Attachment 1_Appendix 1_Report DIII-D 11142021.pdf

PPPL-General Atomics Collaboration

DIII-D Neutral Beam High Voltage Regulation Issue

Phase I - Steady State Model

Rev. 0

November 14, 2021

Prepared by _________________________________________ Bogdan Proca

Power Systems Engineer, PPPL

Reviewed by _________________________________________ John Dellas

Head, Power Systems, PPPL

Reviewed by _________________________________________ Alex Nagy

Head PPPL Technology Collaboration Office, PPPL

Approved by _________________________________________ Craig Burkhart, Director of Engineering, PPPL

Introduction:

The Neutral Beam (NB) Systems, which are used in DIII-D Fusion Energy Research Facility located at General Atomics, are desired to be operated with higher beam voltages. The current beam voltages are varied between 40 kV and 81 kV using a 4CPW1000KB tetrode tube to highly regulate and provide rapid turn on/turn off capability to the beam power [1]. To provide improved operation the input voltage to the tetrode is set to an optimum value by a tap changing autotransformer. This is set at the beginning of the shot and is not changed during a shot. This can become a problem with power line sags when many beams and gyrotrons are being fired in one shot, with over dissipation in the beginning of the shot and insufficient voltage later. The problem will become worse with attempts to operate beams from 85 to 93 kV. This will require some modifications to deal with increased sag and high voltage hold off of the tetrodes in highly modulated beams.

In this work a Simulink model of the NB electrical system is developed, simulation cases are run and results are analyzed in order to identify and understand the cause of the voltage regulation issue.

Preliminary recommendations are made for possible solutions.

Work Description and Deliverables:

In order to evaluate voltage drop and current levels at different points within the NBS (Neutral Beam System), considering time aspects and operating modes, two models can be created using Simulnk software. The scope of work of phase 1 is limited to the development of the first model and the steady-state and slow power variations analysis (several beam lines will be switch on/off alternatively for 5s).

The phase 2 scope will be focused on the development of a transient analysis model to study the dynamic behavior of the neutral beam lines during fast power modulation.

The first model called “Steady-state NBS model” is used to check operating points (voltage drop versus different current load levels with several beam lines in operation). This model does not include the details of the rectifier diode commutations or a detailed model of the DC power cables.

This model is used to run a realistic “worst case” loading scenario to identify any power system issues at macro level.

Based upon the worst case run defined with the results of the Steady-state NBS model (Phase 1), the detailed model for the DC side system will be used to evaluate under voltage and overvoltage limits for the equipment and protection settings.

Phase 1 Scope:

The Phase 1 scope will develop a complete model of the NBS architecture using Simulink with computational time step of 1ms or less. All others systems (P> 1 MW) connected to the 138kV incoming feeder are modeled by a global lumped load.

The current sources are turned on for 1 second and turned off. Several cases with mixing and swapping of beam lines are evaluated. As an example, one case will consist of 4 sources firing out of phase with the second 4. In parallel, transformer T7 is pulsed from 0 kW to 1.5 MW. Also in parallel, load is added to the 12.47 kV line.

Deliverables

The deliverables for Phase 1 are:

• A complete “Steady-state NBS model” on Simulink software.

• This report describing the developed model based upon the input data and detailing the different case scenarios and summarizing the steady state analysis, slow power cycling and any initial findings identified from the worst case scenario.

System description

The following picture is a single line diagram of the neutral beam voltage system.

Figure 1 Single line diagram of the system

The entire system is supplied by a 138kV 3 phase power line from SDE&G with a short circuit power of 4574 MVA. There are two main branches connected to this line:

The NB power supplies

The NB power supply branch include 8 NB power supplies and various smaller loads (represented here as a lumped load). The following picture is a description of one NB power supply (it includes the T6 transformer that supplies all 8 NBPS):

Figure 2 Neutral Beam Power system

Transformer T6 supplies power to all the 8 NB circuits and the additional smaller loads. It is a 3 phase, 110 MVA 138kV/12.47 kV isolation transformer with a short circuit impedance of 8.3%. The transformer’s output is connected to a 10 kA bus through a 0.7 mH surge inductor.

The eight neutral beam power systems are connected through 225 A (00 AWG) power cables to the

12.47 kV Bus and 1200 circuit breakers.

The 12.47 kV is connected to the input of a tap changer autotransformer that can vary its output from 6.2-13.7 kV. There are two types of tap transformers:

- Universal Voltronics (UVC) that can vary its voltage from 6.2-13.7 kV ; these transformers are in the systems supplying the Neutral beams described as 30L, 30R, 330L, 330R (by their angular position)

- Transrex – that can vary its voltage between 6.2 – 12.47 kV ; these transformers are in the systems supplying the Neutral beams described as 150L, 150R, 210L, 210R

The tap changers are the main means of adjusting the voltage to the tetrodes. This voltage is adjusted prior to the pulse and not changed during the pulse.

The output of the tap changers feed step up transformers. The transformers are rated 11.86 MVA and have one 3 phase primary (Y connected) and two secondary (Y and Delta). There are three variants of transformers:

- The original UVC have a turns ratio of 13800V/41000 V and a series impedance of 9%; these are systems 30R and 330R

- The modified UVC have a turns ratio of 13800V/49000 V and a series impedance of 8%; these are systems 30L and 330L

- The Transrex have a turns ratio of 13800V/41000 V and a series impedance of 10%; these are systems 50L, 150R, 210L, 210R

The following table is a summary of the tap changer/ step-up combinations:

Identifier Type

Step up transformer Tap changer

Observation Max Vdc (no load) Impedance(%)

Tap normally used in operation

Impedance(%)

30L UVC 150 kV 8 5 3.6 rebuilt 30R UVC 125 kV 9 11 3.6 330L UVC 150 kV 8 5 3.6 rebuilt 330R UVC 125kV 9 11 3.6

150L Transrex 125 kV 10 11 4 150R Transrex 125 kV 10 11 4 210L Transrex 125 kV 10 11 4 210R Transrex 125 kV 10 11 4

Table 1 Tap-changer/step-up transformer parameters

The outputs of the step up transformers feed two diode bridges connected in series (for a 12 pulse configuration). In one of the two original systems, the manufacturer (UVC) has specified the output of the step-up/diode bridge as being 110 kVdc at no–load and 98 kVdc at 108 A DC.

The rectifiers have a filtering/bulk capacitor bank at their output. Its equivalent capacitance is 27 uF.

There are two high voltage coaxial underground cables (# 2 AWG) connect the capacitors to the tetrode and crowbar assembly. The assembly is shown in the next figure:

Figure 3 Tetrode assembly

There are also two series 1 ohm HV power resistors in series with the cables. The crow bar is connected in between the two resistors as shown in Figure 1.

The last elements prior to the load are the tetrodes. Their details are not included and they are simulated as current series in series with a resistance to simulate their own voltage drop.

The 480 Auxiliary Power Supplies System

The 480 V auxiliary power supply system is show in the next figure:

Figure 4 480 Auxiliary power supplies

Transformer T7 supplies power to the 480V auxiliary power supplies. It is a 3 phase 8 MVA, 138kV/480V tapped transformer with a short circuit impedance of 8.7% nominal (it changes with the tap being used).

The four power supplies are lumped into a single load for the simulation.

Steady-state NBS model

The system is modelled in Simulink (using the Power System Toolbox elements) as shown in the figure below:

Figure 5 Simulink Model of the NB system

The main elements and their parameters are shown below. All parameters reside in the file nb_ss_ini.m that should be run first to initialize the system. The main simulation is steady_state_nb.slx :

a. The 138 kV supply and connecting high voltage lines

The 138kV incoming line from SDE&G is the first element of the simulation. Based on its short circuit power (4574 MVA) and X/R(1.5) , it is modeled as a 2.22 ohm resistor in series with a 8.8 mH inductance.

The supply is modeled as 3 sinusoidal power supplies Y/N connected. Their nominal voltage is 138 kV, nominal frequency of 60 Hz and phase shifted 120 degrees from one another.

Figure 6 138 kV supply and high voltage lines

Figure 7 138 kV supply parameters

The high voltage supply lines are modeled as resistances in series with inductances and in series with each supply

Figure 8 138 kV line parameters

b. Transformer T6

Transformer T6 is the 110 MV step down transformer (138 to 12.47 kV) powering all 8 NB sources:

Figure 9 T6 transformer

It is modeled as a 3 phase Delta/Delta connected isolation transformer (the connection is irrelevant for this model).

Figure 10 Parameters of T6 transformer

c. Transformer T7 Transformer T7 is the 8 MVA step down transformer (138 to 480 V) powering 480 loads

Figure 11 T7 transformer

It is modeled as a 3 phase Wye/Wye connected isolation transformer (the connection is irrelevant for this model).

Figure 12 Parameters of T7 transformer

d. Lumped load on 480 line

The 480V lumped load is connected at the output of the T7 transformer. It can be turned on/off by adjusting the timing of the step switch feeding it (see the next figure).

Figure 13 Lumped load on 480V line

Figure 14 Structure of lumped 480V load

Its parameters are:

Figure 15 Lumped 480V load parameters

e. Lumped load on 12 kV line

The 12 kV lumped load is connected in parallel with the 8 NB systems. It can be turned on/off by adjusting the timing of the step switch feeding it (see the next figure).

Figure 16 Lumped load on 12 kV line

Figure 17 Structure of lumped 12 kV lumped load

Figure 18 Lumped 12 kV load parameters

f. The NB subsystems

There are 8 NB subsystems in parallel representing the 8 NB systems as shown in the following figure:

Figure 19 8 Parallel NB subsystems

Their individual structures are identical, but some of their parameters vary (for the tap changer and for the step-up transformers). The subsystems are labeled as they are referred to in the system schematic (Figure 1).

Figure 20 Internal structure of one NB subsystem (30L) g1. 12 kV power cables (include surge inductor)

Each neutral beam feeder is connected through a surge inductor, two power cable sets (3 lines, 225 A, #00 AWG) with a breaker in between make the connection to the tap changer transformer. They are modelled as a single RL conductor (the breaker is omitted).

Figure 21 12 kV power cables

Their parameters are:

Figure 22 12 kV power cable parameters g2. Autotransformer

The autotransformer is modeled as a 3 phase isolation transformer in which the input and output winding have a connection (Simulink convention).

Figure 23 Autotransformer

Its parameters are shown in the next figure.

Figure 24 Autotransformer parameters g3. Step-up transformer

The Step-up transformer is modelled as a 3 phase 3 winding transformer (input delta and outputs delta and wye).

Figure 25 Step-up transformer

Its parameters are shown in the next figure:

Figure 26 Step up transformer parameters g4. Rectifiers

The rectifiers are Simulink diode bridges with RC snubbers (10k resistance and infinite capacitance – for simulation stability). They have 1 miliOhm internal diode ON resistance and 10 Volt voltage drop.

Figure 27 Rectifiers

Their parameters are:

Figure 28 Rectifier parameters g5. Output capacitor

The output capacitor is modeled as a capacitor in series with an equivalent series resistance (ESR).

The ESR term also contains the current limiting resistor (150 Ohms):

Figure 29 Output capacitor

Figure 30 Capacitor parameters g6. High voltage cable (1000 ft cable)

The high voltage cable is modeled l as a R-L series element with a capacitor in parallel.

Figure 31 High voltage cable

Figure 32 High voltage cable R-L parameters

The capacitor parameter is:

Figure 33 High voltage cable capacitance parameters g7. One ohm resistors

Modeled as one resistors of 2 Ohm value (their value can be modified directly in the block).

Figure 34 One Ohm resistors g8. Tetrodes and load

The tetrodes and the load are modeled as a current source in series with a switch (the switch is turned on slightly before the current source – to avoid numerical instabilities).

Figure 35 Tetrodes and load model

The following elements are part of this model:

- The parallel resistance (rp) is used to represents no load currents .

Figure 36 No load resistance

Resistor MR is used for numerical stability; its value is hard coded as 1e6

Figure 37 Resistor MR

- Resistor MR resistance is modelling the drop across the tetrodes;

Figure 38 Resistor MR Resistance

- The switch is introduced to prevent instabilities of the current source (has no real impact on the simulation). It is shown in the next figure and it uses the Simulink defaults:

Figure 39 Ideal switch

- The time delay is used to insure that the switch is closed prior to the current source being turned on:

Figure 40 Time delay

- The current source block is shown in the following figure:

Figure 41 Current source block

The value of its current is determined externally (top diagram) by the following block:

Figure 42 Current source values and Its parameters are

Figure 43 Current source parameters

There are two current sources, allowing the simulations to run either as 8 simultaneous sources or as 4+4 phase shifted. The source profile is defined as two strings with the same number of elements. One string represents the x-axis (time) and the other represents the current value.

Parameters of steady-state NBS model

This section describes the parameters used in the NBS model. These parameters can be change to generate various simulations. All parameters reside in the file named nb_ss_ini.m

g. The 138 kV supply and connecting high voltage lines The line-line voltages are o Volts V_138=138000; %line-line voltage in volts

The parameters of the 138 kV lines were obtained from conversations with GA engineer are:

o Line resistance in Ohms : R_138_kV=2.22; resistance of the 138kV line in ohms o Line inductance in H: L_138_kV=8.8e-3; %inductance of the 138kV line in ohms

h. Transformer T6

Transformer T6 is the 110 MV step down transformer (138 to 12.47 kV) powering all 8 NB sources.

Most of its parameters were obtained from the nameplate of the transformer or from conversations with GA engineers, while some were assumed for typical transformers of that size (see below):

o Nominal Input Voltage in Volts (for turns ratio and PU calculations): T6_in_v=138000;

(from transformer plate) o Nominal Output Voltage in Volts (for turns ratio and PU calculations): T6_out_v= 12470;

from transformer plate o Transformer KVA rating: T6_kva=110e6; from transformer plate o Short circuit reactance in PU: T6_xc_short=0.083; PU impedance from transformer plate o No load losses as % of rating: T6_nl_loss=1; no load losses in % of kVA - typical value o NL input current in PU: T6_nl_exc=2; no load excitation PU- typical value o Primary resistance T6_winding_R1=0.0058; PU primary winding resistance; - typical value o Secondary resistance T6_winding_R2=0.006; PU secondary winding resistance; - typical value

i. Transformer T7 Transformer T7 is the 8 MVA step down transformer (138 to 480 V) powering 480 loads. Most of its parameters were obtained from the nameplate of the transformer or from conversations with GA engineers, while some were assumed for typical transformers of that size (see below):

o Nominal Input Voltage in Volts (for turns ratio and PU calculations): T7_in_v=138000;

from transformer plate o Nominal Output Voltage in Volts (for turns ratio and PU calculations): T7_out_v= 480;

from transformer plate o Transformer KVA rating: T7_kva=8e6; from transformer plate o Short circuit reactance in PU: T7_xc_short=0.087; PU impedance from transformer plate o No load losses as % of rating: T7_nl_loss=2; no load losses - typical value o NL input current in PU: T7_nl_exc=6; no load excitation PU- typical value o Series winding resistance in PU T7_winding_res=0.02; no load winding resistance PU-typical value

j. Lumped load on 480 line The 480 lumped load is connected at the output of the T7 transformer. Its max power is 3.32 MW.

o Lump load resistance for 480 V: R_load_480=0.144; resistance in Ohms (corresponds to

1.6 MW). The value of this resistance is further decreased when simulating the increase in loads for 2022, 2023 and beyond (0.128 for 1.8 MW, 0.115 for 2.0 MW) o Lump load inductance for 480 V: L_load_480=10e-6; Inductance in Henrys, inconsequential for the overall results

k. Lumped load on 12 kV line

The 12 kV lumped load is connected after the surge inductors (in parallel with the 8 NB systems). Its max power is depends on the working scenario.

Its default parameters are:

o Lump load resistance for 13.8 kV R_load_13kV=9.72; resistance in Ohms (corresponds to 25 MW). The value of this resistance is further decreased when simulating the increase in loads for 2022, 2023 and beyond (6.22 for 25 MW, 4.17 for 37.3 MW and 3.41 for

45.6 MW).

o Lump load inductance for 13.8 kV L_load_13kV=100e-6; Inductance in Henrys, inconsequential for the overall results

l. 12 kV power cables and surge inductor (NB subsystem)

Two power cable sets (3 lines, 225 A, #00 AWG) have their parameters calculated based on typical per foot resistance and inductance:

R_00=0.078e-3; resistance per foot of 0.078 mohm/ft L_00=250e-9; inductance per foot of 250nH/ft and a length of cable length_1 of 100 feet Resulting in o Cable resistance of R_cable_1=R_00*length_1 ;

o L_cable_1=L_00*length_1;

Using the same assumptions as high voltage cable 1 with length_2=100 results in o Cable resistance of R_cable_2=R_00*length_2 ;

o L_cable_2=L_00*length_2;

The length is 100 feet for each cable.

The surge inductors parameters were obtained from GA documentations:

o Surge inductor resistance in Ohms R_surge=0.0157 ; resistance in Ohms o Surge inductor inductance in Henrys L_surge=0.7e-3 ; inductance Henrys

m. Autotransformer

Some of the parameters are common to all 8 autotransformers:

o Nominal input voltage auto_xfer_in_v=12470; from transformer plate o Transformer KVA rating: auto_xfer_kva=13600e3; from transformer plate o No load losses as % of rating auto_nl_loss=0.04; no load losses typical value o NL input current in PU: auto_nl_exc=6; no load excitation PU- typical value o Series winding resistance in PU auto_winding_res=0.04; no load winding resistance PU- typical value

Two of the parameters (the output voltage and the short circuit reactance) are dependent on the transformer type (Transrex or UVC) and on the tap on which they are set.

- The output voltage variable is YYYYY_auto_xfer_out_v

- The short circuit reactance is YYYY_xc_short

- The variable for the tap selection is tap_YYYY,

- YYYY is one of the following: UVC30L, UVC30R, UVC330L, UVC330R, TRX150L, TRX150R, TRX210L, TRX210R.

The tap selection modifies the output voltage as well as the series inductance The values for output voltage and short circuit reactance are taken from the Transrex name plate. The following table shows the dependency on the tap number:

Tap number Output voltage (Volts) Short circuit reactance(PU) 5 7482 0.0852 6 8101 0.0794 7 8729 0.0638 8 9353 0.0482 9 9976 0.0346

10 10288 0.0283 11 10600 0.022 12 10911 0.016 13 11223 0.013 14 11535 0.0065 15 11847 0.0036 16 12158 0.0015 17 12470 0.0001

Table 2 Output voltage and short circuit reactance of Transrex transformer

Tap number Output voltage (Volts) Short circuit reactance(PU)

5 8313 0.0952 6 9006 0.0794 7 9699 0.0636 8 10398 0.0462 9 11084 0.0346

10 11430 0.0253 11 11777 0.022 12 12123 0.016 13 12470 0.0113 14 12816 0.0065 15 13162 0.0036 16 13509 0.0015 17 13855 0.0001

Table 3 Output voltage and short circuit reactance of UVC transformer

n. Step-up transformer

Some of the parameters are common to all 8 step transformers.

o Nominal Input Voltage in Volts (for turns ratio and PU calculations): step_primary_v =13800;

o Transformer KVA rating: step_kva=11860e3;

o No load losses as % of rating: nl_loss=0.03;

o NL input current in PU: nl_exc=6=6;

o Series winding resistance in PU winding_res=0.02;

The Output Voltage and the Short circuit reactance vary with the type of transformer. As no nameplate data was available for these transformers, we relied on the empirical data used by the GA engineers; the results are summarized in the next 3 tables.

The original data consisted of graphs of transformer taps vs DC voltage at no load (columns 1 and 3 in the tables below). Based on the tap and the tap changer data, we estimated the input to the step up transformer (column 2 below).

The output voltage for that tap was then calculated in column 4 as Vout=VDC/2/1.41*1.034 (NL DC voltage for a 12 pulse system; the 1.034 term comes from the fact that the 12 pulses are separated by 30 degrees and as a result, their sum slightly less than their algebraic sum. The rated voltage is then adjusted for a 13.8kV voltage (instead of the one in column2).

Trex

Tap In voltage (V)

DC V no load (kV)

Out voltage NL (kV)

Rated V out @13.8kV(kV)

5 7482 58 21.27 39.22 6 8101 71 26.03 44.35 7 8729 77 28.23 44.64 8 9353 83 30.43 44.90 9 9976 89 32.63 45.14

10 10288 95 34.83 46.72 11 10600 98 35.93 46.78 12 10911 101 37.03 46.84 13 11223 104 38.13 46.89 14 11535 106 38.87 46.50

Table 4 No load Input/Output data of the TREX system

UVC

(V)

DC V no load (kV)

Out voltage NL (kV)

Rated V out @13.8kV(kV)

5 8313 84 30.80 51.13 6 9006 86 31.53 48.32 7 9699 92 33.73 48.00 8 10398 95 34.83 46.23 9 11084 98 35.93 44.74

10 11430 102 37.40 45.15 11 11777 104 38.13 44.68 12 12123 106 38.87 44.24 13 12470 107 39.23 43.42 14 12816 108 39.60 42.64

Table 5 No load Input/Output data of the UVC system

UVC (modified)

(V)

DC V no load (kV)

Out voltage NL (kV)

Rated V out @13.8kV(kV)

5 8313 100 36.67 60.87 6 9006 104 38.13 58.43 7 9699 108 39.60 56.34 8 10398 112 41.07 54.50 9 11084 116 42.53 52.96 Table 6 No load Input/Output data of the modified UVC system

Due to the variation of the output voltage value, the value corresponding to a common operational point was chosen, as shown in the following table (for a 13800 kV input):

Type of transformer Short circuit reactance Output voltage Transrex TREX_imp_pu=0.095 TREX_step_secondary_v= 46840 V UVC UVC_imp_pu=0.0851 UVC_step_secondary_v= 45150 V UVC modified UVC_mod_imp_pu=0.08 UVC_mod_step_secondary_v= 56340 V

Table 7 Output voltage and short circuit reactance of Step up transformers

o. Rectifiers

The rectifiers are hardcoded and their values have minimal influence on the simulations (the voltage drop across the rectifier is embedded into the step up transformer).

p. Output capacitor

The output capacitor parameters are o Initial capacitor voltage in Volts (to reduce transient time at startup): init_dc=78000;

o Capacitance: dc_cap=27e-6;

o Equivalent series resistance in Ohms (current limiting resistor) ESR=150;

q. High voltage cable (1000 ft cable)

The high voltage cable is modeled l as a R-L series element with a capacitor in parallel . Using data from the GA engineers:

o Cable resistance R_1000=0.419;

o Cable inductance L_1000=89.4e-6;

o Cable capacitance C_1000=59.9e-9; Initial capacitor voltage in Volts (to reduce transient time at startup): init_dc=78000;

r. One ohm resistors

As the name implies, they are hardcoded as two 1 ohm resistors.

g8. Tetrodes and load

The tetrodes and the load are modeled as current source in series with a switch and a few elements needed to avoid numerical instabilities. The value of the current (in Amps) as well as the time variations can be modified the values below. The first array shows the time at which the current varies. The second array shows the current values (in this example, the current changes from 0 70).

The first two arrays control 4 of the NB current sources. Arrays 3 and 4 control the other 4 NB current sources, allowing for a phase shift between the two sets of 4 subsystems.

x_time_1 = [0 .8 .80001 1.6 1.60001];

y_current_1 = [0 0 1 1 0 ]*70;

x_time_2 = [0 .8 .80001 1.6 1.60001];

y_current_2 = [0 0 1 1 0 ]*70;

Model validation against measured data

While data was not available for the entire model, there was data available for one of the NB subsystems. The data consisted of voltage and current measurements at the input of the step-up transformer and the DC current of the rectifiers.

The model was adapted to only simulate one system (instead of 8). A crow bar was also added to match one of the data sets. The validation model is shown below:

Figure 44 Validation model

Running the validation

The file containing the model is called validation neutral_beam.

- The file initialization the data (reading the measured data of one of the sets) is called data_ini.m and has to be run first. In this file, change the variable “set” to 1 (line is “set=1’) to run the validation of the first set of data (regular pulse) or to 2 for the second set (set=2)

- Run nb_ini.m or press the button called “variable initialization” in the Simulink diagram to initialize the parameters of the simulation

- Run the simulation

- Plot results by running the file plot_v.m or pressing the “Plot variable” button in the Simulink diagram

There are two sets of data.

a. Regular pulse

The following graphs show:

- measured versus simulated input voltage and current (zoomed around the initiation of the pulse) for one phase (the other phases are similar)

- measured versus simulated dc current

- voltage before the tetrodes (Vin)

Figure 45 Measured vs simulated input voltage for regular pulse data

Figure 46 Measured vs simulated input current for regular pulse data

Figure 47 Measured vs simulated dc current for regular pulse data

Figure 48 Voltage at the tetrodes for regular pulse data

b. Crow bar data

The following graphs show:

- measured versus simulated input voltage and current (zoomed around the closing of the crow bar) for one phase (the other phases are similar)

Figure 49 Measured vs simulated input voltage for crow bar data

Figure 50 Measured vs simulated input current for regular pulse

Simulation scenarios

There are multiple loads connected directly and indirectly to the 138 kV line:

- The 8 NB sources; they are simulated as current sources running at 70 Amps

- The taps are adjusted to 13 for the TREX system, 11 for the original UVC system and 7 for the modified UVC system.

- All 8 NB are firing synchronously, with pulses of 0.8 seconds ON and 0.8 seconds OFF. The 0.8 seconds duration is sufficient for the system to reach steady state.

- Then the 480 V load is fired at 1 second the 12.47 k V at 1.2 seconds and kept ON for the rest of the test.

Scenario a: 2022 operations:

T-6 load 8 NB + 6 gyrotrons + Helicon = 75 MW peak over any 1-2 seconds T-7 load 1.6 MW

Since the NB are adjusted to operate at approximately 50 MW total, this results in a lumped load on the

12.47 kV line of 25 MW.

Scenario b: 2023 operations

T-6 load 8 NB + 8 gyrotrons + Helicon + PH1 LHCD = 87.3 MW peak over 1-2 seconds T-7 load 1.8 MW Since the NB are adjusted to operate at approximately 50 MW total, this results in a lumped load on the

12.47 kV line of 37.3 MW.

Scenario c: beyond 2023 NB power pushed to max 88 kV at 70 amps max. 60 MW 9 gyratrons, helicon, and full LHCD 45.6 MW T-6 load 105.6 MW T-7 load 2.0 MW

The simulation is adjusted to run at 95 kV voltage (at the tetrode input) with a current of 78 A. Since the NB are adjusted to operate at approximately 60 MW total, this results in a lumped load on the 12.47 kV line of 45.6 MW.

This section of the report will only present the results of scenarios in tabular form. The graphical results are shown in Appendix A.

Results for scenario a: 2022 operations

Max Min % difference Voltage of 138 kV line 137400 135600 1.31%

Voltage of 12.47 kV line 12300 11920 3.25% Voltage of 480 V line 476 467 1.89%

Voltage at output of TREX tap changer 11100 10670 3.87% Voltage at output of UVC tap changer 11700 11260 3.76%

Voltage at output of modified UVC tap changer 9600 9150 4.69% DC Voltage at input of tetrode(TREX) 101400 89200 12.03% DC Voltage at input of tetrode(UVC) 103400 91600 11.41%

DC Voltage at input of tetrode(UVC modified) 105400 89300 15.28% Table 8 Range of Voltage variations for test a

Results for scenario b: 2023 operations

The following table shows the min/mx values of voltages at different points in the system as well as the relative difference between them.

Max Min % difference Voltage of 138 kV line 137400 135400 1.46%

Voltage of 12.47 kV line 12300 11873 3.47% Voltage of 480 V line 476 465 2.31%

Voltage at output of TREX tap changer 11100 10630 4.23% Voltage at output of UVC tap changer 11700 11216 4.14%

Voltage at output of modified UVC tap changer 9600 9110 5.10% DC Voltage at input of tetrode(TREX) 101400 88850 12.38% DC Voltage at input of tetrode(UVC) 103400 91250 11.75%

DC Voltage at input of tetrode(UVC modified) 105400 89000 15.56% Table 9 Range of Voltage variations for test b

Results for scenario c: beyond 2023

The following table shows the min/mx values of voltages at different points in the system as well as the relative difference between them.

Max Min % difference Voltage of 138 kV line 137400 134900 1.82%

Voltage of 12.47 kV line 12300 11756 4.42% Voltage of 480 V line 477 463 2.94%

Voltage at output of TREX tap changer 12260 11660 4.89% Voltage at output of UVC tap changer 12540 11920 4.94%

Voltage at output of modified UVC tap changer 10970 10360 5.56% DC Voltage at input of tetrode(TREX) 111950 97400 13.00% DC Voltage at input of tetrode(UVC) 110450 96600 12.54%

DC Voltage at input of tetrode(UVC modified) 120450 101400 15.82% Table 10 Range of Voltage variations for test c

Conclusions and recommendations

Based on the simulated data as well as existing measured data, the following conclusions can be drawn:

1. The steady state model developed in this work simulates well the existing DIII-D Neutral Beam system. While we refer to the model as a steady state, it is developed as a dynamic model without the dynamic details of the neutral beam and high voltage cable.

2. The model was developed using standard Simulink blocks. The block parameters were obtained from nameplate information and from previous measurements performed by the team at DIII-D.

When information was not available, the parameters were assumed from similar systems.

3. The model can be improved by substituting the assumed parameters with more accurate versions.

4. The model was partially validated against two data sets. The data sets contained voltages and currents at the input of one of the step up transformers. One data set contained represented a regular pulse while the other was a crowbar action. There was no DC voltage data available for these sets. The model validated the data well, except for the input currents which had errors in the 10% range. This was explained by the GA team as normal since the current sensors have not been calibrated in a long time and were reading this lower. The range of the current sensors was considerably larger than the measured currents, increasing the possibility of a measurement error.

5. Several simulations scenarios were run. Their purpose was to study the effect of multiple loads (neutral beams and external loads) on the output voltage of the system. The simulation results confirm the relatively large voltage drops at the load (neutral beams). The effect of the loads is cumulative and the model predicts the worst case being when all loads are connected simultaneously.

6. The largest percentage voltage drops happen at the tetrode input (output of the step up-rectifier system).The drop is primarily due to the large impedances of the step-up transformers (8-10%). This drop was predictable from the characteristics of the rectifier system (as specified by their manufacturer). Additionally, being the last drop in the chain, it is also increased by the cumulative effect of the drops in the supply line up to this point.

7. A relatively large voltage drop takes place at the tap changer transformers if they are operated on a lower voltage setting, as the impedance of the transformer increases considerably when operating on a lower tap.

8. The voltage drop on the 12.47 kV and the 138 kV are smaller than those on the step up transformers, but they have a cumulative effect of 4-5% when all loads are fired at the same time. The drop is predictable from the impedance of the transformer and the supply line.

9. There is a secondary 480 V bus that supplies several power supplies used for the NB system.

They are supplied from the 138 kV line through a step down tapped transformer. The bus voltage also registers a drop when the NB system is in full use in addition to the drops generated by its own loads. The drop is relatively small compared to the other drops.

10. The simulations show that the current system operating with all loads simultaneously could provide sufficient voltage for the NB system even if all loads are all fired simultaneously, provided that the transformers are operated on a higher tap and if the voltage is maintained at the current levels (82 kV or less).

11. The simulations show that the system would be able to support operation at an increased level of 95 kV (88 kV after the tetrodes) and currents of 78 A. With the existing system parameters, the steady-state voltage margin on the TREX system is only 1.7% (1.6 kV) with the system operating on the last tap (maximum voltage). Since the simulation does not include transient effects or the tetrode model, this margin may be insufficient for this operation. The UVC-type systems have more output voltage available due to their higher tap changer voltage capability so they are less likely to be at risk.

Based on the above conclusions, we recommend the following:

1. Replace the uncontrolled rectifier system with a phase controlled rectifier (thyristor based) and eliminate (bypass) the tap changer system. This would have the following benefits:

- It would eliminate all the load related drops on the existing tap changer, which are between

2-8% depending to the tap used and the percentage load)

- It would allow a fast dynamic voltage control (in the 3-30 ms range depending on design) over the entire load range

2. As a stop-gap measure to assure operation at higher voltages and currents, the tap changers of the TREX systems need to be replaced with “UVC type” tapped transformers (which allow for step up/down functions). Alternatively, a transformer-rectifier system similar to the modified UVC system would work as well.

3. The DC capacitor capacitance is insufficient to sustain the amount of energy into the neutral beams in the allotted pulse time. We recommend an increase in this capacitance to match the pulse duration.

Appendix A Graphical representations of the simulations

Figure A51 Voltage and current of 138 kV line (instantaneous and RMS values): Scenario a

Figure A52 Voltage and current of output of T6 transformer (instantaneous and RMS values) Scenario a

Figure A53 Voltage and current of 480 V load (instantaneous and RMS values), Scenario a

Figure A54 Voltage and current at output of TREX tap changer(instantaneous and RMS values) , Scenario a

Figure A55 Voltages to tetrodes for TREX, UVC and UVC modified and the current (same for all 3) , Scenario a

Figure A56 Voltage and current of 138 kV line (instantaneous and RMS values): Scenario b

Figure A57 Voltage and current of output of T6 transformer (instantaneous and RMS values) Scenario b

Figure A58 Voltage and current of 480 V load (instantaneous and RMS values), Scenario b

Figure A59 Voltage and current at output of TREX tap changer(instantaneous and RMS values) , Scenario b

Figure A60 Voltages to tetrodes for TREX, UVC and UVC modified and the current (same for all 3) , Scenario b

Figure A61 Voltage and current of 138 kV line (instantaneous and RMS values): Scenario c

Figure A62 Voltage and current of output of T6 transformer (instantaneous and RMS values) Scenario c

Figure A63 Voltage and current of 480 V load (instantaneous and RMS values), Scenario c

Figure A64 Voltage and current at output of TREX tap changer(instantaneous and RMS values) , Scenario c

Figure A65 Voltages to tetrodes for TREX, UVC and UVC modified and the current (same for all 3), Scenario c