Generators

Generators present all type of generation, e.g., both classical and renewable generation

Parameters

Set of parameters used to model DC branches as defined in the input data

name	symb.	unit	type	default	definition
index	$g$	-	Int	-	unique index of the generator
gen_bus	$i$	-	Int	-	unique index of the bus to which the generator is connected to
pg	$P_{g}$	p.u.	Real	-	active power generation - used as input in power flow calculations
qg	$Q_{g}$	p.u.	Real	-	reactive power generation - used as input in power flow calculations, positive sign is an injection
pmin	$\underline{P_{g}}$	p.u.	Real	-	minimum stable operating power of the generator
pmax	$\overline{P_{g}}$	p.u.	Real	-	maximum power rating of the generator
qmin	$\underline{Q_{g}}$	p.u.	Real	-	minimum reactive power of the generator
qmax	$\overline{Q_{g}}$	p.u.	Real	-	maximum reactive power of the generator
gen_status	$\delta_{dc}$	-	Int	-	status indicator of the generator
mbase	$P_{base}$	p.u.	Real	-	MVA base of the generator
vg	$V_{g}^{set}$	p.u.	Real	-	target voltage of generator - used in power flow calculations for PV nodes
mut	$mut_{g}$	-	Int	-	minimum up time for generator used in unit commitment problems, expressed as a multiple of the UC time step
mdt	$mdt_{g}$	-	Int	-	minimum down time for generator used in unit commitment problems, expressed as a multiple of the UC time step
ramp_rate	$\Lambda_{g}$	p.u. / time step	Real	-	ramp rate of the generator used in UC problem
ramprateper_s	$\Lambda_{g}^{s}$	p.u. / s	Real	-	ramp rate of the generator used in frequency constrained UC problem
inertia_constant	$H_{g}$	s	Real	-	inertia constant of the generator used in frequency constrained UC problem
fcr_contribution	$\delta_{g}^{fcr}$	-	Int	-	Indicator if generator g participates in providing frequency containtment reserves
area	$a_{g}$	-	Int	-	Area in which the generator is located, used for tie line contingencies in frequency constrained UC problem
zone	$z_{g}$	-	Int	-	Zone in which the generator is located, used for loss of infeed contingencies in frequency constrained UC problem
model	$m_{g}$	-	Int	-	Generator cost model, 1 = piecewise linear, 2 = polynomial (matpower style)
ncost	$n_{g}$	-	Int	-	Number of polynomial coefficients for generator costs
startup	$c_{g}^{suc}$	Currency	Real	-	Start-up cost in the currency of your choice
shutdown	$c_{c}^{sdc}$	Currency	Real	-	Shut-down cost in the currency of your choice
cost	$c_{g}$	Currency / p.u.	Real	-	Vector with coeffcients of the polynomial cost function
res	$res_{g}$	-	Int	-	True / false indicator for RES generators

Variables

Optimisation variables representing generator behaviour

name	symb.	unit	formulation	definition
pg	$P_{g}$	p.u.	ACP, ACR, LPAC, IVR, SOC, DCP, NF	Active power set point of generator g
qg	$Q_{g}$	p.u.	ACP, ACR, LPAC, IVR, SOC, DCP, NF	Active power set point of generator g
alpha_g	$\alpha_{g}$	-	ACP, ACR, LPAC, IVR, SOC, DCP, NF	On / off status of generator g, binary
beta_g	$\beta_{g}$	-	ACP, ACR, LPAC, IVR, SOC, DCP, NF	Start-up decision for generator g, binary or continous -> setting "relaxucbinaries"
gamma_g	$\gamma_{g}$	-	ACP, ACR, LPAC, IVR, SOC, DCP, NF	Shut-down decision for generator g, binary or continous -> setting "relaxucbinaries"
dpg_up	$\Delta P_{g}^{\uparrow}$	p.u.	ACP, ACR, LPAC, IVR, SOC, DCP, NF	Upwards re-dispatch of generator g
dpg_down	$\Delta P_{g}^{\downarrow}$	p.u.	ACP, ACR, LPAC, IVR, SOC, DCP, NF	Downwards re-dispatch of generator g
pg_droop	$\Delta P_{g}^{fcr}$	p.u.	ACP, ACR, LPAC, IVR, SOC, DCP, NF	FCR contribution of generator g
pgdroopabs	$\Delta P_{g}^{fcr,abs}$	p.u.	ACP, ACR, LPAC, IVR, SOC, DCP, NF	Absolute value of FCR contribution of generator g

Constraints

Active and reactive power limits

\[\begin{align} \underline{P_{g}} &\leq P_{g} \leq \overline{P_{g}} \\ \underline{Q_{g}} &\leq P_{g} \leq \overline{Q_{g}} \\ \end{align}\]

Upwards and downwards redispatch limits

\[\begin{align} 0 &\leq \Delta P_{g}^{\uparrow} \leq \overline{P_{g}} - \underline{P_{g}} \\ 0 &\leq \Delta P_{g}^{\downarrow}\leq \overline{P_{g}} - \underline{P_{g}} \\ \end{align}\]

\[\begin{align} -(\overline{P_{g}} - \underline{P_{g}}) \cdot \delta_{g}^{fcr} &\leq \Delta P_{g}^{fcr} \leq (\overline{P_{g}} - \underline{P_{g}}) \cdot \delta_{g}^{fcr} \\ 0 &\leq \Delta P_{g}^{fcr,abs} \leq (\overline{P_{g}} - \underline{P_{g}}) \cdot \delta_{g}^{fcr} \\ \end{align}\]

Unit commitment constraints

\[\begin{align} \underline{P_{g}} \cdot \alpha_{g,t} &\leq P_{g,t} \leq \overline{P_{g}} \cdot \alpha_{g,t} \\ P_{g,t} - P_{g,t-1} &\leq \Lambda_{g} \alpha_{g,t} + (\underline{P_{g}} - \Lambda_{g}) \\ P_{g,t-1} - P_{g,t} &\leq \Lambda_{g} \alpha_{g,t} + \underline{P_{g}} \cdot \gamma_{g,t} \\ \alpha_{g,t} &\geq \sum_{t'=t+1-mut_{g}}^{t} \beta_{g,t'} \\ 1-\alpha_{g,t} &\geq \sum_{t'=t+1-mdt_{g}}^{t} \gamma_{g,t'} \\ 0 &=\alpha_{g,t-1} - \alpha_{g,t} + \beta_{g,t} - \gamma_{g,t} \\ \end{align}\]