IEEE Exciter Models

These excitation system models implement the IEEE Std 421.5-2016 “IEEE Recommended Practice for Excitation System Models for Power System Stability Studies” (and selected ENTSO-E variants) within RAMSES. Each model is defined using the CODEGEN domain-specific language (DSL) and compiled into Fortran for time-domain simulation. The DSL describes block diagrams as interconnected transfer function primitives (tf1p, tf1p1z, tf1plim, tfder1p, inlim, pictl, etc.), initial conditions, and algebraic constraints — forming a self-contained, portable model definition.

Usage in Dynamic Data Files

Exciter models in RAMSES are defined as sub-records within a SYNC_MACH block using the EXC keyword, followed by the model name and its parameters. They are not standalone records. The EXC line appears after the machine parameters and before the TOR (torque/governor) line. The entire block ends with a single ; after the TOR record.

SYNC_MACH name bus FP FQ P Q SNOM Pnom H D IBRATIO
                    XT  Xl  Xd  X'd  X"d  Xq  X'q  X"q  m  n  Ra  T'do  T"do  T'qo  T"qo
              EXC model_name  param1  param2  ...
              TOR model_name  param1  param2  ... ;

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Model Index

Model Name	Base Type	PSS	OEL / Limiter	IEEE Reference
AC1A	AC type 1	—	—	IEEE 421.5 Type AC1A
AC1A_MAXEX2	AC type 1	—	MAXEX2 field current limiter	IEEE 421.5 Type AC1A
AC1A_OELHQ	AC type 1	—	OELHQ PID OEL	IEEE 421.5 Type AC1A
AC1A_RETRO	AC type 1 (retrofit)	PSS4B (internal)	—	—
AC1A_RETRO_PSS4B	AC type 1 (retrofit)	PSS4B	—	—
AC4A	AC type 4	—	—	IEEE 421.5 Type AC4A
AC8B	AC type 8	—	—	IEEE 421.5 Type AC8B
AC8B_PSS3B_lim	AC type 8	PSS3B	Integral OEL + SCL	IEEE 421.5 Type AC8B
AC8B_lim	AC type 8	—	Integral OEL + SCL	IEEE 421.5 Type AC8B
DC3A	DC type 3	—	—	IEEE 421.5 Type DC3A
ENTSOE_simp	ENTSO-E simplified	IEEEST (internal)	—	ENTSO-E
ENTSOE_lim	ENTSO-E simplified	IEEEST (internal)	Integral OEL	ENTSO-E
EXHQSC	ST type (HQ)	—	Field current db	—
EXHQSC_MAXEX2	ST type (HQ)	—	MAXEX2 + field db	—
EXHQSC_PSS4B	ST type (HQ)	PSS4B	Field current db	—
EXHQSC_PSS4B_MAXEX2	ST type (HQ)	PSS4B	MAXEX2	—
EXHQSC_PSS4B_OELHQ	ST type (HQ)	PSS4B	OELHQ PID OEL	—
EXPIC1	AC/ST (PIC type)	—	—	—
EXPIC1_PSS2B	AC/ST (PIC type)	PSS2B	—	—
EXPIC1_PSS2B_MAXEX2	AC/ST (PIC type)	PSS2B	MAXEX2	—
IEEET5	DC type 5	—	—	IEEE 421.5 Type DC5A (legacy)
SEXS	ST simplified	—	—	CIGRÉ simplified
SEXS_IEEEST	ST simplified	IEEEST	—	CIGRÉ simplified
SEXS_STAB3_lim	ST simplified	STAB3	Integral OEL	—
ST1A	ST type 1	—	—	IEEE 421.5 Type ST1A
ST1A_IEEEST	ST type 1	IEEEST	—	IEEE 421.5 Type ST1A
ST1A_IEEEST_MAXEX2	ST type 1	IEEEST	MAXEX2	IEEE 421.5 Type ST1A
ST1A_PSS2B	ST type 1	PSS2B	—	IEEE 421.5 Type ST1A
ST1A_PSS2B_MAXEX2	ST type 1	PSS2B	MAXEX2	IEEE 421.5 Type ST1A
ST1A_PSS2B_OELHQ	ST type 1	PSS2B	OELHQ PID OEL	IEEE 421.5 Type ST1A
ST1A_PSS3B	ST type 1	PSS3B	—	IEEE 421.5 Type ST1A
ST1A_PSS3B_OELHQ	ST type 1	PSS3B	OELHQ PID OEL	IEEE 421.5 Type ST1A
ST1A_PSS4B	ST type 1	PSS4B	—	IEEE 421.5 Type ST1A
ST1A_PSS4B_MAXEX2	ST type 1	PSS4B	MAXEX2	IEEE 421.5 Type ST1A
ST1A_PSS4B_OELHQ	ST type 1	PSS4B	OELHQ PID OEL	IEEE 421.5 Type ST1A
ST1A_OELHQ	ST type 1	—	OELHQ PID OEL	IEEE 421.5 Type ST1A
ST1A_lim	ST type 1	—	Integral OEL + SCL	IEEE 421.5 Type ST1A
ST2A	ST type 2	—	—	IEEE 421.5 Type ST2A (via EXPIC1)

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AC Exciter Models

AC1A

The AC1A is a rotating AC exciter with a self-excited field winding and non-linear saturation. It corresponds to IEEE Std 421.5-2016 Type AC1A. The generator terminal voltage $V_t$ is compensated for line drop and filtered before being compared with the reference. An AC alternator supplies the field through a rectifier whose output depends on the commutation voltage $V_E$ and field current $I_{fd}$.

Mathematical Description

The voltage regulator processes the error signal through a lead-lag network and a limited amplifier:

$\Delta V = V_{REF} - V_c - V_F - \Delta V_{PSS}$

$V_1(s) = \Delta V \cdot \frac{1 + sT_C}{1 + sT_B}$

$V_A(s) = V_1 \cdot \frac{K_A}{1 + sT_A}, \quad V_{AMIN} \le V_A \le V_{AMAX}$

The AC exciter integrator with saturation and demagnetization:

$V_{FE} = K_D \cdot I_{fd} + \left(K_E + S_E(V_E)\right) V_E$

$\dot{V}_E = \frac{1}{T_E}(V_R - V_{FE}), \quad 0 \le V_E$

$E_{fd} = V_E \cdot \left(1 - \frac{K_C \cdot I_{fd}}{V_E}\right)$

The derivative feedback (rate feedback) path:

$V_F(s) = E_{fd} \cdot \frac{sK_F/T_F}{1 + sT_F}$

where $S_E(V_E)$ is the saturation function interpolated from the two-point saturation characteristic $(V_{E1}, SE_1)$ and $(V_{E2}, SE_2)$.

Signal Flow

1. Line drop compensation (algeq): $V_{c1} = vcomp(V_t, P, Q, K_v, R_c, X_c)$
2. Voltage measurement filter (tf1p): $V_c \leftarrow V_{c1}$ with time constant $T_R$
3. AVR summation (algeq): $\Delta V = V_{REF} - V_c - V_F$
4. Lead-lag compensator (tf1p1z): $V_1 \leftarrow \Delta V$ with $(T_C, T_B)$
5. Amplifier with limits (tf1plim): $V_2 \leftarrow V_1$ with gain $K_A$, time constant $T_A$, limits $[V_{AMIN}, V_{AMAX}]$
6. UEL high-value gate (max1v1c): $V_3 = \max(V_2, V_{UEL})$
7. OEL low-value gate (min1v1c): $V_4 = \min(V_3, V_{OEL})$
8. Output limiter (lim): $V_R = \text{clamp}(V_4, V_{RMIN}, V_{RMAX})$
9. Exciter integrator (inlim): $V_E \leftarrow (V_R - V_{FE})/T_E$
10. Saturation computation (algeq): $V_{FE}$ from $K_D$, $K_E$, $S_E(V_E)$
11. Rectifier output (algeq): $E_{fd} = vrectif(I_{fd}, V_E, K_C)$
12. Derivative feedback (tfder1p): $V_F \leftarrow V_{FE}$ with gain $K_F/T_F$, time constant $T_F$

Parameters

Parameter	Description	Unit/Type
Kv	Voltage compensation gain	pu
Rc	Resistance for line drop compensation	pu
Xc	Reactance for line drop compensation	pu
TR	Voltage transducer time constant	s
KA	Voltage regulator gain	pu
TA	Voltage regulator time constant	s
TB	Lead-lag denominator time constant	s
TC	Lead-lag numerator time constant	s
VAMAX	Maximum regulator output	pu
VAMIN	Minimum regulator output	pu
KE	Exciter constant (self-excitation term)	pu
TE	Exciter time constant	s
KF	Rate feedback gain	pu
TF	Rate feedback time constant	s
VRMAX	Maximum field voltage	pu
VRMIN	Minimum field voltage	pu
VE1	Saturation factor voltage point 1	pu
SE1	Saturation factor at $V_{E1}$	pu
VE2	Saturation factor voltage point 2	pu
SE2	Saturation factor at $V_{E2}$	pu
KC	Commutation factor (rectifier regulation)	pu
KD	Demagnetization factor	pu
VUEL	UEL input signal	pu

Variants

Model	Description
AC1A	Base model — IEEE Type AC1A
AC1A_MAXEX2	Adds MAXEX2 field current limiter; VOEL moves to reference summation point (LV gate removed)
AC1A_OELHQ	Adds Hydro-Québec PID over-excitation limiter (11-point timer)
AC1A_RETRO	Retrofit variant with internal PSS4B; uses first-order AVR without separate exciter block
AC1A_RETRO_PSS4B	Retrofit variant with external PSS4B speed input

Usage Example

SYNC_MACH g1  g1  1. 1.  0.  0.   800. 760. 3. 0. 0.95
                    XT   0.15  1.1  0.25  0.2  0.7  *  0.2  0.1  6.0257  0.  5.00  0.05  *  0.1
              EXC AC1A   0. 0. 0. 0.02 200.0 0.02 10.0 1.0 7.32 -7.32 1.0 1.0 0.03 1.0 6.03 -5.43 4.18 0.1 3.14 0.033 0.2 0.38 99999
              TOR CONSTANT ;

---

AC4A

The AC4A is a simplified static representation of an AC exciter system with an inner-loop voltage-dependent output limit. It corresponds to IEEE Std 421.5-2016 Type AC4A. The upper output limit is a function of field current: $V_{RMAX,eff} = V_{RMAX} - K_C \cdot I_{fd}$.

Mathematical Description

$\Delta V = V_{REF} - V_c$

$V_I = \text{clamp}(\Delta V, V_{IMIN}, V_{IMAX})$

$V_1(s) = V_I \cdot \frac{1 + sT_C}{1 + sT_B}$

$E_{fd}(s) = V_1 \cdot \frac{K_A}{1 + sT_A}, \quad V_{RMIN} \le E_{fd} \le V_{RMAX} - K_C \cdot I_{fd}$

The variable upper limit is updated algebraically at each time step, making AC4A a time-varying limited integrator system.

Signal Flow

1. Line drop compensation (algeq): $V_{c1}$ from terminal measurements
2. Voltage measurement filter (tf1p): $V_c$ with $T_R$
3. AVR summation (algeq): $\Delta V = V_{REF} - V_c$
4. Input limiter (lim): $V_I = \text{clamp}(\Delta V, V_{IMIN}, V_{IMAX})$
5. Lead-lag (tf1p1z): $V_1 \leftarrow V_I$ with $(T_C, T_B)$
6. UEL high-value gate (max1v1c): $V_2 = \max(V_1, V_{UEL})$
7. Variable upper limit (algeq): $uplim = V_{RMAX} - K_C \cdot I_{fd}$
8. Variable-limit amplifier (tf1pvlim): $E_{fd} \leftarrow V_2$ with $K_A$, $T_A$, limits $[V_{RMIN}, uplim]$

Parameters

Parameter	Description	Unit/Type
Kv	Voltage compensation gain	pu
Rc	Line drop compensation resistance	pu
Xc	Line drop compensation reactance	pu
TR	Measurement filter time constant	s
VIMAX	Maximum input error signal	pu
VIMIN	Minimum input error signal	pu
TC	Lead numerator time constant	s
TB	Lag denominator time constant	s
VUEL	UEL signal value	pu
KA	Regulator gain	pu
TA	Regulator time constant	s
VRMAX	Maximum output (at zero field current)	pu
VRMIN	Minimum output	pu
KC	Field current derating factor	pu

Variants

Model	Description
AC4A	Base model — IEEE Type AC4A, no PSS or OEL

Usage Example

SYNC_MACH g1  g1  1. 1.  0.  0.   800. 760. 3. 0. 0.95
                    XT   0.15  1.1  0.25  0.2  0.7  *  0.2  0.1  6.0257  0.  5.00  0.05  *  0.1
              EXC AC4A   0. 0. 0. 0.02 8.0 -8.0 1.0 10.0 0.0 200.0 0.015 4.44 -4.44 0.0
              TOR CONSTANT ;

---

AC8B

The AC8B is a rotating AC exciter with a PID voltage regulator (rather than the proportional-integral amplifier of earlier types). It corresponds to IEEE Std 421.5-2016 Type AC8B. The PID structure — proportional gain $K_{PR}$, integral gain $K_{IR}$, and derivative gain $K_{DR}$ — provides improved transient response compared to Type AC1A.

Mathematical Description

The PID voltage regulator:

$\Delta V = V_c - V_{REF}$

$V_{PID}(s) = K_{PR} \cdot \Delta V + \frac{K_{IR}}{s} \cdot \Delta V + \frac{sK_{DR}/T_{DR}}{1 + sT_{DR}} \cdot \Delta V$

$V_R(s) = V_{PID} \cdot \frac{K_A}{1 + sT_A}, \quad V_{RMIN} \le V_R \le V_{RMAX}$

The AC exciter with variable limits based on maximum field excitation voltage $V_{FEMAX}$:

$V_{FE} = K_D \cdot I_{fd} + \left(K_E + S_E(V_E)\right) V_E$

$\dot{V}_E = \frac{1}{T_E}(V_R - V_{FE}), \quad V_{EMIN} \le V_E \le \frac{V_{FEMAX} - K_D I_{fd}}{K_E + S_E(V_E)}$

Signal Flow

1. Voltage measurement (tf1p): $V_c$ with $T_R$
2. Error signal (algeq): $\Delta V = V_c - V_{REF}$
3. PID derivative part (tfder1p): $x_{der} \leftarrow \Delta V$ with gain $K_{DR}/T_{DR}$
4. PID proportional-integral (pictl): $x_{propint} \leftarrow \Delta V$ with $K_{IR}$, $K_{PR}$
5. PID sum (algeq): $x_{pid} = x_{propint} + x_{der}$, limited to $[V_{PIDMIN}, V_{PIDMAX}]$
6. Amplifier (tf1plim): $V_R \leftarrow x_{pid}$ with $K_A$, $T_A$
7. Exciter integrator (invlim): $V_E$ with variable limits from $V_{FEMAX}$
8. Saturation and rectification (algeq): $V_{FE}$, $E_{fd}$

Parameters

Parameter	Description	Unit/Type
Kv	Voltage compensation gain	pu
Rc	Line drop resistance	pu
Xc	Line drop reactance	pu
TR	Measurement time constant	s
KPR	PID proportional gain	pu
KIR	PID integral gain	pu/s
KDR	PID derivative gain	pu·s
TDR	PID derivative filter time constant	s
VPIDMAX	PID output upper limit	pu
VPIDMIN	PID output lower limit	pu
KA	Amplifier gain	pu
TA	Amplifier time constant	s
VRMAX	Maximum regulator output	pu
VRMIN	Minimum regulator output	pu
KC	Rectifier commutation factor	pu
KD	Demagnetization factor	pu
KE	Exciter self-excitation constant	pu
TE	Exciter time constant	s
VFEMAX	Maximum field excitation voltage	pu
VEMIN	Minimum exciter output	pu
VE1	Saturation voltage point 1	pu
SE1	Saturation factor at $V_{E1}$	pu
VE2	Saturation voltage point 2	pu
SE2	Saturation factor at $V_{E2}$	pu

Variants

Model	Description
AC8B	Base model — IEEE Type AC8B
AC8B_PSS3B_lim	Adds PSS3B dual-input stabilizer and integral OEL + SCL (stator current limiter)
AC8B_lim	Adds integral OEL and SCL without PSS

Usage Example

SYNC_MACH g1  g1  1. 1.  0.  0.   800. 760. 3. 0. 0.95
                    XT   0.15  1.1  0.25  0.2  0.7  *  0.2  0.1  6.0257  0.  5.00  0.05  *  0.1
              EXC AC8B   0. 0. 0. 0.02 1.0 5.0 0.1 0.1 8.0 -8.0 1.0 0.1 6.5 -6.5 0.2 1.0 1.0 0.5 6.5 0.0 4.0 0.3 3.0 0.33
              TOR CONSTANT ;

---

DC Exciter Models

DC3A

The DC3A represents a non-continuously acting (rheostat-type) DC excitation system. It corresponds to IEEE Std 421.5-2016 Type DC3A. Rather than a proportional amplifier, it uses a three-position switch (VRMIN / VRH / VRMAX) driven by an integrator that holds the rheostat position $V_{RH}$. The switch position is determined by whether the error signal $V_{ERR}$ falls inside or outside a deadband $\pm K_V$.

Mathematical Description

$V_{ERR} = V_{REF} - V_c$

The rheostat integrator:

$\dot{V}_{RH} = \frac{K_V \cdot T_{RH}}{V_{RMAX} - V_{RMIN}} \cdot \text{clamp}(V_{ERR}, -K_V, K_V), \quad V_{RMIN} \le V_{RH} \le V_{RMAX}$

The three-position switch:

$V_R = \begin{cases} V_{RMIN} & V_{ERR} < -K_V \\ V_{RH} & |V_{ERR}| \le K_V \\ V_{RMAX} & V_{ERR} > K_V \end{cases}$

The DC exciter with saturation:

$\dot{E}_{fd} = \frac{1}{T_E}\left[V_R - \left(K_E + S_E(E_{fd})\right) E_{fd}\right]$

Parameters

Parameter	Description	Unit/Type
Kvcomp	Voltage compensation gain	pu
Rc	Line drop resistance	pu
Xc	Line drop reactance	pu
TR	Measurement time constant	s
TRH	Rheostat traversal time	s
KV	Sensitivity of non-continuously acting controller	pu
VRMAX	Maximum field voltage	pu
VRMIN	Minimum field voltage	pu
TE	Exciter time constant	s
KE	Exciter self-excitation constant	pu
E1	Saturation voltage point 1	pu
SE1	Saturation factor at $E_1$	pu
E2	Saturation voltage point 2	pu
SE2	Saturation factor at $E_2$	pu

Variants

Model	Description
DC3A	Base model — IEEE Type DC3A, non-continuously acting rheostat controller

Usage Example

SYNC_MACH g1  g1  1. 1.  0.  0.   800. 760. 3. 0. 0.95
                    XT   0.15  1.1  0.25  0.2  0.7  *  0.2  0.1  6.0257  0.  5.00  0.05  *  0.1
              EXC DC3A   0. 0. 0. 0.0 1.0 1.0 1.0 -1.0 0.8 1.0 3.1 0.33 2.3 0.1
              TOR CONSTANT ;

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ST (Static) Exciter Models

ST1A

The ST1A is a static (thyristor) excitation system with two cascaded lead-lag networks in the voltage regulator path and an inner field current limiter (KLR/ILR). It corresponds to IEEE Std 421.5-2016 Type ST1A. The output limits are proportional to terminal voltage $V_t$, and field current derating applies through $K_C$: $uplim = V_t \cdot V_{RMAX} - K_C \cdot I_{fd}$.

Mathematical Description

The voltage regulator with dual lead-lag and instantaneous field current limiting:

$\Delta V = V_{REF} - V_c + V_{PSS} + V_{UEL,path} + V_F$

$V_1 = \text{clamp}(\Delta V, V_{IMIN}, V_{IMAX})$

$V_2(s) = V_1 \cdot \frac{1 + sT_C}{1 + sT_B}$

$V_3(s) = V_2 \cdot \frac{1 + sT_{C1}}{1 + sT_{B1}}$

$V_A(s) = V_3 \cdot \frac{K_A}{1 + sT_A}, \quad V_{AMIN} \le V_A \le V_{AMAX}$

Instantaneous field current limiter:

$V_{LR} = K_{LR}(I_{fd} - I_{LR})$

$V_5 = V_A - \max(V_{LR}, 0)$

Final output with terminal-voltage-dependent limits:

$E_{fd} = \text{clamp}(V_5, V_t \cdot V_{RMIN}, V_t \cdot V_{RMAX} - K_C \cdot I_{fd})$

Derivative feedback:

$V_F(s) = E_{fd} \cdot \frac{sK_F/T_F}{1 + sT_F}$

Signal Flow

1. Line drop (algeq): $V_{c1}$
2. Measurement filter (tf1p): $V_c$ with $T_R$
3. AVR summation (algeq): $\Delta V$, including UEL (mode 1), PSS, and VF
4. Error limiter (lim): $V_1 \in [V_{IMIN}, V_{IMAX}]$
5. UEL gate (mode 2) (max1v1c): HV gate $V_2$
6. First lead-lag (tf1p1z): $V_3$ with $(T_C, T_B)$
7. Second lead-lag (tf1p1z): $V_4$ with $(T_{C1}, T_{B1})$
8. Amplifier (tf1plim): $V_A$ with $K_A$, $T_A$, $[V_{AMIN}, V_{AMAX}]$
9. Field current limiter (algeq, lim): $V_{LR}$, $V_{LRlim}$
10. Limiter subtraction (algeq): $V_5 = V_A - V_{LRlim}$
11. UEL gate (mode 3) (max1v1c): $V_6$
12. OEL gate (min2v): $V_7 = \min(V_6, V_{OEL})$
13. Variable-limit output (limvb): $E_{fd}$ with terminal-voltage-scaled limits
14. Derivative feedback (tfder1p): $V_F$

Parameters

Parameter	Description	Unit/Type
Kv	Voltage compensation gain	pu
Rc	Line drop resistance	pu
Xc	Line drop reactance	pu
TR	Measurement filter time constant	s
UEL	UEL connection mode (1=summation, 2=HV gate after V1, 3=HV gate after VA)	integer
VIMIN	Input error lower limit	pu
VIMAX	Input error upper limit	pu
VUEL	UEL signal value	pu
TC	First lead-lag numerator	s
TB	First lead-lag denominator	s
TC1	Second lead-lag numerator	s
TB1	Second lead-lag denominator	s
KA	Regulator gain	pu
TA	Regulator time constant	s
VAMIN	Regulator lower limit	pu
VAMAX	Regulator upper limit	pu
VRMIN	Output lower limit scaling factor	pu
VRMAX	Output upper limit scaling factor	pu
KC	Field current derating factor	pu
KF	Rate feedback gain	pu
TF	Rate feedback time constant	s
KLR	Field current limiter gain	pu
ILR	Field current limiter reference	pu

Variants

Model	Description
ST1A	Base model — IEEE Type ST1A
ST1A_IEEEST	Adds IEEEST single-input PSS (speed or power input, selectable)
ST1A_IEEEST_MAXEX2	Adds IEEEST PSS + MAXEX2 field current limiter
ST1A_PSS2B	Adds PSS2B dual-input stabilizer
ST1A_PSS2B_MAXEX2	Adds PSS2B + MAXEX2
ST1A_PSS2B_OELHQ	Adds PSS2B + Hydro-Québec PID OEL
ST1A_PSS3B	Adds PSS3B two-channel second-order filter stabilizer
ST1A_PSS3B_OELHQ	Adds PSS3B + OELHQ
ST1A_PSS4B	Adds PSS4B three-band stabilizer
ST1A_PSS4B_MAXEX2	Adds PSS4B + MAXEX2
ST1A_PSS4B_OELHQ	Adds PSS4B + OELHQ
ST1A_OELHQ	Adds OELHQ PID OEL without PSS
ST1A_lim	Integral OEL + stator current limiter (SCL), simplified structure without Kv/Rc/Xc

Usage Example

SYNC_MACH g1  g1  1. 1.  0.  0.   800. 760. 3. 0. 0.95
                    XT   0.15  1.1  0.25  0.2  0.7  *  0.2  0.1  6.0257  0.  5.00  0.05  *  0.1
              EXC ST1A   0. 0. 0. 0.02 1 -0.87 0.87 0.0 1.0 10.0 0.0 1.0 200.0 0.001 7.8 -6.7 0.038 0.0 999.0 0.0 99.0 0.0 0.0
              TOR CONSTANT ;

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ST2A (via EXPIC1)

The EXPIC1 model implements a static exciter with an AC rotating bus-fed rectifier and an integrating (PI-type) amplifier path: $K_A(1 + sT_A)/s$. The output $V_B$ is proportional to the AC voltage phasor magnitude, creating a bus-fed topology analogous to IEEE Type ST2A. When $K_P = K_I = 0$, the rectifier gain is unity.

Mathematical Description

The AC exciter voltage and rectifier:

$V_E = |K_P V_t + jK_I V_t|, \quad V_B = V_E \cdot \left(1 - \frac{K_C I_{fd}}{V_E}\right)^+$

The integrating amplifier:

$G_{amp}(s) = K_A \cdot \frac{1 + sT_A}{s}$

The field voltage integrator:

$\dot{E}_{fd} = \frac{1}{T_E}\left[V_R \cdot V_B - K_E \cdot E_{fd}\right], \quad E_{FDMIN} \le E_{fd} \le E_{FDMAX}$

Signal Flow

1. Voltage measurement (tf1p): $V_c$ with $T_R$
2. Summation (algeq): $\Delta V = V_{REF} - V_c - V_F - \Delta V_{PSS}$
3. UEL gate (max1v1c): clamped to $V_{UEL}$
4. PI amplifier (pictl): $V_A$ with $K_{gain} = K_A \cdot T_A$ and $K_A$
5. Output limiter (lim): $V_R \in [V_{RMIN}, V_{RMAX}]$
6. Rectifier voltage (algeq): $V_E$, $V_B$
7. Field integrator (inlim): $E_{fd}$ from $V_R \cdot V_B - K_E \cdot E_{fd}$
8. Derivative feedback (tfder1p): $V_F$

Parameters

Parameter	Description	Unit/Type
Kvcomp	Voltage compensation gain	pu
Rc	Line drop resistance	pu
Xc	Line drop reactance	pu
TR	Measurement time constant	s
VUEL	UEL signal	pu
KA	Amplifier gain	pu
TA	Amplifier time constant	s
VRMAX	Maximum regulator output	pu
VRMIN	Minimum regulator output	pu
KF	Rate feedback gain	pu
TF	Rate feedback time constant	s
KE	Exciter self-excitation constant	pu
EFDMAX	Maximum field voltage	pu
EFDMIN	Minimum field voltage	pu
TE	Field integrator time constant	s
KP	AC source voltage proportional factor	pu
KI	AC source voltage quadrature factor	pu
KC	Commutation voltage drop factor	pu

Variants

Model	Description
EXPIC1	Base bus-fed static exciter
EXPIC1_PSS2B	Adds PSS2B dual-input stabilizer
EXPIC1_PSS2B_MAXEX2	Adds PSS2B + MAXEX2 field current limiter

Usage Example

SYNC_MACH g1  g1  1. 1.  0.  0.   800. 760. 3. 0. 0.95
                    XT   0.15  1.1  0.25  0.2  0.7  *  0.2  0.1  6.0257  0.  5.00  0.05  *  0.1
              EXC EXPIC1   0. 0. 0. 0.02 0.0 200.0 0.02 99.0 -99.0 0.0 1.0 1.0 8.0 -8.0 0.5 0.0 1.0 0.0
              TOR CONSTANT ;

---

Other IEEE Models

IEEET5

The IEEET5 (also referenced as DC5A in some conventions) is a non-continuously acting exciter similar to DC3A but uses an inner limiter block lim_civ that gates the integrator holding signal within a deadband $\pm K_V$. This creates the three-state (hold/raise/lower) behavior of rheostatic controllers.

Mathematical Description

$V_{ERR} = V_{REF} - V_c$

The integrator for rheostat position:

$\dot{V}_{RH} = \frac{1}{T_{RH}} \cdot V_{ERR}, \quad V_{RMIN} \le V_{RH} \le V_{RMAX}$

The lim_civ block implements the deadband gating so that integration is active only when $|V_{ERR}| > K_V$:

$V_R = \begin{cases} V_{RMIN} & V_{ERR} < -K_V \\ V_{RH} & |V_{ERR}| \le K_V \\ V_{RMAX} & V_{ERR} > K_V \end{cases}$

$\dot{E}_{fd} = \frac{1}{T_E}\left[V_R - \left(K_E + S_E(E_{fd})\right) E_{fd}\right]$

Parameters

Parameter	Description	Unit/Type
Kvcomp	Voltage compensation gain	pu
Rc	Line drop resistance	pu
Xc	Line drop reactance	pu
TRH	Rheostat time	s
KV	Controller sensitivity deadband	pu
VRMAX	Maximum field voltage	pu
VRMIN	Minimum field voltage	pu
TE	Exciter integrator time constant	s
KE	Exciter self-excitation constant	pu
E1	Saturation point 1	pu
SE1	Saturation factor at $E_1$	pu
E2	Saturation point 2	pu
SE2	Saturation factor at $E_2$	pu

Variants

Model	Description
IEEET5	Base model — non-continuously acting DC exciter

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SEXS

The SEXS (Simplified Excitation System) is a minimal two-parameter static exciter model from CIGRÉ publications, widely used for cases where detailed exciter data is unavailable. It has no measurement filter, no line drop compensation, and no rate feedback — just a lead-lag network and a limited first-order block.

Mathematical Description

$\Delta V_{AVR} = V_t - V_o + V_{PSS}$

$G_{lag}(s) = \frac{1 + sT_A}{1 + sT_B}$

$E_{fd}(s) = G_{lag}(\Delta V_{AVR}) \cdot \frac{K_E}{1 + sT_E}, \quad E_{MIN} \le E_{fd} \le E_{MAX}$

where $V_o = V_t + E_{fd,0}/K_E$ is computed from initial conditions to achieve zero initial error.

Parameters

Parameter	Description	Unit/Type
TA	Lead-lag numerator time constant	s
TB	Lead-lag denominator time constant	s
KE	Exciter gain	pu
TE	Exciter time constant	s
EMIN	Minimum field voltage	pu
EMAX	Maximum field voltage	pu

Variants

Model	Description
SEXS	Base simplified exciter
SEXS_IEEEST	Adds IEEEST PSS (multi-mode: speed, power, or accelerating power input)
SEXS_STAB3_lim	Adds STAB3 PSS + integral OEL

Usage Example

SYNC_MACH g1  g1  1. 1.  0.  0.   800. 760. 3. 0. 0.95
                    XT   0.15  1.1  0.25  0.2  0.7  *  0.2  0.1  6.0257  0.  5.00  0.05  *  0.1
              EXC SEXS   0.1 10.0 25.0 0.5 -5.0 5.0
              TOR CONSTANT ;

---

EXPIC1 / EXHQSC

The EXHQSC is a Hydro-Québec static exciter model based on the ST1A topology but extended with an internal field current deadband controller (db block). This controller measures the filtered field current $I_{ff}$ through a first-order filter with time constant $T_I$, compares it against asymmetric limits $[I_{FMIN}, I_{FMAX}]$, and feeds back a corrective signal $V_{lr}$ through a first-order lag, contributing to the amplifier output before the variable-limit clamp.

Mathematical Description

The main AVR path follows ST1A topology with two cascaded first-order blocks (instead of lead-lag):

$V_2(s) = \Delta V \cdot \frac{K_A}{1 + sT_A}$

$V_4(s) = V_2 \cdot \frac{1 + sT_{A1}}{1 + sT_{A2}}$

The field current limiter deadband:

$I_{ff}(s) = I_{fd} \cdot \frac{1}{1 + sT_I}$

$I_{fdb} = db(I_{ff}; I_{FMIN}, K_{MIN}, I_{FMAX}, K_{MAX})$

$V_{lr}(s) = I_{fdb} \cdot \frac{1}{1 + sT_A}$

$E_{fd} = \text{limvb}(V_4 + K_A \cdot V_{lr}; V_{vmin}, V_{vmax})$

where $V_{vmin} = V_t \cdot V_{RMIN} - K_C I_{fd}$ and $V_{vmax} = V_t \cdot V_{RMAX} - K_C I_{fd}$.

Parameters

Parameter	Description	Unit/Type
Kv	Voltage compensation gain	pu
Rc	Line drop resistance	pu
Xc	Line drop reactance	pu
UEL	UEL connection flag	integer
VUEL	UEL signal	pu
TR	Measurement time constant	s
VMIN	Input error lower limit	pu
VMAX	Input error upper limit	pu
TA1	Second filter numerator	s
TA2	Second filter denominator	s
KA	Regulator gain	pu
TA	Regulator time constant	s
VRMIN	Output lower limit factor	pu
VRMAX	Output upper limit factor	pu
KC	Field current derating factor	pu
KF	Derivative feedback gain	pu
TF	Derivative feedback time constant	s
TI	Field current filter time constant	s
IFMIN	Lower deadband threshold	pu
IFMAX	Upper deadband threshold	pu
KMIN	Lower deadband gain	pu
KMAX	Upper deadband gain	pu

Variants

Model	Description
EXHQSC	Base Hydro-Québec static exciter with field current deadband
EXHQSC_MAXEX2	Adds MAXEX2 field current limiter
EXHQSC_PSS4B	Adds PSS4B three-band stabilizer
EXHQSC_PSS4B_MAXEX2	Adds PSS4B + MAXEX2
EXHQSC_PSS4B_OELHQ	Adds PSS4B + OELHQ PID OEL

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ENTSO-E Models

ENTSOE_simp

The ENTSO-E simplified exciter combines a built-in speed-signal PSS with a simple lead-lag AVR and first-order exciter block. It is the standard ENTSO-E model for dynamic studies where detailed exciter data is unavailable.

Mathematical Description

The PSS (speed input $\omega - 1$) uses two washout stages and two lead-lag stages:

$V_{PSS}(s) = (\omega - 1) \cdot \frac{sT_{W1}}{1+sT_{W1}} \cdot \frac{sT_{W2}}{1+sT_{W2}} \cdot K_{S1} \cdot \frac{1+sT_1}{1+sT_2} \cdot \frac{1+sT_3}{1+sT_4}$

The AVR:

$\Delta V_{AVR} = V_t - V_o + V_{PSS}$

$G_{lag}(s) = \frac{1 + sT_A}{1 + sT_B}$

$E_{fd}(s) = G_{lag}(\Delta V_{AVR}) \cdot \frac{K_E}{1 + sT_E}, \quad E_{MIN} \le E_{fd} \le E_{MAX}$

Parameters

Parameter	Description	Unit/Type
TW1	First washout time constant	s
TW2	Second washout time constant	s
KS1	PSS gain	pu
T1	First lead-lag numerator	s
T2	First lead-lag denominator	s
T3	Second lead-lag numerator	s
T4	Second lead-lag denominator	s
VSTMIN	PSS output lower limit	pu
VSTMAX	PSS output upper limit	pu
TA	AVR lead-lag numerator	s
TB	AVR lead-lag denominator	s
KE	Exciter gain	pu
TE	Exciter time constant	s
EMIN	Minimum field voltage	pu
EMAX	Maximum field voltage	pu

Variants

Model	Description
ENTSOE_simp	Base ENTSO-E simplified model with integrated PSS
ENTSOE_lim	Adds integral OEL (same structure as AC8B_lim OEL)

Usage Example

SYNC_MACH g1  g1  1. 1.  0.  0.   800. 760. 3. 0. 0.95
                    XT   0.15  1.1  0.25  0.2  0.7  *  0.2  0.1  6.0257  0.  5.00  0.05  *  0.1
              EXC ENTSOE_simp   10.0 3.0 10.0 0.2 0.1 0.1 0.1 -0.05 0.05 0.05 0.1 25.0 1.0 -10.0 10.0
              TOR CONSTANT ;

---

PSS Models

Power System Stabilizers (PSS) inject an additional signal $V_{PSS}$ at the AVR summation point to damp electromechanical oscillations. All variants listed in the model index table include one of the PSS types described here.

PSS2B — Dual-Input Stabilizer

PSS2B accepts two input signals (typically speed $\omega$ and electrical power $P_e$) and processes them through independent washout chains before combining. It corresponds to IEEE Std 421.5-2016 Type PSS2B.

$V_{S1} = \text{clamp}(VSI_1, V_{S1MIN}, V_{S1MAX})$

Channel 1 (input 1 washout):

$V_{S1} \xrightarrow{sT_{W1}/(1+sT_{W1})} \xrightarrow{sT_{W2}/(1+sT_{W2})} \xrightarrow{1/(1+sT_6)} pss_{3}$

Channel 2 (input 2 washout):

$V_{S2} \xrightarrow{sT_{W3}/(1+sT_{W3})} \xrightarrow{sT_{W4}/(1+sT_{W4})} \xrightarrow{K_{S2}/(1+sT_7)} pss_{6}$

Combination and lead-lag chain (variant M=5, N=1 implemented):

$pss_7 = pss_3 - K_{S3} \cdot pss_6$

$pss_7 \xrightarrow{(1+sT_8)/(1+sT_9)} \xrightarrow{1/(1+sT_9)^4} pss_{12}$

$pss_{13} = pss_{12} + pss_6$

$pss_{13} \xrightarrow{K_{S1}(1+sT_1)/(1+sT_2)} \xrightarrow{(1+sT_3)/(1+sT_4)} \xrightarrow{(1+sT_{10})/(1+sT_{11})} V_{PSS}$

$V_{PSS} = \text{clamp}(V_{PSS,unlim}, V_{STMIN}, V_{STMAX})$

PSS2B Parameters (additional to base exciter):

Parameter	Description
speedinput	Input selection (1=speed+power, 2=power+speed)
TW1, TW2	Channel 1 washout time constants
T6	Channel 1 filter
TW3, TW4	Channel 2 washout time constants
T7, KS2	Channel 2 filter gain and time constant
KS3	Channel coupling gain
T8, T9	Ramp-tracking filter
KS1	Overall PSS gain
T1–T4, T10, T11	Lead-lag time constants
VS1MIN, VS1MAX	Input 1 limits
VS2MIN, VS2MAX	Input 2 limits
VSTMIN, VSTMAX	Output limits

---

PSS3B — Two-Input Second-Order Filter Stabilizer

PSS3B processes two input channels through measurement filters and washout stages, then combines them and applies two cascaded second-order lead-lag filters. It corresponds to IEEE Std 421.5-2016 Type PSS3B.

$V_{SI1} \xrightarrow{1/(1+sT_1)} \xrightarrow{K_{S1} sT_{W1}/(1+sT_{W1})} pss_2$

$V_{SI2} \xrightarrow{1/(1+sT_2)} \xrightarrow{K_{S2} sT_{W2}/(1+sT_{W2})} pss_4$

$pss_5 = pss_2 - pss_4$

$pss_5 \xrightarrow{K_S sT_{W3}/(sT_{W4}+1)} pss_6$

$pss_6 \xrightarrow{\text{TF1: } \frac{A_2 + sA_1 + s^2/A_4}{A_4 + sA_3 + s^2/A_4}} \xrightarrow{\text{TF2: } \frac{A_6+sA_5+s^2/A_8}{A_8+sA_7+s^2/A_8}} V_{PSS}$

$V_{PSS} = \text{clamp}(V_{PSS,unlim}, V_{STMIN}, V_{STMAX})$

PSS3B Parameters (additional):

Parameter	Description
speedinput	Input mode selection
T1, KS1, TW1	Channel 1 filter, gain, washout
T2, KS2, TW2	Channel 2 filter, gain, washout
KS, TW3, TW4	Combined washout gain and time constants
A1–A8	Second-order filter coefficients
VSTMIN, VSTMAX	Output limits

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PSS4B — Three-Band Multi-Input Stabilizer

PSS4B is a three-band stabilizer that separates the speed deviation signal into low-, intermediate-, and high-frequency components. Each band uses a pair of lead-lag filters. This model corresponds to IEEE Std 421.5-2016 Type PSS4B.

The speed signal $\Delta\omega = \omega - 1$ passes through a digital transducer (tf2p2z) to obtain the low/intermediate input. Electrical power $P_e$ passes through two washouts and a low-pass filter to derive the high-frequency component $\Delta\omega_H$.

Low-frequency band ($\Delta\omega_{L-I}$ input):

$pss_4 = \Delta\omega_{L-I} \cdot \frac{K_{L1}(K_{L11} + sT_{L1})}{1 + sT_{L2}}$

$pss_5 = \Delta\omega_{L-I} \cdot \frac{K_{L2}(K_{L17} + sT_{L7})}{1 + sT_{L8}}$

$V_{PSSL} = \text{clamp}\!\left(K_L(pss_4 - pss_5),\, V_{LMin}, V_{LMax}\right)$

Intermediate-frequency band (same $\Delta\omega_{L-I}$ input):

$V_{PSSI} = \text{clamp}\!\left(K_I(pss_7 - pss_8),\, V_{IMin}, V_{IMax}\right)$

High-frequency band ($\Delta\omega_H$ input):

$V_{PSSH} = \text{clamp}\!\left(K_H(pss_{10} - pss_{11}),\, V_{HMin}, V_{HMax}\right)$

$V_{PSS} = \text{clamp}(V_{PSSL} + V_{PSSI} + V_{PSSH},\, V_{STMin}, V_{STMax})$

PSS4B Parameters (additional):

Parameter	Description
H	Generator inertia constant (for high-freq path)
KL1, KL11, TL1, TL2	Low-band filter 1
KL2, KL17, TL7, TL8	Low-band filter 2
KL, VLMax, VLMin	Low-band gain and limits
KI1, KI11, TI1, TI2	Intermediate-band filter 1
KI2, KI17, TI7, TI8	Intermediate-band filter 2
KI, VIMax, VIMin	Intermediate-band gain and limits
KH1, KH11, TH1, TH2	High-band filter 1
KH2, KH17, TH7, TH8	High-band filter 2
KH, VHMax, VHMin	High-band gain and limits
VSTMax, VSTMin	Total output limits

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IEEEST — Single-Input Stabilizer

The IEEEST is a general-purpose single-input PSS with selectable input signal (speed deviation, electrical power, or computed accelerating power). It corresponds to IEEE Std 421.5-2016 Type PSS1A. Two second-order lead-lag filters provide frequency shaping before two first-order lead-lags and a washout stage.

$VS_1 \xrightarrow{\frac{1}{A_2 + sA_1 + s^2/(A_1 A_2)}} \xrightarrow{\frac{A_6 + sA_5 + s^2/(A_3 A_4)}{A_4 + sA_3 + s^2/(A_3 A_4)}} VS_3$

$VS_3 \xrightarrow{\frac{1+sT_1}{1+sT_2}} \xrightarrow{\frac{1+sT_3}{1+sT_4}} \xrightarrow{\frac{K_S sT_5/T_6}{1+sT_6}} V_{PSS}$

$V_{PSS} = \text{clamp}(V_{PSS,unlim}, V_{LSMIN}, V_{LSMAX})$

Input selection (speedinput): 1 = rotor speed deviation, 3 = electrical power, 4 = computed accelerating power ($2H \, d\omega/dt$).

IEEEST Parameters (additional):

Parameter	Description
speedinput	Input mode (1, 3, or 4)
A1–A6	Second-order filter coefficients
T1–T6	Lead-lag and washout time constants
KS	Overall PSS gain
LSMIN, LSMAX	Output limits
KS4	Inertia constant for accelerating power (= 2H)
TW4	Derivative filter time constant

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STAB3 — Power-Input Stabilizer

The STAB3 is a simplified PSS that takes electrical power $P_e$ as input, applies two sequential first-order filters and a washout-type derivative block, producing a stabilizing signal.

$P_e \xrightarrow{1/(1+sT_t)} stab_1 \xrightarrow{1/(1+sT_{X1})} stab_2 \xrightarrow{-K_X s/(1+sT_{X2})} stab_3$

$V_{PSS} = \text{clamp}(stab_3, -V_{LIM}, V_{LIM})$

STAB3 Parameters:

Parameter	Description
Tt	Input measurement time constant
TX1	First filter time constant
KX	Stabilizer gain
TX2	Washout time constant
VLIM	Output limit

---

OEL and Limiter Models

Over-Excitation Limiters (OEL) prevent sustained field current overloads that would thermally damage the field winding. They generate a signal $V_{OEL}$ that reduces the AVR output when field current exceeds thermal limits.

OELHQ — Hydro-Québec PID OEL

The OELHQ OEL is a sophisticated limiter developed by Hydro-Québec. It uses a piece-wise linear timer (11 operating points) to model the thermal capability curve, combined with a hysteresis latch and a full PID controller.

Timer phase: The measured field current $I_{fd,mes}$ (filtered with time constant $T_m$) drives a timer11 block with 11 $(I_{fd}, T_{limit})$ pairs defining the permitted over-current duration. When the accumulated timer exceeds 1.0, the hyst block locks the reference to $I_{FDPL}$ for the remainder of the simulation.

PID phase: Once the timer triggers, the error signal drives a PID controller:

$e_{IFD} = I_{fd,ref} - I_{fd,mes}$

$V_{OEL,der}(s) = e_{IFD} \cdot \frac{sK_{Doel}/T_{Doel}}{1 + sT_{Doel}}$

$V_{OEL,PI}(s) = K_{Poel} \cdot e_{IFD} + \frac{K_{Ioel}}{s} \cdot e_{IFD}, \quad 0 \le V_{OEL,PI} \le V_{OELMAX}$

$V_{OEL} = \text{clamp}(V_{OEL,der} + V_{OEL,PI},\, V_{OELMIN},\, V_{OELMAX})$

$V_{OEL}$ is applied at the AVR LV gate (min2v) or at the reference summation point, reducing the effective reference voltage.

OELHQ Parameters:

Parameter	Description
Tm	Field current measurement filter time constant
IFDTH	Hysteresis upper threshold (= $I_{FDDES}$ at steady state)
IFDPL	Hysteresis lower threshold (permanent limit, e.g. 1.0 pu)
KIoel	OEL integral gain
KPoel	OEL proportional gain
KDoel	OEL derivative gain
TDoel	OEL derivative filter time constant
VOELMAX	Maximum OEL output (= 0 pu in LV gate convention)
VOELMIN	Minimum OEL output (negative, e.g. −0.95 pu)
IFD1–IFD11	Thermal curve current points
TIFD1–TIFD11	Thermal curve time limit points

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MAXEX2 — Field Current Limiter with Timer and Hysteresis

The MAXEX2 is a field current limiter derived from IEEE work, using a simplified three-point piece-wise linear timer instead of the full thermal curve of OELHQ. It is designed for the EXST1/ST1A topology where the OEL output is injected at the reference summation point (not the LV gate).

Timer phase: The measured current $I_{fd,mes}$ (selected as either field current or $E_{fd}$ via parameter IC) drives a timer3 block with three $(I_{fd}, T)$ operating points. The hyst block latches when timer ≥ 1.

Integral phase: Once latched, the error drives a limited integrator:

$e_{IFD} = I_{fd,ref} - I_{fd,mes}$

$\dot{V}_{OEL} = \frac{e_{IFD}}{K_{MX}}, \quad V_{LOW} \le V_{OEL} \le 0$

$V_{OEL}$ is subtracted from the reference ($V_{REF} - V_{OEL}$, i.e. negative reduces reference).

MAXEX2 Parameters:

Parameter	Description
IC	Input selection: 0 = $E_{fd}$, 1 = $I_{fd}$
IFDrated	Rated field current (reference)
IFD1, TIME1	Timer point 1 (current level, allowable duration)
IFD2, TIME2	Timer point 2
IFD3, TIME3	Timer point 3
IFDDES	Desired steady-state field current after limiting
KMX	Integrator time constant inverse (1/KMX = integration rate)
VLOW	Lower limit of OEL output (e.g. −1.0 pu)

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Integral OEL (_lim variants)

The simple integral OEL used in AC8B_lim, ST1A_lim, SEXS_STAB3_lim, and ENTSOE_lim variants computes the over-excitation signal through a clamped integrator acting on the difference between measured field current and $1.05 \cdot I_{FDN}$, with an input clamp at $0.35 \cdot I_{FDN}$.

$\Delta I_{fd,1} = I_{fd} - 1.05 \cdot I_{FDN}$

$\Delta I_{fd,2} = \min(\Delta I_{fd,1},\, 0.35 \cdot I_{FDN})$

$\dot{x}_{OEL} = \frac{\Delta I_{fd,2}}{T_{OEL}}, \quad L_{OEL} \le x_{OEL} \le U_{OEL}$

$V_{OEL} = \text{clamp}(K_{OEL} \cdot x_{OEL},\, OEL_{LI},\, 0)$

A stator current limiter (SCL) with analogous structure acts on $I_{st} = \sqrt{P^2 + Q^2}/V_t$ relative to $1.025 \cdot I_{GN}$.

Integral OEL Parameters (in _lim variants):

Parameter	Description
IFDN	Nominal field current (OEL trigger at 1.05×)
TOEL	OEL integrator time constant
LOEL	OEL integrator lower limit
UOEL	OEL integrator upper limit
KOEL	OEL output gain
OELLI	OEL output lower limit
IGN	Nominal stator current (SCL trigger at 1.025×)
TSCL	SCL integrator time constant
LSCL	SCL integrator lower limit
USCL	SCL integrator upper limit
KSCL	SCL output gain
SCLLI	SCL output lower limit

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For full documentation of the CODEGEN DSL primitives used in these models (tf1p, tf1p1z, tf1plim, inlim, pictl, etc.), see the CODEGEN Blocks Library.