Power Generation Dispatch, Synchronous Turbine Governors & Primary Frequency Control
Parallel Generator Speed-Droop Governor Load Sharing Formula
Calculate Composite Island Frequency Stiffness K_tot (MW/Hz), Settling Bus Frequency f_bus (Hz), Unit 1 Active Load P_1 (MW), and Unit 2 Active Load P_2 (MW).
Why two parallel generators NEVER fight each other under proportional speed droop—and stiffer (smaller R%) governors grab more MW!
Two synchronous generators tied to a common AC bus MUST run at identical electrical frequency, so attempting to run both in zero-droop isochronous mode causes violent hunting as tiny speed-reference mismatches swing megawatts from rail to rail! Primary turbine governors introduce deliberate Speed Droop Regulation R_% (typically 4%–5% frequency drop from no-load f_nl to 100% rated power P_rated), giving each unit a linear Frequency-Response Stiffness K_i = P_rated,i / (f_nl * (R_%,i / 100)) MW/Hz! When a microgrid or islanded industrial plant demands total load P_load (MW) from two units synchronized at identical no-load setpoint f_nl, bus frequency settles smoothly by Delta_f = P_load / (K_1 + K_2) to f_bus = f_nl - Delta_f, splitting load strictly in proportion to each unit’s stiffness: P_1 = K_1 * Delta_f and P_2 = K_2 * Delta_f!
Verify on a 330 MW Islanded Industrial Cogeneration Bus—Unit_1_Rating = 200.0 MW at Droop R_1 = 4.0% (B2, B3 -> K_1 = 83.33 MW/Hz), Unit_2_Rating = 300.0 MW at Droop R_2 = 5.0% (B4, B5 -> K_2 = 100.00 MW/Hz), Synchronized_NoLoad_Freq f_nl = 60.00 Hz (B6), and Total_Plant_Demand = 330.0 MW (B7): Composite Bus Stiffness equals 183.33 MW/Hz (E2), Settling Bus Frequency drops 1.800 Hz to 58.200 Hz (E3), Unit 1 picks up 150.00 MW (75% of rating, E4), and Unit 2 picks up 180.00 MW (60% of rating, E5)!
| Parallel Droop Governor KPI (200 MW @ 4% + 300 MW @ 5%, fnl=60 Hz, 330 MW Load) | Formula | Verified Output |
|---|---|---|
| Composite Bus Stiffness Ktot (MW/Hz) | P1/(fnl*R1%) + P2/(fnl*R2%) | 183.33 MW/Hz (233.33 @ R1 = 2.5%) |
| Settling Bus Frequency fbus (Hz) | fnl - (Total_Load_MW / Ktot) | 58.200 Hz (58.586 Hz @ R1 = 2.5%) |
| Unit 1 Governor Pickup P1 (MW) | K1 * (fnl - fbus) | 150.00 MW (188.57 MW @ R1 = 2.5%!) |
| Unit 2 Governor Pickup P2 (MW) | K2 * (fnl - fbus) | 180.00 MW (141.43 MW @ R1 = 2.5%) |
Primary Speed-Droop Frequency Stiffness & Parallel MW Split Formula
Validate positive unit ratings, Droop R% in [0.5%, 12%], No-Load Frequency in [45, 65] Hz, Total_Demand in [0, P_rated1 + P_rated2], and check that neither unit exceeds 100% nameplate MW before governor limiter saturation!
=LET(pr_a, B2, dr_a, B3, pr_b, B4, dr_b, B5, fn_l, B6, ld_t, B7, IF(OR(pr_a <= 0, dr_a < 0.5, dr_a > 12, pr_b <= 0, dr_b < 0.5, dr_b > 12, fn_l < 45, fn_l > 65, ld_t < 0, ld_t > pr_a + pr_b), "Invalid Governor Input", LET(ka_f, pr_a / (fn_l * (dr_a / 100)), kb_f, pr_b / (fn_l * (dr_b / 100)), df_h, ld_t / (ka_f + kb_f), pa_m, ka_f * df_h, pb_m, kb_f * df_h, IF(OR(pa_m > pr_a, pb_m > pr_b), "UNIT OVERLOAD SATURATION", ROUND(pb_m, 2)))))Stiffer Gas-Turbine Droop Grab Check (Tighten Unit 1 Droop R_1 = 2.5%)
Tighten Unit 1 Droop B3 from 4.0% down to 2.5% (raising K_1 from 83.33 to 133.33 MW/Hz -> Composite Stiffness E2 = 233.33 MW/Hz): Bus Frequency E3 holds tighter at 58.586 Hz, but Unit 1 grabs 188.57 MW (94.3% loaded in E4!) while offloading Unit 2 down to 141.43 MW (E5)!
=IF(ISTEXT(E5), E5, LET(ka_f, B2 / (B6 * (B3 / 100)), kb_f, B4 / (B6 * (B5 / 100)), ROUND(ka_f * (B7 / (ka_f + kb_f)), 2)))Try the example
Use the original values or change them to test your understanding.