EPRI Grid Forming
Context
This model was developed by Electric Power Research Institute (EPRI) and provides a standardized approach for inverter based resources [1]. The original model is described in a report available here.
Model use, assumptions, validity domain and limitations
The model is a positive-sequence RMS model, hence it assumes symmetrical operating conditions and neglects high-frequency dynamics. This type of model is often used in large-scale stability studies, for which it reflects the relevant phenomena. It is not a detailed physical model of the unit. Also for some stability phenomena (e.g. resonance stability) this model is not sufficient and EMT models or other approaches may be necessary. A comparison against EMT is shown in the EPRI documentation. It is also available for PSCAD.
Model description
Difference between grid following and grid forming inverter
A grid-following inverter synchronizes with the power grid’s voltage and frequency using a Phase-Locked Loop (PLL), which tracks the grid’s phase angle and enables the inverter to adjust accordingly. In contrast, a grid-forming inverter can actively establish the grid’s voltage and frequency, allowing it to create or stabilize the grid, particularly in situations where traditional grid infrastructure is weak or absent. Unlike grid-following inverters, grid-forming inverters do not rely on a PLL; instead, they can synchronize with the grid similarly to a synchronous generator. Several approaches can be found in literature, a subset of which is present in the EPRI model.
EPRI GFM operation modes
The Generic EPRI GFM model offers four control modes:
- Droop based, \(\omega_\mathrm{flag}=1\), see Figure 1
- Virtual Synchronous Machine (VSM), \(\omega_\mathrm{flag}=2\), see Figure 2
- Dispatchable Virtual Oscillator (dVOC) based GFM, \(\omega_\mathrm{flag}=3\), see Figure 3
- Phase Locked Loop (Grid following mode), \(\omega_\mathrm{flag}=0\), see Figure 4
Model schema
The different control method diagrams of the GFM is shown below:
Figure 1: Droop mode diagram
Figure 2: VSM mode diagram
Figure 3: dVOC mode diagram
Figure 4: PLL mode diagram
[!NOTE]
The xy reference frame is the real-imaginary coordinate frame of the network, to which all voltage angles are typically referenced, while the dq reference frame functions as the coordinate system of the control. The relative angle between these two reference frames is represented by the control variable \(\theta_\mathrm{inv}\).
D and q reference currents calculation
Figure 5: Calculation of d and q reference currents
Parameters
In [1], per-unit parameters are based on the inverter’s rated apparent power \(S_\mathrm{r}\) in MVA with a default value of 100 MVA.
| name | type | unit | description | typical value |
|---|---|---|---|---|
| \(\Delta\omega_\mathrm{max}\) | float | rad/s | Maximum frequency deviation | \(75.0/\omega_\mathrm{base}\) |
| \(\Delta\omega_\mathrm{min}\) | float | rad/s | Minimum frequency deviation | \(-75.0/\omega_\mathrm{base}\) |
| \(d_\mathrm{d}\) | float | \(pu\) | VSM damping factor | \(0.11\) |
| \(K_\mathrm{1}\) | int | \(pu\) | – (depends on \(\omega_\mathrm{flag}\)) | see Table 3 |
| \(K\mathrm{2}\) | int | \(pu\) | – (depends on \(\omega_\mathrm{flag}\)) | see Table 3 |
| \(K_\mathrm{2}^{\mathrm{dvoc}}\) | int | \(pu\) | – (depends on \(\omega_\mathrm{flag}\)) | see Table 3 |
| \(K_\mathrm{Ii}\) | float | \(pu\) | Current controller integral gain | \(20.0\) |
| \(K_\mathrm{Ip}\) | float | \(pu\) | Active power integral gain | \(20.0\) |
| \(K_\mathrm{Ipll}\) | float | \(pu\) | PLL integral gain | \(700.0\) |
| \(K_\mathrm{Iv}\) | float | \(pu\) | Voltage control integral gain | see Table 2 |
| \(K_\mathrm{Pi}\) | float | \(pu\) | Current controller proportional gain | \(0.5\) |
| \(K_\mathrm{Pp}\) | float | \(pu\) | Active power proportional gain | \(0.5\) |
| \(K_\mathrm{Ppll}\) | float | \(pu\) | PLL proportional gain | \(20.0\) |
| \(K_\mathrm{Pv}\) | float | \(pu\) | Voltage control proportional gain | see Table 2 |
| \(m_\mathrm{f}\) | float | \(pu\) | VSM inertia constant | \(0.15\) |
| \(\omega_\mathrm{drp}\) | float | \(pu\) | Frequency droop | \(0.033\) |
| \(\omega_\mathrm{flag}\) | int | \(pu\) | GFM control type | \(0-3\) |
| \(PQ_\mathrm{flag}\) | bool | \(pu\) | Current priority | false: P priority; true: Q priority |
| \(Q_\mathrm{drp}\) | float | \(pu\) | Voltage droop | \(4.5\) |
| \(R_\mathrm{f}\) | float | \(pu\) | Filter resistance | \(0.0015\) |
| \(T_\mathrm{e}\) | float | \(s\) | Output state time constant | \(0.01\) |
| \(T\mathrm{f}\) | int | \(pu\) | – (depends on \(\omega_\mathrm{flag}\)) | see Table 3 |
| \(T_\mathrm{r}\) | float | \(s\) | Transducer time constant | \(0.005\) |
| \(T_\mathrm{v}\) | int | \(pu\) | – (depends on \(\omega_\mathrm{flag}\)) | see Table 3 |
| \(V_\mathrm{dip}\) | float | \(pu\) | State freeze threshold | \(0.8\) |
| \(X_\mathrm{f}\) | float | \(pu\) | Filter reactance | \(0.15\) |
\(\omega_\mathrm{base}\) is the nominal angular frequency in rad/s.
| name | \(\omega_\mathrm{flag}=0\) | \(\omega_\mathrm{flag} \neq 0\) |
|---|---|---|
| \(K_\mathrm{Iv}\) | \(150.0\) | \(10.0\) |
| \(K_\mathrm{Pv}\) | \(0.5\) | \(3.0\) |
| GFM Control | \(K_\mathrm{d}\) | \(K_\mathrm{1}\) | \(K_\mathrm{2}\) | \(K_\mathrm{2}^{\mathrm{dVOC}}\) |
|---|---|---|---|---|
| PLL | \(0.0\) | \(0.0\) | \(0.0\) | \(0.0\) |
| Droop | \(0.0\) | \(\omega_\mathrm{drp}\) | \(Q_\mathrm{drp}\) | \(0.0\) |
| VSM | \(d_\mathrm{d}\omega_\mathrm{drp}\) | \(\omega_\mathrm{drp}\) | \(Q_\mathrm{drp}\) | \(0.0\) |
| dVOC | \(0.0\) | \(\omega_\mathrm{drp}/s_2^3\) | \(\omega_\mathrm{drp}/s_3\) | see Equation 1 |
\[ \frac{K_2^{dvoc}}{\omega_{drp}} = \frac{4 \cdot 100^4}{100^4 - \left( 2 \cdot \left(100 - 100 \cdot Q_{drp}\right)^2 - 100^2 \right)^2} \tag{1}\]
Inputs
| name | type | unit | description |
|---|---|---|---|
| \(I_\mathrm{x,y}\) | float | \(pu\) | measured current in real/imag. quantities |
| \(\omega_\mathrm{ref}\) | float | \(pu\) | speed reference (difference to nominal) |
| \(P_\mathrm{aux}\) | float | \(pu\) | auxiliary active power |
| \(P_\mathrm{ref}\) | float | \(pu\) | active power setpoint |
| \(Q_\mathrm{aux}\) | float | \(pu\) | auxiliary reactive power |
| \(Q_\mathrm{ref}\) | float | \(pu\) | reactive power setpoint |
| \(V_\mathrm{ref}\) | float | \(pu\) | voltage setpoint |
| \(V_\mathrm{x,y}\) | float | \(pu\) | measured voltage in real/imag. quantities |
Outputs
| name | type | unit | description |
|---|---|---|---|
| \(E_\mathrm{x}\) | float | \(pu\) | output voltage in real quantity |
| \(E_\mathrm{y}\) | float | \(pu\) | output voltage in imag quantity |
Initial equations
\[ s_0 = P_\mathrm{ref} \tag{2}\]
\[ s_1 = Q_\mathrm{ref} \tag{3}\]
\[ s_2 = \theta_\mathrm{loadflow} \tag{4}\]
\[ s_3 = V_\mathrm{ref} \tag{5}\]
\[ s_4 = \omega_\mathrm{grid} - \omega_\mathrm{base} \tag{6}\]
\[ s_5 = \theta_\mathrm{loadflow} \tag{7}\]
\[ s_6 = E_\mathrm{q,loadflow} - v_\mathrm{q,loadflow} - i_\mathrm{q,loadflow}R_\mathrm{f} - i_\mathrm{d,loadflow}X_\mathrm{f} \tag{8}\]
\[ s_7 = E_\mathrm{d,loadflow} - v_\mathrm{d,loadflow} - i_\mathrm{d,loadflow}R_\mathrm{f} + i_\mathrm{q,loadflow}X_\mathrm{f} \tag{9}\]
\[ s_8 = E_\mathrm{q,loadflow} \tag{10}\]
\[ s_9 = E_\mathrm{d,loadflow} \tag{11}\]
\[ s_{10} = i_\mathrm{q,loadflow} \tag{12}\]
\[ s_{11} = i_\mathrm{q,loadflow} \tag{13}\]
\[ s_{12} = i_\mathrm{d,loadflow} \tag{14}\]
\[ s_{13} = i_\mathrm{d,loadflow} \tag{15}\]
The index “loadflow” indicates that this is the solution of a loadflow.
Open source implementations
This model has been successfully implemented in:
| Software | URL | Language | Open-Source License | Last consulted date | Comments |
|---|---|---|---|---|---|
| Open Modelica / Dynawo | Dynawo | modelica | MPL v2.0 | 12/12/2024 | For modeling assumptions and test results, see Dynawo repository. |