Optimal Portfolio of Distinct Frequency-Response Services in Low-Inertia Systems

Requirements for Interdependent Reserve Types

“…To emulate this dependency on nominal PFR reserve, we model the generator's governor ramp rate as being proportional to the nominal PFR reserve R i , as suggested in [11] and [12]. Let's denote the proportionality constant by λ i ≥ 0, which may vary among generators.…”

“…where α(M ) is termed the equivalency ratio and υ(M ) is the frequency response reserve requirement (Rfrr), both of which are functions of the total system inertia. Reference [17] determines these two functions empirically based on simulation studies so that satisfaction of constraint (12) will ensure sufficient reserve to prevent the frequency from violating the minimum frequency threshold of ω min = 59.4Hz in response to an outage of size L, where L = 2750MW in their work. The first three columns of Table I additionally presents the ratio α(M ) υ(M ) , which is approximately constant across all inertia levels.…”

“…ERCOT's real-time co-optimization formulation must include algebraic requirements that couple PFR and FFR reserve. References [10][11][12][13] derive PFR reserve requirements from first principles without accounting for FFR reserve as defined by ERCOT. Although [11] and [12] use a model that incorporates fixed time delays that vary among generators, their model cannot accommodate FFR reserve, which is deployed at a fixed frequency.…”

“…References [10][11][12][13] derive PFR reserve requirements from first principles without accounting for FFR reserve as defined by ERCOT. Although [11] and [12] use a model that incorporates fixed time delays that vary among generators, their model cannot accommodate FFR reserve, which is deployed at a fixed frequency. Reference [13] uses a general model of a generator that is capable of accommodating FFR reserve; however, they utilize a pre-determined frequency trajectory, which would effectively also fix the time that FFR reserve is deployed.…”

“…We claim that this model accurately depicts the ramping limits observed in [8], which are imposed by thermal and stability limitations of a generator. The second PFR reserve limit is termed the proportional PFR reserve limit and assumes that the governor ramp rates vary proportionally with the amount of nominal PFR reserve allocated to a generator, similar to the ramping model used in [11] and [12]. This model represents dynamic generator models that mimic a low pass filter on the droop reference signal.…”