energies Article
Adaptive Gains Control Scheme for PMSG-Based Wind Power Plant to Provide Voltage Regulation Service Jianfeng Dai 1 , Yi Tang 1, * and Jun Yi 2 1 2
*
School of Electrical Engineering, Southeast University, Nanjing 210096, China;
[email protected] China Electric Power Research Institute, Beijing 100192, China;
[email protected] Correspondence:
[email protected]; Tel.: +86-25-8379-0617
Received: 10 January 2019; Accepted: 20 February 2019; Published: 24 February 2019
Abstract: High-penetration wind power will count towards a significant portion of future power grid. This significant role requires wind turbine generators (WTGs) to contribute to voltage and reactive power support. The maximum reactive power capacity (MRPC) of a WTG depends on its current input wind speed, so that the reactive power regulating ability of the WTG itself and adjacent WTGs are not necessarily identical due to the variable wind speed and the wake effect. This paper proposes an adaptive gains control scheme (AGCS) for a permanent magnet synchronous generator (PMSG)-based wind power plant (WPP) to provide a voltage regulation service that can enhance the voltage-support capability under load disturbance and various wind conditions. The droop gains of the voltage controller for PMSGs are spatially and temporally dependent variables and adjusted adaptively depending on the MRPC which are a function of the current variable wind speed. Thus, WTGs with lower input wind speed can provide greater reactive power capability. The proposed AGCS is demonstrated by using a PSCAD/EMTDC simulator. It can be concluded that, compared with the conventional fixed-gains control scheme (FGCS), the proposed method can effectively improve the voltage-support capacity while ensuring stable operation of all PMSGs in WPP, especially under high wind speed conditions. Keywords: permanent magnet synchronous generator (PMSG); droop control; adaptive-gain; voltage support; maximum reactive power capacity (MRPC)
1. Introduction Wind power is increasingly integrated into the modern power system and will be a major source of electrical power in the near future [1–3]. However, the unpredictable nature of wind causes random fluctuations in wind power, which increases the instability risk of wind power grid-connected systems. The voltage of a power system should always be within the allowable range to ensure safe and reliable operation. Recently, variable-speed wind turbine generators (WTGs) such as the permanent magnet synchronous generator (PMSG) and doubly fed induction generator (DFIG) have become more popular because of the maximum power tracking operation and flexible additional controls by using converters [4], in which a PMSG is widely used in the wind power system for its advantages of lower maintenance cost, high reliability and flexible control. However, the fixed reactive power control of the wind turbine (WT) converter causes them not to respond to the system voltage variation. As a result, the voltage of the system will drop significantly without other reactive power compensation devices when an external disturbance occurs, especially in a power system with a high wind power penetration level. In order to minimize this issue and improve the ability of the power grid to accommodate more
Energies 2019, 12, 753; doi:10.3390/en12040753
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wind power, power system operators have imposed strict grid codes for larger wind-power plants (WPPs). One of the mandatory grid codes is that a WPP must be equipped with functions of reactive power and voltage control, including the voltage ride through under fault conditions and reactive power provision under steady states [5–7]. A number of research works on the voltage-supporting schemes of WPPs have been reported. One of the research hotspots is the automatic voltage control (AVC) system for wind power plants, which is used to control the reactive power of reactive power compensation devices in wind power plants according to the dispatching instructions of the power grid [8–10], so as to meet the reactive power and voltage requirements of the grid connection point. In [8], the authors designed a hierarchical automatic voltage control system to support wind power integration, in which the voltage and reactive power distribution inside the wind power plant are optimized and three different control modes are implemented considering all the terminal voltages of WTGs as well as the dynamic var reserves. In [9], the authors proposed a coordination strategy between an automatic voltage regulator (AVR) and power system stabilizer (PSS) of synchronous generators, and fuzzy logic is used to solve the problem. In [10], an automatic voltage control system for power systems with limited continuous voltage control capability is presented. Voltage uncertainty caused by wind power forecasting errors is considered in the optimal voltage/var dispatch by including a security margin in the voltage magnitude constraints. However, the analysis of reactive power compensation and voltage stability in WPP is mostly based on static var compensator (SVC), static var generator (SVG) or on-load tap changer and other local compensation devices for the AVC system mentioned above, and the WTG’s own reactive power capability has not been considered. Actually, the WTG has the ability to generate some reactive power both from the machine-side converter (MSC) and from the grid-side converter (GSC). Therefore, the WTG can be regarded as a continuous reactive power source. The ability of reactive power adjusting under two conditions (with and without crowbar) are analyzed in [11]. In [12], the authors present the supervisory reactive power control scheme in order to regulate the voltage at a remote location. In [13], a dynamic reactive power allocation scheme based on autonomous voltage security regions to accommodate more wind power is proposed in large-scale centralized wind power integration areas. Benders decomposition is used to solve the allocation scheme. However, in the above literature, the fix droop gain of the voltage controller for each WTG is used. As a result, difficulty arises in finding a proper gain of a WTG for various wind conditions. A larger gain has better voltage support performance, but may exceed the maximum reactive power capacity (MRPC) resulting in increasing wear and tear to the converters. Conversely, a small gain ensures stable operation, but the performance of voltage support is limited. More importantly, if the fixed-gains control scheme (FGCS) is applied to a WPP consisting of multiple WTGs, it increases the difficulty of finding the same suitable gain for all WTGs, which have different levels of MRPC due to fluctuating wind speed and wake effects [14–17]. Thus, WTGs in a WPP operate at different maximum output power points, and each WTG has different MRPC depending on the current input wind speed. This means that a larger droop gain is suitable for downstream WTGs that have higher MRPC level, but it is unsuitable for upstream WTGs that have a lower MRPC level, and vice versa. This paper proposes an adaptive droop gains control scheme for PMSG-based WPP that discriminates the PMSG’s contribution to provide voltage regulation service. The proposed control scheme aims to make full use of the MRPC retained in a WPP to improve the voltage support performance while ensuring stable operation of all PMSGs, especially under the high wind speed conditions. To achieve this, the adaptive droop gain of each PMSG is set to be proportional to its current MRPC that is a function of current wind speed and is spatially and temporally dependent due to the wake effect, so that a PMSG with a large MRPC makes a greater contribution to voltage regulation by setting a larger droop gain, and a PMSG with a small MRPC ensures stable operation during voltage control by setting a smaller droop gain. The effect of the proposed adaptive gains control scheme (AGCS) is compared with conventional FGCS and no voltage control loop scheme. The
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validity of this proposed strategy is extensively demonstrated under various wind conditions using a PSCAD/EMTDC simulator. Energies 2019, 01, x FOR PEER REVIEW
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2. Proposed Voltage Support Scheme Based on Adaptive Gains
This section briefly describes the PMSG model used in this paper and the FGCS for reactive This section briefly describes the PMSG model used in this paper and the FGCS for reactive power power voltage control, the overall features of proposed the proposed AGCS are described in detail. andand voltage control, and and thenthen the overall features of the AGCS are described in detail. 2.1.2.1. Permanent Magnet Synchronous Permanent Magnet SynchronousGenerator Generator(PMSG) (PMSG)Model Model A typical of the thePMSG PMSG model is shown in Figure 1, consists which of consists of wind A typicalconfiguration configuration of model is shown in Figure 1, which wind turbines, PMSGs, full-power converters and control systems. The PMSG is operated with a combination turbines, PMSGs, full-power converters and control systems. The PMSG is operated withof a maximum of power point tracking strategy (MPPT) and pitchstrategy control. and Tablepitch 1 gives the parameters of a combination maximum power (MPPT) point tracking control. Table 1 gives PMSG studied in this paper [18]. the parameters of a PMSG studied in this paper [18].
PR + jQR
PLL1
β
PLL2 SVPWM
pitch control
Active power control
PR
ωturref
Po + jQo
Udc
ωtur
Pref
SVPWM
Machine terminal current control
ird
DC bus voltage control
Reactive power control
irdref Udcref
PMPPT
Qref
Q0
Maximum power tracking control
Figure 1. A1.typical configuration ofofthe generator(PMSG) (PMSG)model. model. Figure A typical configuration thepermanent permanentmagnet magnet synchronous synchronous generator Table 1. Parameters of a PMSG used in this paper.
Table 1. Parameters of a PMSG used in this paper. Parameters
Parameters
Units
Values
MVA MVA kV kV p.u. p.u. p.u. p.u. p.u. p.u. p.u. s
2 0.69 2 0.01080.69 0.102 0.0108 0.010.102 0.11 0.01 3
Units
Nominal Apparent Power Nominal Apparent Nominal StatorPower Voltage Nominal Stator Voltage Stator Resistance Stator Leakage Reactance Stator Resistance Rotor Resistance Stator Leakage Reactance Rotor Leakage Reactance Rotor Resistance Inertia Time Constant
Rotor Leakage Reactance Inertia Time Constant
p.u. s
Values
0.11 3
A PMSG controller measures signals such as voltage, current and rotor speed to provide signals A PMSG controller measures signals such as voltage, current and rotor speed to provide for the control system that consist of the MSC and the GSC. A typical GSC control scheme is shown in signals for2.the system thatpower consistofof the MSC the GSC. independently, A typical GSCwhich control scheme is Figure Thecontrol active and reactive a PMSG canand be decoupled is achieved shown in Figurethe 2. active The active and reactive power components of a PMSG ican be decoupled independently, by controlling components id and reactive q of the grid-connected current. which is achieved by controlling the active components i d and reactive components iq of the The mechanical power equation of WTG extracted from the wind is expressed as:
grid-connected current. Pt =
1 ρπr2 v3 C p (λ, β) 2 ed
(1)
where ρ, r, v, Cp , λ and β are the air density, blade length, wind speed, coefficient of performance of Udcref PI PI the wind turbine (WT), tip-speed ratio and blade pitch angle respectively. Udc
igd igq
Qref
PI Q
ωL SVPWM ωL PI eq
Nominal Apparent Power Nominal Stator Voltage Stator Resistance Stator Leakage Reactance Rotor Resistance Rotor Leakage Reactance Inertia Time Constant
MVA 2 kV 0.69 p.u. 0.0108 p.u. 0.102 Energies 2019, 12, 753 4 of 20 p.u. 0.01 p.u. 0.11 s 3 π ( λ +1) (2) C p = signals (0.44 − 0.0167β ) sinvoltage, current and rotor speed to provide A PMSG controller measures such as 2 7.8 − 0.15β
signals for the control system that consist of the MSC and the GSC. A typical GSC control scheme is The expression for λ is shown as: shown in Figure 2. The active and reactive ωpower of a tur PMSG can be decoupled independently, 2πrn tur r = = which is achieved by controlling the λactive components id and reactive components iq (3) of the v v grid-connected where ω tur current. is the angular velocity of the WT; ntur is the pole number of the WT. ed Udcref
PI
PI Udc
ωL
igd
SVPWM
igq
Qref
ωL PI
PI
eq
Q0
Figure Controlstrategy strategy of grid-side Figure 2. 2. Control grid-sideconverter. converter.
At a given wind speed, maximum power can be extracted from a WT for a specific rotor speed and pitch angle. In general, when the WT output is less than the rated power, the pitch angle is maintained at a fixed value. At this point, Cp is a function of λ. By adjusting the angular speed of the wind turbine, the maximum Cp is achieved with maximum power tracking control. So λ and Cp can take an optimal value of λopt and Cpmax , and the output power of each WT can be expressed as: Pt =
1 ρπr2 v3 C pmax (λ, β) = k opt v3 2
(4)
where kopt is the equivalent coefficient to obtain the maximum wind energy. The reactive power capacity of WTG is determined by the active power from the grid-side of the generator and the apparent power of the converter. Assuming that the active power loss is ignored, the reactive power capacity of the WTG can be expressed as: QW = ±
q
2 − P2 SW t
(5)
where SW is the apparent power of the WT converter. It should be emphasized that in extreme cases, when the reactive power shortage is large and all WTGs are running at full power, the upper limit of the full power converter current is reached. Considering that the reactive power adjustment capability of the WTG is closely related to the active power generated, the deloading operation of WTG is considered to increase the reactive power margin. The corresponding deloading adjustment methods include over-speed operation and pitch angle control [19]. Then, the reactive power capacity of WTG can be expressed as QW = ±
q
2 − [(1 − d ) P ]2 = ± SW t
q
2 − (1 − d )2 k 2 v6 SW opt
(6)
where d is the deloading level, and the range of value is usually 0–20%. According to Equation (6), Figure 3 illustrates the allowable range of active and reactive power output of a PMSG under different wind speeds. As can be seen from the figure, when the input wind speed of the WT is higher, the maximum allowable reactive power capacity is smaller, and the reactive power margin can be improved by sacrificing active power to the operation in the deloading operation
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state. Therefore, the reactive power regulation of the WT with low input wind speed is greater than that of the WT with high input wind speed. When the input wind speed of WT is greater than or equal to the rated wind speed, there is almost no reactive power regulation capacity if not sacrificing active Energies output. 2019, 01, x FOR PEER REVIEW 5 of 20 power
Figure 3. Active and reactive power range of the PMSG.
2.2. Conventional Fixed-Gain Voltage Control Scheme This section briefly describes a conventional reactive power and voltage droop control schemes for permanent magnet synchronous generators (PMSGs) [20,21], which uses an additional fixed-gain droop loop, as shown in Figure 4. Qref consists of two terms: Q0 and ΔQ. In general, the value of Q0 is zero.
ΔQi = −
1 (Vsys − Vnom ) R
(7)
where Vnom is the nominalFigure voltage in p.u. atreactive PCC inpower a WPP; Vsys measured voltage in p.u. at 3. Active and range of is thethe PMSG. Figure 3. Active and reactive power range of the PMSG. PCC; and 1/R is the droop loop gain. 2.2. Conventional Voltage Control Scheme Note that theFixed-Gain droop gain 1/R used in (7) is fixed. This means that if the value of 1/R is too large, 2.2. Conventional Fixed-Gain Voltage Control Scheme it is beneficial to improve the voltage regulation ability,power but itand willvoltage make droop the PMSG converters This section briefly describes a conventional reactive control schemes This section briefly describes a conventional reactive power and voltage droop control schemes frequently exceed the limit of maximum reactive power, [20,21], especially in the case extremely narrow for permanent magnet synchronous generators (PMSGs) which uses an of additional fixed-gain for permanent magnet synchronous generators (PMSGs) [20,21], which uses an additional reactive power range of the PMSG, and this phenomenon is more likely to happen when the droop loop, as shown in Figure 4. Qref consists of two terms: Q0 and ∆Q. In general, the value wind of Q0 fixed-gain droop loop, as shown in Figure Qref consists two terms:of Q0 aand ΔQ. Inbut general, the value speed Conversely, a small gain 4. ensures stableof operation PMSG, it provides a is zero.is high. 1 of Q0 is zero. limited contribution for voltage regulation. Therefore, inappropriate droop gain will lead to ∆Qi = − (Vsys − Vnom ) (7) R unsatisfactory results, and the conventional FGCS is unable to ensure both voltage regulation 1 in a WPP; V is the measured voltage in p.u. at where Vnom isand thestable nominal voltageof in ap.u. performance operation PMSG Δ Qiat=PCC −at the − Vnomtime. (7) (Vsyssame ) sys Moreover, it is worth noting that R gain scheme is more inappropriate. PCC; and 1/R isspeed the droop loop frequently, gain. when the wind fluctuates the fixed where Vnom is the nominal voltage in p.u. at PCC in a WPP; Vsys is the measured voltage in p.u. at Q0 Q PCC; and 1/R is the droop loop gain. limiter Note that the droop gain 1/R used in (7) is fixed. This means that if the value of 1/R is too large, 1 Q GSC Vnomthe voltage regulation ability, but refit will make the PMSG converters it is beneficial to improve Controller R ΔQi frequently exceed the limit of maximum reactive power, especially in the case of extremely narrow Vsys reactive power range of the PMSG, and Fix thisgain phenomenon isPmax more likely to happen when the wind speed is high. Conversely, a small gain ensures stable operation of a PMSG, but it provides a Figure Conventional fixed-gain voltage control scheme of a PMSG. gain will lead to limited contribution for4.4.voltage regulation. Therefore, inappropriate Figure Conventional fixed-gain voltage control scheme of a droop PMSG. unsatisfactory results, and the conventional FGCS is unable to ensure both voltage regulation Note that the droop gain 1/R used in (7) is fixed. This means that if the value of 1/R is too large, it performance stable operation of a PMSG at the same time. Moreover, it is worth noting that 2.3. Wake Effectand Model is beneficial to improve the voltage regulation ability, but it will make the PMSG converters frequently when the wind speed fluctuates frequently, the fixed gain scheme is more inappropriate. exceed limit of maximum reactive power, in wake the case of extremely narrow reactive power Thethe Park wake model which is based onespecially the Jensen model is used in this paper [22]. The range of the PMSG, andwind this phenomenon is more to happenthe when the windAssuming speed is high. model obtains the input speed of adjacent WTslikely by considering wake effect. that Q0 Q Conversely, a small gainisensures operation a PMSG, but it provides a limited for the wake wind speed linear stable expansion, and of the windlimiter speed of adjacent WTs contribution is obtained by voltage regulation. Therefore, inappropriate droop gain will lead to unsatisfactory results, and the considering the cumulative effect of multiple shadows and the wind direction. The relationship 1 Qref GSC Vnom conventional unable ensureWTs both can voltage regulation performance and stable operation of a between inputFGCS windisspeed of to adjacent be expressed as: Controller R ΔQi PMSG at the same time. Moreover, it is worth noting that when the wind speed fluctuates frequently, Vsys Fix gain Pmax the fixed gain scheme is more inappropriate. 2.3. Wake Effect Model Figure 4. Conventional fixed-gain voltage control scheme of a PMSG. The Park wake model which is based on the Jensen wake model is used in this paper [22]. The 2.3. Wake Effect Model model obtains the input wind speed of adjacent WTs by considering the wake effect. Assuming that the wakeThe wind speed is linear and the speed wake of adjacent is obtained by considering Park wake modelexpansion, which is based onwind the Jensen modelWTs is used in this paper [22]. The model obtains the input wind speed of adjacent WTs by considering the wake effect. Assuming that the wake wind speed is linear expansion, and the wind speed of adjacent WTs is obtained by considering the cumulative effect of multiple shadows and the wind direction. The relationship between input wind speed of adjacent WTs can be expressed as:
vi = v0 1 −
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2 Dj 2 β a ji j j =1 D j + 2kx ji j ≠i n
2
(8) 6 of 20
where i is the wind speed of theshadows i-th wind ); v0 isThe therelationship wind speed; aj is input the axial thevcumulative effect of multiple andturbine the wind(WTi direction. between induction factorofofadjacent the j-thWTs wind generator (WTGj); Di is the diameter of swept area of the wind speed canturbine be expressed as: i-th wind turbine generator (WTGi); k is the wake-decaying constant; xji is the radial distance between WTGj and WTGi; βji is the ratio between the overlapping area and swept area of WTGi; v u !2 2 u and n is the total number of the WTs. Dj u n u β ji v i = v0 1 − u ∑ 2a j D + 2kx j ji u j=1 a PMSG-Based t 2.4. Adaptive Gains Voltage Support for Wind-Power Plants (WPP) j 6= i
(8)
As mentioned in the previous section, PMSGs within a WPP have different levels of reactive power capability the fluctuation of wind effect.ajThe adaptive where vi is the due windtospeed of the i-th wind turbinespeed (WTi);and v0 isthe the wake wind speed; is theproposed axial induction of the j-th wind turbine generator (WTGj); of swept area of the i-th wind of gainsfactor voltage support scheme aims to improve theDvoltage nadir while ensuring stable operation i is the diameter turbine generator (WTGi); k is the wake-decaying constant; x is the radial distance between WTGj ji a PMSG-based WPP. The configuration of the proposed adaptive gain scheme of a PMSG is shown and WTGi; βji proposed is the ratio scheme, between the the overlapping area and swept of can WTGi; n is the in Figure 5. In the output of the droop controlarea loop be and defined as: total number of the WTs.
(
)
ΔQ = − AGi (vi )Wind-Power Vsys − Vnom Plants (WPP) 2.4. Adaptive Gains Voltage Support for a iPMSG-Based
(9)
As mentioned in the previous section, PMSGs within a WPP have different levels of reactive
To achieve betterdue voltage performance ensure stable at theadaptive same time, power capability to the regulation fluctuation of wind speed and and the wake effect.operation The proposed the control gain support of the voltage deviation loopthe of voltage PMSGi,nadir AGiwhile (vi), isensuring set to be proportional gains voltage scheme aims to improve stable operation ofto a the PMSG-based WPP. The configuration of the proposed adaptive gain scheme of a PMSG is shown in current MRPC of PMSGi, Qi, which can be expressed as: Figure 5. In the proposed scheme, the output of the droop control loop can be defined as: 2 vi 6 AGi (vi ) ∝ Qi = SW2 − (1 − d ) 2 k opt
(10)
∆Qi = − AGi (vi ) Vsys − Vnom
Q0 Vnom
Q limiter Qref
-AGi(vi) ΔQi
Vsys
(9)
Adaptive gain
GSC Controller
Pmax
Figure 5. Proposed adaptive-gain voltage control scheme of a PMSG.
Figure 5. Proposed adaptive-gain voltage control scheme of a PMSG. To achieve better voltage regulation performance and ensure stable operation at the same time, In this paper, to obtain the proportionality constant ofto(10), (10) can betorewritten in the the control gainin of order the voltage deviation loop of PMSGi, AG be proportional the current i (vi ), is set MRPC of PMSGi, Q , which can be expressed as: following form: i
AGi (vi ) ∝ Qi =
q
2 − (1 − d )2 k 2 v 6 SW opt i 1 Q
AGi (vi )=
i
(10)
(11)
R0 Qmax In this paper, in order to obtain the proportionality constant of (10), (10) can be rewritten in the following form: 1 Qi Qi,i (and can be obtained by inserting the cut-in wind speed where Qmax is the maximum value of AG vi ) = (11) R0 Qmax
in to (6). 1/R0 is the maximum droop loop gain. The value of R0 can be determined as different where Qmax is the maximum value of Qi , and can be obtained by inserting the cut-in wind speed in values depending on the design purposes. to (6). 1/R0 is the maximum droop loop gain. The value of R0 can be determined as different values Rearranging (11) gives: depending on the design purposes. Rearranging (11) gives:
2 2 2 6 1 qSW − (1 − d ) k opt vi AGi (vi )= 2 2 − 2 (1 −2 d )6 k2 vi 6 R10 SW opt S − k v W cut − in opt q AG (v ) =
i
i
where vcut-in is the cut-in wind speed.
R0
2 − k 2 v6 SW opt cut −in
(12) (12)
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where vcut-in is the cut-in wind speed. Thus, the output of the adaptive gain droop control loop can be expressed as: Thus, the output of the adaptive gain droop control loop can be expressed as: 2
∆Qi =
2
2
6
S − (1 − d ) k v 21 − (1W− d )2 k2 v 6 opt i Δ1Qi =SW opt i 6 qR0 Vsys SW2 −6 k opt2 vcut − in R0 2 SW − k2opt vcut−in q
(−V V − V ) sys
nom
nom
(13)
(13)
In (13), vi and AGi(vi) are spatially and temporally dependent variables. First, the reason for the In (13), vi and AGi (vi ) are spatially and temporally dependent variables. First, the reason for the spatial dependency is that each PMSG has a spatially different level of current MRPC due to the spatial dependency is that each PMSG has a spatially different level of current MRPC due to the wake wake effect between the adjacent PMSGs. In order to obtain better voltage support performance, a effect between the adjacent PMSGs. In order to obtain better voltage support performance, a larger larger gain is set for a downstream PMSG converter that has a more MRPC (less active power gain is set for a downstream PMSG converter that has a more MRPC (less active power generation), generation), whereas a small gain is set for an upstream PMSG converter that has a less MRPC whereas a small gain is set for an upstream PMSG converter that has a less MRPC (more active power (more active power generation). In addition, the droop gain is set to zero when the wind speed vi is generation). In addition, the droop gain is set to zero when the wind speed vi is greater than or equal greater than or equal to the rated wind speed. This helps PMSG-based WPP to provide more to the rated wind speed. This helps PMSG-based WPP to provide more voltage support and ensure voltage support and ensure stable operation. Second, the reason for the temporal dependency is stable operation. Second, the reason for the temporal dependency is that the input wind speed of that the input wind speed of WT is time-varying. As a result, the MRPC of each PMSG is also WT is time-varying. As a result, the MRPC of each PMSG is also time-varying, and droop gain is time-varying, and droop gain is adjusted adaptively with the change of input wind speed. adjusted adaptively with the change of input wind speed. Therefore, the proposed AGCS can improve Therefore, the proposed AGCS can improve the voltage support and ensure the stable operation the voltage support and ensure the stable operation when set to be proportional to the spatially and when set to be proportional to the spatially and temporally different MRPC. It provides effective temporally different MRPC. It provides effective contribution to voltage regulation by increasing the contribution to voltage regulation by increasing the droop gains depending on the increasing droop gains depending on the increasing MRPC and thus prevents the PMSGs from reaching the MRPC and thus prevents the PMSGs from reaching the maximum reactive power operation limit maximum reactive power operation limit frequently by reducing the droop gains depending on the frequently by reducing the droop gains depending on the decreasing MRPC, which helps avoid the decreasing MRPC, which helps avoid the wear and tear of the PMSG converters. wear and tear of the PMSG converters. 3. Model System 3. Model System Figure 6 shows a test system used in this paper to investigate the performance of the voltage Figure 6 shows a test system used in this paper to investigate the performance of the voltage control schemes. The test system consists of a synchronous generators (SG) of 100 MW [23], a static control schemes. The test system consists of a synchronous generators (SG) of 100 MW [23], a static load of 30 MW and 1 MVAR, and 12 2-MW PMSG-based WPP. In order to differentiate each PMSG, load of 30 MW and 1 MVAR, and 12 2-MW PMSG-based WPP. In order to differentiate each PMSG, each column and each row of the PMSG are numbered from WT1 to WT12 separately, as shown each column and each row of the PMSG are numbered from WT1 to WT12 separately, as shown in in Figure 6. Figure 6.
Figure 6. Test6.system used in thisinpaper. Figure Test system used this paper.
3.1. Synchronous Generators 3.1. Synchronous Generators The SG is a steam turbine generator with a rated capacity of 100 MVA, and it is equipped with The SG is a steam turbine generator with a rated capacity of 100 MVA, and it is equipped with excitation adjustment function. Figure 7 and Table 2 show the IEEE alternator supplied rectifier excitation adjustment function. Figure 7 and Table 2 show the IEEE alternator supplied rectifier excitation system (from [24]) and its coefficients, respectively. excitation system (from [24]) and its coefficients, respectively. SVG, well-known as rapid dynamic reactive power compensation device, is not considered because this paper focuses on the reactive voltage control inside the WPP itself, and thus only the alternator supplied rectifier excitation system is considered. As a result, the voltage at the PCC is not fully recovered to the initial value after the disturbance event.
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VRmax
1+sTC 1+sTB
VM Vref
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VF
KA 1+sTA VRmin
VR eqE
sK F 1+sTF
1 sTE
VE
π
Vf
0
1 + SE
FEX (VE , i f , I N ) If
KD
Figure 7. IEEE alternatorsupplied supplied rectifier excitation system model. Figure 7. IEEE alternator rectifier excitation system model. Table 2. Coefficients of the IEEE alternator supplied rectifier excitation system model.
Table 2. Coefficients of the IEEE alternator supplied rectifier excitation system model. TC
T0C
TB
TB0
KA
TA
KF
TF
TE
SE
KD
KA400
T0.02 A
KF 0.03
T1F
T0.8 E
SE 4.18
KD 0.38
0 0 400 0.02 0.03 1 0.8 4.18 0.38 SVG, well-known as rapid dynamic reactive power compensation device, is not considered because this paper focuses on the reactive voltage control inside the WPP itself, and thus only the 3.2. PMSG-Based WPP rectifier excitation system is considered. As a result, the voltage at the PCC is not alternator supplied fully recovered to the initial value after the disturbance event.
The WPP consists of 12 2-MVA PMSGs. The PMSG is connected to the PCC through the 0.69/35-kV transformer 3.2. PMSG-Based WPPand connected to the grid (modelled by the large SG and the 230/20-kV step-up transformer) through the 35/230-kV transformer. The distance between the adjacent WTs is The WPP consists of 12 2-MVA PMSGs. The PMSG is connected to the PCC through the 1120 m, and the transformer distance between the 35tokV the SGbyisthe 20 large km. SG In PMSG-based WPP, it is 0.69/35-kV and connected thebus gridand (modelled and the 230/20-kV assumed thattransformer) the rated capacity of each WT in a WPP isThe thedistance same, and the operating step-up through the 35/230-kV transformer. between the adjacentparameters, WTs is 1120 m, and the distance between the 35 kV bus and the SG is 20 km. In PMSG-based WPP, it is main circuit and control parameters of each WTG are also the same. assumed that ratedin capacity of 3, each in a WPP is the same, and thewind operating parameters, main and 22 Similarly, as the shown Figure theWT cut-in, rated, and cut-out speeds are 4, 13.2, circuit and control parameters of each WTG are also the same. m/s, respectively. Thus the output of PMSGs in WPP is not at the same level due to the wake effect Similarly, as shown in Figure 3, the cut-in, rated, and cut-out wind speeds are 4, 13.2, and 22 m/s, between the adjacent PMSGs and the input wind speed of WT is time-varying. If the PMSG respectively. Thus the output of PMSGs in WPP is not at the same level due to the wake effect between operates above the realand active power, it speed will not have reactive power regulation capability. The the adjacent PMSGs the input wind of WT is time-varying. If the PMSG operates above voltage the PCC is multiplied withregulation adaptivecapability. gain AGThe i(vi),voltage and this result at is added thedeviation real activeat power, it willpoint not have reactive power deviation to the the reactive power referencewith value. PCC point is multiplied adaptive gain AGi (vi ), and this result is added to the reactive power value.the PMSG controller measures the voltage at the PCC, and then the voltage RMS Inreference this paper, In this the PMSG controller measures the voltage at the PCC, and then the voltage RMS at at the PCC pointpaper, for voltage control is calculated. the PCC point for voltage control is calculated.
4. Case4. Studies Case Studies Time-domain simulations usedto to verify the proposed AGCSinreported in sections. the previous Time-domain simulations are are used verify the proposed AGCS reported the previous The test system is modelled by using a PSCAD/EMTDC simulator [25]. According to the previous sections. The test system is modelled by using a PSCAD/EMTDC simulator [25]. According to the analysis, it canitbecan seenbe that the that performance of AGCS is of closely related to windrelated conditions (i.e., wind previous analysis, seen the performance AGCS is closely to wind conditions direction and wind speed) and the disturbance of reactive power load. Thus, five cases have been (i.e., wind direction and wind speed) and the disturbance of reactive power load. Thus, five cases implemented by varying the above conditions to compare the effectiveness of the proposed AGCS have been implemented by varying the above conditions to compare the effectiveness of the with respect to FGCS, in which 1/R0 is set to the fixed value of 35. In all cases, a static load of 12 MW proposed respect to FGCS,event in which 1/Rto 0 is set to the fixed value of 35. In all cases, a and 9AGCS MVAR with is added as a disturbance at 2 s; due the voltage sags not being particularly large, static load of 12 MW and 9 MVAR is added as a disturbance at 2bes;emphasized due to the that voltage sags not the deloading level d of WTGs are set to 0, namely d = 0, and event it should in the being scenario particularly the deloading level of WTGs are set to 0, = 0, and it should be of thelarge, large voltage drop caused bydshort circuit fault, when thenamely reactivedpower margin of WPP is insufficient, the deloading operation of WTGs can be considered. emphasized that in the scenario of the large voltage drop caused by short circuit fault, when the reactive power margin of WPP is insufficient, the deloading operation of WTGs can be considered. In Case 1 and Case 2 the wind speed is assumed to be constant during the voltage control, and in Case 3 and Case 4 the wind speed is assumed to be increased at the instant of the event, from 13 to 14 m/s. In case 5, a real wind speed pattern is considered, that is, the wind speed is randomly fluctuating within the simulation time.
effects of high wind speed of 13m/s with 45° and 0° wind direction on the voltage control performance. 4.1.1 Case 1: Wind Speed of 13 m/s, and Wind Direction of 45°
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Figure 8 shows the results when the constant wind speed is as high as 13m/s and wind direction is 45°. In this case, the wind speed of WT1, WT2, WT3, WT4, WT8, WT12 is 13 m/s, In Case 1 and Case 2 the wind speed is assumed to be constant during the voltage control, and whereas due to the wake effect in (6), the wind speed of WT5, WT6, WT7, WT11 is 11.68m/s, and in Case 3 and Case 4 the wind speed is assumed to be increased at the instant of the event, from 13 the wind speed of WT9, WT10 is 10.97 m/s, as shown in Table 3. This means that the PMSGs in the to 14 m/s. In case 5, a real wind speed pattern is considered, that is, the wind speed is randomly fourth column and first row have largest active power and thus less MRPC, whereas other PMSGs fluctuating within the simulation time. have larger MRPC. The MRPC of all PMSGs obtained by using (6) and the droop gains obtained by using (12) are shown in Table 4, Figure 8 and Table 5, respectively. The wind speed, MRPC and 4.1. Constant Wind Speed droop gain are divided into three groups. The voltage control capability of a WPP depends on the MRPC of the PMSG which is closely related to wind conditions (i.e., wind direction wind speed). Thus this section describes the effects Table 3. Windand speed of Case 1 (m/s). ◦ ◦ of high wind speed of 13 m/s with 45 and 0 wind direction on the voltage control performance. Col.1
Col.2
Col.3
Col.4
◦ 4.1.1. Case 1: Wind Speed of 13 13 m/s, and Wind 13 Direction13of 45
13 13 11.68 11.68 11.68 Figure 8 shows the results when the constant wind speed is as high as 13 m/s and wind direction 13 11.68 10.97 10.97 ◦
is 45 . In this case, the wind speed of WT1, WT2, WT3, WT4, WT8, WT12 is 13 m/s, whereas due to the wake effect in (6), the wind speed of WT5, WT6, WT7, WT11 is 11.68 m/s, and the wind speed of Table 4. MRPC of Case 1 (Mvar). WT9, WT10 is 10.97 m/s, as shown in Table 3. This means that the PMSGs in the fourth column and Col.2 first row have largest active Col.1 power and thus less MRPC,Col.3 whereas otherCol.4 PMSGs have larger MRPC. The MRPC of all PMSGs obtained and the droop 0.44by using (6)0.44 0.44gains obtained 0.44 by using (12) are shown in 0.44 1.41 MRPC and 1.41droop gain are divided into Table 4, Figure 8 and Table 5, respectively.1.41 The wind speed, 0.44 1.41 1.62 1.62 three groups.
Figure 8. Maximum reactive power capacity (MRPC) of the all PMSGs in case 1. Figure 8. Maximum reactive power capacity (MRPC) of the all PMSGs in case 1. Table 3. Wind speed of Case 1 (m/s). Col.1
Col.1 13 16.04 13 16.04 13 16.04
Table 5. Droop gain of Case 1. Col.2 Col.3 Col.4 13 Col.2 11.68 16.04 11.68 51.40
13 Col.3 11.68 16.04 10.97 51.40
13 Col.4 11.6816.04 10.9751.40
51.40 59.07 Table 4. MRPC of Case 1 (Mvar).
59.07
As shown in Figure 9a, the voltage nadir of three schemes (i.e., no voltage control, FGCS and AGCS) after the disturbance isCol.1 0.889 p.u.,Col.2 0.949 p.u.Col.3 and 0.957Col.4 p.u., respectively. Apparently, the 0.44 scheme 0.44is higher 0.44than that 0.44 steady state voltage of the proposed of the fixed scheme by 0.008 p.u. 1.41 scheme” 1.41 by 0.068 1.41 and higher than that of the “no 0.44 voltage control p.u.. In the case of the same total 0.44 1.41 1.62 1.62 reactive power demand, the proposed scheme shows a better performance on the voltage regulation than that of the FGCS. Table 5. Droop gain of Case 1.
Col.1
Col.2
Col.3
Col.4
16.04 16.04 16.04
16.04 51.40 51.40
16.04 51.40 59.07
16.04 51.40 59.07
WTs (i.e., WT1, WT2, WT3, WT4, WT8, WT12) is constrained to 0.44 Mvar due to the maximum reactive power operating limits. The result is increasing wear and tear to the converters. As shown in Figure 8, Figure 9b and Figure 9c, the adaptive gain and thus the reactive power generation has a large value for the WTs that has smaller input wind speed, depending on the Energies 2019, 12, 753 level of MRPC. The adaptive gains and the reactive power generation of 10 of 20(i.e., spatially different WTs WT1, WT2, WT3, WT4, WT8, WT12) are smaller than that of the FGCS, whereas the adaptive gains and the power generation of other WTs larger than(i.e., that no of the FGCS. This helps Asreactive shown in Figure 9a, the voltage nadir of are three schemes voltage control, FGCSPMSGs and toAGCS) generate certain amount of reactive power, while the stable operationtheofsteady PMSGs afterathe disturbance is 0.889 p.u., 0.949 p.u. and 0.957ensuring p.u., respectively. Apparently, without reactive power limits. In addition, can that be seen WTs state voltage of the proposed scheme is higheritthan of thefrom fixedFigure scheme9c bythat 0.008the p.u.upstream and higher have than by the0.068 downstream at the thesame wind directions, namely, thanless that reactive of the “nopower voltagegeneration control scheme” p.u.. In theWTs case of total reactive power reactive power generation of WTs (i.e.,a WT5, WT7, WT11) larger than that of WTs (i.e., demand, the proposed scheme shows better WT6, performance on the are voltage regulation than that of WT1, WT2, WT3, WT4, WT8, WT12) and are smaller than that of WTs (i.e., WT9, WT10). the FGCS.
(a)
(b)
(c) Figure 9. Results of Case 1. (a) Voltage at PCC, (b) reactive power of PMSGs under the conventional FGCS, (c) reactive power of PMSGs under the proposed AGCS.
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As shown in Figure 9b, for the FGCS, all PMSGs have the same reactive power generation within the MRPC range, whereas the reactive power generated by the fourth column and first row WTs (i.e., WT1, WT2, WT3, WT4, WT8, WT12) is constrained to 0.44 Mvar due to the maximum reactive power operating limits. The result is increasing wear and tear to the converters. As shown in Figures 8 and 9b,c, the adaptive gain and thus the reactive power generation has a large value for the WTs that has smaller input wind speed, depending on the spatially different level of MRPC. The adaptive gains and the reactive power generation of WTs (i.e., WT1, WT2, WT3, WT4, WT8, WT12) are smaller than that of the FGCS, whereas the adaptive gains and the reactive power generation of other WTs are larger than that of the FGCS. This helps PMSGs to generate a certain Energies 2019, 01, x FOR PEER REVIEW 11 of 20 amount of reactive power, while ensuring the stable operation of PMSGs without reactive power limits. In addition, it can be seen from Figure 9c that the upstream WTs have less reactive power generation Figure 9. Results of Case 1. (a) Voltage at PCC, (b) reactive power of PMSGs under the conventional than the downstream WTs at the wind directions, namely, reactive power generation of WTs (i.e., WT5, FGCS, (c) reactive power of PMSGs under the proposed AGCS. WT6, WT7, WT11) are larger than that of WTs (i.e., WT1, WT2, WT3, WT4, WT8, WT12) and are smaller than that of WTs (i.e., WT9, WT10).
4.1.2 Case 2: Wind Speed of 13 m/s, and Wind Direction of 0° ◦
Wind Speed of 13 m/s, and Wind Direction of 0 In4.1.2. this Case case,2:the wind direction is changed to 0°, and the MRPC of the downstream PMSGs is ◦ , and different from thatthe inwind Casedirection 1. The wind speed to of 0each WT shownofinthe Table 6. The PMSGs In this case, is changed theisMRPC downstream PMSGsin is the different from have that in Case active 1. The power wind speed of each WTwhereas is shownother in Table 6. The PMSGs inMRPC. the fourth column largest and less MRPC, PMSGs have larger fourth column havePMSGs largest and activethe power andgains less MRPC, whereas have10 larger The MRPC of all droop are shown in other TablePMSGs 7, Figure andMRPC. Table 8, The MRPC ofThe all PMSGs the droop shown in Table Figure 10 andfour Tablegroups, 8, respectively. respectively. wind and speed, MRPCgains andare droop gain are 7, divided into and each The wind speed, MRPC droop gain are divided into four groups, and each column is regarded as column is regarded as a and group. a group. Table 6. Wind speed of case 2 (m/s). Table 6. Wind speed of case 2 (m/s).
Col.1
Col.1
13 13 13
Col.2
Col.2
11.61 11.61 11.61 11.61 11.61 11.61
13 13 13
Col.3
Col.3
10.93
10.93 10.93 10.93 10.93 10.93
Col.4
Col.4 10.48
10.48 10.48 10.48 10.48 10.48
Table7.7.MRPC MRPCofofCase Case2 2(Mvar). (Mvar). Table Col.1Col.1
Col.2 Col.2
Col.3 Col.3
0.44 0.44 0.44 0.44 0.44 0.44
1.43 1.43 1.43 1.43 1.43 1.43
1.621.62 1.621.62 1.621.62
Col.4 Col.4 1.71 1.71 1.71
1.71 1.71 1.71
Figure 10. MRPC of the all PMSGs in case 2.
Figure 10. MRPC of the all PMSGs in case 2. Table 8. Droop gain of case 2. Col.1
Col.2
Col.3
Col.4
11.85 11.85 11.85
38.5 38.5 38.5
43.62 43.62 43.62
46.04 46.04 46.04
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Table 8. Droop gain of case 2. Col.1
Col.2
Col.3
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11.85 38.5 43.62 46.04 11.85 38.5 43.62 46.04 The comparison of Figure 9c and Figure 11c shows that the MRPCs and the droop gains of 11.85 38.5 43.62 46.04 WTs (i.e., WT1, WT2, WT3) have become larger due to the changes of wind direction. Similarly, the downstream WTs have larger MRPC and the droop gain depends on the spatially different level of MRPC. The adaptive gainsofand the2,reactive generation of 1WTs (i.e.,for WT4, are As Figure 11 shows the result Case which power is identical to case except theWT8, windWT12) direction. smaller than that of the FGCS to avoid maximum reactive output limit, whereas the adaptive gains shown in Figure 11a, the voltage nadirs of three schemes (i.e., no voltage control, FGCS and AGCS) and the reactive power generation of other WTs are larger than that of the FGCS to generate a after the disturbance are 0.889 p.u., 0.95 p.u. and 0.9549 p.u., respectively. Apparently, the steady state certain amount of reactive power. voltage of the proposed scheme is higher than that of the fixed scheme by 0.0049 p.u. and higher than The results of the above two cases clearly indicate that the AGCS can improve the voltage that of “no control scheme” by 0.0659 p.u. the This is because the AGCS releases reactive nadirvoltage and ensure the stable operation by setting spatially dependent gains to PMSGs,more especially power than the FGCS during the disturbance. under high wind speed conditions.
(a)
(b)
(c) Figure 11. of Results Case 2. (a) atVoltage at reactive PCC, (b)power reactive PMSGs the Figure 11. Results Case of 2. (a) Voltage PCC, (b) of power PMSGsofunder theunder conventional conventional FGCS, (c) reactive power of PMSGs under the proposed AGCS. FGCS, (c) reactive power of PMSGs under the proposed AGCS.
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Similarly, as shown in Figure 11b, all PMSGs have the same reactive power generation within the MRPC range for the FGCS, whereas the reactive power generated by fourth column WTs (i.e., WT4, WT8, WT12) is constrained to 0.44 Mvar due to the maximum reactive operating limits. The comparison of Figures 9c and 11c shows that the MRPCs and the droop gains of WTs (i.e., WT1, WT2, WT3) have become larger due to the changes of wind direction. Similarly, the downstream WTs have larger MRPC and the droop gain depends on the spatially different level of MRPC. The adaptive gains and the reactive power generation of WTs (i.e., WT4, WT8, WT12) are smaller than that of the FGCS to avoid maximum reactive output limit, whereas the adaptive gains and the reactive power generation of other WTs are larger than that of the FGCS to generate a certain amount of reactive power. The results of the above two cases clearly indicate that the AGCS can improve the voltage nadir and ensure the stable operation by setting the spatially dependent gains to PMSGs, especially under high wind speed conditions. 4.2. Variable Wind Speed As mentioned above, the performance of voltage control is critically depending on the MRPC, which can be decreased because of an increase in wind speed. Thus, this section investigates the test results for three cases in which the wind speed increases to a high wind speed and with random fluctuations, respectively. 4.2.1. Case 3: Increasing Wind Speed from 13 to 14 m/s and Wind Direction of 45◦ Figure 12 shows the results in which the wind speed starts increasing from 13 to 14 m/s at 4 s, and wind direction is 45◦ . However, only the fourth column and first row WTs (i.e., WT1, WT2, WT3, WT4, WT8, WT12) experience the wind speed reduction during the simulation time due to the travel time of the wake wind, as shown in Table 9 and Figure 12a. Table 9. Wind speed of Case 3 (m/s). Col.1
Col.2
Col.3
Col.4
13→14 13→14 13→14
13→14 11.68 11.68
13→14 11.68 10.97
13→14 11.68 10.97
Because of the wind speed change from 13 to 14 m/s, the WPP has less MRPC than in Case 1, and the droop gains of PMSGs are adaptively changed by using (12), as shown in Tables 10 and 11. Table 10. MRPC of Case 3 (Mvar). Col.1
Col.2
Col.3
Col.4
0.44→0 0.44→0 0.44→0
0.44→0 1.41 1.41
0.44→0 1.41 1.62
0.44→0 1.41 1.62
Table 11. Droop gain of Case 3. Col.1
Col.2
Col.3
Col.4
16.04→0 16.04→0 16.04→0
16.04→0 51.40→66.68 51.40→66.68
16.04→0 51.40→66.68 59.07→76.42
16.04→0 51.40→66.68 59.07→76.42
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Wind speed(m/s)
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(a)
(b)
Droop gain
(c)
(d) Figure 12. Cont.
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(e) Figure ResultsofofCase Case 3. 3. (a) (b)(b) voltage at PCC, (c) reactive powerpower of PMSGs under Figure 12. 12. Results (a)Wind Windspeed, speed, voltage at PCC, (c) reactive of PMSGs the the conventional FGCS, (d) (d) adaptive gain of of PMSGs, (e)(e)reactive under conventional FGCS, adaptive gain PMSGs, reactivepower powerofofPMSGs PMSGsunder under the the proposed AGCS. proposed AGCS.
4.2.2 Case 4: Increasing Windthe Speed fromnadir 13 to 14m/s andand Wind Direction 0° disturbance of wind As shown in Figure 12b, voltage of FGCS AGCS afterofthe speed changes areshows 0.9448the p.u. and 0.957 p.u., respectively. Apparently, steady state voltage of the Figure 13 results of Case 4, which is identical to Case 3the except for the wind direction. proposed scheme is higher than that of the fixed scheme by 0.0122 p.u. Because the input wind speed In this Case, the wind direction is changed to 0°, and only the fourth column WTs (i.e., WT4, WT8, of the upstream WTs the (i.e.,wind fourth column and first row exceeds thedue rated operation speed, the WT12) experience speed reduction during theWTs) simulation time to the travel time of the WTswake output the as maximum power, is no reactive output for the wind, shown inrated Tableactive 12 and Figurethus 13a.there Similarly, the WPPpower has less MRPCcapability than in Case 2, converters of these PMSGs. and the droop gains of PMSGs are adaptively changed by using (12), as shown in Table 13 and Table 14. For the FGCS, the reactive power generated by the fourth column and first row WTs (i.e., WT1, 12. Windto speed of Case 3 (m/s). WT2, WT3, WT4, WT8, WT12) is Table constrained 0 Mvar due to the limit of reactive power. The unfavorable result is increasing wear and tear to the converters. The reactive power generated by other Col.1 Col.2 Col.3 Col.4 WTs is increased due to the larger voltage deviation at PCC caused by the disturbance of increased 13→14 11.61 10.93 10.48 wind speed, as shown in Figure 12c. However, for the 10.93 AGCS, the reactive power generated by the 13→14 11.61 10.48 fourth column and first row WTs (i.e., WT1,11.61 WT2, WT3, 10.93 WT4, WT8, WT12) 13→14 10.48 becomes 0 Mvar because of the adaptive change in droop gain (changed to 0) rather than the reactive power limitation. The reactive power generated by other WTs is increased, only because the voltage deviation at Table 13. MRPC ofthis Caseis3not (Mvar). PCC becomes larger, but also the droop gains of these PMSGs are increased adaptively by using (12), Col.1 Col.2 Col.3 Col.4 as shown in Figure 12d,e, respectively. 0.44→0 1.43 1.62 1.71 0.44→0 1.43 1.62 1.71 4.2.2. Case 4: Increasing Wind Speed from 13 to 14 m/s and Wind Direction of 0◦ 0.44→0 1.43 1.62 1.71
Figure 13 shows the results of Case 4, which is identical to Case 3 except for the wind direction. In this Case, the wind direction is changed to Droop 0◦ , and only the 3. fourth column WTs (i.e., WT4, WT8, Table 14. gain of Case WT12) experience the wind speed reduction during the simulation time due to the travel time of the Col.1 Col.2 Col.3 Col.4 wake wind, as shown in Table 12 and Figure 13a. Similarly, the WPP has less MRPC than in Case 2, 11.85→0 38.5→42.06 43.62→47.65 46.04→50.29 and the droop gains of PMSGs are adaptively changed by using (12), as shown in Tables 13 and 14. 11.85→0 38.5→42.06 43.62→47.65 46.04→50.29 The voltage nadir of FGCS and AGCS after the disturbance speed changes are 0.9456 p.u. 11.85→0 38.5→42.06 43.62→47.65of wind 46.04→50.29 and 0.9549 p.u., respectively. The steady state voltage of the proposed scheme is higher than that of voltage FGCS and AGCSfor after disturbance wind speedpower changes 0.9456 the fixedThe scheme by nadir 0.0093ofp.u.. The reason thethe change trend ofofthe reactive of are FGCS, the p.u. and 0.9549 p.u., respectively. The steady state voltage of the proposed scheme is higher than reactive power and the droop gains of AGCS are the same as described in Case 3. However, compared that of the fixed scheme by 0.0093 p.u.. The reason for the change trend of the reactive power of with the three WT groups in Case 3, the wind speed, MRPC and droop gains are divided into four FGCS, the reactive power and the droop gains of AGCS are the same as described in Case 3. groups in this case, and the biggest difference is that the wind speed, MRPC and droop gains of the However, compared with the three WT groups in Case 3, the wind speed, MRPC and droop gains first row WTs of WPP has undergone major changes due to the wind direction change from 45◦ to 0◦ . are divided into four groups in this case, and the biggest difference is that the wind speed, MRPC and droop gains of the first row WTs of WPP has undergone major changes due to the wind direction change from 45° to 0°.
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Wind speed(m/s)
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(a)
(b)
(c)
(d) Figure 13. Cont.
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(e) 13. Results Case4.4. (a) (a) Wind voltage at PCC, (c) reactive power power of PMSGs FigureFigure 13. Results of of Case Windspeed, speed,(b)(b) voltage at PCC, (c) reactive of under PMSGs the conventional FGCS, (d) adaptive gain of PMSGs, (e) reactive power of PMSGs under the under the conventional FGCS, (d) adaptive gain of PMSGs, (e) reactive power of PMSGs under the proposed AGCS. proposed AGCS.
4.2.3. 4.2.3 CaseCase 5: Real Pattern of Wind Speed, and 5: Real Pattern of Wind Speed, andWind WindDirection Direction of of 00°◦ In reality, the wind speed changes time.InInthis thiscase, case,aareal real wind wind speed have In reality, the wind speed changes all all thethe time. speedpattern patternthat that have (e) ◦ specific statistical features wind direction employed[26], [26], as as shown shown in specific statistical features andand wind direction of of 0 0° is isemployed inFigure Figure14a. 14a. TheFigure voltage nadir of FGCS and AGCS the disturbance are compared as shown 13. Results of Case 4. (a) Wind speed,after (b) voltage at PCC, (c) reactive power of PMSGs under in Figure the be conventional (d) adaptive gain better of PMSGs, (e) reactive of PMSGs the nadir at 14b. It can seen thatFGCS, the AGCS exhibits performance inpower improving theunder voltage Table 12. Wind speed of Case 3 (m/s). PCC. proposed AGCS. Col.1 Col.3 Col.4 It should be emphasized that forCol.2 conventional FGCS the reactive power generated by the 4.2.3 Case 5: Real Pattern of Wind Speed, and Wind Direction of 0° fourth column WTs (i.e., WT4, exceed 13→WT8, 14 WT12) 11.61will frequently 10.93 10.48the limit. This results in not only the wind speed changes all the time. In this real windthe speed pattern have 13voltage →14 11.61 10.93 limiting In thereality, support for the at the PCC point, butcase, alsoa10.48 causing wear outsthat to the PMSG specific statistical features and wind direction is10.93 employed [26], as shown in temporally Figure 14a. dependent 13 →14 11.61 ofvi 0° 10.48 converters. However, for the proposed AGCS, and AGi(vi) are spatially and The voltage nadir of FGCS and AGCS after the disturbance are compared as shown in Figure variables, thus the droop gains of PMSGs are adaptively changed by using (12). Consequently, the 14b. It can be seen that the AGCS exhibits better performance in improving the voltage nadir at 13.gain, MRPC of Case 3 (Mvar). downstream WTs have higherTable droop and the result is that not only the reactive power PCC. generated by the PMSGs does not exceed the MRPC FGCS to avoid the wear outs to the WT converters, It should be emphasized conventional the Col.4 reactive power generated by the Col.1that forCol.2 Col.3 but fourth also provides more effective voltage support for the PCC point, as This shown in Figure 14c and column WTs (i.e., WT4, WT8, WT12) will frequently exceed the limit. results in not only 0.44 →0 shows 1.43 1.62 1.71 Figure 14d. Specifically, thethe AGCS better performance high wind speed. limiting the support for voltage at the PCC point, but also at causing the wear outs to the PMSG 0.44 → 1.435 demonstrate 1.62 are spatially 1.71 The results of Case for 3, Case 4 0and Case the AGCS stable operation of converters. However, the proposed AGCS, vi and AGi(vi)that andensures temporally dependent 0.44→0 1.43 1.62 1.71 variables,tothus the droop gainsouts of PMSGs adaptively changed using (12). Consequently, the by all PMSGs avoid the wear to theare WT converters whilebyimproving the voltage nadir downstream WTs and havetemporally higher droop gain, andgains the result is that at notthe only the reactive powerwhen setting the spatially dependent to PMSGs disturbance instant Table 14. Droop gaintoofavoid Case the 3. wear outs to the WT converters, generated by the PMSGs does not exceed the MRPC wind speed significantly fluctuates.
Wind speed(m/s)
Wind speed(m/s)
but also provides more effective voltage support for the PCC point, as shown in Figure 14c and Col.1 the AGCS Col.2 Col.3 at high wind Col.4 Figure 14d. Specifically, shows better performance speed. The results 11.85 of Case 3, Case 4 and Case 5 demonstrate that the AGCS ensures →0 38.5→42.06 43.62→47.65 46.04→50.29stable operation of all PMSGs to avoid outs→ to42.06 the WT converters while improving the voltage nadir by 11.85the →0 wear 38.5 43.62→47.65 46.04→50.29 setting the spatially gains→ to47.65 PMSGs at46.04 the → disturbance instant when 11.85and →0 temporally 38.5→dependent 42.06 43.62 50.29 wind speed significantly fluctuates.
(a)
(a)
Figure 14. Cont.
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Voltage at PCC(Mvar)
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(b)
(c)
(d) 14. Results of Case 5. (a) Real pattern of wind speed, (b) voltage at PCC, (c) adaptive gain of Figure 14.Figure Results of Case 5. (a) Real pattern of wind speed, (b) voltage at PCC, (c) adaptive gain of PMSGs, (d) reactive power of PMSGs under the proposed AGCS. PMSGs, (d) reactive power of PMSGs under the proposed AGCS.
5. Conclusions
The voltage nadir of FGCS and AGCS after the disturbance are compared as shown in Figure 14b. This paper proposes a control scheme with adaptive gains for a PMSG-based WPP. The droop It can be seen that the AGCS exhibits better performance in improving the voltage nadir at PCC. gains of PMSGs are adjusted adaptively based on the MRPC, which is closely related to input wind It should that for FGCS reactive powerisgenerated by the fourth speed.beToemphasized do this, a function thatconventional relates the droop gainthe to the wind speed used. The different column WTs (i.e., WT4, WT8, WT12) will frequently exceed the limit. This results in not onlyTo limiting gains are set to be proportional to the spatially and temporally different levels of MRPC. improve the voltage-supporting capacity, the droop gains of downstream WTs are adjusted to a the support for the voltage at the PCC point, but also causing the wear outs to the PMSG converters. larger value due to the larger MRPC; then, to ensure stable operation of all PMSGs, the droop gains However, for the proposed AGCS, vi and AGi (vi ) are spatially and temporally dependent variables, of upstream WTs are adjusted to a smaller value due to the smaller MRPC. thus the droop gains of PMSGs are adaptively changed by using (12). Consequently, the downstream Various simulation results demonstrate that the proposed scheme has better performance than WTs have the higher droop gain, and result is that not the only the reactive generated bystable the PMSGs conventional FGCS inthe terms of improving voltage nadir atpower PCC and ensuring does not exceed the MRPC to avoid the wear outs to the WT converters, but also provides operation of all PMSGs in WPP under load disturbance and various wind conditions (i.e., different more effective voltage support for the PCC point, as shown in Figure 14c,d. Specifically, the AGCS shows better performance at high wind speed. The results of Case 3, Case 4 and Case 5 demonstrate that the AGCS ensures stable operation of all PMSGs to avoid the wear outs to the WT converters while improving the voltage nadir by setting the spatially and temporally dependent gains to PMSGs at the disturbance instant when wind speed significantly fluctuates.
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5. Conclusions This paper proposes a control scheme with adaptive gains for a PMSG-based WPP. The droop gains of PMSGs are adjusted adaptively based on the MRPC, which is closely related to input wind speed. To do this, a function that relates the droop gain to the wind speed is used. The different gains are set to be proportional to the spatially and temporally different levels of MRPC. To improve the voltage-supporting capacity, the droop gains of downstream WTs are adjusted to a larger value due to the larger MRPC; then, to ensure stable operation of all PMSGs, the droop gains of upstream WTs are adjusted to a smaller value due to the smaller MRPC. Various simulation results demonstrate that the proposed scheme has better performance than the conventional FGCS in terms of improving the voltage nadir at PCC and ensuring stable operation of all PMSGs in WPP under load disturbance and various wind conditions (i.e., different wind direction, wind speed increase and wind speed fluctuation). The advantage of the proposed scheme is that it not only improves the voltage nadir by making full use of the WPP reactive capacity but also presents PMSGs at a high wind speed from exceeding the maximum reactive capacity. Moreover, the proposed scheme has application potential in a power system with high wind power penetration. Author Contributions: J.D. and Y.T. conceived and designed the study; J.D. analyzed the data, performed the experiments and wrote the paper; J.Y. provided some actual wind power parameters and checked the results of this work. All the authors read and approved the final manuscript. Funding: This research and the APC were funded by [the Technology Project of the State Grid Electric Power Company (Study on power generation control system and operation control strategy of super-high-ratio new energy grid)”. Conflicts of Interest: The authors declare no conflict of interest.
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