating unit operates at the rated condition of 0.3 (p.u.) and the simulation time t = 100 s, a downward step disturbance is applied to the system, and the disturbance value is set at 0.0036 (p.u.) simultaneously. By constantly changing the extraction power of the unit, the output of the steam turbine was studied, and the results are shown in Figure 11b. According to the information in the figure, it can be known that when the system is disturbed by the frequency, the unit is in the deep peak-shaving and steam extraction heating condition. With the continuous increase in the steam extraction power, the original output power of the unit affected by the primary frequency regulation is greater than the initial value and then gradually less than the initial value, even approaching the stable combustion boundary. From the output power of 0.283 (p.u.) corresponding to the extraction power of 0.05 (p.u.) to the output power of 0.194 (p.u.) corresponding to the extraction power of 0.15 (p.u.), it can be concluded that in this situation, as the extraction power increases, the oscillation of the output power at t = 100 s will intensify. Meanwhile, the mechanical power output in the steady state may be lower than the steady-state combustion boundary. If the extraction power is further increased, the system will face extremely unstable factors. Under this premise, the extraction power needs to be limited to within 0.15 (p.u.).

4. Simulation of the Influence of Primary Frequency Modulation Parameters on the Frequency Modulation Process of the Unit

4.1. The Influence of Frequency Modulation Dead Zone Parameter Setting on Frequency Modulation Process

The adjustment coefficient was set to 4.5%, the frequency-modulation-limiting parameter was set to 4.44%, and the size of the frequency modulation dead zone was changed. The simulation results of the primary frequency modulation action are shown in Figure 12.

According to the information in the figure, it can be concluded that with the expansion of the dead zone of frequency modulation, the response of the heating unit to the grid frequency disturbance gradually weakens. However, when the frequency modulation dead zone setting exceeds a certain threshold, if the frequency disturbance amplitude of the power grid is less than the preset dead zone range, the speed control system of the heating unit will remain in a non-action state. Although this setting effectively reduces the frequent adjustment problem caused by grid frequency disturbance, it also causes the system to lose the primary frequency regulation function, thus affecting the frequency stability of the grid.

4.2. The Influence of Frequency-Modulation-Limiting Parameter Settings on the Frequency Modulation Process

Set the frequency modulation dead zone to 0.033 Hz, the modulation coefficient to 4.5%, and change the frequency modulation amplitude limit. The simulation results of one frequency modulation action process are shown in Figure 13.

From the information in the figure, it can be seen that as the frequency-modulation-limiting parameter increases, the sensitivity of the heating unit to power grid frequency disturbances significantly increases, and its power regulation amplitude shows a clear increasing trend.

4.3. The Impact of Setting the Adjustment Coefficient on the Frequency Modulation Process

Set the frequency modulation dead zone to 0.033 Hz, the frequency modulation amplitude limit to 4.44%, and change the modulation coefficient. The simulation results of one frequency modulation action are shown in Figure 14.

According to the information in the figure, it can be seen that there is a significant negative correlation between the frequency response characteristics of the heating unit and the adjustment coefficient; that is, as the adjustment coefficient increases, the dynamic response amplitude of the unit to power grid frequency disturbances shows a clear attenuation trend. When the adjustment coefficient value is too small, the primary frequency regulation has a significant impact on the unit, and the system is prone to excessive overshoot and prolonged regulation time, which will directly affect the transient stability of the power grid frequency and, in severe cases, may lead to system frequency instability.

5. The Influence of Random Intermittent Coupling Disturbance on the Frequency Modulation of the System When the Source and Load Are on Both Sides

The influence of a random intermittent coupling disturbance on the frequency modulation of the system when the source and load are on both sides

5.1. The Influence of Frequency Regulation Dead Zone Parameter Settings on Disturbances in Industrial Extraction Units

Set the adjustment coefficient to 4.5%, the frequency-modulation-limiting parameter to 4.44%, and change the size of the frequency modulation dead zone. The results are shown in Figure 15.

According to the information in the figure, it can be inferred that when the frequency modulation dead zone value is too small, the system will exhibit significant dynamic response overshoot during the disturbance recovery process, manifested as a significant increase in the maximum overshoot of the high-voltage control valve opening signal and a prolonged adjustment time, directly affecting the operational stability of the unit. On the other hand, when the frequency regulation dead zone is set too large, although it can effectively reduce the response frequency of the unit to small fluctuations in the grid frequency, it will significantly weaken the system’s ability to regulate the set frequency disturbance, resulting in a decrease in the margin of grid frequency stability and an increase in the risk of system instability. Therefore, the optimization setting of the frequency regulation dead zone needs to strike a balance between the sensitivity of unit regulation and system stability; that is, setting 0.033 Hz~0.10 Hz is more appropriate.

5.2. The Influence of Frequency-Modulation- and Amplitude-Limiting Parameter Settings on Disturbances in Industrial Extraction Units

Set the adjustment coefficient to 4.5% and the frequency dead zone to 0.033 Hz, and change the frequency modulation amplitude limit. The simulation calculation results are shown in Figure 16.

From the information in the figure, it can be seen that the larger the frequency-modulation- and amplitude-limiting parameters were set, the greater the impact of power grid frequency disturbance on the unit. When the frequency-modulation- and amplitude-limiting parameters are set to the maximum, the system will exhibit an obvious dynamic response overshoot during the disturbance recovery process. The maximum overshoot of the high-voltage control valve-opening signal will significantly increase, and the adjustment time will be prolonged, directly affecting the operational stability of the unit. However, when the frequency-modulation-limiting parameter was set to decrease, the frequency modulation performance of the unit showed a gradually decreasing trend. Therefore, it was more appropriate to set the frequency-modulation- and amplitude-limiting parameters of the heating unit at 2.22% to 4.44%.

5.3. The Impact of Setting the Adjustment Coefficient of Industrial Steam Extraction Units on Disturbances

Set the frequency-modulation-limiting parameter to 4.44% and the frequency modulation dead zone to 0.033 Hz, and change the modulation coefficient. The simulation results are shown in Figure 17.

According to the information in the figure, it can be seen that there was a nonlinear relationship between the setting of the adjustment coefficient and the dynamic response characteristics of the heating unit. When the value of the adjustment coefficient was small, the impact intensity of power grid frequency disturbance on the unit significantly increased. When the adjustment coefficient is set to its maximum value, the system will experience significant dynamic response overshoot during the disturbance recovery process, where the maximum overshoot of the high-voltage control valve opening signal significantly increases, the adjustment time is prolonged, and the operational stability of the unit is affected. In addition, although a smaller difference coefficient was beneficial for improving the dynamic response speed of the unit and enabling the system to recover to the pre-disturbance state more quickly, it will significantly reduce the system’s anti-interference ability to small disturbances in the power grid, resulting in frequent fluctuations in the operating conditions of the unit. Therefore, the optimization setting of the adjustment coefficient needs to seek the optimal balance between dynamic response speed and operational stability, which is more suitable to be set between 4.5% and 10%.

Based on the above analysis, the influence of industrial steam extraction unit parameter changes is summarized in

Table 2. The influence of industrial steam extraction unit parameter changes.

Parameter	The Impact of Parameter Variation
Frequency regulation dead zone parameter (0.0016 Hz$\to$0.30 Hz)	Set too small: The system exhibits significant dynamic response overshoot during recovery from disturbances, manifested as a substantial increase in the maximum overshoot of the high-pressure control valve-opening signal and an extension of the regulation time.
	Set too large: It effectively reduces the unit’s responsiveness to minor grid frequency fluctuations but significantly undermines the system’s regulatory capacity against set frequency disturbances, thereby increasing the risk of system instability.
Frequency-modulation- and amplitude-limiting parameter (0.56%$\to$5.5%)	Set too large: The impact of grid frequency disturbances on the unit is bigger. When it is set to its maximum value, the system exhibits noticeable dynamic response overshoot during disturbance recovery, characterized by a significant increase in the maximum overshoot of the high-pressure control valve opening signal and an extended regulation time.
	Set too small: The frequency regulation performance of the unit gradually diminishes.
Adjustment Coefficient (3%$\to$10%)	Set too small: The impact of grid frequency disturbances on the unit becomes significantly more pronounced. A smaller droop coefficient helps improve the dynamic response speed of the unit, allowing the system to return to its pre-disturbance state more quickly. It markedly reduces the system’s resistance to minor grid disturbances, resulting in frequent fluctuations in the unit’s operating conditions.
	Set too large: The system exhibits significant dynamic response overshoot during disturbance recovery, characterized by a substantial increase in the maximum overshoot of the high-pressure control valve opening signal and an extended regulation time.

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6. Conclusions

(1)

Under deep peak-shaving conditions (30~50% rated power), the model can effectively characterize the nonlinear characteristics of the unit and the critical problem of low-load stable combustion. As the peak-shaving depth increases, the dynamic process fluctuations of the system intensify, but the model still has a reliable ability to analyze the dynamic characteristics of all operating conditions.

(2)

The setting of frequency modulation dead zone, amplitude-limiting parameters, and modulation coefficient has a significant impact on the dynamic response of the system: a frequency modulation dead zone that is too small (<0.033 Hz) leads to frequent adjustments and increased overshoot, while a frequency modulation dead zone that is too large (>0.10 Hz) weakens the frequency modulation function and needs to be optimized within the range of 0.033–0.10 Hz; Increasing the frequency-modulation-limiting parameter (>4.44%) will enhance system sensitivity, but it may cause power overshoot and prolong the adjustment time. It is recommended to control it between 2.22% and 4.44%. The adjustment coefficient is negatively correlated with dynamic response. If it is too small (<4.5%), it will exacerbate system shock, while if it is too large (>10%), it will reduce anti-interference ability. It is recommended to take 4.5%~10% to balance response speed and stability.

(3)

The increase in frequency disturbance amplitude (>0.0040 p.u.) significantly increases the frequency modulation pressure, resulting in an increase in power overshoot and a prolonged adjustment time. The sudden change in extraction volume under heating mode has a nonlinear effect on the frequency modulation process: as the extraction volume increases, the power deviation compensation ability is limited, and it is easy to trigger low-load instability. When the extraction volume decreases, the frequency regulation process becomes stable, but the risk of overshoot increases. It is necessary to optimize the extraction regulation strategy in conjunction with the heating demand.

(4)

In the scenario of source-load-coupling disturbance caused by the random fluctuation of new energy output, both robustness and sensitivity should be taken into account when setting the frequency modulation parameters. The simulation results show that a reasonable matching of dead zone and limiting parameters (such as a dead zone of 0.033 Hz and a limiting parameter of 4.44%) can effectively suppress dynamic overshoot and shorten the regulation time while maintaining grid frequency stability. In addition, a moderate increase in the adjustment coefficient (up to 10%) can enhance the system’s anti-interference ability and reduce the frequency of operating conditions under small disturbances.

(5)

By comparing step disturbance test data from actual units, the simulation accuracy of the model across a wide load range was validated. The influence mechanism of peak-shaving depth variation on nonlinear fluctuations during frequency regulation was analyzed, revealing the coupling relationship between abrupt changes in heating steam extraction and frequency disturbances. The impact of frequency regulation dead band, amplitude limiting, and droop coefficients on dynamic response characteristics was systematically investigated, leading to the proposal of an optimized parameter range that balances response speed and stability. Under combined stochastic and intermittent disturbance scenarios from both source and load sides, the enhancement effect of parameter configuration on system anti-interference capability was evaluated, providing theoretical support for the design of frequency regulation control strategies in industrial steam extraction units.

(6)

From the perspective of practical impacts on grid operators, the integration of high shares of renewable energy—primarily wind and solar—is accelerating the transition toward a new-type power system. However, the inherent randomness, intermittency, and variability of these sources pose significant challenges to grid security and stability, among which frequency stability stands out as a critical issue. In this context, the core objective of this study is to deeply exploit the potential of conventional thermal power units, particularly the vast fleet of combined heat and power units, to compensate for the shortage of frequency regulation resources caused by renewable integration. The practical applications of this research include enhancing the frequency stability in grids with high renewable penetration, precisely unlocking the flexible frequency regulation capabilities of CHP units, and facilitating the accommodation of renewable energy.

(7)

The current research has certain limitations: it does not cover scenarios involving units of different capacities and types or multi-energy coupling, the parameter analysis of thermoelectric decoupling equipment remains at a qualitative stage, and there is a lack of research on coordination mechanisms with flexible resources, such as electrochemical energy storage and demand-side response. Subsequent efforts should include conducting cross-regional, multi-unit, joint-frequency regulation experiments, building a wide-area collaborative regulation platform based on actual grid demands and renewable energy volatility characteristics, deepening the quantitative analysis of key frequency regulation parameters, and exploring multi-time-scale collaborative scheduling strategies for heating units and distributed energy resources. These steps aim to enhance the system’s generalization capability, engineering applicability, and full-scenario adaptability in integrated source-grid-load-storage scenarios.