JP2707680B2 - Speed calculation device and speed control device for induction motor - Google Patents
Speed calculation device and speed control device for induction motorInfo
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- JP2707680B2 JP2707680B2 JP1031734A JP3173489A JP2707680B2 JP 2707680 B2 JP2707680 B2 JP 2707680B2 JP 1031734 A JP1031734 A JP 1031734A JP 3173489 A JP3173489 A JP 3173489A JP 2707680 B2 JP2707680 B2 JP 2707680B2
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- Prior art keywords
- temperature
- speed
- stator
- motor
- secondary resistance
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Description
【発明の詳細な説明】 〔産業上の利用分野〕 本発明は、インバータで駆動される誘導電動機の速度
制御装置に関し、特に速度センサを用いずに精度よく速
度制御する装置に関する。Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a speed control device for an induction motor driven by an inverter, and particularly to a device for accurately controlling the speed without using a speed sensor.
〔従来の技術〕 従来より、かご形誘導電動機の特徴である堅牢さを活
かした、耐環境性や構造的自由度の大きい駆動システム
が、すべての産業分野で要望されている。速度センサを
用いない速度制御装置は、このような要望に適合するも
のである。[Prior Art] Conventionally, there has been a demand in all industrial fields for a drive system that utilizes the robustness characteristic of a squirrel-cage induction motor and has a high degree of environmental resistance and structural flexibility. A speed control device not using a speed sensor meets such a demand.
従来、速度センサを用いない誘導電動機の速度制御装
置として、誘導電動機の電圧と電流から求めたトルク電
流と磁束および二次抵抗値、すなわち回転子巻線抵抗値
から演算したすべり周波数によって、電動機駆動周波数
を補償し、電動機の速度制御を行う装置があった。Conventionally, as a speed control device for an induction motor that does not use a speed sensor, the motor drive is performed by a slip frequency calculated from a torque current, a magnetic flux, and a secondary resistance value obtained from a voltage and a current of the induction motor, that is, a rotor winding resistance value. There were devices that compensated the frequency and controlled the speed of the motor.
この場合のすべり周波数の演算方法について説明す
る。A method of calculating the slip frequency in this case will be described.
インバータで駆動される誘導電動機の回転数ｎ（rp
m）は、一般に駆動周波数ｆ（Hz）と電動機のすべり周
波数fs（Hz）によって表される。The rotation speed n (rp) of the induction motor driven by the inverter
m) is generally represented by the drive frequency f (Hz) and the slip frequency f s (Hz) of the motor.
周波数ｆはインバータから直接に得られるため、すべ
り周波数fsを何らかの手段によって得ることができれ
ば、回転数ｎを知ることができ、これを速度制御に用い
ることが可能となる。 Since the frequency f is obtained directly from the inverter, if it is possible to obtain by any means the slip frequency f s, it is possible to know the rotational speed n, it is possible to use this to speed control.
すべり周波数fsは、電動機の磁束φとトルクに相当す
るトルク電流Iqおよび二次抵抗R2によって次のように表
される。Slip frequency f s is the torque current I q and the secondary resistor R 2 corresponds to the magnetic flux φ and a torque of the motor is expressed as follows.
磁束φ、トルク電流Iqは電動機の電圧と電流とから演
算することができるから、二次抵抗値R2が分かれば、す
べり周波数fsを演算することができる。 Flux phi, because the torque current I q can be calculated from the voltage and current of the motor, knowing the secondary resistance R 2, it can be calculated slip frequency f s.
ところが、二次抵抗値R2は回転子の巻線抵抗値である
ため、これを直接固定子側で観測することは困難であ
る。However, the secondary resistance R 2 is for a winding resistance value of the rotor, it is difficult to observe at this directly stator side.
二次抵抗値R2のある基準温度における値を知ることは
できるが、温度によって変化するために、実際の運転に
おいてfsを正しく演算することができない。例えば回転
子の温度が100℃変われば、回転子導体として用いられ
る銅やアルミニウムからなる二次抵抗値は40％程度変化
し、また、回転子の温度は運転によって通常100〜150℃
の温度上昇がある。Although it is possible to know the value at the reference temperature with the secondary resistance R 2, in order to vary with temperature, it is impossible to correctly calculating the f s in the actual operation. For example, if the temperature of the rotor changes by 100 ° C., the secondary resistance of copper or aluminum used as the rotor conductor changes by about 40%, and the temperature of the rotor is usually 100 to 150 ° C. depending on the operation.
Temperature rise.
このように、従来の装置では、すべり周波数の演算に
二次抵抗の設定値を用いていたため、回転子の温度が変
化すると、実際の二次抵抗値と設定の二次抵抗との差異
によって、実際のすべり周波数と差異を生じ、速度を精
度よく補償できない欠点があった。As described above, in the conventional apparatus, since the set value of the secondary resistance is used in the calculation of the slip frequency, when the temperature of the rotor changes, the difference between the actual secondary resistance value and the set secondary resistance causes There is a drawback that a difference from the actual slip frequency occurs and the speed cannot be compensated with high accuracy.
そこで本発明は、速度センサを用いずに精度よく速度
制御を行うことを目的とし、すべり周波数を精度よく演
算しようとするものである。Therefore, an object of the present invention is to precisely perform speed control without using a speed sensor, and to accurately calculate a slip frequency.
この目的を達成するため、本発明の誘導電動機の速度
演算装置は、電動機の磁束φ、トルク電流Iq及び電動機
の二次抵抗値R2よりすべり周波数fsを演算し、求められ
たすべり周波数fsと電動機駆動周波数ｆとの差に基づい
て電動機の回転速度fnを演算する回転速度演算装置にお
いて、前記電動機の固定子に設けた温度センサと、この
温度センサによって検出された固定子の温度θsと固定
子の基準温度θS0とに基づいて温度補償分Δθrを次式 Δθr＝（１＋krs）（θs−θs0） ここで、krsは回転子温度と固定子温度の差（θr−θ
s）÷固定子の温度上昇値（θs−θs0） により演算する温度補償分演算手段と、この温度補償分
演算手段の出力Δθrと前記基準温度θS0における二次
抵抗値R20とから次式 R2＝R20（１＋k0Δθr） により温度補償後の二次抵抗値R2を算出する手段とを備
え、この温度補償後の二次抵抗値R2に基づいて前記すべ
り周波数fsを演算することを特徴とする。To this end, the speed calculation device of the induction motor of the present invention, the magnetic flux φ of the motor, and calculates the slip frequency f s from the secondary resistance R 2 of the torque current I q and the electric motor, the obtained slip frequency in the rotational speed calculating apparatus for calculating a rotational speed f n of the motor based on the difference between f s and the motor drive frequency f, a temperature sensor provided in the stator of the electric motor, the stator is detected by the temperature sensor Based on the temperature θ s and the stator reference temperature θ S0 , a temperature compensation component Δθ r is given by the following equation: Δθ r = (1 + k rs ) (θ s −θ s0 ) where k rs is the rotor temperature and the stator temperature. Difference (θ r −θ
s ) ÷ Temperature compensation portion calculation means for calculating the temperature rise value of the stator (θ s −θ s0 ), the output Δθ r of the temperature compensation portion calculation means, the secondary resistance value R 20 at the reference temperature θ S0 , Means for calculating the temperature-compensated secondary resistance value R 2 from the following equation: R 2 = R 20 (1 + k 0 Δθ r ), and the slip frequency is calculated based on the temperature-compensated secondary resistance value R 2. It is characterized in that f s is calculated.
本発明は、温度変化を補償した二次抵抗値を用いたす
べり周波数の演算値によって、電動機の速度を精度よく
推定するものである。The present invention accurately estimates the speed of an electric motor by calculating a slip frequency using a secondary resistance value that compensates for a temperature change.
前記のように、二次抵抗値R2は温度によって大きく変
化する。したがって、二次抵抗値R2の温度による変化を
補正できれば、すべり周波数fsを正しく演算でき、速度
もまた正しく演算できる。As described above, the secondary resistance R 2 varies greatly with temperature. Therefore, if correct changes due to temperature of the secondary resistance R 2, correctly calculating the slip frequency f s, the speed can be calculated also correctly.
第１図は本発明の速度演算を示すブロック図である。 FIG. 1 is a block diagram showing the speed calculation of the present invention.
駆動周波数ｆ、電動機の電圧、電流から演算されたト
ルク電流の演算値Iq、磁束演算値φ、および固定子の温
度検出値θsを入力信号とし、回転数に相当した周波数f
n＝ｆ−fsを出力する。The drive frequency f, the voltage of the motor, the arithmetic value I q of the torque current computed by the current, the magnetic flux calculation value phi, and the temperature detection value theta s of the stator as an input signal, corresponding to the rotational speed and the frequency f
and outputs a n = f-f s.
すべり周波数は より演算される。The slip frequency is It is calculated by
ここで二次抵抗値設定のための回転子の基準温度をθ
r0、このときの二次抵抗値をR20とすると、任意の温度
における二次抵抗値R2は一般に、次のように表される。Here, the reference temperature of the rotor for setting the secondary resistance is θ
r0, the secondary resistance value at this time is R 20, secondary resistance R 2 at any temperature is generally expressed as follows.
R2＝R20（１＋k0Δθ0） ……（３） ただし、Δθr＝θr−θr0 k0＝1/（225＋θr0）（二次導体がアルミニウムのと
き） さて、本発明は固定子温度の検出値θsから回転子温
度θrを推定しようとするものである。回転子の温度上
昇と固定子の温度上昇は、近似的には比例関係にあるか
ら、θr≒θsと置いても、R2の温度変化をかなり補償す
ることができる。しかし、通常、運転中は固定子温度よ
り回転子温度が高くなる場合が多く、この分を補償すれ
ば、二次抵抗値の推定精度は更に向上する。R 2 = R 20 (1 + k 0 Δθ 0 ) (3) where Δθ r = θ r −θ r0 k 0 = 1 / (225 + θ r0 ) (when the secondary conductor is aluminum) The present invention is fixed. it is intended to estimate the rotor temperature theta r from the detection value theta s child temperature. Since the temperature rise of the rotor and the temperature rise of the stator are approximately proportional to each other, even if θ r ≒ θ s is set, the temperature change of R 2 can be considerably compensated. However, during operation, the rotor temperature is often higher than the stator temperature, and if this is compensated for, the accuracy of estimating the secondary resistance value is further improved.
第２図は固定子温度と回転子温度の測定例である。固
定子巻線に定格電流を流し、始動より温度上昇特性を測
定したものである。測定の便宜上、回転子は拘束されて
いる。すなわち、固定子温度より、回転子温度がかなり
高いことがわかる。FIG. 2 is an example of measurement of the stator temperature and the rotor temperature. The rated current was applied to the stator winding, and the temperature rise characteristics were measured from the start. The rotor is constrained for measurement convenience. That is, it is understood that the rotor temperature is considerably higher than the stator temperature.
また、第２図より回転子温度と固定子温度の差（θr
−θs）は、固定子の温度上昇値（θs−θs0）（ここで
θs0は固定子の基準温度）にほぼ比例することが分か
る。From FIG. 2, the difference between the rotor temperature and the stator temperature (θ r
−θ s ) is almost proportional to the stator temperature rise value (θ s −θ s0 ) (where θ s0 is the stator reference temperature).
したがって、θr−θs＝krs（θs−θs0）とおいて、
ΔθrおよびR2を次のように推定することができる。Therefore, assuming that θ r −θ s = k rs (θ s −θ s0 ),
Δθ r and R 2 can be estimated as follows.
Δθr＝（１＋krs）（θs−θs0） ……（４） R2＝R20（１＋k0Δθr） ……（５） krsとして、回転子と固定子の温度差θr−θsが大き
い領域での値をとれば、温度の影響が大きい領域でのR2
を効果的に推定することができる。Δθ r = (1 + k rs ) (θ s −θ s0 ) (4) R 2 = R 20 (1 + k 0 Δθ r ) (5) Let k rs be the temperature difference θ r − between the rotor and the stator. If the value is taken in the region where θ s is large, R 2 in the region where the effect of temperature is large
Can be estimated effectively.
第２図における破線は、krsとしてＡ点のデータを用
いて回転子温度を推定した場合である。これより、効果
的に回転子温度の推定がなされることが分かる。The broken line in FIG. 2 indicates a case where the rotor temperature is estimated using the data at point A as krs . From this, it can be seen that the rotor temperature is effectively estimated.
このような固定子温度の検出値を用いた二次抵抗値の
温度変化の補正によって、温度変化の主たる要因である
周囲温度の変化、固定子の温度上昇値を補正し、さらに
固定子と回転子の温度差も配慮されているから、精度よ
く二次抵抗値を演算することができる。したがって、こ
れを用いた速度推定値も精度よく演算されることは明白
である。By correcting the temperature change of the secondary resistance value using the detected value of the stator temperature, the change of the ambient temperature and the temperature rise value of the stator, which are the main factors of the temperature change, are corrected. The secondary resistance value can be calculated with high accuracy because the temperature difference between the terminals is taken into account. Therefore, it is clear that the speed estimation value using this is also accurately calculated.
第３図に、本発明をインバータでV/f制御される誘導
電動機の速度制御装置に適用した場合を示す。FIG. 3 shows a case where the present invention is applied to a speed control device of an induction motor that is V / f controlled by an inverter.
図において、１はインバータであり、周波数指令信号
f1より電圧指令器11を介して周波数に比例した電圧指令
信号Ｖが与えられ、また、周波数指令信号f1が与えられ
ている。In the figure, reference numeral 1 denotes an inverter, which is a frequency command signal.
f 1 is the voltage command signal V in proportion to the frequency through the voltage command 11 given from, also, the frequency command signal f 1 is given.
誘導電動機２には、温度センサ32が装備されている。
一点鎖線で示される部分３は、本発明の速度演算器30の
関連する部分で、トルク電流・磁束演算器31、固定子温
度を検出する温度センサ32、電流センサ33、電圧センサ
34からなっている。また、電圧センサを省略して、イン
バータへの交流電圧指令値を用いることもできる。The induction motor 2 is equipped with a temperature sensor 32.
A part 3 indicated by a dashed line is a related part of the speed calculator 30 of the present invention, and includes a torque current / magnetic flux calculator 31, a temperature sensor 32 for detecting a stator temperature, a current sensor 33, and a voltage sensor
It consists of 34. Alternatively, the voltage sensor may be omitted and an AC voltage command value to the inverter may be used.
一点鎖線で囲まれる４は速度制御部であり、速度設定
器40、速度偏差演算器41、速度制御器42、速度偏差加算
器43からなっている。Reference numeral 4 surrounded by an alternate long and short dash line denotes a speed controller, which comprises a speed setter 40, a speed deviation calculator 41, a speed controller 42, and a speed deviation adder 43.
速度演算部３で演算された速度に相当する周波数信号
fnは、速度偏差演算器41で速度指令信号f* nと比較さ
れ、速度制御器42で速度補正信号fsが出力される。速度
補正信号fsは速度指令信号f* nに加算されて、インバー
タの実際の周波数指令信号f1となる。A frequency signal corresponding to the speed calculated by the speed calculator 3
f n is compared with the speed difference calculator 41 and the speed command signal f * n, the speed correction signal f s by the speed controller 42 is outputted. The speed correction signal f s is added to the speed command signal f * n, the actual frequency command signal f 1 of the inverter.
すなわち、速度演算部３で演算された速度信号fnと速
度指令信号f* nの偏差が０になるようにインバータの周
波数指令が調節される。In other words, the frequency command of the inverter so that the deviation of the speed signal f n and the speed command signal f * n calculated by the speed calculating unit 3 becomes zero is adjusted.
第４図は本発明の効果を表す速度特性を実施例につい
て示したものである。回転数指令を50％とし、負荷トル
クに対して示した。特性は本発明を適用した場合の速
度制御特性であり、回転子の温度変化０〜100℃に対し
て速度制御特性は、斜線の範囲にあった。特性は二次
抵抗の温度による変化を補償しない場合で、特性−１
は回転子温度が基準温度よりほぼ50℃低い場合、特性
−２は基準温度よりほぼ50℃高い場合のそれぞれ速度制
御特性である。FIG. 4 shows a speed characteristic showing the effect of the present invention for the embodiment. The rotation speed command is set to 50%, and is shown with respect to the load torque. The characteristics are the speed control characteristics when the present invention is applied, and the speed control characteristics are in the range indicated by oblique lines with respect to a temperature change of the rotor of 0 to 100 ° C. The characteristic is a case where the change due to the temperature of the secondary resistance is not compensated.
Is a speed control characteristic when the rotor temperature is approximately 50 ° C. lower than the reference temperature, and a characteristic-2 is a speed control characteristic when the rotor temperature is approximately 50 ° C. higher than the reference temperature.
本発明の温度補償を行うことにより、従来方法では定
格負荷時で温度変動により±１％の速度変動があったの
に対し、本発明の二次抵抗値の温度補償を行うことによ
り、±0.2％以下の速度変動に抑えることができた。By performing the temperature compensation of the present invention, in the conventional method, the speed fluctuation of ± 1% due to the temperature fluctuation at the rated load, but by performing the temperature compensation of the secondary resistance value of the present invention, ± 0.2%. % Or less.
本発明は、電動機の電圧、電流から演算される速度信
号に基づいて速度制御する装置において、従来速度演算
において精度上問題であった二次抵抗の温度変化を固定
子温度の検出値によって修正することにより、精度の高
い速度演算値を得て、電動機に速度センサを設けずに、
誘導電動機の堅牢な製造的特徴を活かした精度の高い速
度制御を行うことができる。The present invention relates to an apparatus for controlling speed based on a speed signal calculated from a voltage and a current of a motor, and corrects a temperature change of a secondary resistance, which has conventionally been a problem in accuracy in speed calculation, by a detected value of a stator temperature. As a result, a high-accuracy speed calculation value is obtained, and the motor is not provided with a speed sensor.
Accurate speed control can be performed by utilizing the robust manufacturing characteristics of the induction motor.
第１図は本発明の速度演算を示すブロック図、第２図は
固定子巻線温度と回転子温度の測定例を示すグラフ、第
３図は本発明を適用した誘導電動機の速度制御装置の実
施例を示すブロック図、第４図は本発明の効果を表す速
度制御特性を実施例について示したグラフである。 1:インバータ、11:電圧指令器 2:誘導電動機 3:速度演算部、30:速度演算器 31:トルク電流・磁束演算器 32:温度センサ、33:電流検出器 34:電圧センサ 4:速度設定器、41:速度偏差演算器 42:速度制御器、43:速度偏差加算器 5:電源FIG. 1 is a block diagram showing speed calculation of the present invention, FIG. 2 is a graph showing an example of measurement of stator winding temperature and rotor temperature, and FIG. 3 is a diagram showing a speed control device of an induction motor to which the present invention is applied. FIG. 4 is a block diagram showing an embodiment, and FIG. 4 is a graph showing speed control characteristics showing the effect of the present invention for the embodiment. 1: Inverter, 11: Voltage commander 2: Induction motor 3: Speed calculator, 30: Speed calculator 31: Torque / magnetic flux calculator 32: Temperature sensor, 33: Current detector 34: Voltage sensor 4: Speed setting , 41: Speed deviation calculator 42: Speed controller, 43: Speed deviation adder 5: Power supply
Claims (2)
の二次抵抗値R2よりすべり周波数fsを演算し、求められ
たすべり周波数fsと電動機駆動周波数ｆとの差に基づい
て電動機の回転速度fnを演算する回転速度演算装置にお
いて、前記電動機の固定子に設けた温度センサと、この
温度センサによって検出された固定子の温度θsと固定
子の基準温度θS0とに基づいて温度補償分Δθrを次式 Δθr＝（１＋krs）（θs−θs0） ここで、krsは回転子温度と固定子温度の差（θr−
θs）÷ 固定子の温度上昇値（θs−θs0） により演算する温度補償分演算手段と、この温度補償分
演算手段の出力Δθrと前記基準温度θS0における二次
抵抗値R20とから次式 R2＝R20（１＋k0Δθr） により温度補償後の二次抵抗値R2を算出する手段とを備
え、この温度補償後の二次抵抗値R2に基づいて前記すべ
り周波数fsを演算することを特徴とする誘導電動機の速
度演算装置。A slip frequency f s is calculated from a magnetic flux φ of the motor, a torque current I q and a secondary resistance value R 2 of the motor, and based on a difference between the determined slip frequency f s and the motor drive frequency f. in the rotational speed calculating apparatus for calculating a rotational speed f n of the motor, a temperature sensor provided in the stator of the electric motor, to a reference temperature theta S0 and the stator temperature theta s stator detected by the temperature sensor based temperature compensation amount [Delta] [theta] r the following equation Δθ r = (1 + k rs ) (θ s -θ s0) in here, k rs difference of the rotor temperature and the stator temperature (theta r -
θ s ) ÷ Temperature compensation component computing means that computes the temperature rise value of the stator (θ s −θ s0 ), the output Δθ r of the temperature compensation component computing device and the secondary resistance value R 20 at the reference temperature θ S0 . Means for calculating the temperature-compensated secondary resistance value R 2 from the following equation: R 2 = R 20 (1 + k 0 Δθ r ), and the slip is performed based on the temperature-compensated secondary resistance value R 2. speed calculation device of the induction motor, characterized by calculating the frequency f s.
転速度に基づいて誘導電動機の速度制御を行う速度制御
系を備えたことを特徴とする誘導電動機の速度制御装
置。2. A speed control device for an induction motor, comprising a speed control system for controlling the speed of the induction motor based on the rotation speed obtained by the speed calculation device according to claim 1.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP1031734A JP2707680B2 (en) | 1989-02-09 | 1989-02-09 | Speed calculation device and speed control device for induction motor |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP1031734A JP2707680B2 (en) | 1989-02-09 | 1989-02-09 | Speed calculation device and speed control device for induction motor |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH02211087A JPH02211087A (en) | 1990-08-22 |
| JP2707680B2 true JP2707680B2 (en) | 1998-02-04 |
Family
ID=12339269
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP1031734A Expired - Fee Related JP2707680B2 (en) | 1989-02-09 | 1989-02-09 | Speed calculation device and speed control device for induction motor |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JP2707680B2 (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2021002897A (en) * | 2019-06-19 | 2021-01-07 | 東芝三菱電機産業システム株式会社 | Motor controller, motor system, calculation method of rotor winding secondary resistance value and rotor winding temperature estimation method |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| IT1271194B (en) * | 1994-06-24 | 1997-05-27 | Finmeccanica Spa | ASYNCHRONOUS MOTOR SPEED REGULATION SYSTEM WITH TEMPERATURE COMPENSATION |
| JP2004173422A (en) | 2002-11-20 | 2004-06-17 | Fanuc Ltd | Controller for induction motor |
| CN110557075A (en) * | 2019-10-08 | 2019-12-10 | 珠海格力电器股份有限公司 | motor torque determination method and device and motor control system |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS6036716A (en) * | 1983-08-08 | 1985-02-25 | Nissan Motor Co Ltd | Apparatus for preventing over-cooling of engine used for driving vehicle |
| JPS60131088A (en) * | 1983-12-20 | 1985-07-12 | Hitachi Ltd | Controller of induction motor |
| JPS60176488A (en) * | 1984-02-21 | 1985-09-10 | Mitsubishi Electric Corp | Speed controller of induction motor |
| JPS6277894A (en) * | 1985-09-30 | 1987-04-10 | Yaskawa Electric Mfg Co Ltd | Controlling device for induction motor |
-
1989
- 1989-02-09 JP JP1031734A patent/JP2707680B2/en not_active Expired - Fee Related
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2021002897A (en) * | 2019-06-19 | 2021-01-07 | 東芝三菱電機産業システム株式会社 | Motor controller, motor system, calculation method of rotor winding secondary resistance value and rotor winding temperature estimation method |
Also Published As
| Publication number | Publication date |
|---|---|
| JPH02211087A (en) | 1990-08-22 |
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| LAPS | Cancellation because of no payment of annual fees |