Dissertation Defense Compensation of Electric Arc Furnaces Based

Dissertation Defense Compensation of Electric Arc Furnaces Based on La. Grange Minimization by: Leonard W. White May 7, 2012

Introduction Electric Arc Furnaces (EAFs) are among the largest loads connected to the gird. They are disruptive to the grid and are generally compensated – Static Compensators (STATCOMs) being the most common equipment used. The standard compensation strategy uses the Clarke transformation to derive the compensation values. A detailed look into the operation of the compensation systems reveals a different, and more effective, compensation strategy is available. During the following presentation, we will: • Review the operation of, and problems with, the Clarke transformation as applied to EAFs. • The particular nature of EAF waveforms. • Develop the La. Grange minimization compensation strategy. • Review two operating EAFs, one without compensation. • Develop and validate accurate EAF and STATCOM models. • Compare and contrast the dq 0 compensation scheme with the La. Grange schemes on an identical model platform. May 7, 2012 Dissertation Defense 2

The Clarke Transformation: The Clarke transformation ‘converts’ a 3 -phase system into an equivalent 2 -phase system. It was developed in 1932 by Edith Clarke. It works by projecting 3 -phase values – either voltage or current – onto a set of orthogonal axes. The d axis is aligned with the Va axis of the original system. The Vb values and the Vc values are each projected onto the d and q axes and summed with the other projected values on that axis. The system does not have to be balanced for the transformation to be applied – as shown here: If the system is balanced, there is no residue, that is, the d and q values are all that you get. If the system is not balanced, there is a residue, called the “zero” or 0 component. Mathematically, the transformation looks like this: May 7, 2012 Dissertation Defense 3

The Clarke Transformation, Con’t: These elements are the sine and cosine values of the 120 angles assumed to be between the vectors. Or The coefficient is added so that the power represented by this system is invariant across the two spaces. There is an inverse transformation that reverses the operation. The transformation is well-known and finds application, especially where there is need to decouple real and reactive power. . . Which can be easily done to the transformed variables with simple operations. . Let’s take a look at the output of the Clarke transformation when the input is an unbalanced 3 -phase set of currents. . May 7, 2012 Dissertation Defense 4

The Clarke Transformation, Con’t: Allow the inputs to be the following values: The example set is composed of currents; a voltage waveform set would look the same. , i. e. , there is no loss of generality. The following operations will be performed: 1. Transform the set, point-by-point, into dq 0 space. 2. Plot the transformed set of values, Id , Iq , and I 0 in time domain on the same set of axes. 3. Examine the plotted values for meaning. May 7, 2012 Dissertation Defense 5

The Clarke Transformation, Con’t: The direct axis component is in black. Iq Id The quadrature axis component is in red. The zero component is in green. If we also have a dq 0 set of voltage waveforms we know the following is true at any instant of time from instantaneous power theory: And for the power in the zero component: I 0 At any instant of time we know the dq 0 values of I and V. We also know the relationship between the dq values of I and V. So we can compute P and Q. . We do not know the value of And now, the problem: May 7, 2012 . . And there is no way to determine it ! Dissertation Defense 6

The Clarke Transformation, Con’t: The implications are the following: § We cannot compensate for zero component current using dq 0. § We cannot compensate for zero component power using dq 0. Power involves the product of voltage and current and, since zero component voltage is typically quite small, power is not a serious issue. Compensating for zero component current is a different problem and one of extreme interest in the operation of Electric Arc Furnaces. A brief summary: A Clarke transformation based compensation strategy will work quite well in any application where the unbalance components are small. We can’t extract complete compensation information with the use of the dq 0 approach. It is less than ideal when there are significant levels of unbalance in the system. Mathematically, when the Clarke transformation is employed in a compensation scheme a Degree of Freedom has been lost. Once lost, it can not be recovered. . Aside: Two additional degrees of Freedom are lost if the angles between the waveforms is not 120. This is a relatively minor issue. May 7, 2012 We will look at this in a more detail when we compare dq 0 to La. Grange compensation. Dissertation Defense 7

The Clarke Transformation, Con’t: It does not matter if the system is a 3 -wire or a 4 -wire system. § In one case the unbalance current circulates. . . § In the other it returns through a common connection. . . The point is that the unbalance current is simply not accessible for compensation by use of the Clarke transformation. Next, we will take a detailed look at EAF waveforms …. And, as we will see, these waveforms do not match many of the fundamental constraints that were applied in the development of the Clarke transformation …. May 7, 2012 Dissertation Defense 8

EAF Waveforms: Kobe-Weiland Copper Accurate data from EAFs is difficult to obtain. The subject EAF is used to melt copper for recycle; it is rated at 4 MW, with a dedicated 88 k. V transmission line used to supply the EAF only. The input voltage to the EAF transformer is 12. 47 gnd. Y/7. 2 k. V. Real-time metering data were obtained from the EAF, using a Fluke 443. Eight separate data sets, each containing: Two (2) full cycles with a resolution of 2. 4 electrical: § Four (4) voltages – Each phase plus neutral to ground. § Three (3) currents – Each phase. Data captured in this way is extremely reliable and provides hard information about actual EAF operations. The following is a sample of captured EAF data: May 7, 2012 Dissertation Defense 9

EAF Waveforms, Con’t: Current Waveforms Voltage Waveforms Data presented is from data set No. 8. All captured data sets are ‘similar. ’ When the current waveforms are summed we see that there is a considerable amount of unbalance current …. May 7, 2012 Dissertation Defense 10

EAF Waveforms, Con’t: The degree of current unbalance can be seen by looking at the individual ABC waveforms plus the sum plotted on a common axis set: We’ll see this plot later. . Again, all captured data sets are ‘similar. ’ May 7, 2012 Dissertation Defense 11

EAF Waveforms, Con’t: The overall relationship of arc voltage vs. arc current can be seen in the following plots …. These plots are similar to lissajous figures and clearly show that the v-I relationship is complex. The multiple crossings indicate the presents of harmonic content. Overall, the relationship can go from lead-to-lag and vice-versa several times in a cycle. So we see that, in general: May 7, 2012 “lead” and “lag” are steady state concepts; the idea here is that the voltage: current relationship changes over a single cycle. Dissertation Defense 12

EAF Waveforms, Con’t: § The waveforms are non-sinusoidal. § The waveforms are non-periodic. § The waveforms have no obvious symmetry. § The peak values of the waveforms are different from phase-to-phase. § The peak values of the waveforms are different from cycle-to-cycle. § There are multiple zero-crossing points within one cycle. § The waveforms do not originate from a system in the “steady-state” as this is usually defined. § The voltage/current waveforms vary widely in their lead/lag relationship. i. e. , they are not identical from cycle-to-cycle Current waveforms Conclusion : § Any analysis that depends on assumptions contrary to the above will be flawed. § Any compensation scheme based upon assumptions contrary to the above will be not provide the expected corrections. May 7, 2012 Dissertation Defense 13

La. Grange Minimization: Consider another approach to the problem of instantaneous power: Partition currents into two parts: (1) A part that contributes to only ‘Active’ power. (2) A part that contributes to only ‘Passive’ power. The concept is to minimize the active currents while guaranteeing that the passive currents do not contribute to active power over all three phases. That is: Minimize: Subject to: May 7, 2012 Dissertation Defense 14

La. Grange Minimization, Con’t: Introduce a La. Grange operator, , and rewrite the current and constraint equations as a combined set: The object is to determine such that: First, expand F to obtain: May 7, 2012 Dissertation Defense 15

La. Grange Minimization, Con’t: In matrix format: Solving the set for gives: From which the passive currents are: And the active currents are: May 7, 2012 Dissertation Defense 16

La. Grange Minimization, Con’t: Some comments: 1. No assumptions about the nature of the input waveforms were made by the derivation method. 2. The solution is unconstrained mathematically, but there may be constraints imposed by the electrical topology and Kirchhoff’s Laws. 3. There is a second derivation that involves the neutral conductor for application in wye connected systems where there is neutral control. Next, confirm the validity of the method with the two methods of computing instantaneous power. Power under this method is defined as: For reference, the other two methods of expressing the same power are: The following plot shows all three for the same 3 - , V-I, input data set May 7, 2012 Dissertation Defense 17

La. Grange Minimization, Con’t: Black Pen - Widest Yellow Pen – Middle Red Pen - Narrow instantaneous power is the same at all points of the data set The implication is that if we remove the passive current from the input current waveform the overall input power will remain unchanged. May 7, 2012 Dissertation Defense 18

La. Grange Minimization, Con’t: In summary: 1. Complex power under La. Grange is the same as for either the ABC or dq 0 power theories. 2. La. Grange minimization requires no real power. 3. For a balanced set of current waveforms La. Grange minimization provides equivalent compensation to dq 0. 4. For a un-balanced set of current waveforms La. Grange minimization provide optimal compensation as based on the derivation method. The next step is to devise a validation method and compare La. Grange to dq 0 …. May 7, 2012 Dissertation Defense 19

Validation of La. Grange Minimization: The original concept was to locate an EAF with STATCOM compensation and to perform the following steps: § Duplicate the physical STATCOM in PSCad § Duplicate the STATCOM control system in PSCad. § Collect voltage and current data from the EAF. § Apply the model using the dq 0 compensation technique. § Apply the model using the La. Grange compensation technique. § Compare and contrast the two techniques …. Ameri. Steel in Charlotte, NC The following was accomplished: § A steel plant was located with a 33 MVA EAF and a 20 MVA STATCOM. § A non-disclosure agreement was executed between the company and NCSU. § Site visits were made; unprecedeted access was given to all EAF and STATCOM documentation. And then a problem developed: The plant Owner does not have the compensation scheme or control system documentation. Further, this information was not available from the STATCOM manufacturer (ABB). May 7, 2012 Dissertation Defense 20

Validation of La. Grange Minimization, Con’t: In the face of this problem, a new validation scheme was devised: § Duplicate the physical STATCOM in PSCad. § Devise a control scheme that would work with both dq 0 and La. Grange. § Use an EAF model. § Apply the model using the dq 0 compensation technique. § Apply the model using the La. Grange compensation technique. § Compare and contrast the two techniques …. This was accomplished …. § Some comments: The original idea was to use a ‘canned’ STATCOM model but there were several problems. No information about the internal workings of ‘canned’ models. The models use the Clarke transformation as a part of their internal control scheme. Aside: For La. Grange to be valid the dq 0 transformation must be avoided anywhere in the scheme…. § The PSCad EAF model has serious problems that keep it from meeting the validation requirements of the work. May 7, 2012 Dissertation Defense More a bit later …. 21

The EAF and EAF power supply system: The following diagram shows the overall arrangement of the EAF in relation to the utility system and compensating STATCOM: Utility Point of Delivery (POD) EAF & EAF transformer Utility transmission system Filter @ carrier frequency Utility Power Factor correction capacitor(s) STATCOM /w DC link Starting with the STATCOM model. . May 7, 2012 Dissertation Defense 22

A NPC STATCOM model So – a STATCOM model and an EAF model were written from the basic concepts. Both were then validated. First the STATCOM model …. The starting point was the electric utility point of delivery. Harmonic content information was obtained - at a time when the EAF was not in operation. the highlighted harmonics are those that were at lease 0. 1% of the total magnitude. these input harmonics were scaled to match the delivery point voltage. . . . and then duplicated in the utility source model. . May 7, 2012 Dissertation Defense 23

A NPC STATCOM model, Con’t: The result was the final PSCad model of the utility source: Switching is included so that the model can either provide a pure sine wave – for initial testing – and the actual more complex waveform for final model validation. Overall, the system looks like this: . . . The next step is the STATCOM itself. . May 7, 2012 Dissertation Defense 24

A NPC STATCOM model, Con’t: The inverter section of the STATCOM is a standard Neutral Point Clamped topology. . Component values are taken from the documentation for the actual plant. . Gates are controlled by use of a standard two-tier, phase-locked, Pulse Width Modulation scheme with the carrier at 1, 500 Hz. Same as Ameri. Steel STATCOM May 7, 2012 Dissertation Defense 25

A NPC STATCOM model, Con’t: Output of the carrier generator looks like this: The relations that are used to generate the gating signals is: This is at reduced frequency (600 Hz) to better display the waveforms Using this carrier with a simulated reference waveform. . May 7, 2012 Dissertation Defense 26

A NPC STATCOM model, Con’t: An early test of the gating signals – at reduced carrier frequency for better visualization – looked like this: For all three phases, the overall gating looks like this: A master control line is included to allow the STATCOM to be turned on/off at specific instants in time. . May 7, 2012 Dissertation Defense 27

A NPC STATCOM model, Con’t: The overall current regulator looks like this: This is the value of the series inductance This scales the actual voltage back to the reference voltage There’s one of these for each of the three phases. . May 7, 2012 Dissertation Defense 28

STATCOM model validation: In order to validate the model it is necessary to direct the STATCOM to deliver positive and negative reactive power at the rating of the STATCOM. . Starting with the dq 0 matrix equation, solved for currents. . And forcing P to be zero, gives: Which is incorporated into the following compensation strategy: Desired reactive power from the STATCOM Desired phase currents that will accomplish this goal. . May 7, 2012 Dissertation Defense 29

STATCOM model validation: Directing the model to deliver -20 MVA then switch to +20 MVA produces: Power waveforms: Note the accuracy of the directed output …. Voltage & current waveforms : May 7, 2012 Dissertation Defense 30

STATCOM model validation: And, the other direction, from +20 MVA to -20 MVA: Power waveforms: Voltage & current waveforms : May 7, 2012 Dissertation Defense 31

STATCOM model validation: The STATCOM model has been validated. . In summary: § The STATCOM model produces negative reactive power at its design rating. . § The STATCOM model produces positive reactive power at its design rating. . § The STATCOM model will smoothly transition between the two extremes in either direction. . Next, onward to the EAF arc model. . May 7, 2012 Dissertation Defense 32

The EAF model: The existing PSCad EAF model is unsuitable for the work because: § It’s a 3 -phase model. . § It provides equal loading on all phases. . § It is undocumented. . Originally used for flicker studies. It does not provide the unbalance that we need to demonstrate the advantages of the La. Grange method. . The PSCad EAF model created as a part of this work overcomes all these disadvantages. The original model is based on the following non-linear differential equation set: The base publication references an harmonic domain solution but this was not actually used in the solution of the set. These equations were solved by several different methods in Mat. Lab and then, once the final solution method was chosen, in PSCad. . May 7, 2012 Dissertation Defense 33

The EAF model, Con’t: The Mat. Lab solution attempts to duplicate the work of the original source publication with a method other than a harmonic domain solution. . The following solution methods were used: § § § Euler’s method Runge-Kutta, 4 th order Modified Euler Method (Heun’s Method) In the publication, the model is driven by a sinusoidal current source. . Note that this is not the way a “real” arc functions. More later. . The Runge-Kutta and the Modified Euler method both provided results that identically matched the referenced publication. . Reasons: The Euler method did not provide accurate results – as expected. . 1. Fast. . 2. Sufficient accuracy – a 2 nd order solution. . The Modified Euler method was selected as the best solution method. . 3. Fully discrete. . 4. Does not require interpolation of values at each step. . May 7, 2012 Dissertation Defense 34

The EAF model, Con’t: The results from the Mat. Lab solution: These results identically match those from the source publication. . Again, this solution is driven by a pure sine wave. . Onward to the PSCad solution. . May 7, 2012 Dissertation Defense 35

The EAF model, Con’t: The PSCad solution drives the equation set with the actual current through the arc. The arc current is determined by application of the circuit constraints. . This is more difficult. A flow chart of the final solution looks like this: Provisions are made for the introduction of Gaussian noise. § Gauss noise will be useful for future work, especially with flicker analysis. . The results of the PSCad solution look like this: May 7, 2012 Dissertation Defense 36

The EAF model, Con’t: The results from the PSCad solution: Note the differences in the Voltage, Current, and Arc Radius waveforms. . May 7, 2012 The V vs. I relationship remains similar to the original plot. . Dissertation Defense 37

The EAF model, Con’t: A 3 -phase validation was performed. . For this validation, 3 copies the following circuit were used. The arcs are wye-connected. Each source is phase shifted by 120 from the other: The line currents looked like this: Comments: Which is very close to the original on-site data captured from the working 4 MW Electric Arc Furnace at Kobe. . 1. The Kobe data scale has been reduced so that the size is closer to the model graph. . 2. No Gauss noise has been added to the model. . 3. The model has been submitted to IECON 2012 for publication as “A single phase PSCad electric arc furnace model. ” The EAF model is ready to applied to the dq 0 to La. Grange comparison, but first. . May 7, 2012 Dissertation Defense 38

The EAF model, Con’t: A RSCad solution: This is not a part of the present work. It was completed by Saman Babaei as an independent validation that the solution method can be programmed in RSCad and used on the Real Time Digital Simulator (RTDS). As an aside, the source for this simulation is somewhat stiffer than the source that was used for the PSCad model. . Note the differences in the Voltage and current waveforms. . May 7, 2012 The V vs. I relationship remains similar to the original plot. . Dissertation Defense 39

The dq 0 to La. Grange Comparison: To compare the two compensation methods the STATCOM must be programmed to remove reactive power using, (1) the dq 0 approach and then, (2) the La. Grange approach. . The equations for the dq 0 approach are the following: With Which gives: Note the ‘ 0’ component !!!! Which reduces to the following implementation: May 7, 2012 This is the standard dq 0 compensation approach. . Dissertation Defense 40

The dq 0 to La. Grange Comparison, Con’t: The matrix equation for the La. Grange passive current is the following: Which expands to: Which reduces to the following implementation for passive currents: May 7, 2012 Dissertation Defense 41

The dq 0 to La. Grange Comparison, Con’t: This is the La. Grange compensation approach. . Both these circuits were implemented in the same PSCad model, with a switching arrangement to select between the two. . May 7, 2012 Dissertation Defense 42

The dq 0 to La. Grange Comparison, Con’t: The remainder of graphs are presented with the following timing: § The model starts at time t=0. § The STATCOM starts at time t=0. 2 S with dq 0 compensation § The STATCOM switches at time t=1. 20 S from dq 0 to La. Grange compensation. First, a test to see how the model deals with a fixed 20 MVA reactive load: The ripple gradually vanishes as the dc offset decays. . STATCOM turns on May 7, 2012 Switch from dq 0 to La. Grange Dissertation Defense This confirms that both compensation schemes are operating properly. . 43

The dq 0 to La. Grange Comparison, Con’t: Next, a test showing the EAF load. . This graph shows power delivered by the utility: STATCOM turns on Switch from dq 0 to La. Grange A smoothed plot will show the changes more clearly. . The real power from the utility increases with La. Grange compensation. The reactive power from the utility decreases with La. Grange compensation. May 7, 2012 Dissertation Defense 44

The dq 0 to La. Grange Comparison, Con’t: Smoothed power from the utility: STATCOM turns on Switch from dq 0 to La. Grange Amount of the real power increase: 500 k. W (1. 6%) This clearly shows the advantage of the La. Grange compensation scheme. . Amount of the reactive power decrease: 1 MVA (11%) Taking a detailed look at the power increase. . May 7, 2012 Dissertation Defense 45

The dq 0 to La. Grange Comparison, Con’t: A detail of the power increase: The power is not only higher but it also appears to be smoother. . STATCOM turns on Switch from dq 0 to La. Grange To put this into perspective, the increase translates into approximately 27 tons/day of additional steel production. . The implication is that La. Grange compensation will make the arc more stable as compared to dq 0 compensation. . Taking a look at the utility line voltage. . May 7, 2012 Dissertation Defense 46

The dq 0 to La. Grange Comparison, Con’t: A detail of the Utility line voltage (Phase A, RMS): STATCOM turns on Switch from dq 0 to La. Grange The line voltage appears to be a bit smoother under La. Grange control. . The line voltage actually falls a bit when La. Grange is applied. This is due to the relatively low X/R ratio of the entire system – around 3: 1 – and is a reflection of the increase in real power delivery. The increased ‘smoothness’ of the line voltage implies that flicker will probably be lower under La. Grange control. . Taking a look at the input current to the system. . May 7, 2012 Dissertation Defense 47

The dq 0 to La. Grange Comparison, Con’t: A detail of the Utility line current fundamental: The line current appears to be smoother under La. Grange control. . STATCOM turns on Switch from dq 0 to La. Grange A look at the harmonic content will reveal a slight decrease in 3 rd harmonic content and no significant increases elsewhere. . Taking a look at the power to the arc itself. . May 7, 2012 Dissertation Defense 48

The dq 0 to La. Grange Comparison, Con’t: A detail of the powers to the arc: STATCOM turns on Switch from dq 0 to La. Grange The real power to the arc increases by the same amount as the power delivered by the utility. . The reactive power to the arc increases; this additional reactive power is delivered by the STATCOM. . taking a look at the STATCOM. . May 7, 2012 Dissertation Defense 49

The dq 0 to La. Grange Comparison, Con’t: A detail of the STATCOM output: Reactive power increase matches increased reactive power to the arc. . Note that STATCOM is delivering rated MVA…. Average real power is zero for both schemes. . STATCOM turns on Switch from dq 0 to La. Grange taking a look at the STATCOM DC Bus. . May 7, 2012 Dissertation Defense 50

The dq 0 to La. Grange Comparison, Con’t: A detail of the STATCOM DC Bus: Minor shift in DC bus voltage. . Switch from dq 0 to La. Grange There is a bit more variability in the DC bus under La. Grange. . But the change in the DC component itself is very minor. A summary. . May 7, 2012 Dissertation Defense 51

Conclusions: The following conclusions are drawn from this work: 1. The dq 0 compensation scheme, as based on the Clarke transformation is valid where the system is balanced; when the system is not balanced the dq 0 scheme does not compensate for all currents. 2. The La. Grange compensation scheme delivers optimal compensation currents independent of balance of currents or voltages. 3. The La. Grange compensation scheme delivers more energy to the arc than does dq 0 compensation. 4. The La. Grange compensation scheme delivers more consistent power to the arc than does dq 0 compensation. 5. The La. Grange compensation scheme reduces the magnitude of the input current to the system. 6. The La. Grange compensation scheme reduces the variability of real power to the arc. 7. Under balanced conditions the dq 0 and La. Grange compensation schemes give the same results. 8. The real power delivered by either the dq 0 or the La. Grange compensation scheme is zero. 9. Physically the equipment used by both the dq 0 or the La. Grange compensation schemes is identical. Only software changes are needed to switch between the two schemes. May 7, 2012 Dissertation Defense 52

Specific Contributions of the Work: 1. Provides a detailed theoretical analysis and comparison of the Clarke-based dq 0 compensation scheme as compared with the La. Grange approach. 2. Demonstrated why the Clarke-based dq 0 scheme does not and can not provide complete compensation in unbalanced situations. Such situations are the norm for EAF operation. 3. Provides theoretical proof demonstrating that under balanced conditions the ‘passive current’ of La. Grange is equivalent to the ‘reactive current’ of the classical approach. 4. Developed the equations for the La. Grange minimization method for use when compensator neutral control is available. 5. Provides a realistic, practical, validated working model of an EAF that can be used in any configuration in a compensation model. 6. Adapts theoretical La. Grange compensation method to a validated, working, compensation strategy. 7. Clearly demonstrates the superiority of the La. Grange compensation approach over the Clarke-based dq 0 compensation scheme in a validated one-on-one comparison. May 7, 2012 Dissertation Defense 53

Additional Work Proposed: • Apply the La. Grange technique to a RTDS, as it is unlikely that a manufacturing plant will allow a shutdown for software modifications without real time modeling. Alternately, a joint effort with a STATCOM manufacturer and a steel mill might prove effective. • It appears that the La. Grange approach will also improve flicker. Unfortunately, no IEC 61000 -4 -15 validated flickermeter model is available for PSCad. Such a model should be written and the possible improvements to flicker be evaluated. Aside: this work has already begun. There already two flickermeter papers that have come from this work: May 7, 2012 [1] L. W. White and S. Bhattacharya, "A Discrete Matlab - Simulink Flickermeter Model for Power Quality Studies, " Instrumentation and Measurement, IEEE Transactions on, vol. 59, pp. 527 -533, 2010. [2] D. Fregosi, L. W. White, J. Watterson, and S. Bhattacharya, "Digital Flickermeter design and implementation based on IEC Standard, " in Energy Conversion Congress and Exposition (ECCE), 2010 IEEE, 2010, pp. 4521 -4526. Dissertation Defense 54

Questions ?