A Secondary Control Method for VSG Based on Improved Model Reference Adaptive

Abstract

The present invention discloses a secondary control method for VSG based on improved model reference adaptive control. An island main unit model including a VSG control loop, a double closed-loop of voltage and current, and an inverter main circuit is established. A damping enhancement module is added to the active power control part of the VSG to enhance damping and ensure power sharing. The model reference adaptive control technology based on multi-input multi-output is used to restore the frequency and voltage. At the same time, the least squares method is introduced in the design of the adaptive controller to reduce the optimization calculation error caused by system uncertain factors such as load changes, equipment aging, and system parameter changes. The present invention improves the model reference adaptive control technology, ensures the stability of the system, no longer requires communication, does not require estimating the parameters of the system model, reduces the computational burden, and the damping enhancement module enhances the VSG damping, reduces oscillations, thereby ensuring the stability of voltage and frequency, and at the same time realizes active power sharing.

Description

Technical Field

[0001] The present invention relates to the technical field of inverter control, and particularly relates to a VSG secondary control method based on improved model reference adaptive. Background Art

[0002] With the popularization of new energy technologies, the new generation of power systems puts forward the requirement of developing towards intelligence. How to reasonably use clean energy has become the main research direction of many scholars. However, clean energy is vulnerable to environmental influences, and the traditional centralized power supply method is no longer the first choice. Therefore, the concept of distributed generation (DG) has been proposed.

[0003] Due to the inherent characteristics of power electronic components, their anti-interference ability is poor, resulting in low-quality output electrical energy. If the low-quality electrical energy is output to the power grid, it will pollute the power grid and even cause the power grid to collapse. The quality of electrical energy depends on two important indicators, namely voltage amplitude and frequency. How to ensure the stability of these two parameters is the key to improving the quality of electrical energy.

[0004] By simulating the transient characteristics of a synchronous generator, the VSG uses an algorithm to obtain a mathematical model similar to the active frequency modulation, reactive voltage regulation, and rotor motion equation of a synchronous generator, enabling the inverter to simulate the speed governor and excitation regulator of a synchronous motor to achieve primary control, that is, frequency modulation and voltage regulation. When connected to the grid, it reduces the impact on the power grid and ensures the stable operation of the system; in the island mode, it can achieve stable operation of multiple VSGs in parallel, providing a way for new energy consumption.

[0005] Grid regulation can be divided into primary, secondary, and tertiary regulation. For primary control, the traditional droop control-based method is prone to causing frequency and voltage deviations. Therefore, secondary control aims to restore the voltage and frequency to their rated values. Tertiary control is the overall regulation of the power grid, involving factors such as new energy access, remaining capacity, and power grid topology, mainly solving power grid economic problems and optimization problems. And the problems existing in VSG secondary control:

[0006] 1. Stability problem: Traditional secondary control may cause oscillations or instability during generator operation. This may lead to the instability of the power system and even trigger system collapse.

[0007] 2. Accuracy problem: Traditional control methods may not be able to accurately track system changes or maintain good performance under different operating conditions.

[0008] 3. Robustness problem: Traditional methods may not be robust enough to system parameter changes or external disturbances, resulting in performance degradation or system out-of-control.

[0009] 4. Insufficient frequency response: Traditional secondary control may have insufficient response to frequency changes. Especially when the system is subject to large load changes or faults, it may not be able to quickly restore the system frequency to a stable state.

[0010] 5. Degraded tracking performance: Traditional secondary control may experience degraded performance in tracking the target frequency or voltage, especially when system parameters change significantly or the external environment changes.

[0011] 6. High communication cost: The communication system may have transmission delays, which can affect the real-time nature of control signals. Especially when high-frequency control is required, the delay may cause the performance of the control system to degrade or become unstable. The communication link may fail or be interrupted, resulting in the control signal not being transmitted in a timely manner. This may cause the control system to fail, affecting the stability and reliability of the system.

[0012] Model Reference Adaptive Control (MRAC) aims to make the output of the system as close as possible to the output of a defined reference model. It is an adaptive control strategy that can adapt to changes in the system's dynamic characteristics and unknown disturbances to achieve good tracking performance. In model reference adaptive control, the reference model is used to describe the behavior of an ideal system, usually a linear time-invariant system, and its output is the desired ideal trajectory or response. The goal of the controller is to adjust the system's parameters so that the system output is as close as possible to the output of the reference model.

[0013] Least Square Method (LSM) adaptive control is used to handle dynamic systems with unknown dynamics or unknown model parameters. It designs a controller based on the estimated model and adjusts the controller's parameters accordingly to adapt to system changes and meet the stability and performance requirements of the system. It is usually used for nonlinear, time-varying, or uncertain systems. Summary of the Invention

[0014] Object of the Invention: To solve the problem of voltage and frequency deviation in the islanded microgrid with VSG control in the prior art, the present invention discloses a VSG secondary control method based on improved model reference adaptation. A damping enhancement module is added to the active power control part of the VSG to enhance damping and ensure power sharing. The model reference adaptive control technology based on multiple input and multiple output is used to restore frequency and voltage. At the same time, the least square method is introduced in the design of the adaptive controller to reduce the optimization calculation error caused by system uncertainties such as load changes, equipment aging, and system parameter changes.

[0015] Technical Solution: The present invention discloses a VSG secondary control method based on improved model reference adaptation, including the following steps:

[0016] Step 1: Add an energy storage unit on the inverter side. Based on droop control, introduce the VSG algorithm to simulate the rotor equation of a synchronous generator, endowing the inverter with virtual inertia, obtaining the VSG rotor motion equation, and constructing the VSG active - frequency loop;

[0017] Step 2: Based on the rotor motion equation obtained in Step 1, and at the same time, the voltage loop of the VSG adopts Q - V droop control to obtain the VSG output voltage expression, and construct the VSG reactive - voltage loop;

[0018] Step 3: Represent the relationship between the active or reactive power of the VSG and the line impedance by using a bus system with a distributed generation DG unit and an idle bus, establish a VSG small - signal power model to represent the active and reactive power of the VSG, and at the same time obtain the relationship between the active power and the VSG frequency, and the reactive power and the VSG voltage;

[0019] Step 4: Based on the VSG active - reactive power model proposed in Step 3, add a damping enhancement module in the VSG active - power control to achieve equal sharing of active power in the VSG secondary control;

[0020] Step 5: Based on the damping enhancement module designed in Step 4, design an improved model reference adaptive controller, design the control law by the least - squares method, realize the recovery of the VSG frequency and voltage, and achieve the VSG secondary control.

[0021] Furthermore, the expression of the VSG active - frequency loop in Step 1 is:

[0022]

[0023] where, T m 、T e 、T d are the mechanical torque, electromagnetic torque and damping torque of the synchronous generator respectively; P and P0 are the output active power and rated active power respectively; ω n 、ω0 are the VSG output angular frequency and rated angular frequency respectively; J and D are the VSG moment of inertia and damping coefficient respectively; δ is the electrical angle;

[0024] In actual operation, the change in the DG angular frequency is small, i.e., ω≈ω0. At the same time, define the input power P0 as the DG input power reference value P * , the DG output power is P, and denote m as the VSG droop coefficient. Since the steady - state performance of the system is analyzed, the dynamic performance of the VSG is not considered. Then the relationship between active power and frequency under steady state is:

[0025] P = P * -m(ω n -ω0) (2)

[0026] Furthermore, the VSG reactive power - voltage loop expression in step 2 is as follows:

[0027] V = V0 - n(Q - Q0) (3)

[0028] where n is the reactive power droop coefficient; Q and Q0 are the VSG output reactive power and rated reactive power respectively; V and V0 are the VSG output voltage and rated voltage respectively.

[0029] Furthermore, the VSG output active and reactive powers in step 3 are expressed as:

[0030]

[0031]

[0032] where U g is the amplitude of the AC bus voltage, V is the amplitude of the inverter output voltage, R g and X g are the line resistance and inductance respectively, and δ is the power angle; since δ is small, then sinδ≈δ and cosδ≈1. When the line impedance is inductive, i.e., R g ≈0, the inverter output active power P and reactive power Q can be expressed as:

[0033]

[0034]

[0035] Therefore, the relationship between the active frequency and reactive voltage of VSG can be expressed as:

[0036] ω n = ω0 - k p (P - P * ) (9)

[0037] V = V0 - k q (Q - Q * ) (10)

[0038] ω n and ω0 are the VSG output angular frequency and rated angular frequency respectively; P * , Q * are the reference active power and reactive power respectively; k p , k q are the VSG active and reactive power droop coefficients; assuming there are small perturbations near the equilibrium point, defined as (δ e , U ge , V e ), then the above formula can be rewritten as:

[0039] ΔP = k pe ΔV + k pd Δδ (11)

[0040] ΔQ = k qe ΔV + k qd Δδ (12)

[0041] Δω n = Δω0 - k p (ΔP - ΔP * ) (13)

[0042] ΔV = ΔV0 - k q (ΔQ - ΔQ * ) (14)

[0043] where

[0044] assuming ω0, V0, P * , Q * are constants, so the deviation terms in Δω n and ΔV can be ignored. To filter out the high - frequency components caused by load imbalance in the measured power element, low - pass filters LPFs are used in the power control loop, and these filters introduce a multi - time - scale separation between the inner voltage and current loops and the outer power loop.

[0045] Furthermore, the design of the damping enhancement module in step 4 is as follows:

[0046] When the active power deviates, without losing the damping characteristics, feed - forward damping is utilized, and the feed - forward damping is expressed as:

[0047] ω d = G c (s)(P m - P e ) (15)

[0048] where G c (s)= k p + k dq H(s)s, in the formula, k p , k dq are control parameters, and N d is used to limit the bandwidth of G c (s).

[0049] Furthermore, after adding the damping enhancement module, the specific process of realizing active - power sharing in VSG secondary control is as follows:

[0050] The simplified representation of the improved VSG active - power loop is:

[0051]

[0052] Among them, ω m is the rotor speed, D is the damping coefficient, and P dmp is the damping expressed in power, and ω g is the grid frequency;

[0053] Define the grid voltage:

[0054]

[0055] The inner product of the vector e g is expressed as: It is expressed as:

[0056]

[0057] The derivative is:

[0058]

[0059] Among them, θ g and θ m are phase angles;

[0060] Therefore, the internal voltage amplitude V of the VSG dmp is:

[0061] That is, V dmp =-DE g (ω g -ω m )cos(θ g -θ m ) (20)

[0062] To improve the flexibility of the damping term, a low-pass filter is added:

[0063]

[0064] Among them is the filter time constant;

[0065] From the above formula, let

[0066]

[0067] Among them, e vsg·3ph =[e avsg e bvsg e cvsg T is the three-phase voltage of the VSG;

[0068] To increase the damping enhancement ability of the VSG, a feedforward term is used in the enhanced module of the active power control and renamed ω​d , referred to as the enhanced signal:

[0069]

[0070] where θ vsg is the voltage phase of the VSG, and V vsg is the output voltage of the VSG;

[0071] Taking the derivative of the above equation gives:

[0072]

[0073] Considering θ vsg ≈ θ g Then

[0074] ω d = ∫(V vsg (ω vsg - ω g ))dt (25)

[0075] The above equation contains (ω vsg - ω g ) transferred from the integral term, which means that when the secondary control controller is activated, it has the ability to make ω g equal to ω vsg . Therefore, after the system frequency is stabilized, the active power is evenly distributed.

[0076] Furthermore, the improved model reference adaptive controller designed in step 5 is:

[0077] At the steady-state operating point, the linearized model of the VSG is obtained as:

[0078]

[0079] where Then In the formula, ω p and ω q are the cut-off frequencies of the active and reactive loops;

[0080] By defining the state vector The state-space representation of the system under study is:

[0081]

[0082] where

[0083]

[0084] where y(t) and v(t) are the system output and control input respectively. The characteristic equation of the above closed-loop system is:

[0085] s3 +as 2 +bs + c = 0 (28)

[0086] where

[0087] a = (2 + k q k qe )ω f

[0088] b = (k p k pd + k q k qe ω f + ω f )ω f

[0089]

[0090] ω f is the cut-off frequency of the filter;

[0091] (1) Reference model design:

[0092] Since the state space is a third-order system, consider the following reference model:

[0093]

[0094] where x m (t) and r(t) are the reference model state variable and the reference signal respectively, a m1 , a m2 , a m3 are three positive real numbers selected based on time-domain performance criteria, including phase and gain margins. The tracking error e(t) is defined as:

[0095] e(t) = x m (t) - x(t) (30)

[0096] Let e(t) → 0, that is, A depends on the parameters of the feeder. Since the system parameters k p , k q , ω p , ω q are self-designed variables, so B is a known quantity;

[0097] (2) Controller design

[0098] Considering the damping enhancement signal, the general structure of the adaptive controller is:

[0099] u(t) = k x (t)x(t) + k r r(t) + ω d (31)

[0100] where k x , k r are gains to be determined, which ideally make ω d a known damping enhancement signal;

[0101] To make the closed-loop system track the reference model such that:

[0102]

[0103]

[0104] Accordingly, design a corresponding adaptive mechanism to estimate the controller parameters

[0105] (3) Adaptive mechanism design

[0106] The system dynamic error is defined as:

[0107]

[0108] where are all error gains;

[0109] (4) Parameter estimation

[0110] Use the least squares method to update the system parameters regularly to reflect the dynamic changes of the system, and estimate the controller parameters to enable the system to track the reference model, thereby achieving adaptive control of the dynamic system:

[0111] The objective function of the least squares method is the sum of the squares of the error terms, that is:

[0112]

[0113] Substitute the error terms to get:

[0114]

[0115] Take the partial derivatives with respect to k x , k r respectively to obtain:

[0116]

[0117] Set the partial derivatives to 0 to obtain:

[0118]

[0119] Adopt the gradient descent method to minimize the loss function J(k x , k r ), and thus obtain k x , k rThe update rule is as follows:

[0120]

[0121]

[0122] where α is the learning rate, which controls the step size of each update; by iteratively updating the parameters until the loss function converges or the maximum number of iterations is reached, the optimal k can be found x and k r .

[0123] Beneficial effects:

[0124] 1. The present invention adopts a secondary control method of a virtual synchronous generator based on improved model reference adaptive to solve the secondary control problem under the peer-to-peer architecture in an islanded microgrid. First, an islanded main generator set model including a VSG control loop, a voltage-current double closed loop, and an inverter main circuit is established. A damping enhancement module is added to the VSG active power control part, and the model reference adaptive control technology based on multi-input multi-output is used to restore the frequency and voltage. At the same time, the least square method is introduced in the design of the adaptive controller to reduce the optimization calculation error caused by system uncertain factors such as load changes, equipment aging, and system parameter changes. The present invention improves the model reference adaptive control technology to cope with the voltage and frequency deviation problems caused by non-linearity and system uncertainty in the VSG during the operation of the microgrid, and ensures the stability of the system. At the same time, due to the introduction of the adaptive mechanism, compared with the traditional control, the secondary control of the VSG no longer requires communication. And the parameters of the controller are directly adjusted, so there is no need to estimate the parameters of the system model, reducing the computational burden.

[0125] 2. While implementing the secondary control of the VSG, the present invention introduces a damping enhancement module to adapt to the active power sharing problem of the VSG under the improved MRAC controller. While enhancing the damping, the oscillation problem in the system can be suppressed, and at the same time, the system dynamic response is improved, and the reference signal can be tracked more accurately. The damping enhancement module enhances the damping of the VSG, reduces the oscillation, thereby ensuring the stability of the voltage and frequency, and at the same time achieving active power sharing.

[0126] 3. The control strategy proposed by the present invention can realize the secondary control of the virtual synchronous generator and effectively eliminate unknown disturbances, enabling the system to operate at the rated voltage and frequency, and ensuring the stability of the system. It mainly relies on local sensor data and control algorithms for parameter estimation and adjustment, without the need for real-time data exchange with external systems or devices. The least square method is used to more accurately estimate the parameters of the system, thereby improving the control performance. Thus, the problems of high communication cost and low reliability caused by the common use of communication in traditional secondary control are solved. Description of the drawings

[0127] Figure 1 It is the secondary control structure diagram of the virtual synchronous generator based on improved model reference adaptive control;

[0128] Figure 2 It is the operation process of the improved model reference adaptive controller;

[0129] Figure 3 It is the control block diagram of the improved model reference adaptive controller;

[0130] Figure 4 It is the connection diagram of the distributed microgrid studied in the embodiment of the present invention. Specific implementation manners

[0131] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and cannot be used to limit the protection scope of the present invention.

[0132] The present invention discloses a VSG secondary control method based on improved model reference adaptive control, and the specific steps are as follows:

[0133] Step 1: The essence of VSG is to add an energy storage unit on the inverter side. On the basis of droop control, the VSG algorithm is introduced to simulate the rotor equation of the synchronous generator, endowing the inverter with virtual inertia and improving the anti-interference ability. Thus, the VSG rotor motion equation is obtained, and the VSG active-power / frequency loop is constructed.

[0134] The expression of the VSG active-power / frequency loop is:

[0135]

[0136] where T m , T e , T d are the mechanical torque, electromagnetic torque and damping torque of the synchronous generator respectively; P and P0 are the output active power and rated active power respectively; ω n , ω0 are the VSG output angular frequency and rated angular frequency respectively; J and D are the VSG moment of inertia and damping coefficient respectively; δ is the electrical angle;

[0137] In actual operation, the change of the DG angular frequency is small, i.e., ω≈ω0. At the same time, the input power P0 is defined as the DG input power reference value P * , the DG output power is P, and m is denoted as the VSG droop coefficient. Since the steady-state performance of the system is analyzed, the dynamic performance of the VSG is not considered, and the relationship between active power and frequency under steady state is:

[0138] P = P * -m(ω n -ω0).

[0139] Step 2: Based on the rotor motion equation obtained in Step 1, while the voltage loop of the VSG adopts Q-V droop control to obtain the VSG output voltage expression, a VSG reactive power-voltage loop is constructed.

[0140] The expression of the VSG reactive power-voltage loop is:

[0141] V = V0 - n(Q - Q0)

[0142] where n is the reactive power droop coefficient; Q and Q0 are the VSG output reactive power and rated reactive power respectively; V and V0 are the VSG output voltage and rated voltage respectively.

[0143] Step 3: According to Step 1 and Step 2, the relationship between the VSG active or reactive power and the line impedance can be represented by using a bus system with distributed generation (DG) units and an idle bus. A VSG power small-signal model is established to represent the VSG active and reactive powers. At the same time, considering the influence of the line impedance, the relationships between the active power and the VSG frequency, and the reactive power and the VSG voltage can be obtained.

[0144] The VSG output active and reactive powers are expressed as:

[0145]

[0146]

[0147] where U g is the amplitude of the AC bus voltage, V is the amplitude of the inverter output voltage, R g and X g are the line resistance and inductance respectively, and δ is the power angle; since δ is small, then sinδ ≈ δ, cosδ ≈ 1. When the line impedance is inductive, that is, when R g ≈ 0, the inverter output active power P and reactive power Q can be expressed as:

[0148]

[0149]

[0150] Therefore, the relationship between the VSG active power and frequency and the reactive power and voltage can be expressed as:

[0151] ω n = ω0 - k p (P - P * )

[0152] V = V0 - k q (Q - Q * )

[0153] ω n, ω0 are the output angular frequency and the rated angular frequency of the VSG respectively; P * , Q * are the reference active power and reactive power; k p , k q are the active and reactive droop coefficients of the VSG; Assume that there are small perturbations near the equilibrium point, defined as (δ e , U ge , V e ), then the above formula can be rewritten as:

[0154] ΔP = k pe ΔV + k pd Δδ

[0155] ΔQ = k qe ΔV + k qd Δδ

[0156] Δω n =Δω0 - k p (ΔP - ΔP * )

[0157] ΔV = ΔV0 - k q (ΔQ - ΔQ * )

[0158] Where

[0159] Assume that ω0, V0, P * , Q * are constants. Therefore, the deviation terms in Δω n and ΔV can be ignored. To filter out the high-frequency components caused by load imbalance in the measured power element, low-pass filters (LPFs) are usually used in the power control loop. These filters introduce a multi-time scale separation between the inner voltage and current loops and the outer power loop, and the latter is more than ten times slower than the inner voltage and current loops. Therefore, the inner loop is often ignored in the modeling process of the microgrid. This paper specifically studies the design of the power loop adaptive controller.

[0160] Step 4: Based on the VSG active and reactive power model proposed in Step 3, in the VSG active power control, a damping enhancement module is added. In this module, the damping control is improved, and at the same time, the grid frequency does not need to be measured, the governor characteristics are not changed, and the inertial response of the VSG is not disturbed. The ultimate goal is to achieve active power sharing in the VSG secondary control.

[0161] The damping enhancement module is:

[0162] When the active power deviates, without losing the damping characteristics, this paper selects feedforward damping, and the feedforward damping is expressed as:

[0163] ωd = G c (s)(P m - P e )

[0164] where G c (s) = k p + k dq H(s)s, where k p 、k dq are control parameters, and N d is used to limit the bandwidth of G c (s) to achieve the elimination of high - frequency noise.

[0165] The simplified active - power loop of the improved VSG can be expressed as:

[0166]

[0167] where ω m is the rotor speed, D is the damping coefficient, and P dmp is the damping in terms of power, and ω g is the grid frequency.

[0168] Define the grid voltage:

[0169]

[0170] The inner product of the vector e g is expressed as:

[0171]

[0172] The derivative is:

[0173]

[0174] where θ g 、θ m are phase angles.

[0175] Therefore, the internal voltage amplitude V dmp of the VSG is:

[0176] That is, V dmp = - DE g (ω g - ω m )cos(θ g - θ m )

[0177] To improve the flexibility of the damping term, a low - pass filter is added:

[0178]

[0179] wherein is the filter time constant.

[0180] From the above formula, let:

[0181]

[0182] where e vsg·3ph =[e avsg e bvsg e cvsg T is the three-phase voltage of the VSG.

[0183] In order to increase the damping enhancement ability of the VSG, the feedforward term of the above formula is used in the enhancement module of the active power control system and renamed as ω d , which is called the enhancement signal.

[0184]

[0185] where θ vsg is the voltage phase of the VSG, and V vsg is the output voltage of the VSG.

[0186] Deriving the above formula gives:

[0187]

[0188] Considering that θ vsg ≈θ g Then:

[0189] ω d =∫(V vsg (ω vsg -ω g ))dt

[0190] The above formula contains (ω vsg -ω g ) transferred from the integral term, which means that when the secondary control controller is activated, it has the ability to make ω g equal to ω vsg . Therefore, after the system frequency is stabilized, the active power is evenly distributed.

[0191] Step 5: Based on the damping enhancement module designed in Step 4, improve the model reference adaptive control and combine it to achieve the recovery of the VSG frequency and voltage, realize the secondary control of the VSG, and at the same time make the system have strong anti-interference ability.

[0192] ​Since the proposed MRAC is adaptive, it can compensate for the adverse effects of uncertainties, including the unmodeled dynamics due to neglecting the inner-loop dynamics. Through the static droop control in the VSG control, the steady-state values of the DG operating frequency and voltage amplitude are achieved. Therefore, at the steady-state operating point, the linearized model of the VSG can be obtained as follows:

[0193]

[0194] where then In the formula, ω p and ω q are the cut-off frequencies of the active and reactive loops, respectively.

[0195] By defining the state vector the state-space representation of the system under study is:

[0196]

[0197] where

[0198]

[0199] where y(t) and v(t) are the system output and control input, respectively. The characteristic equation of the above closed-loop system is:

[0200] s 3 + as 2 + bs + c = 0

[0201] where

[0202] a = (2 + k q k qe )ω f

[0203] b = (k p k pd + k q k qe ω f + ω f )ω f

[0204]

[0205] ω f is the cut-off frequency of the filter.

[0206] The coefficients of the characteristic equation determine the transient response of the system and thus the stability of the closed loop. The system under study is a two-input two-output (TITO) system. Therefore, the control input can independently adjust the two outputs.

[0207] (1) Reference model design:

[0208] Since the state space is a third-order system, consider the following reference model:

[0209]

[0210] where x m (t) and r(t) are the reference model state variable and the reference signal respectively, and a m1 , a m2 , a m3 are three positive real numbers selected based on time-domain performance criteria (such as settling time, rise time, overshoot, and frequency-domain specifications), including phase and gain margins. The above equation has a completely decoupled structure and can provide acceptable performance even in the presence of unknown dynamics. The tracking error e(t) is defined as:

[0211] e(t) = x m (t) - x(t)

[0212] Let e(t) → 0, that is, A depends on the parameters of the feeder. Since the system parameters (k p , k q , ω p , ω q ) are self-designed quantities, B is a known quantity.

[0213] (2) Controller design

[0214] Consider the general adaptive controller structure as:

[0215] u(t) = k x (t)x(t) + k r r(t) + ω d

[0216] where k x , k r are undetermined gains, and ideally, ω d is a known damping enhancement signal.

[0217] To make the closed-loop system track the reference model such that:

[0218]

[0219]

[0220] Thus, design the corresponding adaptive mechanism to estimate the controller parameters

[0221] (3) Adaptive mechanism design

[0222] The system dynamic error is defined as:

[0223]

[0224] Among them

[0225] (4) Parameter estimation

[0226] The system parameters are updated regularly using the least squares method to reflect the dynamic changes of the system. The role of the least squares method in model reference adaptive control is to enable the system to track the reference model by estimating the parameters of the controller, thereby achieving adaptive control of the dynamic system.

[0227] The objective function of the least squares method is the sum of the squares of the error terms, that is:

[0228]

[0229] Substituting the error terms gives:

[0230]

[0231] Taking partial derivatives with respect to k x and k r yields:

[0232]

[0233] Setting the partial derivatives to 0 gives:

[0234]

[0235] The gradient descent method is used to minimize the loss function J(k x , k r ). From this, the update rules for k x and k r are:

[0236]

[0237]

[0238] where α is the learning rate, which controls the step size of each update; by iteratively updating the parameters until the loss function converges or reaches the maximum number of iterations, the optimal k x and k r can be found.

[0239] The connection diagram of the distributed microgrid studied in the embodiments of the present invention is as shown in Figure 4As shown. The proposed improved MRAC control method is applied to an autonomous AC microgrid composed of four different DGs. When any one of the DGs is subjected to an external disturbance, the adaptive controller calculates the error based on the actual output of the system and the model reference signal. According to the error signal, the parameters of the controller are adjusted using an adaptive algorithm (least squares method). The adaptive algorithm adjusts the parameters according to the magnitude and direction of the error signal, so that the output of the faulty DG gradually approaches the desired model reference signal. According to the update rule of the adaptive algorithm (gradient descent method), the parameters of the controller are updated in real time. Secondly, based on the updated parameters and the state of the DG, a control signal is generated to regulate the faulty DG, making its output approach the model reference signal and regulating the operation of the system in real time. This process is continuous, and the controller continuously adjusts according to the actual response of the DG to maintain the stability of the system. At the same time, the damping enhancement module adjusts the control signal according to the state of the DG to improve the damping characteristics of the system.

[0240] The above embodiments are only for illustrating the technical concept and features of the present invention, and the purpose is to enable those who are familiar with this technology to understand the content of the present invention and implement it accordingly, and it cannot be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit and essence of the present invention should be covered within the protection scope of the present invention.

Claims

1. A secondary control method for VSG based on improved model reference adaptive, characterized in that It includes the following steps: Step 1: Add an energy storage unit to the inverter side. On the basis of droop control, introduce the VSG algorithm, simulate the rotor equation of a synchronous generator, endow the inverter with virtual inertia, obtain the VSG rotor motion equation, and construct the VSG active-power - frequency loop; Step 2: Based on the rotor motion equation obtained in Step 1, and at the same time, the voltage loop of the VSG adopts Q-V droop control to obtain the VSG output voltage expression, and construct the VSG reactive-power - voltage loop; Step 3: Use a bus system with a distributed generation DG unit and an idle bus to represent the relationship between the VSG active or reactive power and the line impedance, establish a VSG small-signal power model to represent the VSG active and reactive powers, and at the same time obtain the relationship between the active power and the VSG frequency, and the relationship between the reactive power and the VSG voltage; Step 4: Based on the VSG active and reactive power model proposed in Step 3, add a damping enhancement module in the VSG active power control to achieve active power sharing in the VSG secondary control; The damping enhancement module is: When the active power deviates, without losing the damping characteristics, use feedforward damping, and the feedforward damping is expressed as: ω d = G c (s)(P m - P e ) (15) where G c (s) = k p + k dq H(s)s, where k p 、k dq are control parameters, and N d is used to limit the bandwidth of G c (s); After adding the damping enhancement module, the specific process of achieving active power sharing in the VSG secondary control is as follows: The improved VSG active power loop is simplified as: where ω m is the rotor speed, D is the damping coefficient, P dmp is the damping expressed in power, and ω g is the grid frequency; Define the grid voltage: vector e g inner product is expressed as: The derivative is: where θ g and θ m are phase angles; Therefore, the internal voltage amplitude V of the VSG dmp is as follows: To improve the flexibility of the damping term, add a low-pass filter: wherein is the filter time constant; From the above formula, let where e vsg·3ph = [e avsg e bvsg e cvsg T is the three-phase voltage of the VSG;​ To increase the damping enhancement ability of the VSG, a feedforward term is used in the enhancement module of the active power control and renamed as ω d , which is called the enhancement signal: Among them, θ vsg is the voltage phase of the VSG, and V vsg is the output voltage of the VSG; Take the derivative of the above formula to get: Considering θ vsg ≈ θ g Then ω d = ∫(V vsg (ω vsg - ω g ))dt (25) The above equation includes (ω vsg - ω g ) transferred from the integral term, which means that when the secondary control controller is activated, it has the ability to make ω g equal to ω vsg . Therefore, after the system frequency is stabilized, the equal sharing of active power is achieved; Step 5: Based on the damping enhancement module designed in Step 4, design an improved model reference adaptive controller based on multi-input multi-output, design the control law using the least squares method, realize the recovery of the VSG frequency and voltage, and achieve the VSG secondary control; The improved model reference adaptive controller is: At the steady-state operating point, the VSG linearized model is obtained as: Among them then where ω p and ω q are the cut-off frequencies of the active circuit and the reactive circuit; By defining the state vector The state space representation of the system under study is as follows: Where Where, y(t) and v(t) are the system output and control input respectively, and the characteristic equation of the closed-loop system is: s 3 +as 2 +bs + c = 0 (28) Where a = (2 + k q k qe )ω f b = (k p k pd + k q k qe ω f + ω f )ω f ω f is the cut-off frequency of the filter; (1) Reference model design: Since the state space is a third-order system, consider the following reference model: where x m (t) and r(t) are the reference model state quantity and the reference signal respectively, and a m1 , a m2 , a m3 are three positive real numbers selected based on the time-domain performance criteria, including phase and gain margins, and the tracking error e(t) is defined as: e(t) = x m (t) - x(t) (30) Let e(t) → 0, that is, A depends on the parameters of the feeder. Since the system parameters k p 、k q 、ω p 、ω q are self-designed variables, B is a known variable; (2) Controller design Considering the damping enhancement signal, the general adaptive controller structure is: u(t) = k x (t)x(t) + k r r(t) + ω d (31) where k x and k r are gains to be determined, which ideally make ω d a known damping enhancement signal; To make the closed-loop system track the reference model such that: Accordingly, a corresponding adaptive mechanism is designed to estimate the controller parameters (3) Adaptive mechanism design The system dynamic error is defined as: wherein are all error gains; (4) Parameter estimation Use the least squares method to update the system parameters regularly to reflect the dynamic changes of the system, and estimate the parameters of the controller to enable the system to track the reference model, thereby realizing the adaptive control of the dynamic system: The least squares method objective function is the sum of the squares of the error terms, that is: Substitute the error terms to get: Derive the partial derivatives with respect to k x and k r respectively, and we get: Let the partial derivative be 0 to get: The gradient descent method is used to minimize the loss function J(k x ,k r ), and the update rules for k x and k r are as follows: where α is the learning rate, controlling the step size of each update; by iteratively updating the parameters until the loss function converges or reaches the maximum number of iterations, the optimal k can be found x and k r .

2. The secondary control method of VSG based on improved model reference adaptive according to claim 1, characterized in that The VSG active-power - frequency loop expression in Step 1 is: Among them, T m , T e , T d are the mechanical torque, electromagnetic torque, and damping torque of the synchronous generator, respectively; P and P0 are the output active power and rated active power, respectively; ω n , ω0 are the output angular frequency and rated angular frequency of the VSG, respectively; J and D are the moment of inertia and damping coefficient of the VSG, respectively; δ is the electrical angle; In actual operation, the angular frequency change of the DG is small, i.e., ω≈ω0. At the same time, the input power P0 is defined as the reference value P of the DG input power * , the DG output power is P, and m is denoted as the VSG droop coefficient. Since the steady-state performance of the analysis system is considered, the dynamic performance of the VSG is not considered. Then, the relationship between active power and frequency under steady state is: P = P * -m(ω n - ω0) (2) 3. The VSG secondary control method based on improved model reference adaptive according to claim 1, characterized in that The VSG reactive-power - voltage loop expression in Step 2 is: V = V0 - n(Q - Q0) (3) Where, n is the reactive droop coefficient; Q and Q0 are the VSG output reactive power and rated reactive power respectively; V and V0 are the VSG output voltage and rated voltage respectively.

4. The secondary control method of VSG based on improved model reference adaptive according to claim 1, characterized in that The VSG output active and reactive powers in Step 3 are expressed as: Among them, U g is the amplitude of the AC bus voltage, V is the amplitude of the inverter output voltage, R g and X g are the line resistance and inductance respectively, and δ is the power angle; since δ is small, then sinδ≈δ and cosδ≈1. When the line impedance is inductive, that is, when R g ≈0, the active power P and reactive power Q output by the inverter can be expressed as: Therefore, the relationship between the VSG active frequency and reactive voltage can be expressed as: ω n = ω0 - k p (P - P * ) (9) V = V0 - k q (Q - Q * ) (10) ω n , ω0 are the output angular frequency and rated angular frequency of the VSG respectively; P * , Q * are the reference active power and reactive power; k p , k q are the active and reactive droop coefficients of the VSG; assuming there is a small disturbance near the equilibrium point, defined as (δ e , U ge , V e ), then the above equation can be rewritten as: ΔP = k pe ΔV + k pd Δδ (11) ΔQ = k qe ΔV + k qd Δδ(12) Δω n = Δω0 - k p (ΔP - ΔP * ) (13) ΔV = ΔV0 - k q (ΔQ - ΔQ * ) (14) Among them Assume that ω0, V0, P * , Q * are constants, so the bias terms in Δω n and ΔV can be neglected. To filter out the high-frequency components caused by load imbalance in the measured power element, low-pass filters LPFs are used in the power control loop, and these filters introduce a multi-time scale separation between the inner voltage and current loops and the outer power loop.

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