1. Introduction
Wind power penetration in power systems has been globally increasing due to technical advances that have made the technology economically viable over the last decade. For example, the EU has set a goal of supplying 100% of electrical energy by renewable energy sources by 2050 and half of this energy will be supplied by wind power generation [1].
In order to keep the frequency within the acceptable ranges in a conventional power system, synchronous generators (SGs) with spinning reserves inherently respond to the frequency excursion and restore the reduced frequency to the nominal value by using the reserves.
On the other hand, variable-speed wind generators (VSWGs) have been widely used to extract maximum energy from wind [2, 3]. To do this, VSWGs operate at a maximum power point tracking (MPPT) control mode, where they adjust the rotor speed depending on the wind speed. However, the MPPT control decouples the wind generators (WGs) from the system frequency and thus causes a reduction in the system inertia. Therefore, the reliability of a power system will be jeopardized, particularly in the case of high wind penetration.
The frequency support scheme of the WG can be divided into two groups: inertial control and primary control. If a disturbance occurs, the former uses only the kinetic energy stored in the rotating masses, whilst the latter uses both the kinetic energy and the reserve power that is de-loaded. This paper addresses only the inertial control of a WG and thus it is assumed that the WGs are operating in the MPPT control mode before a disturbance.
A significant amount of research on the inertial control scheme has been proposed for the doubly-fed induction generators (DFIGs) [4-8]. An inertial control loop was designed using the rate of change of the frequency (ROCOF) [4, 5]. The ROCOF loop generates additional power during the initial period of the disturbance and helps increase the frequency nadir. However, incremental power from the ROCOF loop decreases as time goes on. Moreover, the contribution of the ROCOF loop becomes negative after the frequency rebound. Thus, both the ROCOF and frequency deviation loops were used to improve the frequency support of DFIGs [6-8]. The frequency deviation loop generates an additional power reference proportional to the frequency deviation, and thus mitigates the negative power reference from the ROCOF loop after the frequency nadir.
This paper proposes an inertial control algorithm of a DFIG-based WPP using the maximum ROCOF and the frequency deviation loops. The proposed algorithm replaces the ROCOF loop in the conventional inertial control algorithm with the maximum ROCOF loop to retain the maximum value of the ROCOF and eliminate the negative effect after the frequency rebound. Thus, the algorithm releases more kinetic energy both before and after the frequency rebound and increases the frequency nadir more than the conventional inertial control algorithm. The performance of the algorithm is investigated with a model system, which consists of five SGs and a 100 MW WPP with 20 DFIGs using an EMTP-RV simulator. The wind speed of each DFIG was calculated considering the cumulative impact of multiple shadowing and the effect of the wind direction.
2. Proposed Inertial Control of a DFIG-based WPP
This paper proposes an inertial control algorithm of a WPP, which consists of multiple DFIGs. The following two subsections will describe the conventional and proposed inertial algorithms that will be implemented in each DFIG. Then, the wake model used in this paper will be explained.
2.1 Conventional inertial control of a DFIG [6-8]
Fig. 1 shows a conventional inertial controller of a DFIG that uses the ROCOF and frequency deviation loops. In the top loop of Fig. 1, ΔPin depends on the ROCOF with K, which is the gain of the ROCOF loop, i.e.,
Fig. 1.Conventional inertial controller
On the other hand, in the bottom loop of Fig. 1, ΔP depends on the frequency deviation with R, which is the droop gain of the loop, i.e.,
The relationship between the mechanical power, Pm, and Pref of a DFIG can be represented by
where J is the moment of inertia (kg·m2) of the rotor and ωr is the rotor speed of the WG.
If the system frequency drops below its nominal value for a disturbance such as a generator tripping, ΔPin and ΔP become positive values, and consequently Pref increases. Thus, the kinetic energy stored in the rotating mass in the DFIG is released and consequently ωr decreases according to (3).
At the initial stage of the disturbance, the contribution of the ROCOF loop becomes dominant, because the ROCOF has a large value and so does ΔPin. As the frequency decreases further, ΔPin decreases. In addition, ΔPin becomes a negative value after the frequency rebound. This has a negative impact on the inertial control of a DFIG.
To clearly illustrate the performance of the conventional algorithm, a test result is shown in Fig. 2, where a disturbance occurs at 30 s. As mentioned above, ΔPin decreases with time and becomes a negative value after the frequency rebound. On the other hand, ΔP remains a positive value. The additional power of the supplementary loops for the conventional algorithm helps increase the frequency nadir.
Fig. 2.Results for the conventional algorithm
2.2 Proposed inertial control of a DFIG
In order to provide a greater contribution to frequency support, this paper replaces the ROCOF loop in the conventional controller in Fig. 1 with the maximum ROCOF loop, but leaves the frequency deviation loops intact. Fig. 3 shows the proposed inertial controller. The maximum ROCOF loop calculates the ROCOF, selects the maximum value of the previous ROCOF values, and then multiplies −K to obtain ΔPin,max. Thus, ΔPin,max remains a positive constant value with time after a short time, whereas ΔPin in Fig. 1 decreases with time and becomes a negative value after the frequency rebound. Consequently, the proposed inertial controller can arrest the frequency nadir more effectively than the conventional controller.
Fig. 3.Proposed inertial controller of a DFIG
On the other hand, the proposed algorithm releases a large amount of kinetic energy stored in the rotating mass and thus ωr might decrease below the minimum operating speed. Typically, the operating range of the rotor speed is 0.68-1.32 pu. To prevent the rotor speed from decreasing below 0.68 pu, the additional control loops are disabled if ωr reaches 0.68 pu.
Fig. 4 shows a test result for the proposed algorithm. Note that ΔPin, max remains a positive constant value with time whilst ΔPin in Fig. 2(b) decreases with time and becomes a negative value after the frequency rebound. ΔP in Fig. 4(c) is similar to that in Fig. 2(c). Thus, the additional power of the supplementary loops for the proposed algorithm is larger than the conventional algorithm. Therefore, the proposed algorithm can improve the frequency nadir more than the conventional algorithm.
Fig. 4.Results for the proposed algorithm
2.3 Wake effect
The WGs in a WPP generate electricity by extracting the kinetic energy from wind. Thus, the upstream WGs will impact the wind speed approaching at the downstream WGs. This shadowing effect is known as the wake effect [9]. Therefore, the different wind speeds approaching the WGs will result in different operating conditions such as the rotor speed and the power production of WGs.
In this paper, the wind speeds of WGs are calculated by considering the cumulative impact of multiple shadowing and the effect of the wind direction. The wind speed of a WGj, vj, can be represented by
where vj0 is the incoming wind speed at WGj without any shadowing, xkj is the radial distance between WGk and WGj, vwk(xkj) is the speed of the wind arriving at WGj from the shadowing, WGk, β k is the ratio of part of the area of WGj under the shadow of WGk to its total area, and n is the total number of WGs.
3. Model system
Fig. 5 shows a model system used to investigate the performance of the proposed inertial control algorithm. The model system consists of five SGs with a total of 850 MVA, a load of 600 MW and 9 MVAr, and a 100 MW DFIGbased WPP. The detailed information of these will be described in the following subsections.
Fig. 5.Model system
3.1 Synchronous generators
The five SGs connect to the model system and consist of one 100 MVA SG, one 150 MVA SG, and three 200 MVA SGs. As the governor model of SGs, an IEEEG1 model is used (see Fig. 6) and the parameters are shown in Table 1. The droop coefficient, R, of each SG is set to 5%.
Fig. 6.IEEEG1 steam governor model
Table 1.Coefficients of the IEEEG1 model
3.2 Wind power plant
As shown in Fig. 5, the WPP consists of five feeders, and four 5 MW DFIGs are connected to each feeder. The distance between the neighboring WGs is 9D (1,080 m), where D is the diameter of the swept area of the blades. The two 60 MVA substation transformers are connected to the on-shore grid through a 22 km-long submarine cable.
Fig. 7 shows the power curve of a DFIG, where the cutin, rated, and cut-out wind speed are 4 m/s, 10.5 m/s, and 25 m/s, respectively. PMPPT for the MPPT control (as in [10]) was set to
where kg is a function of the parameters, such as the gearratio, blade length, and blade profile. In this paper, the operating range for the rotor speed of the DFIG is set to the range of 0.68-1.32 pu for reliable operation.
Fig. 7.Power curve of the WG
4. Case studies
To simulate the frequency drop case, SG5 is assumed to be tripped out at t = 30 s; it supplies 70 MW to the load in the steady state. In this paper, the R and K gains of the auxiliary loops are set to 0.1 and 10, respectively. Three cases are chosen and Table 2 shows the wind speeds of the WGs for the three cases calculated using (4). The performance of the proposed algorithm is compared with that of ‘without (w/o) inertial control’ and the conventional algorithm. In this paper, the supplementary loops of both the conventional and proposed algorithms are disabled if the rotor speed reaches 0.68 pu.
Table 2.Wind speeds of WGs for three cases considering the wake effect
4.1 Case 1: Wind speed of 8.25 m/s, wind direction of 0°
Fig. 8 shows the results for case 1. Fig. 8(a) shows the system frequencies. The frequency nadirs for ‘w/o inertial control’, the conventional, and the proposed algorithms are 59.28 Hz, 59.48 Hz, and 59.52 Hz, respectively. The frequency nadir for the proposed algorithm is the largest because the former releases the most kinetic energy. From the view point of the nadir-based frequency response (NBFR), the NBFRs of ‘w/o inertial control’, the conventional, and the proposed algorithms are 9.77 MW/0.1 Hz, 13.48 MW/0.1 Hz, and 14.70 MW/0.1 Hz, respectively.
Fig. 8.Results for case 1
Fig. 8(b) shows the active power of the WPP. The maximum values of the active power for the conventional and proposed algorithms are 43.91 MW and 47.28 MW, respectively. The active power for the proposed algorithm is larger than that of the conventional algorithm because the additional power of the supplementary loops for the proposed algorithm is larger than that of the conventional algorithm, as shown in Figs. 8(c) and 8(d).
Fig. 8(c) shows ΔPin, max and ΔPin. As expected, ΔPin, max remains constant with time, whereas ΔPin decreases with time. The additional power of the supplementary loops for the proposed algorithm is larger than that for the conventional algorithm as shown in Fig. 8(d).
Figs. 8(e) and 8(f) show the rotor speeds of the four columns for the conventional and proposed algorithms, respectively. For the proposed algorithm, the rotor speeds of the WGs at only the third and fourth columns reach 0.68 pu at 31.59 s and 34.61 s, respectively, whereas for the conventional algorithm, the rotor speeds at the third and fourth columns reach 0.68 pu at 31.80 s and 37.93 s, respectively. This is because the input wind speeds of the third and fourth columns are smaller than the first and second columns due to the wake effect. This will cause a sudden decrease in the active power of the WPP twice, as shown in Fig. 8(b).
4.2 Case 2: Wind speed of 10.31 m/s, wind direction of 0°
Fig. 9 shows the results for case 2, which is identical to case 1 except for the wind speed. As shown in Fig. 9(a), the frequency nadirs for ‘w/o inertial control’, the conventional, and the proposed algorithms are 59.31 Hz, 59.53 Hz, and 59.59 Hz, respectively. Similar to case 1, the frequency nadir for the proposed algorithm is the largest. The NBFRs for ‘w/o inertial control’, the conventional, and the proposed algorithms are 10.22 MW/0.1 Hz, 15.01 MW/0.1 Hz, and 17.00 MW/0.1 Hz, respectively.
Fig. 9.Results for case 2
As shown in Fig. 9(b), the maximum values of the active power for the conventional and proposed algorithms are 67.36 MW and 72.02 MW, respectively. The active power of the WPP for the proposed algorithm is larger than the conventional algorithm. Fig. 9(c) shows ΔPin, max and ΔPin. As in case 1, ΔPin, max remains a positive value with time whereas ΔPin decreases with time. As shown in Fig. 9(d), the additional power of the supplementary loops for the proposed algorithm is larger than that of the conventional algorithm during the disturbance.
The rotor speeds of the four columns for the conventional and proposed algorithms are shown in Figs. 9(e) and 9(f), respectively. The rotor speeds of the four columns remain larger than 0.68 pu because the wind speed in case 2 is higher than in case 1
4.3 Case 3: Wind speed of 10.31 m/s, wind direction of 90°
Fig. 10 shows the results for case 3, which is identical to case 2 except for the wind direction. As shown in Fig. 10(a), the frequency nadirs for ‘w/o inertial control’, the conventional, and the proposed algorithms are 59.29 Hz, 59.51 Hz, and 59.57 Hz, respectively. The frequency nadir for the proposed algorithm is the largest because the released kinetic energy is the largest. The NBFRs for ‘w/o inertial control’, the conventional, and the proposed algorithms are 9.79 MW/0.1 Hz, 14.42 MW/0.1 Hz, and 16.32 MW/0.1 Hz, respectively. Note that the frequency nadirs and NBFR of the inertial control algorithm in case 3 are slightly smaller than in case 2 because the wake effect in case 3 is larger than that in case 2 due to the different wind direction.
Fig. 10.Results for case 3
The maximum values of the active power of the WPP for the conventional and proposed algorithms are 62.26 MW and 66.90 MW, respectively. As in the previous two cases, the additional power of the supplementary loops for the proposed algorithm is larger than that of the conventional algorithm. As shown in Fig. 10(d), the additional power of the supplementary loops for the proposed algorithm is larger than that of the conventional algorithm.
The rotor speeds of the five rows for the conventional and proposed algorithms are shown in Figs. 10(e) and 10(f), respectively. The rotor speeds of the WGs at only the fifth row reach 0.68 pu at 35.14 s whereas the rotor speeds for the conventional algorithm do not reach 0.68 pu. This is because the input wind speeds of the WGs at the fifth row are lower than the other rows due to the severe wake effect in this case (the 90° wind direction). Thus, the active power of the WPP suddenly decreases at once, as shown in Fig. 10(b).
The results of the three cases clearly indicate that the inertial control algorithms can give more contribution if the WPP have more kinetic energy in the rotating masses.
5. Conclusion
This paper proposes an inertial control algorithm of a WPP using the maximum ROCOF and frequency deviation loops. The algorithm replaces the ROCOF loop in the conventional inertial control algorithm with the maximum ROCOF loop to retain the maximum value of the ROCOF and eliminate the negative effect after the frequency rebound. Thus, the algorithm can release more kinetic energy both before and after the frequency rebound and increase the frequency nadir more than the conventional inertial control algorithm.
The test results clearly show that the proposed algorithm is able to increase the frequency nadir by releasing more kinetic energy than a conventional algorithm and make the frequency rebound faster than the conventional algorithm.
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