Stepwise Inertial Control of a Doubly-Fed Induction Generator to Prevent a Second Frequency Dip

Abstract

To arrest a frequency nadir, a stepwise inertial control (SIC) scheme generates a constant active power reference signal of a wind turbine generator (WTG) immediately after a disturbance and maintains it for the predetermined time. From that point, however, the reference of a WTG abruptly decreases to restore the rotor speed for the predefined period. The abrupt decrease of WTG output power will inevitably cause a second frequency dip. In this paper, we propose a modified SIC scheme of a doubly-fed induction generator (DFIG) that can prevent a second frequency dip. A reference value of the modified SIC scheme consists of a reference for the maximum power point tracking control and a constant value. The former is set to be proportional to the cube of the rotor speed; the latter is determined so that the rotor speed does not reach the minimum operating limit by considering the mechanical power curve of a DFIG. The performance of the modified SIC was investigated for a 100 MW aggregated DFIG-based wind power plant under various wind conditions using an EMTP-RV simulator. The results show that the proposed SIC scheme significantly increases the frequency nadir without causing a second frequency dip.

1. Introduction

Power generation in a power system should match the power consumption to maintain the frequency within the allowed limits at all times. When a large disturbance occurs, such as a generator tripping, the system frequency is reduced. In this case, the kinetic energy (KE) stored in the rotating masses of the synchronous generators (SGs) is intrinsically released; the SGs with spinning reserve then take part in the frequency control by increasing mechanical power to recover the frequency to the nominal value [1].

Over the last decade, the installed capacity of a wind turbine generator (WTG) has rapidly increased on account of its technological advances and economic viability. The total worldwide installed capacity of a WTG increased to 336 GW in 2014 [2]; it is expected to increase to 832 GW by 2020 and to 3,702 GW by 2050 [3].

The variable speed WTG, one of the most popular WTG types, adjusts the rotor speed depending on the wind speed to capture the maximum energy from the wind. This is called the maximum power point tracking (MPPT) operation. However, because WTGs do not respond to the frequency deviation due to the MPPT operation, the frequency stability will significantly worsen in a power system with high wind penetration [4]. To minimize this problem, WTGs are encouraged or forced to participate in the frequency control of a power system [5].

Many frequency-based inertial control (FBIC) schemes of variable speed WTGs have been proposed that release the KE stored in the rotating masses using frequency to support frequency control [6-10]. The FBIC schemes employ two kinds of auxiliary loops based on the rate of change of frequency (ROCOF) [6] and/or the ROCOF loop with the frequency deviation loop [7]. These schemes can halt the frequency nadir by releasing the KE stored in the WTGs. However, the frequency should be measured in real-time to calculate the frequency deviation and/and the ROCOF. In addition, because the additional power is determined not by the KE in the WTGs but by the frequency, the contribution to frequency support is limite/d. On the other hand, to give more contribution to the frequency support, the droop gain was adjusted depending on the rotor speed of WTGs [8]; the maximum ROCOF instead of the ROCOF was used to improve the response of the ROCOF loop [9]; the loops gains were dynamically changed by using a fuzzy controller to maintain the power system frequency [10].

A stepwise inertial control (SIC) scheme [11] has been suggested that produces and maintains constant power for a predefined time after a disturbance. Because the SIC scheme releases more power than FBIC schemes at the initial stage of a disturbance, the frequency nadir is enhanced. However, because the scheme results in a significant loss of KE, the rotor speed may decrease below the minimum operating speed limit. To avoid this, the stepwise decrease of the output for a predetermined time is inevitable for recovering the rotor speed. This might cause a subsequent disturbance to the power system and a second frequency dip may occur. Thus, difficulties can arise in determining the amount and duration of increase/decrease to avoid a second frequency dip.

In this paper, we propose a modified SIC scheme that can increase the frequency nadir without causing a second frequency dip. To achieve this, the reference signal of the proposed modified scheme consists of the reference signal for an MPPT operation and a constant value. The former is set to be proportional to the cube of the rotor speed; the latter is determined so that the rotor speed does not reach the minimum operating limit by considering the mechanical power curve of a doubly-fed induction generator (DFIG). The performance of the modified SIC was investigated for a model system consisting of a 100 MW DFIG-based WPP and four SGs under various wind speeds using an EMTP-RV simulator.

 

2. Modified Stepwise Inertial Control for a DFIG

2.1 Conventional SIC scheme of a DFIG [11]

Fig. 1 depicts the operational characteristics of the conventional SIC scheme of a DFIG [11]. Immediately after a disturbance, the power reference value, Pref, is switched from PMPPT to Pstep, which are the reference values for the MPPT operation and for SIC, respectively. In addition, PMPPT is set to be proportional to the cube of the rotor speed, as in [12].

Fig. 1.Operational characteristics of the conventional SIC of a DFIG [11]

In this scheme, Pstep has two operational periods - an overproduction period (TOP) and an underproduction period (TUP) - as shown in Fig. 1(b). From the moment a disturbance occurs, ΔPOP is added to P0, which is Pref prior to the disturbance. This means that Pref abruptly jumps from point A to point B. Then, this value is maintained for TOP, which means that Pref is maintained from point B to point C. This improves the frequency nadir because a large amount of additional power is released from a DFIG for TOP. In the meantime, the rotor speed, ω, is significantly reduced from the optimum rotor speed, ωopt. The reduction in rotor speed depends on both ΔPOP and TOP. After some time, Pref should be decreased so that ω does not decrease below the minimum operating limit, ωmin; otherwise, the WTG will stop. To achieve this, Pref is changed from P0 + ΔPOP to P0−ΔPUP (half of ΔPOP); i.e., Pref is abruptly decreased from point C to point D. Then, Pref is maintained for TUP (twice more than TOP), indicating movement of point D to point E. After TUP, Pref is returned to point A, and ω will eventually recover to ωopt.

We will explain the dynamic behavior of the rotor speed during the SIC (see Fig. 1(c)). The relationship between the rotor speed and the mechanical and electrical power can be expressed by

where Pm and Pe are the respective mechanical input power and electrical output power of a WTG.

The instant a disturbance occurs, Pe abruptly increases from point A to point B. Then, ω decreases because Pe is greater than Pm. For TOP, point B moves to point C. After TOP, Pe is abruptly reduced from point C to point D. If Pe at point D is less than Pm at the same rotor speed of D, ω will increase. If Pe is returned to the MPPT operation (point A) after TUP, ω will eventually return to ωopt.

In the case of the conventional SIC scheme [11], careful attention should be given to determining TOP (from points B to C) and ΔPUP (from points C to D). If a too lengthy TOP is selected, ω will decrease below ωmin and thus cannot be recovered. In addition, Pe at point D should be smaller than Pm at the corresponding rotor speed. Thus, if a too small ΔPUP is selected, ω will not be recovered because Pe is still larger than Pm. Moreover, if too much ΔPUP is selected, it will cause a severe subsequent disturbance to the power system and a second frequency dip will inevitably occur.

2.2 Modified SIC to prevent a second frequency dip

Fig. 2 depicts characteristics of the modified SIC scheme. Unlike the conventional scheme, the proposed SIC scheme sets Pref as the summation of PMPPT and the constant value; i.e.,

Fig. 2.Operational characteristics of the modified SIC

where ΔP is the constant additional power.

Note that the modified SIC scheme adds a constant value to PMPPT, whereas the conventional scheme switches Pref from PMPPT to a constant reference. PMPPT in (2) will decrease with time because ω will decrease with time during the inertial control. Thus, as shown in Fig. 2(b), Pref will monotonously decrease (from point B to point C) after an abrupt increase (from point A to point B) when a disturbance occurs. Inclusion of PMPPT in Pref will help ω to slowly decrease and reach ω* because Pref decreases with time. Pref in the form of Fig. 2(b) is effective in terms of causing no second frequency dip because there is no abrupt reduction in Pref. However, a too large ΔP will cause a second frequency dip because ω will reach ωmin very quickly and the inertial control should be disabled. Thus, determination of ΔP will be explained hereafter so that ω will not reach ωmin.

In Fig. 2(c), the dotted red line and solid blue line show Pe during the inertial and MPPT control, respectively.

The modified scheme determines ΔP so that the area of the top shaded region is the same as that of the bottom shaded region; i.e.,

The top region can be regarded as a deceleration area; the bottom region can be regarded as an acceleration area. Thus, if the areas of the two regions are the same, the rotor speed will reach the new equilibrium point, ω*.

Rearranging (3) yields

Note that ΔP in this scheme depends on the KE stored in the rotor. This means a WTG operating at a higher wind speed will generate a greater value of ΔP and will thus contribute more to the frequency control.

For the modified SIC scheme, ΔP can be analytically determined, whereas ΔPOP, ΔPUP, TOP, and TUP, should be heuristically determined in the conventional SIC scheme. In addition, the modified scheme can significantly improve the frequency nadir without causing a second frequency dip.

 

3. Model system

To investigate the performance of the modified SIC scheme, a model system shown in Fig. 3 was selected. The model system consists of four SGs, one 100 MW aggregated DFIG-based WPP, and a static load of 500 MW and 164 MVAr. In this paper, to benchmark the Korean power system that has a low ramping capability, for simplicity, all SGs are modelled as steam turbine generators. Detailed information on the SGs and WPP is described in the following subsections.

Fig. 3.Model system

3.1 Synchronous generators

The four SGs, specifically two 200 MVA SGs and two 150 MVA SGs, are included in the model system; they are all steam turbine generators. Their steam turbine governor model is the IEEEG1 steam model. The droop gains are set to 5%, which is a typical droop setting of the SGs in the Korean power system. The steam turbine governor model is shown in Fig. 4; the governor coefficients are shown in Table 1.

Fig. 4.IEEEG1 steam governor model

Table 1.Coefficients of the IEEEG1 steam governor model

3.2 DFIG-based wind power plant

Fig. 5 shows characteristics of the DFIG used in this paper. The operational rotor speed of the DFIG ranges from 0.7 p.u. to 1.25 p.u. As shown in Fig. 5(b), the cut-in, rated, and cut-out wind speeds are 4 m/s, 11 m/s, and 25 m/s, respectively.

Fig. 5.Characteristics of a DFIG

 

4. Case studies

As a disturbance, a SG4 supplying 50 MW is tripped out at 40s. The performances of the conventional and proposed SIC schemes are compared for wind speeds of 11 m/s, 9 m/s, and 7 m/s. For the conventional SIC, TOP and TUP are set to 10 s and 20 s, respectively, and ΔPOP and ΔPUP are set to be 0.1 p.u. and 0.05 p.u., respectively, as in [11].

Table 2 shows the estimated values of ΔP, P*, and ω*, which are the respective constant output power, output power, and rotor speed of the new equilibrium point after a disturbance. Figs. 6-8 show the results of cases 1, 2, and 3, respectively. The solid, dashed, and dash-dotted lines are the results for the modified SIC, conventional SIC, and the state without inertial control, respectively.

Table 2.Estimated values for the proposed SIC

Fig. 6.Results for case 1

Fig. 7.Results for case 2

Fig. 8.Results for case 3

4.1 Case 1: Wind speed of 11 m/s

Fig. 6 shows the results for case 1. The wind speed in this case is the rated wind speed, which means that the maximum KE is stored in the rotating mass in the WPP. As shown in Fig. 6(a), after a disturbance, the frequencies are restored after a significant reduction due to the primary control of SGs and/or SIC of a WPP. Note that the secondary frequency control is not considered in this paper and thus the frequencies are not completely recovered to the nominal value of 60 Hz. The frequency nadirs for the state without inertial control, the conventional SIC, and the modified SIC are 59.33 Hz, 59.50 Hz, and 59.69 Hz, respectively. The frequency nadirs of the conventional and proposed SIC schemes are higher than that of the state without inertial control. However, the frequency nadir of the proposed SIC is higher than that of the conventional SIC because the former releases more KE than that of the latter (see Fig. 6(b)). In addition, as expected, a second frequency dip does not appear for the modified SIC, whereas a second frequency dip appears for the conventional SIC. This is because the power output for the modified SIC monotonously decreases with time, as explained in Section 2.

As shown in Fig. 6(b), for the conventional SIC, the WPP output increases and reaches 107 MW at 40.3 s. This means that 0.1 p.u. is added to the MPPT reference prior to a disturbance. This reference value is maintained for 10.0 s. Then, the WPP output is abruptly reduced to 92 MW at 50.4 s and is maintained for 20 s. This abrupt significant reduction of output power causes a second frequency dip. However, the WPP output of the modified SIC step-wisely increases to 132 MW at 40.7 s, which means that 0.36 p.u. is added to the MPPT reference. Then, the output decreases and reaches approximately 92 MW, which has an approximate 6% error. This is because the damping effect of the WTG is not considered when the additional power is calculated.

As shown in Fig. 6(c), for the conventional SIC, the rotor speed decreases from 40 s to 50 s; it is then restored from 50 s to 70 s. On the other hand, for the proposed SIC, the rotor speed decreases more significantly than the conventional SIC because it releases more KE than that of the conventional SIC. The rotor speed reaches 1.03 p.u., which has a 3% error.

4.2 Case 2: Wind speed of 9 m/s

Fig. 7 shows the results for case 2. The wind speed in case 2 is less than that of case 1, which means the WPP contains smaller KE than case 1. As shown in Fig. 7(a), the frequency nadirs for the state without inertial control, the conventional SIC, and the modified SIC are 59.34 Hz, 59.51 Hz, and 59.60 Hz, respectively. As in case 1, the frequency nadir for the modified SIC is the largest. In addition, a second frequency dip does not occur for the modified SIC; however, it occurs for the conventional SIC.

The WPP output of the conventional SIC increases by 63 MW at 40.4 s; this output is maintained until 50.0 s, as shown in Fig. 7(b). Note that the same value of 0.1 p.u. is added to the MPPT reference prior to a disturbance. Then, the WPP output is rapidly reduced to 48 MW at 50.4 s and remains constant for 20s. As in case 1, the abrupt reduction causes a second frequency dip. In the case of the modified SIC, the output power step-wisely increases and reaches 71.85 MW at 40.5 s. This means that 0.19 p.u. is added in case 2 and is smaller than in case 1 on account of the smaller KE. Then, the WPP output decreases and reaches approximately 51.1 MW.

The rotor speed for the conventional SIC decreases from 40 s to 50 s; it then recovers from 50 s to 70 s because of the rapid reduction of output power. However, for the modified SIC, the rotor speed continuously decreases and reaches approximately 0.86 p.u.

4.3 Case 3: Wind speed of 7 m/s

Fig. 8 shows the results for case 3. The wind speed in case 3 is less than the previous two cases; moreover, the KE stored in the rotor is smaller. The frequency nadirs for the state without inertial control, the conventional SIC, and the modified SIC are 59.34 Hz, 59.51 Hz, and 59.42 Hz, respectively. In this case, the frequency nadir for the conventional SIC is the highest, which is unlike the previous two cases. This is because the conventional SIC increases the same amount of power — i.e., 0.1 p.u. — which is a too great value for the wind speed of 7 m/s. Thus, the rotor speed decreases below the minimum operating limit (see Fig. 8(c)). However, the modified SIC adds only 0.059 p.u. (see Table 2); thus, no second frequency dip occurs. In addition, the rotor speed does not reach the minimum operating limit.

 

5. Conclusions

In this paper, we propose a modified SIC scheme that can improve the frequency nadir without causing a second frequency dip. The power reference of the modified SIC is the sum of the constant power reference and the power reference for the MPPT control. Because the reference of the modified SIC monotonously decreases, no second frequency dip is caused. The constant additional power is analytically determined by considering the mechanical and electrical power curves depending on the wind speed to prevent a second frequency dip.

The simulation results clearly indicate that the proposed SIC determines the additional power increase depending on wind conditions and thus successfully increases the frequency nadir without causing a second frequency dip regardless of wind conditions.