Renewable Modelling · GSC Current Loop

GSC Current-Loop Tuning in EMTP®

RL plant, IMC gains, feed-forward and dq decoupling

The grid-side converter (GSC) inner current loop is the fast control layer that forces the converter current to follow its dq references. In EMTP®, the loop is tuned from the RL plant seen between the converter and the grid — not the converter’s choke alone, but the whole impedance path including the transformers and the grid equivalent — so its internal-model-control gains depend on the network strength. Because the converter acts at its own terminals while the currents are measured after the choke, the voltage reference adds a dq decoupling term and a feed-forward of the measured terminal voltage to the PI correction to improve tracking — and both matter most in a weak grid.

Reading time ≈ 18 min · RL plant, IMC gains & feed-forward

The GSC inner current loop is the fast layer that forces the actual current to follow the dq references the outer loops produce. Two ideas shape how it is tuned. First, the loop is not tuned in isolation: it controls the RL plant seen from the converter voltage source to the measured-current point — the converter choke, the transformer impedance and the relevant grid-side equivalent used for the study — so its gains depend on the network, not on the converter hardware alone. Second, because the converter acts at its own terminals while the currents and voltages are measured after the choke and network impedance, the voltage reference needs feed-forward compensation and dq decoupling on top of the PI. Both points come into their own in a weak grid.

Abbreviations used on this page

GSCGrid-side converter

IMCInternal model control

d–qDirect / quadrature rotating frame

PIProportional–integral controller

PIDProportional–integral–derivative controller

\(\alpha_c\)Current-loop bandwidth

\(R,\ L\)Series resistance and inductance (choke + transformers + grid)

\(\omega L\)dq cross-coupling reactance

PCCPoint of common coupling

SCRShort-circuit ratio (grid strength)

FRTFault ride-through

EMTP®Electromagnetic Transients Program

Key idea

The GSC inner loop controls an RL plant — \(G(s)=1/(R+sL)\), where \(\underline{Z}=R+j\omega L\) is the impedance from the converter to the grid, including the choke filter and the transformers / grid. So the gains depend on more than the converter hardware.
The PI gains follow IMC tuning straight from that plant (\(k_p=\alpha_c L\), \(k_i=\alpha_c R\)) and a chosen bandwidth — but because \(R\) and \(L\) include the grid, a weak vs strong grid changes the effective plant and the tuning.
The converter acts at its terminals but currents are measured after the choke, so the voltage reference adds, to the PI correction, a dq decoupling term (\(\pm\omega L\,i\)) that separates the axes and a feed-forward of the measured terminal voltage that anticipates the drop — improving response, decoupling and stability, especially in weak grids.
The gains are fixed during a study but set per project from the short-circuit strength at the PCC; PI (not PID) is used because derivative action is too sensitive to switching / measurement noise; and the current limiter is dynamic, allocating the limited current by priority and FRT.

Key terms used on this page

01Inner current loop

The fast loop that forces the converter current to follow its dq reference by setting the converter voltage.

02RL plant

The series resistance–inductance the current sees, \(1/(R+sL)\); the “plant” the current loop controls.

03Choke filter

The converter-side reactor; part of the series impedance but not all of it.

04Grid impedance

\(\underline{Z}=R+j\omega L\) including transformers and the network, added to the choke.

05IMC tuning

Gains computed from the plant and a chosen bandwidth: \(k_p=\alpha_c L\), \(k_i=\alpha_c R\).

06Decoupling term

The \(\pm\omega L\,i\) cross term added so the d and q current loops act independently.

07Feed-forward compensation

Adding the measured terminal voltage to the converter reference so the PI handles only the error.

08Weak grid

A network with high impedance (low short-circuit strength), where the terminal voltage is sensitive to current.

09Short-circuit strength

How “stiff” the grid is at the PCC; it sets the effective impedance the loop sees.

10Dynamic current limiter

A limiter whose allocation depends on fault mode, priority rules, FRT logic and available capability.

11Effective plant

The total \(R,\ L\) seen by the loop — converter choke plus transformers plus grid — not the choke alone.

12PI vs PID

PI is preferred here; derivative (D) action is too sensitive to switching and measurement noise.

Section 1

Inside the GSC inner current loop

The inner loop’s job is simple to state — force the actual current to follow the current reference the outer loops produce — but doing it well needs two pieces of physics that the “fast PI” picture leaves out: the plant the loop actually controls, and the difference between where the converter acts and where the measurements are taken. Get those right and the loop is well-behaved across operating points and grid conditions; get them wrong and it can be sluggish or, in a weak grid, unstable.

Two things to get right

(1) Tune the loop from the RL plant seen by the converter, which includes the grid, not just the choke. (2) Add feed-forward and decoupling so the PI only has to handle the genuine current error.

Section 2

The plant the loop controls: an RL system

Between the converter output and the grid is a series impedance, and the current through it responds to the converter voltage as a first-order RL system. The transfer function from converter voltage to current is:

\[ G(s) = \frac{i}{v} = \frac{1}{R + sL}, \qquad \underline{Z} = R + j\omega L \]

\(G(s)\): transfer function from converter voltage to current
\(\underline{Z}=R+j\omega L\): series impedance from the converter to the power system
\(R,\ L\): total series resistance and inductance — the choke filter and the transformers and grid
\(\omega\): fundamental angular frequency

The key point: \(\underline{Z}\) is not the choke reactor alone. It includes the grid impedance and the transformers, so the “plant” the current loop controls is the whole path from the converter to the network.

What “plant” means here

Here, plant means the controlled electrical system seen by the current regulator — the effective \(R\) and \(L\) between the converter voltage source and the measured-current point — not the renewable park as a whole. \(R\) and \(L\) represent the effective resistance and inductance the current loop actually sees.

This is the same kind of RL current plant met on the full-scale converter through its interface filter — only here the impedance explicitly carries the transformers and grid as well as the choke. The RL form is a practical tuning model, not an exact description: in weak grids, long cables, filters, transformer saturation, control delays and control interactions can make the real response more complex than a simple first-order RL plant, so it is a sound starting point that still needs validation for the specific network.

Section 3

Why the gains depend on grid strength

Because the plant includes the grid, the gains depend on how strong the grid is. A stronger grid gives a stiffer voltage reference and a lower effective sensitivity, so the current response is faster and better behaved; a weaker grid makes converter current changes move the terminal voltage more strongly, so the current-loop tuning needs more care. Even with identical converter hardware, the effective \(R\) and \(L\) seen by the controller change with the network. Importantly, this dependence is handled at tuning time: the gains are normally selected for the project study condition using the assumed grid strength and impedance — they are not necessarily adaptive during the EMT run.

Tuning is network-dependent

The current loop is tuned for the network it lives in. The same converter on a strong grid and on a weak grid is, to the controller, two different plants.

Section 4

IMC tuning of the current loop

Internal model control tuning chooses the PI gains from the assumed RL plant and a desired closed-loop bandwidth. Given that plant, the gains follow directly — the same logic used on the machine side — computed from the plant parameters and the chosen bandwidth:

\[ k_p = \alpha_c L, \qquad k_i = \alpha_c R \]

\(k_p,\ k_i\): proportional and integral gains of the inner current loop
\(\alpha_c\): desired current-loop bandwidth
\(L,\ R\): inductance and resistance of the RL plant (choke + transformers + grid)

The gains come from the RL dynamics of the GSC output path and a chosen bandwidth — far better than guessing PI values, and the reason the tuning tracks the effective plant.

The one remaining choice is the bandwidth \(\alpha_c\) itself, and in practice it is fixed from the GSC rise time rather than picked in the abstract. For the first-order closed loop that IMC produces, the bandwidth and the current rise time are two views of the same speed, tied by roughly \(\alpha_c \approx 2.2 / t_r\), so specifying how quickly the grid-side current should reach its reference sets \(\alpha_c\) — and, through \(k_p=\alpha_c L\) and \(k_i=\alpha_c R\), the gains follow. A faster target rise time raises the bandwidth and the gains; a slower one relaxes them, trading response speed for margin against noise and switching content. In short, \(\alpha_c\) is the selected current-loop bandwidth — the speed of response: a higher \(\alpha_c\) gives faster tracking but can reduce robustness where control delays, measurement filters, PLL interaction or grid weakness are significant.

Section 5

Outer-loop gains versus inner-loop gains

It is worth separating the two sets of gains, because they are tuned for different purposes. The outer-loop gains shape the supervisory behaviour: the dc-voltage error creates \(i_d^{*}\), the voltage / reactive request creates \(i_q^{*}\), and these gains set the dc-link regulation speed and the voltage / reactive support. The inner-loop gains do one thing — force the actual current to follow its reference — and are tuned from the RL electrical plant. So the outer loop is tuned from the desired supervisory dynamics, the inner loop from the electrical plant; they are not tuned for the same job.

Section 6

Why feed-forward compensation is needed

Here is the crux. The voltage command is applied by the converter at its output terminals, but the measured current is shaped by the choke filter, the transformer and the network impedance between the converter and the measurement point — so the point where the converter acts is not the point where the current is measured. Across that intervening impedance there is a voltage drop:

\[ \Delta v = R\,i + L\frac{di}{dt} \]

\(\Delta v\): voltage drop between the converter terminal and the measurement point
\(R,\ L\): resistance and inductance of the intervening impedance
\(i\): current through the impedance

There is also a dq cross-coupling between the axes due to the rotating frame. So the converter terminal voltage is not the measured terminal voltage; to produce the right current at the measured point, the controller must anticipate these effects.

That anticipation is exactly what feed-forward compensation provides. The PI controller only corrects the current error; feed-forward adds the measured terminal voltage and the expected coupling terms directly, so the converter does not have to “discover” the required voltage through feedback alone. The PI is then left to handle only the genuine current error.

Section 7

The feed-forward and decoupling terms

In a rotating dq frame the d-axis and q-axis currents are coupled through \(\omega L\) terms, so a change on one axis disturbs the other. The decoupling terms compensate this cross-coupling, so a d-axis current command does not unnecessarily disturb the q-axis, and vice versa. The converter voltage reference therefore has three parts: the PI correction from the current error, a decoupling term for the dq cross-coupling, and a feed-forward term for the measured terminal voltage. Written out for the two axes (the exact signs follow the chosen convention):

\[ v_{dg}^{*} = \mathrm{PI}(e_d) + \omega L\,i_{qg} + v_{d}, \qquad v_{qg}^{*} = \mathrm{PI}(e_q) - \omega L\,i_{dg} + v_{q} \]

\(v_{dg}^{*},\ v_{qg}^{*}\): converter dq voltage references
\(\mathrm{PI}(e_d),\ \mathrm{PI}(e_q)\): PI acting on the current errors \(e_d=i_{dg}^{*}-i_{dg}\), \(e_q=i_{qg}^{*}-i_{qg}\)
\(\pm\,\omega L\,i\): dq decoupling term (cross-axis current × reactance)
\(v_{d},\ v_{q}\): feed-forward of the measured terminal voltage

The signs of the \(\omega L\) decoupling terms depend on the dq convention and the current direction; the control principle is unchanged. The PI is no longer working alone: the decoupling and feed-forward terms account for the known physics, which improves dynamic response, decoupling, stability and tracking accuracy — provided the measured quantities are accurate and the delays are small.

Table 1 — The three parts of the GSC inner-loop converter voltage reference.
Term	Origin	Purpose
PI correction	the current error \(i^{*}-i\)	drives the actual current to its reference
Decoupling term	the cross-axis current, \(\pm\omega L\,i\)	cancels the dq cross-coupling so the two axes act independently
Feed-forward term	the measured terminal voltage, \(v_d,\ v_q\)	anticipates the terminal voltage so the PI handles only the error

The reference is built in a clean sequence: current error → PI correction → dq decoupling term → terminal-voltage feed-forward → converter voltage reference → PWM / average-value execution. Feed-forward is a useful compensation path, not a free win: where the measured quantities are accurate and the delays small it improves tracking, but poorly filtered or delayed feed-forward can add phase error, so it still needs validation.

Section 8

Why this matters most in weak grids

In a strong grid the voltage behind the filter is relatively stiff, so even a simpler control can work reasonably. In a weak grid the terminal voltage is far more sensitive: current changes create larger voltage interactions, the external impedance matters more, and an aggressive current-loop bandwidth, feed-forward delay, PLL dynamics and measurement filtering can all interact with the grid impedance and destabilise the converter much more easily. So the practical message is that in a weak grid the current-loop tuning and the compensation matter a great deal more — which is why manufacturers tune their models to the expected project short-circuit strength, and why the tuning should be validated in EMT across the expected range of grid strengths and operating points.

Section 9

Project-set gains

Because the effective plant is network-dependent, the gains are normally set per project: chosen from the short-circuit strength at the point of common coupling, checked in studies, and adjusted if needed. In this generic model they do not change online during a simulation — they are fixed controller parameters chosen to work well for the expected network strength and operating range. The important distinction is that the gains are constant during the study but not universal across projects.

Section 10

Why PI, not PID

PI control is normally used because derivative action amplifies switching ripple and measurement noise — both of which abound in a converter. With filtered signals and fast electrical loops, PI is usually enough and far easier to tune robustly, so the derivative term is generally left out of converter current control.

Section 11

The current limiter is dynamic

One more detail completes the picture: the current limiter between the outer and inner loops is dynamic, not a fixed static clip. The inner loop tracks the limited references, not the unlimited outer-loop commands: when the outer loops ask for \(i_d^{*}\) and \(i_q^{*}\), the limiter decides what combination is physically allowed before those references reach the inner loop, and during a fault it can change the demanded dq currents. That decision depends on the fault mode, the priority rules and the available converter capability. The detailed current-priority behaviour — how the limited current is shared during ride-through — is covered on the GSC fault-behaviour page; here it is enough that the inner loop receives already-limited references.

Section 12

Key points

The GSC inner loop tracks the dq current references from the outer loops.
The controlled plant is an effective RL impedance \(1/(R+sL)\) — the choke, the transformers and the grid, not the choke alone.
IMC tuning gives \(k_p=\alpha_c L\) and \(k_i=\alpha_c R\), so the gains depend on the network strength.
dq decoupling (\(\pm\omega L\,i\)) compensates the cross-axis coupling so the two axes act independently.
Feed-forward adds the measured terminal voltage so tracking is faster and more robust — most of all in a weak grid.

References

EMTP® Documentation and Application Notes. Powersys / EMTP®.

Built on EMTP® · Expert spotlight

Henry Gras

Chief Operating Officer, PGSTech · Montréal, Canada

Henry Gras delivers the EMTP® University course “EMT Simulation and Analysis of Large-Scale Power Systems with Renewables” and works daily with the tool this article is written around.

Henry is based in Montréal, where he is Chief Operating Officer of PGSTech, the company responsible for EMTP® engineering services, commercialisation and continuing software development. He holds a master’s degree from Polytechnique Montréal, where he worked on electrical-machine research, and previously completed an engineering degree at École Centrale de Lyon in France.

Readers who want a structured programme on EMT simulation of large-scale power systems with renewables will find his EMTP® University course an excellent next step.

Henry’s technical expertise covers electromagnetic transient simulation, renewable-energy integration, power-system modelling, electrical machines, protection and specialist transient studies including TRV, transformer energisation, ferroresonance, insulation coordination and power quality.

Part 11 Reading now

GSC Current-Loop Tuning and Feed-Forward

The RL plant, IMC gains and the feed-forward decoupling that shape the grid-side current loop.

Series progress 11 of 30

Part 12

GSC Fault Behaviour: FRT and Decoupled Sequence Control

Why fault-ride-through needs current priority, and why unbalance calls for decoupled sequence control.