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CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 3, NO. 2, JUNE 2017
A Hybrid Dynamic Demand Control Strategy for Power System Frequency Regulation Qingxin Shi, Student Member, IEEE, Hantao Cui, Student Member, IEEE, Fangxing Li, Fellow, IEEE, Yilu Liu, Fellow, IEEE, Wenyun Ju, Student Member, IEEE, and Yonghui Sun, Member, IEEE
Abstract—The rapid increase in renewable energy integration brings with it a series of uncertainty to the transmission and distribution systems. In general, large-scale wind and solar power integration always cause short-term mismatch between generation and load demand because of their intermittent nature. The traditional way of dealing with this problem is to increase the spinning reserve, which is quite costly. In recent years, it has been proposed that part of the load can be controlled dynamically for frequency regulation with little impact on customers’ living comfort. This paper proposes a hybrid dynamic demand control (DDC) strategy for the primary and secondary frequency regulation. In particular, the loads can not only arrest the sudden frequency drop, but also bring the frequency closer to the nominal value. With the proposed control strategy, the demand side can provide a fast and smooth frequency regulation service, thereby replacing some generation reserve to achieve a lower expense. Index Terms—Dynamic demand control, frequency regulation, hybrid control, responsive load, turbine governor.
I. I NTRODUCTION
F
REQUENCY stability is a critical concern regarding power system operation. Frequency fluctuation or deviation is a result of unbalance between generation and load demand. The power unbalance might be caused by the large generator unit trip, tie-line trip or sudden change of loads, etc. [1]. In the power industry, the frequency regulation is divided into three levels. Primary frequency regulation (PFR) is an automatic decentralized control that adjusts the generator units to quickly arrest the frequency excursion within a few seconds. Secondary frequency regulation (SFR) is typically a centralized automatic control that adjusts the generator output reference to bring the frequency back to its target value. Tertiary frequency regulation (TFR) refers to manual adjustment in the commitment of generator units or coupon-based demand response program [2]–[4]. This control is used to Manuscript received July 30, 2016; revised Oct. 11, 2016; accepted December 9, 2016. Date of publication June 30, 2017; date of current version April 24, 2017. This work was supported by the Engineering Research Center Program of the National Science Foundation and the Department of Energy of USA under NSF Award Number EEC-1041877 and the CURENT Industry Partnership Program. Q. Shi (corresponding author, e-mail:
[email protected]), H. Cui, F. Li, Y. Liu and W. Ju are with Department of Electrical Engineering and Computer Science, the University of Tennessee, Knoxville. TN 37996, USA. Y. Sun is with the College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China. DOI: 10.17775/CSEEJPES.2017.0022
restore the PFR and SFR reserves and to manage congestions in transmission networks. In recent years, the development of renewable energy source integration and power market has brought about several challenges to the frequency stability. 1) The intermittent nature of renewable energy always causes a mismatch between power generation and demand. Therefore, frequency fluctuation is likely to occur [5]. 2) Some synchronous generators are replaced by converterbased energy sources, such as wind inverters and photovoltaic inverters, which cause a decrease in system total mechanical inertial [5]–[7]. 3) The hourly-based energy market is likely to cause a mismatch between generation and load in the first few minutes of an hour [8]. Confronted by the above challenges, dynamic demand control (DDC) has been proposed to mitigate the short-term frequency fluctuation [9]. Some residential loads with thermal storage feature can be switched off for a short period when the frequency drops below a threshold and switched back on again when the frequency recovers. These loads are called responsive loads, and can be seen in electric water heaters (EWH) and heating, ventilation, and air-conditioners (HVAC) [8]–[10]. Switching off EWH or HVAC for a few minutes hardly affects customers’ living comfort because the water temperature or air temperature almost remains constant. If the control scheme is properly designed, the aggregated responsive loads can act as a frequency reserve and thus help reduce the capacity of generator spinning reserve for frequency regulation. The DDC strategy can be classified into decentralized control [8]–[12], centralized control [13]–[15] and hybrid/ distributed control [16], [17]. Decentralized control has received a great deal of attention because it does not require any communication infrastructure. A controller device is installed between the load and the household power outlet [9]. If a frequency drop is detected, the controller compares it with the pre-defined frequency set-point and decides whether to switch off the load or to adjust its power consumption. These control algorithms usually set random frequency set-points or random time delays for each load controller [8]–[12]. Consequently, we can avoid the synchronous disconnection of a large number of loads and the resultant frequency overshoot. Some technical concerns, however, still exist in the literature. First, such studies fail to verify how the aggregated responsive loads provide the accurate power compensation in reaction to diff-
2096-0042 © 2017 CSEE
SHI et al.: A HYBRID DYNAMIC DEMAND CONTROL STRATEGY FOR POWER SYSTEM FREQUENCY REGULATION
erent levels of frequency deviations [8], [11]. Second, some simulation studies ignore the frequency droop characteristics of the generators [9], [11]. Furthermore, other simulation studies do not consider the detailed dynamic system model [9]– [12]. As a result, the conclusions are not adequate to reflect practical industry cases. This paper proposes a DDC strategy for frequency regulation. When an under-frequency disturbance happens, the load controller first forecasts the frequency nadir in order to decide whether to perform PFR (1st level). After the frequency enters the steady-state, the controller then decides whether to participate in SFR (2nd level) to bring the frequency closer to the nominal value. In this DDC strategy, the control parameters are sent from the control center, while the load controller acts in a decentralized manner. Therefore, it is a hybrid control strategy. The simulation study considered a detailed power system model, which includes a turbine governor, exciter, synchronous generator, and network topology. Consequently, the simulation result will fully represent the practical power system frequency response. The rest of the paper is organized as follows. Section II introduces the characteristics of the system frequency response, which is the theoretical basis of the frequency regulation. Section III proposes the DDC strategy, including PFR and SFR. In particular, the least square (LS)-based frequency nadir forecast method is introduced. Section IV verifies the control strategy through time-domain simulation and analyzes how to determine appropriate control parameters. Finally, Section V concludes the paper and suggests some future research directions.
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of the transfer function model is reduced, as shown in Fig. 1(b) [18]. ΔPd
ΔP
Δf
1 2Hs+D
ΔPg
1+FHTRs 1+TRs
Km
1 1+TCs
1 R
1 1+TGs
(a)
ΔPd
ΔP
ΔPg
1 2Hs+D
Δf
Km(1+FHTRs) R(1+T Rs) (b) Fig. 1. The system frequency response model. (a) Full model. (b) Reduced order model. TABLE I PARAMETERS OF THE T URBINE G OVERNOR Parameter Governor time constant TG Steam chest time constant TC Reheat time constant TR High-pressure turbine fraction FH Mechanical power gain factor Km Inertia constant H Governor speed regulation R Load damping coefficient D
Typical Value 0.2 s 0.3 s 10 s 0.3 0.95–1 3–6 s 0.05 1.0
II. P RINCIPLE OF S YSTEM F REQUENCY R ESPONSE Power system frequency dynamics result from power unbalance. When the system neglects local frequency differences caused by electromechanical transients and oscillations, it is naturally governed by the physics of motion. Expressing this law regarding deviations from the nominal values gives [1]: d∆f (t) + D∆f (t) (1) dt where ∆Pg (t) is the generator mechanical power deviation from the pre-disturbance value, ∆Pd (t) is the load demand deviation from the pre-disturbance value, and ∆f (t) is the system frequency deviation from the nominal value at time t (∆f (t) = f (t) − 60). Note: power and frequency variables are in per-unit value. H is the system total inertia constant. D is the system total load damping coefficient, which mainly results from generators and frequency-dependent loads such as induction motors. The system frequency response model is expressed as lumped generator turbine governor and lumped frequencydependent load, as is shown in Fig. 1(a), where ∆P = Pg − Pd = ∆Pg − ∆Pd represents the power unbalance that is caused by generation decrease or sudden load change. ∆P can be both positive and negative. The typical parameters of the turbine governor are shown in Table I [18], [19]. Since TG and TC are much smaller than TR , we can neglect these two parts in order to simplify the analytical study. Then the order ∆Pg (t) − ∆Pd (t) = 2H
When a negative ∆P happens, the system frequency experiences a drop and enters a new equilibrium. Similar to the step response of the generic 2nd -order dynamic system, the system frequency response can be characterized by three time-domain parameters: frequency nadir fnadir (equivalent to maximal overshoot), time to reach frequency nadir tnadir , and steady-state frequency fss . According to Fig. 1(b), the Laplace transform of the frequency response is calculated [18]: ∆f (s) =
Rωn2 Km (1 + FH TR s) ∆P · DR + Km s (s2 + 2ςωn s + ωn2 )
(2)
where ωn is the oscillation frequency and ζ is the damping coefficient. These are calculated from the turbine governor parameters, namely, DR + Km 2HRTR 2HR + (DR + Km FH ) ς= ωn . 2 (DR + Km )
ωn2 =
(3)
The time-domain frequency deviation is obtained by inverse Laplace transform, ∆f (t) = 60 ·
R∆P 1 + ae−ςωn t sin (ωr t + ϕ) DR + Km
where a and ωr are given by,
(4)
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s
60.00
(5)
Frequency (Hz)
1 − 2TR ςωn + TR2 ωn2 a= 1 − ς2 p ωr = ωn 1 − ς 2 (ς < 1).
At the frequency nadir, the derivative of the frequency curve should be 0, that is, d∆f (t)/dt = 0. Therefore tnadir is obtained by 1 ωr TR −1 tnadir = tan . (6) ωr ςωn TR − 1 The steady-state frequency deviation of the new equilibrium is R∆P R∆P ≈ 60 · . (7) ∆fss = 60 · DR + Km DR + 1 Based on (4) and (6), we can make the following observation on the system frequency response: 1) tnadir depends on turbine governor parameters, generator inertia, and system damping. tnadir is unrelated to ∆P . 2) If ∆P is multiplied by a coefficient k, the frequency response ∆f (t) is also multiplied by k in real time. 3) According to the above two points, ∆fnadir is proportional to ∆P if the dynamic system parameters (presented in Table I) remain constant. The analytical expression of ∆fnadir is omitted here due to its complexity. III. DYNAMIC D EMAND C ONTROL S TRATEGY The decentralized DDC is able to participate in both the primary frequency regulation [8], [10] and secondary frequency regulation [9]. An intrinsic concern with decentralized DDC is that an individual load controller does not “know” the action of other controllers. Consequently, the aggregated responsive loads may provide excessive or insufficient power compensation and fail to bring the frequency back to the nominal value. Therefore, the DDC algorithm should have adaptive characteristics and coordinate with the turbine governor control. In this paper, a hybrid DDC method is proposed. When the system frequency falls below the frequency dead-band, we can forecast the frequency nadir (fnadir ) through a number of frequency measurement data. If the forecast fnadir is not low enough, then the DDC only needs to participate in the SFR; it will wait until the new frequency steady-state is reached and then bring the frequency back to the frequency dead-band. If fnadir is low enough, then the DDC needs to participate in the PFR at first; some responsive load will be switched off immediately. The next two subsections will explain the algorithms of the frequency nadir forecast and demand control, respectively. A. Frequency Nadir Forecast Based on the three items of the conclusion made in Section II, the LS-based method is proposed for forecasting fnadir . As is shown in Fig. 2, the t0 − tnadir segment of nonlinear curve f (t) can be fitted by a quadratic curve. For the next frequency disturbance, it is possible to roughly forecast fnadir before it actually happens. By assuming the system total inertia to be constant, we can forecast fnadir in three steps:
Initial freauency Frequency sample LS-fitted frequency
59.98 59.96 59.94 59.92 59.90
0
1
2
3
t0
Fig. 2.
4 5 Time (s)
6
7
8
tnadir
LS-fitted base frequency curve.
1) Base Frequency Curve (fb (t)) Fitting Small frequency disturbances often happen because of small load step changes. As is shown in Fig. 2, N frequency samples {fb (t1 ), fb (t2 ), . . . fb (tN )} (N > 3) are selected from the data segment between t0 and tnadir . The curve fb (t) is fitted by a quadratic function: fb (t) = ab2 t2 + ab1 t + ab0 .
(8)
The coefficient vector A is determined by, F = TA
(9)
where, 2 f (t1 ) t1 F = ... , T = ... f (tN ) t2N
tN
1 ab2 .. and A = a . b1 . ab0 1
−1
T TF
t1 .. .
2) Coefficient Solution A is solved by LS method: ˆ = T TT A
(10)
ˆ = [ˆ where A ab2 a ˆb1 a ˆb0 ]T . Then the LS-fitted base frequency curve is, fˆb (t) = a ˆb2 t2 + a ˆb1 t + a ˆb0 . (11) Since tN = tnadir , the minimal value of the quadratic function fˆb (t) is equal to the nadir of fb (t). a ˆ2 fˆnadir = fˆb,min = a ˆb0 − b1 4ˆ ab2
(12)
3) Frequency Nadir Forecast As is shown in Fig. 3, when a larger disturbance ∆P happens (called “current disturbance curve”), the frequency response curve is proportional to the base frequency curve. The new frequency curve f (t) is f (t) = a2 t2 + a1 t + a0 = λ · fb (t)
(13)
where λ = a2 /ˆ ab2 . Before the frequency nadir is reached, we select M frequency samples from t0 − tM segment (tM < tnadir ) with the same sampling rate as 1). The coefficient λ is estimated by a linear regression: ˆ= λ
M X n=1
f (tn ) · fb (tn )/
M X
n=1
fb2 (tn ).
(14)
SHI et al.: A HYBRID DYNAMIC DEMAND CONTROL STRATEGY FOR POWER SYSTEM FREQUENCY REGULATION
Frequency (Hz)
60
t0 tm tnadir
random value, (15)
Time (s) Base disturbance curve
fnadir
Current disturbance curve To be forecast
Fig. 3.
∆PPFR poff = min ,1 Presp total ( if U (0, 1) ≤ poff , switch off if U (0, 1) > poff , remain on.
Frequency response for different power disturbances.
The accuracy of the frequency measurement device is essential for frequency nadir forecast. Nowadays, the accuracy of frequency disturbance recorder (FDR) is ± 0.0005 Hz or better [20]–[23], which is sufficient for frequency regulation. Furthermore, since the load controller only needs part of the functions of the FDR (i.e., GPS receiver is unnecessary), we can expect that the expense of a load controller is acceptable.
For example, there are 1000 responsive loads for PFR and each has a power rating of 2 × 10−5 p.u.. Thus, the total frequency reserve power is 0.2 p.u.. At a frequency disturbance event, suppose 0.14 p.u. (70%) of the loads should be switched off according to (16). Thus each load is switched off at a probability of 70% according to (17). We can expect that there are around 700 loads being switched off. In order to demonstrate the accuracy of SDM, a Monte Carlo simulation is performed for 1,000 times and the discrete probability distribution of “off” loads is counted each time, as shown in Fig. 4. We can observe that the probability of providing the expected power reduction with ± 5% error (665–735 loads) is 98.1%. Therefore, the aggregated loads are able to provide real power compensation that is roughly proportional to the frequency deviation, acting as a very large-scale energystorage battery with frequency droop control.
∆PPFR = kPFR ·
∆fˆnadir 60
(16)
where kPFR is the load-frequency sensitivity factor of PFR (MW/Hz or p.u./p.u.). kPFR depends on the available power of the responsive load, and is sent from the control center. Furthermore, in this hybrid control scheme, since a responsive load neither communicates with the control center nor with other loads, the difficulty is in making the aggregated responsive loads provide the accurate power compensation given by (16). A stochastic decision method (SDM) is proposed. That is, each load should be switched off at a specified probability (poff ). The mathematical implementation is that the load makes an “on/off decision” according to a uniformly distributed
Probability (%)
B. Dynamic Demand Control The frequency nadir indicates how serious this frequency disturbance is. First, if at the time step t0 the measured frequency falls below the dead-band (59.95 Hz), this indicates a “suspicious” under-frequency disturbance. Then the controller starts to sample the frequency with a time interval of 0.1 s for a 1.5 s duration (Tsamp ). When Tsamp is expired, the controller immediately forecasts the frequency nadir using the latest frequency data between t0 and t0 + Tsamp to decide whether to perform PFR. Furthermore, when the frequency reaches the steady state fss , the controller will also decide whether to perform SFR. 1) Primary Frequency Regulation (PFR) Case 1: If fˆnadir ≥ 59.75 Hz, the frequency deviation is not serious enough. The turbine governors themselves are adequate to arrest the frequency deviation. Case 2: If fˆnadir < 59.75 Hz, the frequency deviation requires an immediate load control. The amount of load to be switched off is determined by (16),
(17)
18 16 14 12 10 8 6 4 2 0
喡650 650-655 655-660 660-665 665-670 670-675 675-680 680-685 685-690 690-695 695-700 700-705 705-710 710-715 715-720 720-725 725-730 730-735 735-740 740-745 745-750 喣750
Finally, the forecast frequency nadir is given by (15): a ˆ2 ˆ· a fˆnadir = λ ˆb0 − b1 . 4ˆ ab2
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Nunber of OFF Load
Fig. 4.
Probability of off-loads among 1000 loads.
2) Secondary Frequency Regulation (SFR) The turbine governor control can arrest a sudden frequency drop. However, according to (7), it will result in a steady-state frequency deviation ∆fss . If fss < 59.95 Hz, it is necessary for the DDC to participate in SFR and replace some capacity of spinning reserve for a short while. Generally, DDC should satisfy two main technical requirements: 1) Steady-state requirement, which is bringing the frequency to within the frequency dead-band (i.e., 59.95 Hz); 2) Dynamic requirement, which is providing a smooth frequency response and avoiding big overshoot. For the steady-state requirement, the responsive load reduction is determined by (18). ∆fss (18) 60 where kSFR is the load-frequency sensitivity factor of SFR (MW/Hz or p.u./p.u.). kSFR is also sent from the control center. Similar to PFR loads, each SFR load should be switched off according to (17) (by just replacing ∆PPFR with ∆PSFR ). ∆PSFR = kSFR ·
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Consequently, the total load power reduction is close to ∆PSFR . One problem is to determine a sufficient kSFR that can bring the frequency to within the dead-band fdb . Since the frequency increment ∆f = ∆fdb,min − ∆fss is caused by ∆PSFR (fdb,min is the lower bound of fdb ), (7) can be modified as: ∆f = 60 ·
∆f (DR + 1) R∆PSFR or ∆PSFR = . DR + 1 60R
(19)
Therefore, kSFR should ensure that ∆PSFR offsets the generator power reduction. Substituting (18) into (19) gives kSFR
∆f ∆f (DR + 1) ≥ . 60 60R
(20)
That is, kSFR ≥
DR + 1 . R
(21)
It should be noticed that (21) is derived from an aggregated system frequency response model shown in Fig. 1. In practice, since the system contains multiple generators, R represents the system equivalent frequency droop, which is the weighted average of each generator droop value [18]. As for the dynamic requirement, a uniformly-distributed time delay Tdelay2 is introduced to ensure a ramp increment of the power reduction. For the responsive load i, the random time delay is generated by (22). i Tdelay2 ∼ U (0, Tdelay2,max )
C. Summary The whole DDC algorithm is summarized in Fig. 6. In the steady-state, the time step for frequency measurement is 1 second. First, a low-frequency snapshot (< 59.95 Hz) is detected, which indicates a suspicious under-frequency event. The time step for frequency measurement is switched to 0.1 second. After a sampling time of 1.5 s, the controller forecasts fnadir . Second, if fˆnadir < 59.75 Hz, the controller performs PFR immediately. Third, when the steady-state frequency is reached, the controller determines whether to perform SFR according to the measured frequency f (t). Note: The “steadystate” is identified by the formula |fmav (t)−fmav (t−∆t)| < ε, where fmav is the moving average frequency of the latest few samples and ∆t = 1 s. Besides, in a large-scale system, the possibility of large frequency deviation is quite low. In most cases, the DDC perhaps only needs to perform the SFR. By defining appropriate load-frequency sensitivity factor and time delay, the aggregated responsive loads can achieve similar results to generators with AGC control. Normal state Next 1 s time step f(t)
