Adaptive method for aggregation of distributed loads to provide emergency frequency support

Abstract

Systems and methods are disclosed for power management by estimating power contingency of a grid at a cloud control center; performing decentralized real-time measurement and making local decisions at one more computer controlled outlets connected to the grid; and aggregating distributed loads to provide emergency frequency support to the grid.

Claims

1. A method for power management, comprising: estimating power contingency of a grid at a cloud control center; performing decentralized real-time measurement and making local decisions at one or more locally or remotely controlled outlets connected to the grid; and aggregating distributed loads to provide emergency frequency support to the grid, wherein the control center aggregates the locally or remotely controlled outlets into hierarchical blocks based on appliance types and locations.

2. The method of claim 1, wherein in the cloud control center, performing decision-making for frequency control by determining one or more flexible loads to shed based on the power system state, total amount of flexible loads, importance of the flexible loads, and possible contingencies.

3. The method of claim 1, wherein in the cloud control center, performing decision-making for frequency control by analyzing switching-off conditions of the computer controlled outlets and send the conditions to the computer controlled outlets.

4. The method of claim 1, comprising continuously measuring a frequency of the grid at the locally/remotely controlled outlets.

5. The method of claim 4, comprising switching off one or more appliances when switching-off conditions are satisfied, or when switching-off commands sent from the cloud control center.

6. The method of claim 1, wherein the locally/remotely controlled outlets measure voltage, current, active power, reactive power, frequency, rate of frequency change (ROFC), and switch status one or more plugged-in appliances in real-time continuously.

7. The method of claim 1, wherein from measurements sent from the outlets and a total power of each block, and total power of all blocks are used to control and manage the outlets.

8. The method of claim 1, comprising updating power system model and parameters.

9. The method of claim 1, comprising determing a frequency response in the time domain as $\Delta f\left(t\right)=-\frac{R\Delta P}{\mathrm{DR}+K_m}\left[1+\alpha e^{-\zeta {\omega }_{n}t}\sin \left({\omega }_{r}t+\varnothing \right)\right]$ $\mathrm{where}$ $\alpha =\sqrt{\frac{1-2T_R{\mathrm{\zeta \omega }}_n+T_R^2{\omega }_n^2}{1-{\zeta }^2}}$ ${\omega }_r={\omega }_n\sqrt{1-{\zeta }^2}$ $\varnothing ={\varnothing }_1-{\varnothing }_2={\tan }^{-1}\left(\frac{T_R{\omega }_r}{1-{\mathrm{\zeta \omega }}_n{T}_R}\right)-{\tan }^{-1}\left(\frac{\sqrt{1-{\zeta }^2}}{-\zeta }\right)$ ${\omega }_n=\sqrt{\frac{\mathrm{DR}+K_m}{2\mathrm{HR}.Math.T_R}}$ $\zeta =\frac{2\mathrm{HR}+\left(\mathrm{DR}+K_m{F}_H\right)T_R}{2\left(\mathrm{DR}+K_m\right)}{\omega }_n$ Δf (t) is the frequency change; R is a constant of the governor speed-droop control; ΔP is the initial power loss; D is the amount of load damping which indicates the sensitivity of the load in response to frequency change; K.sub.m is the power gain factor; H is the equivalent inertia constant of the system; ΔP.sub.sp is the change of the generator power set point; F.sub.H is the fraction of the power generator by the reheat turbine.

10. The method of claim 1, comprising receiving an initial power loss AP at time t.sub.0=0, and determining a rate of frequency change (ROFC) g (t) as: $g\left(t\right)=\frac{d\Delta f\left(t\right)}{\mathrm{dt}}=-\frac{{\mathrm{\alpha \omega }}_{n}R\Delta P}{\mathrm{DR}+K_m}{e}^{-\zeta {\omega }_{n}t}\sin \left({\omega }_{r}t+{\varnothing }_1\right)]$

11. The method of claim 1, 3, when the ROFC is zero, comprising determining a minimumn frequency f.sub.nadir and a time t.sub.nadir taken to reach f.sub.nadir: $t_{\mathrm{nadir}}=\frac{\pi -{\varnothing }_1}{{\omega }_r}=\frac{1}{{\omega }_r}{\tan }^{-1}\left(\frac{T_R{\omega }_r}{\zeta {\omega }_n{T}_R-1}\right)$

12. The method of claim 1, comprising determining f.sub.nadir as: $f_{\mathrm{nadir}}=f_n-\frac{R\Delta P}{\mathrm{DR}+K_m}\left[1+\alpha e^{-{\mathrm{\zeta \omega }}_n{t}_{\mathrm{nadir}}}\sin \left({\omega }_r{t}_{\mathrm{nadir}}+\varnothing \right)\right]$ where f.sub.n, is the pre-contingency frequency of the steady state.

13. The method of claim 1, comprising ensuring a system frequency does not drop to below a under frequency load shedding (UFLS) point while minimizing the amount of load shedding by the controlled outlets.

14. The method of claim 1 or 8, comprising determining a threshold power loss ΔP.sub.s, as $\Delta P_s=\frac{\left(f_n-f_s\right)\times \left(\mathrm{DR}+K_m\right)}{R\times \left[1+\alpha e^{-{\mathrm{\zeta \omega }}_n{t}_{\mathrm{nadir}}}\sin \left({\omega }_r{t}_{\mathrm{nadir}}+\varnothing \right)\right]}$ where f.sub.s is the minimal frequency allowed for the frequency control strategy.

15. The method of claim 1, comprising determining a minimal controllable power ΔP.sub.v, to be shed to prevent the frequency from dropping below f.sub.s as: $\Delta P_v=\{\begin{array}{cc}\Delta P_{\mathrm{ma}x}-\Delta P_s& \mathrm{if}\Delta P_{\mathrm{ma}x}>\Delta P_s\\ 0& \mathrm{if}\Delta P_{\mathrm{ma}x}\le \Delta P_s\end{array}$ where a maximum amount of sudden power deficit induced among all the contingencies is P.sub.max.

16. The method of claim 1 or 5 comprising determing the frequency value f.sub.x, and related ROFC value g.sub.x, after the loss of power ΔP.sub.s, at time at any time t.sub.x as $f_x=f_n-\frac{R\Delta P_s}{\mathrm{DR}+K_m}\left[1+\alpha e^{-\zeta {\omega }_n{t}_x}\sin \left({\omega }_r{t}_x+\varnothing \right)\right]$ $g_x=\frac{{\mathrm{\alpha \omega }}_{n}R\Delta P_s}{\mathrm{DR}+K_m}{e}^{-\zeta {\omega }_n{t}_x}\sin \left({\omega }_r{t}_x+{\varnothing }_1\right)$

17. The method of claim 1 or 5 comprising locally determining the switching as: if the real-time frequency measurement is f.sub.x, and at the same time the ROFC measurement is lower than g.sub.x, the switching-off condition is satisfied, for robustness, the locally/remotely controlled outlet will switch off when the switching-off condition is satisfied for multiple times.

Description

BRIEF DESCRIPTIONS OF FIGURES

(1) FIG. 1 shows an exemplary smart outlet network

(2) FIG. 2 shows an exemplary Smart outlet structure

(3) FIG. 3 shows an exemplary frequency response model of power system

(4) FIG. 4 shows an exemplary system dynamics following a power deficit

(5) FIG. 5 shows an exemplary relationship between the ROFC and frequency drop

(6) FIG. 6 shows an exemplary control strategy of the cloud control center

(7) FIG. 7 shows an exemplary smart outlet control strategy for frequency regulation

(8) FIG. 8 shows an exemplary frequency drop in case of 633 MW power loss

(9) FIG. 9 shows an exemplary sensitivity analysis for the relationship between the ROFC and frequency drop

(10) FIG. 10 shows an exemplary frequency regulation performance of the instant method with sufficient load

(11) FIG. 11 shows an exemplary influence of the amount of controllable power

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS

(12) For simplicity, the following adaptive frequency control method for utilizing aggregated flexible load demand to provide emergency frequency support service is based on the smart outlet network illustrated in FIG. 1. The smart outlet network consists of a large number of smart outlets, the communication network and a cloud control center. The smart outlet basically consists of a Microcontroller Unit (MCU), a measurement module, a control module, and a communication module, as shown in FIG. 2. The smart outlet can measure the voltage, current, frequency and power of the appliance connected to it using the measurement module, control the switching (e.g., on/off) of the appliance using the control module, communicate with the cloud control center using the communication module. All the computation work of the smart outlet is conducted using the MCU. A smart outlet collects to the network router via wireless communication (e.g., Wifi and Lora) or wired communication (e.g., Ethernet). The cloud control center can receive, store, and analyze the measurements sent from the smart outlets, send the control and setting commands to the smart outlets.

(13) Based on the smart outlet network, an adaptive method for aggregation of distributed loads to provide emergency frequency support is instant. It combines the centralized online contingency estimation and parameter setting at the cloud control center, with the decentralized real-time measurement and local decision-making of smart outlets. The detail is explained as follows.

(14) Determination of Minimal Controllable Load Required

(15) This section presents the calculation of the amount of load curtailment in case of a serious contingency, e.g., a sudden loss of the generator or increase of the load. Based on the frequency response model of the power system in FIG. 3 [4], the frequency will decrease rapidly until a minimum frequency (denoted by f.sub.nadir) is reached due to the inertia of the generators and the frequency response of the load demands. Then the frequency will increase until a new equilibrium is achieved. A typical power system frequency dynamics in response to severe power loss is shown in FIG. 4. In FIG. 3, ΔP.sub.G(t) is the total increase of the power generation in per unit at time t; ΔP.sub.D(t) is the total increase of load demand in per unit at time t; D is the amount of load damping which indicates the sensitivity of the load in response to frequency change; Δf(t) is the frequency change in per unit; H is the equivalent inertia constant of the system; ΔP.sub.SP is the change of the generator power set point; F.sub.H is the fraction of the power generator by the reheat turbine; T.sub.R is the average reheat time constant; K.sub.m is the power gain factor; R is a constant of the governor speed-droop control. It takes time to change the generator power set point, and ΔP.sub.SP is ignored in most cases.

(16) When a power mismatch between the generation and load demand suddenly happens, the system frequency will experience a dynamic change until a new equilibrium is reached. Using the Laplace transform, the frequency response to the power imbalance in the frequency domain can be calculated as

(17) $\begin{array}{cc}\Delta f\left(s\right)=\frac{R{\omega }_n^2}{\mathrm{DR}+K_m}.Math.\frac{1+T_{R}s}{s^2+{\mathrm{\zeta \omega }}_{n}s+{\omega }_n^2}.Math.\frac{-\Delta P}{s}& \left(1\right)\\ \mathrm{where}& \\ {\omega }_n=\sqrt{\frac{\mathrm{DR}+K_m}{2\mathrm{HR}.Math.T_R}}& \left(2\right)\\ \zeta =\frac{2\mathrm{HR}+\left(\mathrm{DR}+K_m{F}_H\right)T_R}{2\left(\mathrm{DR}+K_m\right)}{\omega }_n& \left(3\right)\end{array}$

(18) Based on (1), the frequency response in the time domain can be computed by inverse Laplace transform,

(19) $\begin{array}{cc}\Delta f\left(t\right)=-\frac{R\Delta P}{\mathrm{DR}+K_m}\left[1+\alpha e^{-\zeta {\omega }_{n}t}\sin \left({\omega }_{r}t+\varnothing \right)\right]\mathrm{where}& \left(4\right)\\ \alpha =\sqrt{\frac{1-2T_R{\mathrm{\zeta \omega }}_n+T_R^2{\omega }_n^2}{1-{\zeta }^2}}& \left(5\right)\\ {\omega }_r={\omega }_n\sqrt{1-{\zeta }^2}& \left(6\right)\\ \varnothing ={\varnothing }_1-{\varnothing }_2={\tan }^{-1}\left(\frac{T_R{\omega }_r}{1-{\mathrm{\zeta \omega }}_n{T}_R}\right)-{\tan }^{-1}\left(\frac{\sqrt{1-{\zeta }^2}}{-\zeta }\right)& \left(7\right)\end{array}$

(20) When there are multiple sudden power changes at different times, the frequency response is

(21) $\begin{array}{cc}\Delta f\left(t\right)=-\underset{j}{.Math.}\frac{R\Delta P\left(t_j\right)}{\mathrm{DR}+K_m}\left\{1+\alpha e^{-{\mathrm{\zeta \omega }}_n\left(t-t_j\right)}\sin \left[{\omega }_r\left(t-t_j\right)+\varnothing \right]\right\}& \left(8\right)\end{array}$
where ΔP(t.sub.j) is the sudden power loss at time t.sub.j.

(22) Given the initial power loss ΔP at time t.sub.0=0, the rate of frequency change (ROFC) g(t) can be calculated as

(23) $\begin{array}{cc}g\left(t\right)=\frac{d\Delta f\left(t\right)}{\mathrm{dt}}=-\frac{\alpha {\omega }_{n}R\Delta P}{\mathrm{DR}+K_m}{e}^{-\zeta {\omega }_{n}t}\sin \left({\omega }_{r}t+{\varnothing }_1\right)& \left(9\right)\end{array}$

(24) When the ROFC is zero, the minimum frequency f.sub.nadir is obtained. Thus, the time t.sub.nadir taken to reach f.sub.nadir can be computed as follows

(25) $\begin{array}{cc}{t}_{\mathrm{nadir}}=\frac{\pi -{\varnothing }_1}{{\omega }_r}=\frac{1}{{\omega }_r}{\tan }^{-1}\left(\frac{T_R{\omega }_r}{\zeta {\omega }_n{T}_R-1}\right)& \left(10\right)\end{array}$

(26) Thus, f.sub.nadir can be obtained based on the following equation [5].

(27) $\begin{array}{cc}{f}_{\mathrm{nadir}}=f_n-\frac{R\Delta P}{\mathrm{DR}+K_m}\left[1+\alpha e^{-{\mathrm{\zeta \omega }}_n{t}_{\mathrm{nadir}}}\sin \left({\omega }_r{t}_{\mathrm{nadir}}+\varnothing \right)\right]& \left(11\right)\end{array}$
where f.sub.n is the pre-contingency frequency of the steady state, and it is typically 1 in per unit.

(28) One principle of the instant method is to ensure the system frequency does not drop to the point of conventional under frequency load shedding (UFLS) while minimizing the amount of load shedding by the smart outlets. The starting frequency of the UFLS can be different for different systems. For safety, a frequency slightly higher than the starting frequency of the UFLS, denoted as f.sub.s, is chosen as the objective for the frequency control. Hence, the threshold power loss ΔP.sub.s which makes the frequency drop to f.sub.s as the nadir frequency can be calculated as

(29) $\begin{array}{cc}\Delta P_s=\frac{\left(f_n-f_s\right)\times \left(\mathrm{DR}+K_m\right)}{R\times \left[1+\alpha e^{-\zeta {\omega }_n{t}_{\mathrm{nadir}}}\sin \left({\omega }_r{t}_{\mathrm{nadir}}+\varnothing \right)\right]}& \left(12\right)\end{array}$

(30) The cloud control center can receive the measurements from the widely distributed smart outlets and predict the possible contingencies. Assume the maximum amount of sudden power deficit that could be induced among all the contingencies is ΔP.sub.max. The minimal controllable power ΔP.sub.v that needs to be shed to prevent the frequency from dropping below f.sub.s is calculated as

(31) $\begin{array}{cc}\Delta P_v=\{\begin{array}{cc}\Delta P_{\mathrm{ma}x}-\Delta P_s& \mathrm{if}\Delta P_{m\mathrm{ax}}>\Delta P_s\\ 0& \mathrm{if}\Delta P_{\mathrm{ma}x}\le \Delta P_s\end{array}& \left(13\right)\end{array}$

(32) Switching-Off Conditions of Smart Outlets

(33) An adaptive and robust control strategy for the smart outlets is instant. A typical relationship between the ROFC and the frequency can be represented as shown in FIG. 5. Right after the loss of power ΔP.sub.s at time at any time t.sub.x, the corresponding frequency value f.sub.x and ROFC value g.sub.x can be obtained as

(34) $\begin{array}{cc}{f}_x=f_n-\frac{R\Delta P_s}{\mathrm{DR}+K_m}\left[1+\alpha e^{-\zeta {\omega }_n{t}_x}\sin \left({\omega }_r{t}_x+\varnothing \right)\right]& \left(14\right)\\ g_x=-\frac{\alpha {\omega }_{n}R\Delta P_s}{\mathrm{DR}+K_m}{e}^{-\zeta {\omega }_n{t}_x}\sin \left({\omega }_r{t}_x+{\varnothing }_1\right)& \left(15\right)\end{array}$

(35) Thus, the control strategy of the smart outlets in response to the frequency drop is described as follows. If the real-time frequency measurement is f.sub.x, and at the same time the ROFC measurement is lower than g.sub.x, the switching-off condition is satisfied. For robustness, the smart outlet will switch off when the switching-off condition is satisfied for multiple times.

(36) TABLE-US-00001 TABLE I Switching-off conditions of the smart outlets Frequency range Switching-off conditions [f.sub.n, m, ∞) N/A [f.sub.x, 1, f.sub.n, m) ROFC < g.sub.x, 1 [f.sub.x, 2, f.sub.x, 1) ROFC < g.sub.x, 2 . . . . . . [f.sub.x, n, f.sub.x, n−1) ROFC < g.sub.x, n [f.sub.s, f.sub.x, n) ROFC < 0 (−∞, f.sub.s) Unconditional switching-off

(37) Further, the control strategy is elaborated considering more practical factors as follows. (1) The power system frequency may fluctuate in the normal operation. The smart outlets should not switch off within this normal range in order to avoid the mis-tripping caused by noises or measurement errors. (2) In the curve shown in FIG. 5, there is an infinite number of the (f.sub.x, g.sub.x) pairs. It is not realistic to store every pair, as the storage within the smart outlet is limited. Also, the control strategy should not be too complicated. Thus, the frequency range between f.sub.s and f.sub.n is divided into a number of pieces, and the switching-off conditions of the smart outlets are presented in Table I.

(38) Overall Control Strategy

(39) The overall control strategy consisting of the cloud control center and the smart outlets are explained as follows. The smart outlets measure the voltage, current, active power, reactive power, frequency, ROFC and switch status, etc. of the plugged-in appliances in real-time continuously. Also, the smart outlets periodically send the measurements to the cloud to keep the control center updated about the statuses of smart outlets. The control center aggregates the widely distributed smart outlets into hierarchical blocks considering the types of appliances and their locations. Based on the measurements sent from the smart outlets, the total power of each block, as well as the total power P.sub.total of all the blocks, can be obtained. These blocks serve as the basis for the control and management of the smart outlets. The blocks are not fixed but can dynamically change, merge or divide as needed.

(40) The cloud control center has communication with the control center of the power system and can even be regarded as part of the power system energy management system (EMS). Based on the information from the control center of the power system, the cloud control center can update its power system model and parameters, including the equations (1)-(14).

(41) The major control strategy of the cloud control center is described in FIG. 6. Since the power system state estimation is updated every a few minutes, the control strategy shown in FIG. 6 needs to be updated every a few minutes in accordance with the state estimation. Also, when there are abundant controllable loads, i.e., P.sub.total>ΔP.sub.max−ΔP.sub.s, only a selected amount of smart outlet load blocks are needed to prevent the system frequency from decreasing to below f.sub.s, and the relatively non-critical load blocks can be chosen with a priority. For the rest load blocks, they can stand by, be used to prevent the frequency drop, or be used for frequency restoration.

(42) Based on the parameter setting sent from the control center, the flow chart of the smart outlet control is shown in FIG. 7.

(43) Case Studies

(44) In order to verify the performance of the instant control method for emergency frequency support, case studies are performed using a modified IEEE 24-bus system. The original system [6] has 32 generators, and in this modified system the three generators on bus 23 are removed and an interconnection line between bus 23 and an external system is added. Assume the rated power of the interconnection line is 1000 MVA, thus the tripping of the interconnection line is often most serious single contingency.

(45) The parameters used in the power system frequency dynamics model are explained as follows. The inertia constant H and the constant of the governor speed-droop control R are 5.8 s and 1/17 for a generator whose rated power is less than 100 MW, respectively; 8.1 s and 1/20 for rated power between 100 MW and 200 MW, respectively; 9.3 s and 1/22 for rated power larger than 200 MW, respectively. D is 2.5, F.sub.H is 0.3, TR is 8 and Km is 0.95. Based on the above parameters, it is calculated that t.sub.nadir is 3.72 seconds. 49.1 Hz is chosen as the desired nadir frequency, the threshold power loss ΔP.sub.s is 633 MW which makes the frequency drop to the minimum frequency 49.1 Hz, as shown in FIG. 8.

(46) The sensitivity analysis for the relationship between the ROFC and the frequency drop is conducted for different power loss cases, as shown in FIG. 9. It can be seen that at any frequency (e.g., 59.2 Hz), the ROFC for a higher power loss is larger than the ROFC for a lower power loss, which validates the ROFC can be used an accurate index for detecting and responding to a contingency.

(47) Thus, the specific switching-off conditions of the smart outlets can be obtained as in Table II.

(48) TABLE-US-00002 TABLE II Specific switching-off conditions of the smart outlets Condition number Frequency range Switching-off conditions 1 [49.8, 49.9) ROFC < −0.528 Hz/s 2 [49.7, 49.8) ROFC < −0.476 Hz/s 3 [49.6, 49.7) ROFC < −0.421 Hz/s 4 [49.5, 49.6) ROFC < −0.363 Hz/s 5 [49.4, 49.5) ROFC < −0.300 Hz/s 6 [49.3, 49.4) ROFC < −0.231 Hz/s 7 [49.2, 49.3) ROFC < −0.150 Hz/s 8 [49.1, 49.2) ROFC < 0 9  [−∞, 49.1) Unconditional switching-off

(49) TABLE-US-00003 TABLE III Influence of measurement error on the smart outlet response Maximum random error (%) Response rate 0 1.00000000 10 0.99899502 20 0.99899732 30 0.99899217

(50) The developed smart outlets in Section III reports a frequency and a related ROFC value every 16 ms, and based on them check if any of the switching-off conditions is satisfied. The smart outlet will turn off the switch when the switching-off conditions are satisfied for 3 times.

(51) Based on Table II, the response of the smart outlets in case of a sudden power loss can be analyzed. A random frequency measurement error is added to each point of the frequency drop curve in FIG. 8 within the range [49.8 Hz, 49.9 Hz) to generate a new frequency drop curve with errors. The generated frequency drop curve with errors is tested based on condition 1 in Table II to check whether the switching-off condition can be satisfied for 3 times. For each case of error, 10 million frequency drop curves with errors are generated and tested to calculate the response rate. The simulation results are shown in Table III. It can be shown that the instant control strategy for smart outlets is very robust and it can act very accurately (around 99.9% probability) even in case of very significant measurement noise or errors, e.g., 30% noises.

(52) Case studies are conducted to verify the frequency regulation performance of the instant method when the available load is sufficient, as in FIG. 10. When the power of the interconnection line is 1000 MW, the minimal controllable power that needs to be curtailed is 367 MW; and the minimal controllable power will decrease to 67 MW when the power of the interconnection line is 700 MW. It is shown in FIG. 10 for these two cases that the frequency will not drop below 49.1 Hz, and the system is secure with the power provided by the outlets.

(53) Also, sensitivity studies are carried out to check the influence of different amount of controllable power on the contingency. Assume a sudden power loss of 1000 MW, the system frequency dynamics in case of different amounts of controllable load is presented in FIG. 11. It can be seen when the amount of controllable load is not sufficient, it is unable to prevent the frequency from dropping below 49 Hz, but it can reduce the speed of frequency drop; with the increase of the amount of controllable load, the system is increasingly secure.