Frequency Regulation Control and Parameter Optimization of Doubly-Fed Induction Machine Pumped Storage Hydro Unit

Since doubly-fed induction machine pumped storage hydro (DFIM-PSH) unit can adjust active power flexibly through adjustable-speed operation, it has frequency regulation capability in both generating and pumping modes. In order to explore the frequency regulation capability of DFIM-PSH unit under different working conditions, this paper develops a frequency control module for DFIM-PSH unit in pumping mode, which is quite different from that in generating mode, and then optimizes the frequency control parameters aimed at minimizing the frequency deviation in multiple operating conditions. Based on the dynamic model of the DFIM-PSH unit, the system frequency response model is built to analyze the influence of parameters on frequency dynamic characteristics. An optimization method of frequency control parameters is developed based on improved particle swarm optimization algorithm to maximize its frequency regulation capability under different operating conditions while ensuring safe and stable operation. Finally, a four-machine two-zone power system model with a DFIM-PSH unit is simulated, and the simulation results show that the proposed strategy can make the DFIM-PSH unit have great frequency regulation performance in a wide range of operating conditions.

will not participate in the frequency regulation due to its 23 inability to adjust active power continuously in the pumping 24 mode [1], [2], [3]. 25 The associate editor coordinating the review of this manuscript and approving it for publication was Jiefeng Hu . New PSH power station based on doubly-fed induction 26 machine (DFIM) (DFIM-PSH) can not only overcome the 27 disadvantages of traditional PSH unit including low effi-28 ciency and inability to adjust power in the pumping mode, 29 but also has more flexible power regulation capability since it 30 can realize variable-speed operation [4], [5], [6]. Therefore, 31 it can be seen that DFIM-PSH unit is equipped with addi-32 tional frequency regulation capacity and frequency regulation 33 potential through variable-speed operation, which provides a 34 feasible scheme for relieving the increasing frequency regu-35 lation pressure of the grid. However, since control strategies 36 adopted by DFIM-PSH unit will lead to the decoupling of 37 unit's speed and the grid's frequency, the unit cannot auto-38 matically participate in frequency adjustment, which needs 39 is constructed for the unit in pumping mode, where frequency 95 deviation is converted into additional speed and active power 96 instructions and then the flexible power regulation ability of 97 DFIM-PSH can be played through the coordination between 98 converter and reversible pump/turbine, and the module's 99 mechanism and characteristics of frequency regulation can 100 be analyzed in detail. Secondly, by constructing the system 101 frequency response model with DFIM-PSH, the root-locus 102 method is used to analyze the influence of frequency control 103 parameters on frequency dynamic characteristics, and the 104 recommended range of each frequency control parameter is 105 given. Accordingly, aiming at minimizing the frequency devi-106 ation with DFIM-PSH under multiple operating conditions, 107 an optimization method for frequency control parameters is 108 developed based on improved particle swarm optimization 109 algorithm to maximize its frequency regulation capability 110 under different operating conditions while ensuring safe and 111 stable operation. Finally, a four-machine two-zone power 112 system model with DFIM-PSH is simulated, and the system's 113 dynamic frequency responses under traditional frequency 114 control and the proposed control are compared, verifying 115 the effectiveness and robustness of the proposed frequency 116 control strategy when the unit is under different operating 117 conditions and different disturbances. As the prime mover/load of DFIM-PSH, reversible pump/ tur-129 bine can realize the switch between turbine and pump modes 130 by changing the direction of rotation. Based on the IEEE 131 nonlinear model, its mathematical model can be established 132 as [16]: To simplify the analysis, the ideal model is often used to 135 describe it: Here, prefix is used to represent change, q is the relative 138 value of flow, H is the relative value of head, z is the relative 139 value of guide vane opening, p mech is the relative value of 140 mechanical power, ω r is the relative value of speed, h 0 is 141 the relative value of initial head, h 1 is the relative value of 142 Here, i r is the actual value of rotor current, i * r is the reference  Currently, the power priority control strategy is mostly 191 adopted to realize the regulation of DFIM-PSH's speed and 192 power [11], [18], as shown in Fig. 1(a). The active and reac-193 tive power are set as the control target of the converter, which 194 can be adjusted rapidly by altering rotor current. At the same 195 time, the optimal speed calculated according to active power 196 instructions is set to be adjusted by changing the guide vane 197 opening of turbine. Under such control structure, the rapid 198 and flexible adjustment of active power can be guaranteed in 199 priority, so power priority control strategy is adopted when 200 the unit is in generating mode.

201
Although the power priority control strategy can accelerate 202 the response of active power, it cannot facilitate the accurate 203 and rapid tracking of rotor speed. In pumping mode, since 204 it is usually required that the unit can directly control the 205 speed to the optimal [19], [20], speed priority control strategy 206 is selected here. The optimal speed is calculated according 207 to the real-time active power at first, and then given to the 208 converter as the priority control object for rapid adjustment. 209 Meanwhile, the active power is precisely adjusted through the 210 controller in pump, as shown in Fig. 1(b).  respectively, f is the frequency deviation, P 0_ref is the initial 220 active power reference, and s is the differential operator.

221
In pumping mode, since the unit's active power is con-222 trolled through the pump/turbine, if the traditional frequency 223 control strategy is still adopted, the regulating speed will be 224 significantly slower than that in generating mode, so the rapid control block diagram is shown in Fig. 2 and K ωd , K ωp are the proportion and differential coefficients 243 of frequency control modules at active power controller and 244 speed controller, and ω 0_ref is the initial speed reference.

247
After adopting the above frequency control modules, DFIM-248 PSH can not only provide support for frequency regula-249 tion by changing the output power in generating mode, but 250 also participate in frequency regulation as a variable load in 251 pumping mode. The frequency regulation characteristics of 252 DFIM-PSH can be reflected by the relationship between the 253 change of frequency f and the change of unit's active power. 254 In generating mode, the additional active power instruction 255 generated by DFIM-PSH due to frequency control can be 256 expressed as: At this point, DFIM-PSH controls the output active power 259 through the converter, and then further realizes the energy 260 exchange with the grid. Combined with the response model 261 of converter, the transfer function between the unit's active 262 power and frequency can be deduced: In pumping mode, since the active power and speed control 265 channels are both equipped with additional frequency con-266 trol modules, DFIM-PSH can not only directly adjust active 267 power through the frequency control module in pump/turbine, 268 but also can indirectly change it by altering speed through the 269 module in converter at the same time. The additional active 270 power and speed instructions of DFIM-PSH generated by 271 frequency control can respectively be expressed as follows: 272 According to (1), the active power output of the pump 275 can be described as a polynomial related to the rotational 276 speed. For simplification, the active power change caused 277 by the speed deviation ω r can be described as P mech = 278 k ω r by linearization, where k is the slope of the polynomial 279 curve at the optimal running point of pump. For convenience, 280 the transfer function between active power and frequency is 281 derived based on the ideal model of pump/turbine: In order to study the influence of DFIM-PSH on the frequency 287 dynamic response of the system, this paper establishes 288 the system frequency response model including DFIM-PSH 289   Table 1.

298
It should be noted that H is the equivalent inertia time  In generating mode, DFIM-PSH works as power supply, 309 and the frequency deviation can be expressed as: In pumping mode, DFIM-PSH works as load, and the 314 frequency deviation can be expressed as: Here, S N is the rated apparent power of the whole system, S TN 319 and S HN are respectively the rated apparent power of thermal 320 power and hydropower units, S DN is the rated apparent power 321 of DFIM-PSH, H T and H H are respectively the equivalent 322 inertia time constant of thermal power and hydropower units, 323 and m and n are the number of thermal power and hydropower 324 units, respectively.

325
By substituting (7) and (10) into (11) and (12), the specific 326 expression of frequency deviation when DFIM-PSH is in gen-327 erating and pumping modes can be obtained. Furthermore, 328 the frequency dynamic response indices including the max-329 imum frequency deviation rate d f/dt| max , the steady-state 330 frequency deviation f st , and the maximum frequency devia-331 tion f max can be derived based on inverse Laplace transform 332 mentioned in [22]. In general, the addition of proportional 333 control in frequency controller increases the system's damp-334 ing, which is conducive to reducing f max and f st . On the 335 other hand, the differential part increases the inertia of the 336 system to improve the frequency stability of the system by 337 decreasing d f/dt| max . According to the analysis above, larger frequency control 343 parameters can help to improve the frequency regulation 344 ability of DFIM-PSH. However, since the speed and active 345 power of the unit will be affected by frequency control param-346 eters, too large parameters will result in excessive response 347 and further make speed difficult to restore. Therefore, the 348 selection of frequency control parameters should be on the 349 basis of ensuring the safe and stable operation of DFIM-PSH 350 and thus take the goal of realizing the optimal capability of 351 frequency regulation into consideration.

352
Therefore, based on (11) and (12), the zero-pole trajecto-353 ries of the transfer function of frequency deviation when each 354 frequency control parameter changes from 0 to ∞ are plotted 355 using the generalized root-locus method, and the influence of 356 each parameter on the stability of frequency response and its 357 dynamic performance is observed. Figs. 4 and 5 show the root 358  In generating mode, the frequency control parameters to be 361 determined include K p and K d . As can be seen from Fig. 4(a),  on the premise of ensuring system's stability. Accordingly, 389 the zero-pole trajectories with dual channels are drawn as 390 shown in Fig. 5.

VOLUME 10, 2022
Similarly, taking the system's stability as the basic goal 392 and considering the dynamic performance requirements of 393 inertia response and primary frequency regulation response, 394 the preliminary selection of each frequency control param-395 eter is made. As can be seen from Fig. 5(a), when 9.51 < 396 K ωd < 24, the system is underdamped with damping ratio 397 over 0.707 and overshoot below 5%, so that the maximum 398 frequency deviation and the stability time will be reduced in 399 the corresponding frequency regulation process. According Here, ω rmin and ω rmax are respectively the minimum and  calculation formula of frequency dynamic response indices 444 given in [22], deleting the particles with high values of f max 445 and d f/dt| max before the simulation model is invoked can 446 help to improve the quality of initial particles, so as to accel-447 erate the convergence of the algorithm. Fig. 6 shows the 448 convergence of the algorithm before and after improvement. 449 The parameters optimized in generating mode can be listed as 450 follow: K p = 21.47, K d = 11.15, and those in pumping mode 451 are K pp = 21.78, K pd = 3.85, K ωp = 15.3, K ωd = 11.98.

453
A simulation model of a DFIM-PSH connected to an 454 improved four-machine two-area power system, as shown 455 in Fig. 7, is built on PSCAD/EMTDC, and the dynamic 456 frequency response is observed by setting load disturbance. 457 The specific simulation parameters are shown in Table 2. For 458 simplicity, the optimal running point tracking is not consid-459 ered in the process of frequency regulation.   active power instruction of DFIM-PSH is set as −0.8 p.u., 470 and the corresponding optimal speed instruction is 1.02 p.u..

471
After operating for 20 s, 10% load increase is set. The responses of system frequency, unit's speed and active 473 power when DFIM-PSH adopts different frequency control 474 strategies in pumping mode are shown in Fig. 8. The speed 475 channel can make the unit change its active power input 476 rapidly by greatly adjusting speed, to suppress the change of 477 frequency quickly at the early stage of frequency regulation, 478 VOLUME 10, 2022 dual channel control can effectively combine the advantages 495 of these two channels to achieve better effects.

496
In Fig. 9, the frequency responses of DFIM-PSH with 497 different frequency control parameters when only the speed 498 channel or the active power channel functions are compared. 499 The corresponding dynamic response indices of frequency 500 are compared as shown in Table 3 to analyze the effect of each 501 parameter. It can be found that larger K ωp of speed channel 502 can contribute to smaller d f/dt and f max , but the increment 503 of K ωd will not promote the reduction of f max obviously. 504 As for the active power channel, larger K pd can also help to 505 reduce d f/dt and f max , while since differential control has 506 weak effect in late regulation stage when the deviation rate 507 of frequency becomes small, it cannot further promote the 508 reduction of f st . As the effect of active power channel can 509 last for a relatively long time, the reduction of f st can be 510 realized by selecting larger K pp .  are simulated. At 20 s, 10% load increase is provided, and 529 the responses of each physical quantity with DFIM-PSH 530 adopting different frequency control parameters are shown in 531 Figs. 10-13. It can be seen that compared with the traditional 532 frequency control parameters (Parameter I), the optimized 533 parameters can help to reduce f max , f st , and d f/dt more 534 significantly. At the same time, DFIM-PSH can maintain 535 safe and stable operation under different working conditions 536 and maintain the speed and power within allowable ranges 537 in the whole regulation process. In other words, the opti-538 mized frequency control parameters in this paper have a good 539 robustness.

540
In generating mode, the unit's speed can be rapidly 541 adjusted under the action of frequency control modules, 542 which provides great active power instantaneously in the 543 initial stage of frequency regulation, thus making f max and 544 d f/dt reduced significantly. At the same time, the con-545 stant increase of output active power also leads to obvi-546

585
In this paper, considering the operation characteristics of 586 DFIM-PSH in pumping mode, the frequency control strat-587 egy which are based on the coordination of converter and 588 pump/turbine are proposed. Furthermore, based on the anal-589 ysis of its mechanism and characteristics, a system frequency 590 response model with DFIM-PSH is built, and the influence of 591 frequency control parameters on frequency dynamic response 592 characteristics is analyzed using root-locus method. To give 593 full play to the frequency regulation ability of DFIM-PSH 594 under different working conditions on the basis of stable 595 operation, this paper further presents optimization method 596 of frequency control parameters based on improved particle 597 swarm optimization algorithm, which is aimed at minimiz-598 ing the frequency deviation with DFIM-PSH under multiple 599 working conditions. The main conclusions can be drawn as 600 follows:

601
(1) The frequency control module of DFIM-PSH in pump-602 ing mode established in this paper, where the frequency devi-603 ation is turned into auxiliary speed and active power instruc-604 tions and then adjusted by the coordination of converter and 605 pump/turbine, can help to significantly reduce d f/dt and 606 f max by rapidly adjusting speed at the initial stage of fre-607 quency regulation, and reduce f st by continuously changing 608 active power at the frequency recovery stage.

609
(2) The optimization method of frequency control param-610 eters based on improved PSO, which is aimed at minimizing 611 the overall effects of frequency regulation when the unit 612 is under multiple working conditions and takes the change 613 of speed and active power within allowable ranges as con-614 straints, has great robustness when DFIM-PSH is under dif-615 ferent working conditions or suffers from different load dis-616 turbances. The overall frequency control strategy can improve 617 the frequency regulation ability of DFIM-PSH by reducing 618 d f/dt, f max , and f st , so as to improve the frequency 619 characteristics of power grid.