Energy-Efficient Control Strategy for PMSM With Superconductive Stator Winding IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 25, NO. 3, JUNE 2015 用超導體定子繞組的永磁同步馬達節能控制策略

Outline INTRODUCTION SPMSM LOSSES IN THE MACHINE OPTIMIZED CURRENT SHAPE CONTROL STRATEGY & CONCLUSION 優化電流波形

INTRODUCTION

Introduction Besides the good electrical parameters the manufacturers are capable of producing high quality tapes in long length configurations. Further advantages are low weight, high mechanical strength and no aging attrition However, in comparison to the DC modus, ac operations show significant losses in the superconductor [6], [7]. 超導體線圈優點 除了良好的電氣參數的廠家能夠生產長長度配置高品質的磁帶。 進一步的優點是重量輕，機械強度高，沒有老化磨耗[1]。 然而，相較於直流作案，交流操作顯示在超導體顯著損失[6]，[7]。

Introduction report on measuring ac transport losses of superconducting pancake coils (YBCO HTS) using electrical as well as calorimetric measurement arrangements. The electrical set-up consists of an ac power supply and a high accuracy DAQ (Data Acquisition) measurement system [10] In this contribution, a general loss overview of an ac powered superconductive machine is given. An optimization criterion is given, based on the most dominating factor of influence to the system efficiency. In contrast to earlier works the macroscopic loss behavior of the superconductor is in the fore, in particular the transfer of loss behavior to a control scheme. 在扁平線圈（YBCO HTS）的交流電傳輸損失 測量超導使用電以及熱量計量的報告。電的建立由一個交流電源和一個高準確度的DAQ（數據採集）測量系統[10] 在這方面的貢獻，交流供電超導體馬達的一般損失。優化影響到系統效率的最主要的因素。與早期的超導體的損失中脫穎而出，特別是損失的控制方案的轉移。

Superconductive Whereas "ordinary" or metallic superconductors usually have transition temperatures (temperatures below which they superconduct) below 30 K (−243.2 °C), and must be cooled using liquid helium in order to achieve superconductivity, HTS have been observed with transition temperatures as high as 138 K (−135 °C), and can be cooled to superconductivity using liquid nitrogen. 而“普通”或金屬超導體通常具有轉變溫度（溫度低於它們超導）低於30度（-243.2℃）， 並且必須使用液態氦以實現超導被冷卻，高溫超導已觀察到轉變溫度高如138 K（-135℃），並且可以使用液氮冷卻到超導性。

SPMSM

Machine Concept The concept of a permanent magnet synchronous machine with superconductive stator winding (SPMSM) is based on a standard permanent magnet synchronous machine (PMSM) where the excitation is induced by magnets on the rotor of the machine. The stator consists of several superconductive windings which are powered by ac current. The windings are separated from the back iron of the machine and the rotor by means of a cryostat (see Fig. 1). 機械結構 永磁同步機的有超導定子繞組（SPMSM）的概念是基於在激磁感應磁體上的轉子 標準永磁同步電機（PMSM）。 定子是由交流電供電的多個超導線圈。繞組被從機器和轉子的背鐵以低溫恆溫器的裝置（參照圖1）隔開。

PMSM Equations The well-known stator flux components in the rotor based coordinate system (d/q-system) are as follows: For the PMSM in the d/q-frame the resulting rotor based stator voltage equations are 永磁同步馬達方程式 在基於坐標系統（D/ Q系統）的轉子的公知的定子磁通方程式如下： Sd定子 sq轉子 對於在d/q框架所產生的基於轉子定子電壓方程 是永磁同步電機 其中ω是電氣角速度和Rs是定子電阻。

PMSM Equations The first terms of (2) are the voltage drops over the stator resistance Rs. The second terms represent the voltage drops over the assigned inductances, and the last one stands for the voltage sources. The voltage sources form, together with the respective currents, the electric output power of the machine 圖2的第一項是電壓下降在定子電阻R s。 第二項表示電壓下降通過指定的電感，和最後一個手段的電壓源。電壓源的形式，連同相應電流，機器的電輸出功率

PMSM Equations The scaling of Pel with 3/2 results from the amplitude normalized space vector calculation. With the simplification that friction does not exist in the system the internal torque Mi is equivalent to the mechanical torque Pel與3/2為振幅歸空間向量計算的比例結果。 與摩擦不存在於系統中的簡化內部轉矩Mi是等同於機械轉矩 P為極數

PMSM Equations Depending on the electro mechanic layout of the machine the inductance ratio Ld/Lq can vary. For Ld/Lq = 1 or isd = 0 the internal torque is 根據機器的電感比Ld/Lq可以變化的電機械佈局。 對於LD/ LQ-=1或ISD=0內部轉矩

PMSM to SPMSM Transfer The variables are the resistance, the inductances and the flux of the permanent magnets. The inductance of the superconductive stator windings shows nearly the same behavior as with normal conductive material Also the flux of the permanent magnets is not influenced by the superconductor. At standstill the current is in the windings is a DC value and it is mainly dominated by the contact circuit resistance between the normal conductive supply and the superconductive windings. In normal ac operation the resistance depends on the electrical frequency, the flux of the permanent magnets and the current. A detailed explanation is given in chapter 4. PMSM到SPMSM的轉移 變量是電阻，電感和永久磁鐵的磁通。 超導定子繞組的電感顯示幾乎相同的行為與正常導電材料另外的永久磁鐵的磁通不通過超導體的影響。 在靜止時的電流是在繞組是一個直流值，它主要是佔主導地位的正常導電電源和超導線圈之間的接觸電阻電路。 在正常的交流操作的阻力取決於電頻率，永久磁鐵和電流的通量。詳細解釋見第4章。

LOSSES IN THE MACHINE 機械損失

The main losses in the machine are: • AC losses in the superconductor. • Iron losses in the back iron and in the stator teeth. • Iron losses in the magnet supporting structure of the rotor. • Cryostat losses. • Friction losses.

The ac losses can be divided in four different types: • Hysteresis losses. • Coupling losses. • Eddy current losses. • Ferromagnetic losses. AC損耗可以在四種不同類型可分為： •磁滯損耗。 •耦合損耗。 •渦流損耗。 •鐵磁損失。

The hysteresis losses are generated directly in the superconductor layer and are based on the magnetic flux. If the flux is generated by the superconductor itself, the hysteresis losses are known as “current transport losses.” When an external magnetic source is responsible for the flux the losses are called “magnetization losses.” 磁滯損耗是直接在超導體層中產生，並且基於磁通上。 如果是由超導體本身產生的磁通，磁滯損耗被稱為“當前的傳輸損耗”。 當外部磁源是負責磁通的損失被稱為“磁化損失”。

A superconductive tape consists of several layers A superconductive tape consists of several layers. Between these layers resistance coupled boundary layers appear. The boundary layers can exist between superconductive layers and between normal conductive materials. The impact of the current flows through these boundary layers is called coupling losses. 超導體由一層一層相疊成。 之間的這些層的電阻加上邊界層出現。 該邊界層存在於超導層之間的和正常的導電材料之間 電流流過這些邊界層的損耗被稱為耦合損耗。

Especially the “current transport losses” are influenceable by the power electronics. The dependencies of the transport current losses per volume and cycle in thin strips [8] are 特別是超導體的傳輸損失，對於電路的影響很大 Ic是臨界電流 imn是標準電流大小

OPTIMIZED CURRENT SHAPE 優化電流波形

In the case of a SPMSM it is useful to establish a resistance Rsc as a function of derivation and the instantaneous value of i(t) 在一個SPMSM的情況下，它建立一個電阻的AAA作為推導函數和XXX的瞬時值是有益 其中c是常數，取決於超導線圈的設計。

In general, the dissipated power is defined as the mean value over the period T of the instantaneous power p(t) 在一般情況下，耗散功率被定義為瞬時功率p(t)的週期T的平均值

Together with (7) the resulting dissipated power Ploss is The general equation (9) represents the dissipated power in the superconductor as a function of the current i(t) and a material- /geometry based constant c. 耗散功率Ploss 公式（9）代表的耗散功率在超導體作為電流i（t）和一個材料 - /幾何基於常數c的函數。

Dependence on the Current Shape In the case of a sinusoidal current the following losses are calculated in accordance to equation (9) 依據當前狀態 在一個正弦電流的情況下，下面的損失計算根據等式（9）

Dependence on the Current Shape The same behavior results from the microscopic loss calculation in (6). The equations referring to the triangular and rectangular shaped current types are solved following the same principle All three types of current deliver exactly the same loss dependencies. For the validation of the approximation theory of (7) with the results from (10) and (11), some loss measurements at superconducting coils were carried out. 從微損失計算相同的行為的結果（6）中。按照相同的原理參照三角形和矩形形狀的當前類型方程 所有這三種類型的電流提供完全相同的損失依賴關係。對於（7）與來自（10）和（11）的結果，證明了超導線圈進行的損耗測量在近似理論的正確性。

Loss Measurement at SC-Coils The losses in the superconducting coil are measured by means of an electrical setup [10]. The high-speed data recorder HBM GEN3i with a high precision current transducer handles the power calculation. 測量超導體線圈的損耗 在超導線圈中的損耗通過電設置[10]的方法測量的。高速數據記錄儀HBM GEN3i具有高精度電流傳感器處理功率計算。 [10]測量和傳輸交流損耗的計算，在第二代高溫超導扁平線圈 材料 絕緣層的厚度 內部線圈內徑 外徑 匝數

Loss Measurement at SC-Coils With a fit of parameter c, the equation (10) gives a good approximation of the losses. For low currents, equation (10) delivers lower losses than the measurements. The inaccuracy of the measurement heavily influences the results in the low current area. 圖為每個週期標準化損失相對於電流的大小。 黑色線是公式（10）給出的損耗的良好近似。但對於低電流。測量的精準度很大地影響。

Loss Measurement at SC-Coils At a fixed operation point of 35 A the losses of the superconductor, which is powered with a rectangular shaped current, are 66% and the sinusoidal are 40% smaller than the losses generated by the triangular shaped current. 可以清楚地看到，在此表示的損失是不同的。這是由於這樣的事實，即在RMS值取決於電流的形狀。 三角形電流提供最高和矩形狀的最低損失。正弦型是在兩者之間。在這個曲線圖還等式（10）給出的損耗對於不同的電流形狀的良好近似。 在的超導體，其供電用rectangularshaped電流的35 A中的損失的固定操作點，是66％，而正弦比由三角形電流產生的損失小40％。

Optimization Criterion Together with equations (3) and (4), which show that the output power of the SPMSM depends on the RMS value of the current, and the equations (10) and (11), where the losses in the superconductor depend on the magnitude of the current, this results in an optimization criterion. For the maximum output power at lowest losses it follows: 在超導體的損耗取決於幅度的電流，因此導出一個優化準則。為最大輸出功率在最低損失它如下：(在電流的RMS值)

CONTROL STRATEGY & CONCLUSION 控制策略

Optimized Current Waveform This condition strongly restricts the possibilities of creating a suitable current waveform for this application. The induced voltage of the SPMSM has to be a trapezoidal waveform. In order to ensure a constant torque, the current waveform should be an intermittent rectangular signal. 優化的電流波形 這個條件強烈限制了創造了此應用的合適的電流波形的可能性。該SPMSM的感應電壓必須是一個梯形波。為了確保恆定的扭矩，電流波形應該是一種間歇的矩形信號。

Optimized Current Waveform

Examination of the Control Performance Fig. 10 can be seen that the system behavior consisting of the power electronics, the SPMSM and the control strategy is stable. Also, the step response shows good results. The output power is nearly constant whereby the torque of the machine also has to be constant at a given speed. 測試的控制性能 啟動程序 空轉 扭矩步進穩態運行 圖。10可以看出，該系統行為構成的電力電子技術，所述SPMSM和控制策略是穩定的。另外，步進響應顯示了良好的效果。輸出功率為幾乎恆定，由此在機器的扭矩也必須恆定在給定的速度。

Examination of the Control Performance The loss reduction depends on the utilization of the superconductor and the topology of the power electronics. In this case the loss reduction is 減少損耗取決於超導體的利用率和功率電子的拓撲結構。在這種情況下，減少43%的損耗

CONCLUSION In this contribution the machine model transfer from a normal conductive PMSM to a superconductive SPMSM is shown. A new approach of superconductive resistance dependencies is given and verified with measurements on a superconducting pancake coil. The obtained optimization criterion is transposed to a new control strategy for superconductive permanent magnet synchronous machines. The ac losses are reduced by up to 43% depending on the topology of the power electronics and the operating point in comparison to a normal sinusoidal control strategy. 在這方面的貢獻從正常導電PMSM機器控制方法轉移到到SPMSM。 超導體依賴的新方法，並給出與超導扁平線圈測量驗證。 所獲得的最優化準則被調換到了超導永磁同步電機一個新的控制策略。交流損失減小到43％

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