Configuration method of PSS lead-lag compensator parameters

. Power System Stabilizer (PSS) is an important measure to increase damping and suppress low frequency oscillations of power system. During PSS test, the time constant of lead-lag compensator need to be configured, considering the inefficiency and optimization problem when configuring parameters empirically, this paper proposes automatic configuration method of PSS parameters based on Matlab, by setting the expected phase value at each frequency and constructing the objective function with the sum of phase differences square, the automatic calculation of PSS parameters under specific phase requirements at each frequency can be realized, the detailed steps of this method are given, and the method is verified during the PSS test of an 300Mw thermal-power generating unit finally.


Introduction
Low-frequency oscillation largely affects the stable operation of the power system. The main reason of lowfrequency oscillation are negative-damping mechanism [1] , forced-oscillation mechanism [2] , nonlinear-mechanism [3] and strong-resonance mechanism [4] , the negativedamping mechanism is a classic theory when studying low-frequency oscillation. Due to the phase-lag characteristics of the automatic regulator, excitation system and generator rotor winding, negative-damping torque is produced, which bring negative-damping of power system. For this reason, the power system stabilizer (PSS) is usually added to the regulator. PSS is an additional control device that adjusts the output rotor voltage with automatic-regulator to achieve the purpose of damping power system and other oscillations. Currently, PSS2B model is widely used in the world. The PSS2B model has two input signals: speed and electric power. Only by correctly configuring the leadlag time constant of the PSS2B model, can PSS have its due effect. At present, EXCEL table is often used to adjust the time constant during PSS test, which takes a lot of time and can not get the best effect. This paper proposes an automatic calculation method based on Matlab, and the new method is verified during PSS test.

2.1The Transfer Function of PSS2B Model
PSS2B model's transfer function is shown in Figure 1. ω is signal of generator's speed, Pe is signal of generator's power, Tω1 ～ Tω4 is time constants of blocking compensator, T 1 ~ T 5 and T 10 are time constants of leadlag compensator (two or three-order compensation compensator may be used), T 6 T 7 are inertial time constants, T 8 , T 9 are time constants of torsional vibration filter, T 11 ~ T 14 are lead-lag time constants of automatic voltage regulator, M, N are the orders of torsional vibration filter, P M is mechanical input power, Pa is accelerating power, K s1 is gain of PSS, K s2 is gain of inertial compensator, K s3 is gain of power combination, K is gain of automatic voltage regulator, K A is gain of excitation system's power, K G is gain of generator, T A is the time constant of power amplification compensator, Td' is time constant of generator, T j is time constant of the total shaft, the T r is sampling time constant of generator's output voltage.
The accelerating power variation ΔP a can be synthesized using signals of output power variation ΔP e and speed variation Δω, ΔP a is input signal of the threeorder lead-lag compensation compensator, U pss can be got from the output of three-order lead-lag compensation compensator, which is added to the voltage reference value of the automatic voltage control loop. Physical concept of PSS2B model is clear, three-order lead-lag compensator has strong ability of phase correction and strong practicality.

The phase compensation principle of the PSS2B model
The phase relationship of each physical quantity in the PSS2B model is shown in Figure 2. Without compensation, as a result of the automatic voltage regulator control, the electromagnetic torque ΔT e2 lags the power (Δδ), Component of the torque in the ω-axis direction is negative, providing negative damping. PSS provides ΔU PSS signal which is added to automatic voltage regulator by sampling and processing some input signals. The ΔU PSS signal can provide positive damping through the lagging of the excitation system of electromagnetic torque ΔT PSS in Δω axis component is positive.  Figure 1 Transfer function of PSS2B model contains lag angel of PSS itself and the inherent lag angle of the excitation system without compensation [5] .

During PSS test, '
Ex  is obtained by frequency sweep, and the time constant of PSS lead-lag compensator is configured to meet the requirements [6] .

Configuration method of PSS2B model's parameter
The transfer function of PSS2B model as shown in figure 1, ω input branch is designed to suppress the Counter-modulation of PSS, during oscillation of active power, ΔPm equals zero, considering the configuration of PSS parameters is based on Pe axis, so lag angel of PSS itself can be expressed as, Where T 1 ~ T 4 and T 7 are always set as 6 empirically, and the value of K s2 is calculated from the inertia moment of total shaft and T 7 . The phase-frequency characteristic value after compensation has been stipulated clearly in DLT 1231-2018 "Guide for Setting Test of Power System Stabilizer ", the lead-lag compensator time constant T 1 ~ T 6 values should be configured during PSS test to meet the requirements. Therefore, how to configure the time constant quickly and effectively is a problem that needs to be studied and solved.

Multivariate optimization function under constraints
MATLAB fmincon() function can deal with the multivariate optimization problem, fmincon() function is structured as fmincon (FUN, X0, A, B, Aeq, Beq, LB, UB), where FUN is the objective function and X0 is the initial value of the variable to be solved. The inequality constraints to be satisfied for variables is given by A and B (AX < B), the equality constraints to be met for variables is given by Aeq and Beq (AeqX = Beq), and the boundary conditions to be met for variables are given by LB and UB (LB < X <UB).
The optimization results are affected by the form of objective function directly. In this paper, the sum of difference squares between expected phase value and actual phase value at each frequency point is used as the optimization function. The expected phase angel 0   of Δ T PSS lagging -ΔP e at 20 discrete frequency points between 0.1 ~ 2.0 HZ is set firstly, then the objective function myfun () is defined as sum of difference squares between expected phase value 0   and actual phase value   ,

Configuration method of PSS2B's lead-lag compensator time constant
The configuration method of PSS2B lead-lag compensator time constant is shown in Figure 3. The first step is to set the desired phase angle 0   at each frequency point, Secondly the phase frequency value of the excitation system without compensation ' Ex  is obtained by frequency sweep and objective function myfun ( ) can be got according to (2), thirdly the optimal value of time constant can be obtained based on section 2.1 by using MATLAB fmincon() function. Fourthly time constants obtained in the previous step are substituted to calculate the actual phase value of each frequency point, whether the actual value meets the requirements is determined in the fifth step, the time constant value can be taken as the PSS setting value when requirements are met, otherwise, the second step is returned to modify the expected value of the phase angle at the frequency point where the requirement can not be met.

Test Verification
The proposed configuration method of PSS lead-lag compensator time constant is verified in the PSS test of a 1 000 MW generator unit. The main parameters of the unit are shown in Table 1, the uncompensated phasefrequency characteristics of the excitation system are shown in Table 2.  Figure 4 shows the waveform of field voltage when K s1 = 32. As can be seen from figure 4, the field voltage diverges to a certain extent, so the critical gain of Ks1 is 32. Generally, 1/3 ~ 1/5 of the critical gain is taken as the value of Ks1 [6] , so Ks1 is set as 8.  As can be seen from figure 5 and figure 6, under the same generator voltage change, the amplitude and times of active power oscillation are greatly reduced with PSS, indicating that the PSS lead-lag time constant configuration method proposed in this paper is effective.