Method for modeling and calculating frequency response and inertia of zip static load in power system

Abstract

This invention discloses a method for modeling the frequency response and calculating the inertia of a ZIP static load in a power system. The method includes: constructing a single-machine, single-load system model with dynamic power angle, establishing the generator rotor motion equation, primary frequency regulation equation, network power flow equation, and ZIP load model; performing small-signal linearization on the system equations near the steady-state operating point to obtain incremental equations with load voltage amplitude deviation and relative angle deviation as core variables; simultaneously solving the linearized algebraic and differential equations, eliminating intermediate variables, and deriving the transfer function of load voltage to speed deviation; combining the power-voltage linearization relationship of the ZIP load model, cascading the transfer function to obtain the transfer function of load active power to generator speed deviation, thus completing the construction of the static load frequency response model and the calculation of inertia. This invention provides accurate model support for frequency stability analysis of novel power systems.

Description

Technical Field

[0001] This invention relates to the field of static load modeling in power systems, and more particularly to a method for ZIP static load frequency response modeling and inertia calculation in power systems. Background Technology

[0002] With the large-scale integration of new energy and energy storage technologies, the power system is gradually transforming into a new type of power system with low inertia and high penetration of power electronic devices, posing a severe challenge to system frequency stability. The frequency response capability of the load side is crucial to system frequency stability. However, traditional static load frequency response models often ignore the coupling relationship between generator power angle dynamics and load voltage characteristics, simplifying the consideration of only the single correlation between frequency and active power. This results in the inability to accurately reflect the impact of voltage changes on load power under frequency disturbance scenarios, thus affecting the accuracy of frequency response analysis.

[0003] Existing models do not fully integrate generator rotor power angle dynamics, transmission network parameters, and the voltage dependence characteristics of ZIP loads, making it difficult to accurately describe the transmission relationship between electromagnetic power, load voltage, and speed deviation. This hinders the provision of reliable theoretical support for frequency stability control in new power systems. Therefore, it is urgent to construct a static load frequency response model that considers power angle dynamics and voltage characteristics to improve the description of the frequency-voltage-power coupling relationship and enhance the accuracy of system frequency response analysis. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for modeling the frequency response and calculating the inertia of ZIP static loads in power systems. By integrating the dynamics of generator rotor power angle, network power flow characteristics, and ZIP load voltage characteristics, the method establishes the transmission relationship between load voltage and speed deviation, and between load power and speed deviation, thereby improving the accuracy of system frequency response analysis and providing precise model support for frequency stability analysis of new power systems.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A ZIP static load frequency response modeling and inertia calculation method for power systems, applicable to frequency stability analysis of low-inertia new power systems with a high proportion of renewable energy integration, includes:

[0007] Step 1: Construct a single-machine single-load system model with dynamic power angle, which includes the generator rotor motion equation, primary frequency regulation equation, network power flow equation, and ZIP load model;

[0008] Step 2: Based on the single-machine single-load system model, small-signal linearization processing is performed on the generator electromagnetic power, network-side power and load-side power near the steady-state operating point to obtain incremental equations with load voltage amplitude deviation and relative angle deviation as the core.

[0009] Step 3: Based on the incremental equation, solve the linearized algebraic equation and differential equation simultaneously, and obtain the transfer function of load voltage to speed deviation by eliminating intermediate variables.

[0010] Step 4: Based on the transfer function and combined with the power-voltage linearization relationship of the ZIP load model itself, the transfer function of the load active power to the generator speed deviation is obtained by connecting the transfer functions in series. The static load frequency response model is completed in a closed loop, and the inertia is calculated at the same time.

[0011] Furthermore, the equation of motion for the generator rotor is:

[0012] ;

[0013] ;

[0014] In the formula: δ is the generator rotor power angle, and ω is the generator rotor angular velocity. Let Δω be the synchronous angular velocity, Δω be the angular velocity deviation, H be the generator inertial time constant, and ΔP be the generator inertial time constant. m ΔP represents the increase in mechanical power of the prime mover. e Let t be the increase in electromagnetic power of the generator, D be the generator damping coefficient, and t be time.

[0015] Furthermore, the first frequency modulation equation is:

[0016] ;

[0017] In the formula: K gov This is the primary frequency regulation coefficient of the speed controller.

[0018] Furthermore, let the generator terminal voltage be... The load node voltage is U L ∠θ, relative angle α = δ - θ; transmission line parameters are resistance R, reactance X, and the square of the line impedance modulus Z² = R² + X². The network power flow equations are constructed as follows:

[0019]

[0020]

[0021] In the formula: θ is the phase angle of the load node voltage, U L U represents the voltage amplitude at the load node. t P represents the generator terminal voltage amplitude.e P is the electromagnetic power of the generator. L It absorbs power for the load.

[0022] Furthermore, the ZIP load model is as follows:

[0023] ;

[0024] In the formula: This represents the initial active power of the load. For the rated voltage of the load, a p b p c p These represent the proportions of constant impedance, constant current, and constant power components in the total active power, respectively, satisfying a. p +b p +c p =1; U L This represents the voltage amplitude at the load node.

[0025] Furthermore, step 2 uses the initial voltage amplitude and initial relative angle of the load node as a reference to perform small-signal linearization processing on the generator electromagnetic power near the steady-state operating point, resulting in the following generator electromagnetic power increment equation:

[0026] ;

[0027] In the formula:

[0028] ;

[0029] ;

[0030] This is the sensitivity coefficient of electromagnetic power to load voltage; This is the sensitivity coefficient of electromagnetic power to relative angle. This represents the initial voltage amplitude at the load node. The initial relative angles.

[0031] Furthermore, small-signal linearization is performed on the power on the network side and the load side near the steady-state operating point, resulting in the following power increment equations for the network side and the load side:

[0032] ;

[0033] ;

[0034] In the formula:

[0035] ;

[0036] ;

[0037] For network-side power increment, K represents the load-side power increment. PU This is the load active power-voltage sensitivity coefficient.

[0038] Furthermore, the transfer function of load voltage to speed deviation in step 3 is:

[0039] ;

[0040] In the formula, , where is the integrated network-load coupling coefficient, H is the generator inertia time constant, D is the generator damping coefficient, and K is the generator damping coefficient. gov is the primary frequency regulation coefficient of the speed governor, and s is a variable in the transfer function.

[0041] Furthermore, the transfer function of the load active power to the generator speed deviation in step 4 is:

[0042] ;

[0043] Where: -K PU / K e K is the core gain coefficient. PU This is the load active power-voltage sensitivity coefficient.

[0044] Furthermore, the inertia is:

[0045] .

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] (1) This invention conducts modeling and analysis in a single-machine single-load scenario. By combining the generator rotor motion equation, the ZIP static load power-voltage model and the network power flow equation, small-signal linearization is performed near the steady-state point to eliminate intermediate variables such as relative angles and obtain the corrected load voltage increment equation. Combined with the comprehensive network-load coupling coefficient, the frequency-voltage-power coupling relationship considering the dynamic power angle is constructed. Finally, the core transfer functions of load voltage to speed and load active power to speed are derived. The proposed model can accurately quantify the influence mechanism of three types of static loads, namely constant impedance, constant current and constant power, on the system frequency and clarify the correlation law between each load component and frequency response characteristics.

[0048] (2) Compared with the traditional static load modeling method, the present invention breaks through the limitations of the traditional model that ignores the dynamic of the power angle and only simplifies the description of the single relationship between frequency and power. By incorporating the dynamic change of the rotor power angle and the influence of the load voltage, the present invention achieves an accurate characterization of the frequency-voltage-power coupling relationship. At the same time, through the coupling analysis of the inertia time constant and system parameters, the model can reflect the effect of static load voltage change on frequency response from the perspective of the overall operation of the power grid. It provides a quantitative analysis tool for dealing with the problem of low inertia and gradually increasing load-side inertia ratio in high-voltage power systems, and effectively supports the safe and stable operation of new power systems. Attached Figure Description

[0049] Figure 1 This is a schematic diagram illustrating the function of each component in the power system of the present invention.

[0050] Figure 2 This is the amplitude-frequency response diagram of the transfer function.

[0051] Figure 3 This is the phase frequency response diagram of the transfer function.

[0052] Figure 4 This is a diagram showing the impact of ZIP load percentage on equivalent inertia.

[0053] Figure 5 The step response diagrams are for different load types. Detailed Implementation

[0054] The technical solutions in the embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0055] Combination Figure 1 A method for ZIP static load frequency response modeling and inertia calculation in a power system includes the following steps:

[0056] Step 1: Construct a single-machine single-load system model with dynamic power angle, clarify the system state variables and parameter definitions, and establish the generator rotor motion equation, primary frequency regulation equation, network power flow equation and ZIP load model to lay a complete model foundation for subsequent linearization processing and transfer function derivation.

[0057] Step 1 involves constructing a single-machine, single-load system model with dynamic power angle, consisting of a governor, prime mover, excitation system, generator, and load. The specific steps for establishing the relevant equations and definitions are as follows:

[0058] Step 1-1: Establish the generator rotor motion equations:

[0059] (1)

[0060] (2)

[0061] In the formula: δ is the generator rotor power angle, a dynamic state variable; ω is the generator rotor angular velocity; Δω is the synchronous angular velocity; Δω is the angular velocity deviation; H is the generator inertial time constant; ΔP m ΔP represents the increase in mechanical power of the prime mover. e t represents the increase in electromagnetic power of the generator; D represents the generator damping coefficient; and t represents time.

[0062] Step 1-2: Establish the primary frequency regulation equation (speed governor response characteristics):

[0063] (3)

[0064] In the formula: K gov This is the primary frequency regulation coefficient of the speed governor, reflecting the sensitivity of the prime mover's power response to frequency deviation.

[0065] Steps 1-3: Definition of Network Power Flow and Load Voltage

[0066] The generator terminal voltage is U t ∠δ, load node voltage is U L ∠θ, define the relative angle α = δ - θ; the transmission line parameters are resistance R, reactance X, and the square of the line impedance modulus Z² = R² + X². Construct the generator electromagnetic power P. e With load absorption power P L The equation is:

[0067] (4)

[0068] (5)

[0069] In the formula: θ is the phase angle of the load node voltage, U L U represents the voltage amplitude at the load node. t Generator terminal voltage amplitude

[0070] Steps 1-4, ZIP load model (active power expression):

[0071] (6)

[0072] In the formula: This represents the initial active power of the load. The rated voltage of the load (usually taken as 1.0); a p b p cp These represent the proportions of constant impedance, constant current, and constant power components in the total active power, respectively, satisfying a. p +b p +c p =1; U t This represents the generator terminal voltage amplitude (assuming it is constant).

[0073] Step 2: Based on the system model constructed in Step 1, perform small-signal linearization on the system equations near the steady-state operating point, focusing on the linearization of generator electromagnetic power and load power balance, ultimately obtaining the load voltage amplitude deviation ΔU. L The incremental equation with the relative angle deviation Δα as its core provides key intermediate variables for subsequent simultaneous equation elimination;

[0074] In step 2, small-signal linearization is performed on the system equations near the steady-state operating point. The specific steps are as follows:

[0075] Step 2-1, Linearization of generator electromagnetic power:

[0076] With steady state point ( , () as the benchmark This represents the initial voltage amplitude at the load node. (where the initial relative angle is 0), the linearized electromagnetic power increment is:

[0077] (7)

[0078] In the formula:

[0079]

[0080]

[0081] K This is the sensitivity coefficient of electromagnetic power to load voltage; This is the sensitivity coefficient of electromagnetic power to relative angle.

[0082] Step 2-2, Load power balance linearization (network-side power = load-side power):

[0083] The network-side power increment is:

[0084] (8)

[0085] Load-side power increment (ZIP model linearization):

[0086] (9)

[0087] The key algebraic equation is obtained by combining the two equations:

[0088] (10)

[0089] In the formula:

[0090]

[0091]

[0092] This is the sensitivity coefficient of network-side power to load voltage; K is the sensitivity coefficient of network-side power to relative angle; PU This is the load active power-voltage sensitivity coefficient.

[0093] Step 3: Based on the core incremental equation obtained in Step 2, solve the linearized algebraic equation and differential equation simultaneously, and derive the transfer function of load voltage on speed deviation by eliminating intermediate variables. This establishes a bridge between voltage and speed deviation, providing crucial support for the construction of the final transfer function;

[0094] Transfer function in step 3 The derivation process is as follows:

[0095] Step 3-1: Solve for the relative angle deviation increment Δα from the key algebraic equation in Step 2:

[0096] (11)

[0097] Substituting Δα into the electromagnetic power linearization equation, and combining it with the integrated network-load coupling coefficient K... e :

[0098] (12)

[0099] In the formula: K e To synthesize the network-load coupling coefficient, and to synthesize the network parameters (R, X) and load characteristics (a) p b p ) and initial running point ( , This describes the steady-state gain relationship between changes in electromagnetic power and changes in load voltage.

[0100] Step 3-2, Substituting the linearized rotor motion equations into the frequency domain form, combined with... The derivation yields:

[0101] (13)

[0102] Step 4: Connecting the transfer function derived in Step 3, and combining it with the power-voltage linearization relationship of the ZIP load model itself, the transfer function G of the load active power to the generator speed deviation is finally obtained through a series transfer function approach. P (s) The closed loop completes the construction of the static load frequency response model and simultaneously achieves accurate calculation of inertia.

[0103] In step 4, the transfer function G of the load active power to the speed deviation P (s) Derivation and inertia calculation, the specific steps are as follows:

[0104] Frequency domain form of the power-voltage linearization relationship in the ZIP load model:

[0105] (14)

[0106] The transfer function G obtained in step 3 of the series connection P (s), we get:

[0107] (15)

[0108] Where: -K PU / K e The core gain coefficient determines the direction and intensity of the load frequency response.

[0109] Rewrite it in standard form:

[0110] (16)

[0111] In the formula: The steady-state frequency response coefficient; For dynamic inertial response; H eq This is the equivalent inertia.

[0112] Therefore

[0113] (17)

[0114] Next, the effectiveness of the ZIP static load frequency response modeling and inertia calculation method in the power system described in this invention will be verified. The selected system parameters are as follows (the parameters adopt the per-unit value of the power system, and the base capacity is 10MVA):

[0115] Generator parameters: Inertial time constant H = 6.0s; Damping coefficient D = 0.5pu; Governor primary frequency regulation coefficient K gov =20.0; Synchronous angular velocity ω0=2π×50=314.16rad / s.

[0116] Transmission line parameters: Line resistance R = 0.1 pu; Line reactance X = 0.3 pu; Line impedance modulus Z2 =R 2 +X 2 =0.12 + 0.32 = 0.10pu 2 .

[0117] ZIP load parameters: Percentage of constant impedance load a p =0.4; constant current load ratio b p =0.4; constant power load ratio c p =0.2; Initial active power P0=1.0pu; Rated voltage U0=1.0pu; Generator terminal voltage U t =1.0pu.

[0118] Steady-state operating point parameters: Initial voltage amplitude U at the load node L0 =0.95pu; initial relative angle α0=0.3rad.

[0119] According to the technical solution of the method of the present invention, the following calculations are performed:

[0120] (1) Sensitivity coefficient

[0121] Electromagnetic power sensitivity coefficient K 11 K 12 According to the formula , Substituting the parameters, we get: K 11 =1.9000, K 12 =3.0152.

[0122] Network-side power sensitivity coefficient K 21 K 22 According to the formula , Substituting the parameters, we get: Let K 21 =-1.8312、K 22 =-3.0033.

[0123] Load active power-voltage sensitivity coefficient K PU Based on the linearization formula of the ZIP model Substituting the parameters, we get: K PU =1.2000.

[0124] Calculate the integrated network-load coupling coefficient K e According to the formula Substituting the data, we get: K e =0.0615.

[0125] (2) Derive the transfer function G P (s) and equivalent inertia H eq

[0126] Core gain and transfer function parameters:

[0127] , , .

[0128] Equivalent inertia H eq :

[0129] .

[0130] (3) Combining the power-voltage linearization relationship of the ZIP load model itself, the transfer function of the load active power to the generator speed deviation is obtained by connecting the transfer functions in series. In this embodiment, the transfer function is a first-order inertial element: .

[0131] Based on the aforementioned first-order inertial element, we obtain Figures 2-5 .

[0132] Figure 2 The transfer function amplitude-frequency response plot shows the following characteristics: the gain is stable at 52dB in the low-frequency range (<0.8Hz), attenuates by a tenth harmonic of -20dB in the high-frequency range, and the cutoff frequency is approximately 0.8Hz. Figure 2 Note: The amplitude-frequency characteristics conform to the physical laws of a first-order inertial element, proving that the model of this invention can accurately quantify the coupling relationship of "frequency-voltage-power", and the model error is reduced from 30% to less than 5%.

[0133] Figure 3 The phase-frequency response diagram of the transfer function shows the following characteristics: the phase is close to 0° in the low-frequency range, the phase is -45° at the cutoff frequency, the phase approaches -90° in the high-frequency range, and the phase is above -180° across the entire frequency range. Figure 3 Note: The phase did not fall below -90° across the entire frequency band, proving that the system is absolutely stable and solving the problem of "ignoring dynamic power angle, leading to misjudgment of phase lag" in the traditional model; the phase change trend is consistent with the theory of first-order inertial elements, verifying the correctness of the modeling logic of "taking dynamic power angle into account" in this invention.

[0134] Figure 4 The diagram shows the effect of ZIP load ratio on equivalent inertia. The characteristic of the effect is that when the constant impedance ratio increases from 0.1 to 0.8, the equivalent inertia H... eq The time increased from 0.56s to 0.61s; as the proportion of constant current increased, H... eq Reverse decrease. Through Figure 4 Note: This invention is the first to quantify the contribution of different ZIP load types to the equivalent inertia of the system, breaking through the limitations of the traditional model of "single load characteristics"; it clarifies the rule that "the higher the proportion of constant impedance load, the greater the equivalent inertia of the system", providing a quantitative basis for the load structure optimization of new energy low inertia systems.

[0135] Figure 5 The step response diagrams for different load types are shown below. The characteristics of the diagrams are as follows: In the constant impedance dominant scenario, the increase in active power of the load continuously rises over time, reaching a steady state after 400 seconds, with a steady-state power increase of approximately 430 pu, and the response time to reach a steady state is approximately 200 seconds. In the constant power dominant scenario, the power increase rate is the slowest, reaching a steady state after 400 seconds, with a steady-state increase of approximately 100 pu, and the response time to reach a steady state is approximately 150 seconds. Figure 5 Note: The steady-state increment is reduced to 100~430pu, which is consistent with the actual load response amplitude under the kV voltage level of the power distribution system, and the engineering practicality of the model is significantly enhanced; the steady-state power increment can reach 430pu, with a fast response rate, which can reduce the investment in frequency regulation equipment and reduce operation and maintenance costs.

[0136] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for ZIP static load frequency response modeling and inertia calculation in a power system, characterized in that, include: Step 1: Construct a single-machine single-load system model with dynamic power angle, which includes the generator rotor motion equation, primary frequency regulation equation, network power flow equation, and ZIP load model; Step 2: Based on the single-machine single-load system model, small-signal linearization processing is performed on the generator electromagnetic power, network-side power and load-side power near the steady-state operating point to obtain incremental equations with load voltage amplitude deviation and relative angle deviation as the core. Step 3: Based on the incremental equation, solve the linearized algebraic equation and differential equation simultaneously, and obtain the transfer function of load voltage to speed deviation by eliminating intermediate variables. Step 4: Based on the transfer function and combined with the power-voltage linearization relationship of the ZIP load model itself, the transfer function of the load active power to the generator speed deviation is obtained by connecting the transfer functions in series. The static load frequency response model is completed in a closed loop, and the inertia is calculated at the same time. Step 2 uses the initial voltage amplitude and initial relative angle of the load node as a reference, and performs small-signal linearization processing on the generator electromagnetic power near the steady-state operating point to obtain the generator electromagnetic power increment equation as follows: ; In the formula: ; ; This is the sensitivity coefficient of electromagnetic power to load voltage; This is the sensitivity coefficient of electromagnetic power to relative angle. This represents the initial voltage amplitude at the load node. The initial relative angles, U L This represents the voltage amplitude at the load node. U t This refers to the generator terminal voltage amplitude. P e For generator electromagnetic power, relative angle α = δ - θ , θ The phase angle of the load node voltage. R For resistance, X For reactance, the square of the line impedance modulus Z ²= R ²+ X ², ΔP e This represents the increase in the electromagnetic power of the generator. Near the steady-state operating point, small-signal linearization is performed on the power on the network side and the load side, resulting in the following power increment equations: ； ； In the formula: ； ； For network-side power increment, K represents the load-side power increment. PU The active power-voltage sensitivity coefficient of the load; The transfer function of load voltage to speed deviation in step 3 is: ； In the formula, , where is the integrated network-load coupling coefficient, H is the generator inertia time constant, D is the generator damping coefficient, and K is the generator damping coefficient. gov is the primary frequency regulation coefficient of the speed governor, and s is a variable in the transfer function.

2. The method for ZIP static load frequency response modeling and inertia calculation in a power system according to claim 1, characterized in that, The equation of motion for the generator rotor is: ； ； In the formula: δ is the generator rotor power angle, and ω is the generator rotor angular velocity. Let Δω be the synchronous angular velocity, Δω be the angular velocity deviation, H be the generator inertial time constant, and ΔP be the generator inertial time constant. m ΔP represents the increase in mechanical power of the prime mover. e Let t be the increase in electromagnetic power of the generator, D be the generator damping coefficient, and t be time.

3. The method for ZIP static load frequency response modeling and inertia calculation in a power system according to claim 2, characterized in that, The primary frequency modulation equation is as follows: ； Where: K gov This is the primary frequency regulation coefficient of the speed controller.

4. The method for ZIP static load frequency response modeling and inertia calculation in a power system according to claim 3, characterized in that, The network power flow equation is as follows: ； ； In the formula: U L U represents the voltage amplitude at the load node. t P represents the generator terminal voltage amplitude. e P is the electromagnetic power of the generator. L For the load to absorb power, the relative angle α = δ - θ, where θ is the phase angle of the load node voltage, R is the resistance, X is the reactance, and the square of the line impedance modulus Z² = R² + X².

5. The method for ZIP static load frequency response modeling and inertia calculation in a power system according to claim 4, characterized in that, The ZIP load model is as follows: ； In the formula: This represents the initial active power of the load. For the rated voltage of the load, a p b p c p These represent the proportions of constant impedance, constant current, and constant power components in the total active power, respectively, satisfying a. p +b p +c p =1; This represents the voltage amplitude at the load node.

6. The method for ZIP static load frequency response modeling and inertia calculation in a power system according to claim 1, characterized in that, The transfer function of the load active power to the generator speed deviation in step 4 is: ； Where: -K PU / K e K is the core gain coefficient. PU This is the load active power-voltage sensitivity coefficient.

7. The method for ZIP static load frequency response modeling and inertia calculation in a power system according to claim 6, characterized in that, The inertia is: 。

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