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  • GridKit/Model/PhasorDynamics/Stabilizer/IEEEST

‎GridKit/Model/PhasorDynamics/Stabilizer/IEEEST/README.md‎

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@@ -4,7 +4,7 @@ Standard IEEE power system stabilizer: 4th-order notch filter, two lead–lag
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blocks, washout, and output limiter.
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Notes:
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- $V_{cl}$, $V_{cu}$, and $T_{delay}$ are accepted for input-format
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- $V_{\mathrm{cl}}$, $V_{\mathrm{cu}}$, and $T_{\mathrm{delay}}$ are accepted for input-format
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compatibility but are not modeled.
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- A zero denominator time constant bypasses its corresponding lead–lag or
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washout block.
@@ -17,26 +17,26 @@ Figure 1: Stabilizer IEEEST model. Figure courtesy of [PowerWorld](https://www.p
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## Model Parameters
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Symbol | Units | JSON | Description | Typical Value | Note
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-------------|--------|----------|--------------------------------------|---------------|------
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$A_1$ | [s] | `A1` | Notch denominator coefficient | 1.013 |
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$A_2$ | [s²] | `A2` | Notch denominator coefficient | 0.013 |
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$A_3$ | [s] | `A3` | Notch denominator coefficient | 0.0 |
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$A_4$ | [s²] | `A4` | Notch denominator coefficient | 0.0 |
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$A_5$ | [s] | `A5` | Notch numerator coefficient | 1.013 |
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$A_6$ | [s²] | `A6` | Notch numerator coefficient | 0.113 |
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$T_1$ | [s] | `T1` | Lead–lag 1 numerator time constant | 0.0 |
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$T_2$ | [s] | `T2` | Lead–lag 1 denominator time constant | 0.02 |
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$T_3$ | [s] | `T3` | Lead–lag 2 numerator time constant | 0.0 |
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$T_4$ | [s] | `T4` | Lead–lag 2 denominator time constant | 0.0 |
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$T_5$ | [s] | `T5` | Washout numerator time constant | 1.65 |
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$T_6$ | [s] | `T6` | Washout denominator time constant | 1.65 |
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$K_s$ | [p.u.] | `Ks` | Stabilizer gain | 3.0 |
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$L_s^{\min}$ | [p.u.] | `Lsmin` | Minimum stabilizer output limit | -0.1 |
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$L_s^{\max}$ | [p.u.] | `Lsmax` | Maximum stabilizer output limit | 0.1 |
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$V_{cl}$ | [p.u.] | `Vcl` | Lower input cutout threshold | 0.0 | Accepted but not modeled
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$V_{cu}$ | [p.u.] | `Vcu` | Upper input cutout threshold | 0.0 | Accepted but not modeled
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$T_\text{delay}$ | [s] | `Tdelay` | Input delay | 0.0 | Accepted but not modeled
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Symbol | Units | JSON | Description | Typical Value | Note
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------------------------|----------|----------|--------------------------------------|---------------|------
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$A_1$ | [sec] | `A1` | Notch denominator coefficient | 1.013 |
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$A_2$ | [sec²] | `A2` | Notch denominator coefficient | 0.013 |
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$A_3$ | [sec] | `A3` | Notch denominator coefficient | 0.0 |
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$A_4$ | [sec²] | `A4` | Notch denominator coefficient | 0.0 |
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$A_5$ | [sec] | `A5` | Notch numerator coefficient | 1.013 |
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$A_6$ | [sec²] | `A6` | Notch numerator coefficient | 0.113 |
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$T_1$ | [sec] | `T1` | Lead–lag 1 numerator time constant | 0.0 |
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$T_2$ | [sec] | `T2` | Lead–lag 1 denominator time constant | 0.02 |
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$T_3$ | [sec] | `T3` | Lead–lag 2 numerator time constant | 0.0 |
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$T_4$ | [sec] | `T4` | Lead–lag 2 denominator time constant | 0.0 |
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$T_5$ | [sec] | `T5` | Washout numerator time constant | 1.65 |
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$T_6$ | [sec] | `T6` | Washout denominator time constant | 1.65 |
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$K_s$ | [p.u.] | `Ks` | Stabilizer gain | 3.0 |
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$L_s^{\min}$ | [p.u.] | `Lsmin` | Minimum stabilizer output limit | -0.1 |
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$L_s^{\max}$ | [p.u.] | `Lsmax` | Maximum stabilizer output limit | 0.1 |
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$V_{\mathrm{cl}}$ | [p.u.] | `Vcl` | Lower input cutout threshold | 0.0 | Accepted but not modeled
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$V_{\mathrm{cu}}$ | [p.u.] | `Vcu` | Upper input cutout threshold | 0.0 | Accepted but not modeled
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$T_{\mathrm{delay}}$ | [sec] | `Tdelay` | Input delay | 0.0 | Accepted but not modeled
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### Parameter Validation
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#### Differential
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Symbol | Units | Description
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----------------------|--------|------------
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$x_1, x_2, x_3, x_4$ | [-] | Notch filter states
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$x_5$ | [-] | Lead–lag 1 state
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$x_6$ | [-] | Lead–lag 2 state
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$x_7$ | [-] | Washout state
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Symbol | Units | Description | Note
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----------------------|--------|-----------------------|------
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$x_1, x_2, x_3, x_4$ | [-] | Notch filter states | States 1–4 in Fig. 1
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$x_5$ | [-] | Lead–lag 1 state | State 5 in Fig. 1
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$x_6$ | [-] | Lead–lag 2 state | State 6 in Fig. 1
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$x_7$ | [-] | Washout state | State 7 in Fig. 1
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For reduced-order notch filters, unused notch states remain in the fixed
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component state vector and are pinned by algebraic residuals.
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#### Algebraic
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Symbol | Units | Description
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-----------|--------|------------
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$v_4$ | [p.u.] | Notch filter output
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$v_5$ | [p.u.] | Lead–lag 1 output
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$v_6$ | [p.u.] | Lead–lag 2 output
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$v_7$ | [p.u.] | Unlimited stabilizer signal
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$V_{ss}$ | [p.u.] | Limited stabilizer signal (model output)
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Symbol | Units | Description | Note
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---------------------|--------|------------------------------------------|------
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$v_4$ | [p.u.] | Notch filter output |
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$v_5$ | [p.u.] | Lead–lag 1 output |
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$v_6$ | [p.u.] | Lead–lag 2 output |
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$v_7$ | [p.u.] | Unlimited stabilizer signal |
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$V_{\mathrm{ss}}$ | [p.u.] | Limited stabilizer signal (model output) |
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### External Variables
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#### Differential
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None.
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#### Algebraic
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Symbol | Units | Description
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-------|--------|------------
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$u$ | [p.u.] | Stabilizer input signal
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Symbol | Units | Description | Note
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-------|--------|-------------------------|------
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$u$ | [p.u.] | Stabilizer input signal |
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## Model Equations
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-T_6 v_7 + K_s T_5(v_6 - x_7) & T_6 \ne 0 \\
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K_s v_6 - v_7 & T_6 = 0
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\end{cases} \\
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0 &= -V_{ss} + \text{clamp}(v_7, L_s^{\min}, L_s^{\max})
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0 &= -V_{\mathrm{ss}} + \text{clamp}(v_7, L_s^{\min}, L_s^{\max})
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\end{aligned}
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```
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The output limiter uses GridKit's smooth
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[Clamp](../../../../CommonMath.md#derived-functions).
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[clamp](../../../../CommonMath.md#derived-functions).
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## Initialization
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States and derivatives initialize to the steady state implied by the attached
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input $u$:
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Initialization is performed by evaluating the steady-state residuals in
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dependency order. Let subscript $0$ denote initial values and set all internal
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derivatives to zero. States and derivatives initialize to the steady state
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implied by the attached input $u$:
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```math
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\begin{aligned}
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0 & \text{otherwise}
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\end{cases}
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&
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V_{ss} &= \text{clamp}(v_7, L_s^{\min}, L_s^{\max})
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V_{\mathrm{ss}} &= \text{clamp}(v_7, L_s^{\min}, L_s^{\max})
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\end{aligned}
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```
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## Model Outputs
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Output | Units | Description | Note
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-------|--------|---------------------------|-----
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-------|--------|---------------------------|------
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`vss` | [p.u.] | Limited stabilizer signal | Exported through `output` when assigned

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