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A New Load Shedding Scheme for Limiting Underfrequency
Copyright © IFAC 12th Triennial World Congress, Sydney, Australia, 1993
A NEW LOAD SHEDDING SCHEME FOR LIMITING UNDERFREQUENCY W.R. Lachs, D. Prasetljo and D. Sutanto School of Electrical Engineering, The University of New SouJh Wales. p.a . Box 1. Kensington. NSW 2033. Australia
Abstract. Under-frequency load shedding acts to alleviate load-generation imbalance following a sudden loss of large amounts of generation. Loads are shed at pre-scheduled locations throughout the power system. This, unfortunately, does not adequately correct for the effects of the location of the disturbance on the power system. It would be better if load shedding were to occur at locations close to the lost generation so reducing the reactive power losses associated with transmitting larger amounts of power to the disturbed location. A new hierarchical load shedding scheme is proposed, based on frequency, voltage and rate of frequency decline, which utilizes a distributed intelligence to shed load according to the actual system state at each locality.
Key Words: Underfrequency Load Shedding, Distributed Intelligence, Loss of Generation, Operational Security, Transient Stability.
1. INTRODUCTION
2.1. freQuency Decline
Energy cannot be stored on an AC system, yet there must constantly be a balance between load and generation to control frequency. The continuing variations in system load are matched by governor actions on generator prime movers. To allow this control many generators operate below their rated output, thereby carrying "spinning reserve" and the governors respond to frequency variations to sustain the balance between load and generation. When there had been an unexpected loss of generators substantially in excess of the "spinning reserve", the large frequency fall could cause a power system collapse. Although it does not happen often that there is a simultaneous loss of generators which could precipitate such a collapse, under-frequency load shedding (UR.,S) has been widely used to quickly restore the load-generation balance and prevent dangerous frequency excursions. At the time when UFLS schemes were introduced power systems were much more compact so that the reduced frequency level on the loss of generators was uniform throughout these networks. Now, with extensive interconnected transmission networks, there is a finite time delay after a major loss of generation before the lower frequency reaches the network extremities. The sudden shock following the loss of generation can produce abrupt changes of transmission line loadings which in turn can produce oscillations between remote groups of generators scattered throughout the extensive power grid. In spite of its radically altered frequency characteristic, ULFS uses the same approach as that adopted for the compact network, namely to scatter load shedding relays throughout the entire grid. Although with the more extensive networks many more generators would need to be lost to produce a dangerous frequency excursion, there can be a danger in adopting the underfrequency load shedding methods of a compact network. The following questions arise with this UFLS should there be a large loss of generation: i. Could frequency drop so quickly for such a loss of generation that its descent would not be arrested in time with UFLS? ii. Could the frequency wave emanating from the lost generators unduly delay load shedding at the more distant locations? ill. Is there much benefit in load shedding at locations quite distant from the lost generation? To examine these questions, studies using a transient stability programme have been undertaken to evaluate both the existing and a new proposed scheme for underfrequency load shedding.
For constant system voltage, the frequency decline of compact single-area power systems can be approximated, Caprio & Marconato (J 979), by: f(t) = fo +
~ (I + Cf e-~oontsin( 0001+4»)
(J)
where fo ,MlG and K are the rated frequency, size of disturbance and system stiffness respectively, and Cf, ~ ,oon ' 000 and 4> are constants related to system inertia, gain and time-constants of primary frequency controller and the load damping coefficient. When the disturbed system is elastic, oscillations can produce a different frequency decline in each area. AREA 1 708MW
AREA 2 7l0MW
Fig.l . Single line diagram of a two-area elastic power system The system in Fig. I consists of two areas connected by weak: ties. For a generator loss of MlG in Area 2, the frequency declines in Area I, fl (I), and in Area 2, f2(1), (assuming constant system voltage and load and negligible turbine-governor response in the first instance) are given by : MlGsinooot fl (t) = fave(t)+ (2) 2ltoooM2(1 +m)
(3)
2. LOAD SHEDDING PARAMETERS Events following loss of generation can be characterized by two quantities: system-wide frequency decline and regional voltage reductions. The first quantity indicates active power deficit in the system and the second quantity indicates reactive power deficit at locations near the disturbance. Both quantities can be used as control parameters for load shedding and the following subsections describe these parameters.
813
(4)
where fave(1) is the average system frequency, M I and M2 are the composite inertia coefficient of Area 1 and 2 respectively, m=MI!M2 and
0)0
is frequency of electromechanical oscillation.
2.2. Rate of Frequency Decline
3.3. Distribution of Load Shedding
Time derivatives of equations (2) to (4) give the rate of frequency declines : dfl (t) dfave(t) APGcosO>ot -- - --- + (5) dt dt 21tM2(1 +m)
Voltage reduction can be the control parameter to identify the most affected locations and to quantify the amount of load shedding at each. To obtain a better voltage profile after load shedding, the amount of load shed at node i , (t1Pi) , would be:
mAPGcosO>ot
t1Pi = (6)
(10)
i=1 (7)
With APG negative in equations (2) to (7), in the first instance df/dt at the disturbed area is maximum and greater than the average df/dt while it is zero in the undisturbed area. Only after a delay related to the period of oscillation, will the undisturbed area have a frequency decline. In other words, one can postulate that there is a wave of frequency decline emanating from the disturbed area, propagating to the other area. Load shedding schemes with rate of frequency reduction relays are likely to operate with a delay in distant areas, so prolonging the overall active power deficit and adding to the frequency fall. Not only can the rate of frequency decline (df/dt) allow an evaluation of the output of the generation loss, but when measured immediately afterwards, can identify the deficient area 2.3. Voltage Reduction Following loss of a large power station, both active and reactive power outputs are lost, causing nearby voltage levels to instantly fall. The largest voltage reductions will occur at substations fed by transmission lines that have had the highest load increases, those supplying the generation deficient area Hence, voltage reduction at a node conveys simple but useful information on system state in terms of its location, and can be used to determine both the amount and location of load shedding to alleviate not only active power deficit, but also minimise reactive power losses by curtailing the power imports. It should not be overlooked that such a disturbance causes transient effects, including oscillations of generators and fluctuations of voltage and frequency levels. For this reason the measurement of voltage reduction used for load shedding should be the level recorded immediately after the disturbance. PROPOSED LOAD SHEDDING
» xl:PLS
L,[t1 Vi x OQi/oVil
21tM2(1+m)
3.
t1Vi x OQi/oVi N
ARRANGEMENT
The UFLS scheme has been a subject of much research for more than forty years, Carlin & Blackburn (1944), Geirich (1955) and Lokay & Burtnyk (1968). ULFS sheds predetermined loads throughout the entire network with frequency reduction as the control parameter. Some later load shedding schemes use the rate of frequency decline as well as the frequency fall, IEEE Working Group (1975) and IEEE Task Force (1985). Lachs (1985) proposed the use of strategic load shedding which uses the reduction of transmission voltage level to quantify the amount of load shedding at each location. This type of load shedding regains the system-wide control of reactive power following catastrophic disturbances . A similar approach is proposed with load shedding for controlling the effects of the loss of a large amount of generation. 3.1. Priority List The load blocks already prioritised and chosen for the existing ULFS would be used with the propsal. But each load block would need to be monitored, so that if shedding were to be necessary only a total amount equal to the lost generation would be interrupted. 3.2. Total Amount of Load to be Shed When the power system has an amount spinning reserve (SR) on top of system load and losses, the total load to be shed, after loss of generation would be: l:PLS=t1PG - KMSS (8) where l:PLS is the required amount of load shed, t1PG is the output of the lost generation, K is system stiffness and MSS is the desired steady state frequency after load shedding. With a smaller reserve than generation lost, more load must be shed: (9) l:PLS>(t1PG-SR) + (t1PG - K MSS)
814
where t1 Viis voltage reduction at node i, OQi/oV i is the sensitivity of voltage at node i to change of reactive power, N is the total number of load nodes with significant voltage reduction and LPt.s is given by equation (8) or (9). To be effective, the distribution of system-wide load shedding by equation (10) requires an hierarchical scheme. In modern power systems employing EMS facilities, information required for calculating equations (8) to (10) is readily available. Some time delays should be allowed for system-wide load shedding. However, when the speed of frequency decline is fast, immediate load shedding is required to arrest the decline. Fast load shedding is more effective when in the deficient area. Additional load shedding to precisely balance the lost generation would be directed by the hierarchical control. 3.4. Local Load Shedding elLS) The larger the amount of generation that is lost, the more dangerous the frequency fall. For the very severe disturbances when large amounts of generation are lost concurrently, almost invariably in the one region, it is imperative to respond more quickly if collapse is to be avoided. Because of the low probability of such events, existing ULFS make no special provisions for them. Specifically to cater for this on a large interconnected grid, a new type of shedding - local load shedding is proposed. The Local Load Shedding (LLS) would capitalise on the distinctive pattern of parameter changes. Specifically within the region where the generators are lost, there would be a sharp rate of frequency decline and a sudden voltage dip. In more distant regions , because of the inter-tie elasticity, the initial rate of frequency decline would be less as well as a less pronounced voltage dip. By suitable calibration of relays to measure the initial frequency decline and the initial voltage reduction, they could actuate the LLS. As an added safeguard, no shedding would occur unless frequency had fallen below 49Hz. For such a critical loss of generation, LLS would function in less than 15 cycles after the disturbance, sufficiently fast to retard the rate of frequency decline. 3.5. System-wide Load Shedding (SLS) Because of its fast action, LLS would restrict the largest frequency deviation, but would not fully compensate for the total quantity of generation lost. Nonetheless, the LLS action would provide sufficient time for follow-up action of a hierarchical control, which, using equations (8) to (10), could evaluate the total extra quantity of System-wide Load Shedding (SLS). With the less dangerous rate of frequency decline following the LLS , the SLS could function one second or more after the initial disturbance. This would permit the delays associated with the evaluation of the precise amount of load shedding and the transmission of signals needed to activate auxiliary relays and circuit breakers at the different substations, in effect, a distributed intelligence. 4. SIMULATION RESULTS 4. 1. Proposed Load Shedding Scheme on a Two-area System Simulation studies on the system in Fig. l have have been made to compare ULFS with the new load shedding scheme in an elastic power system . Each area has three generators Gl = GIl = 900MVA, G2 = G12 = 625MVA and G3 =GJ3=275 MVA, with Area 1 load 950MW and Area 2 load 1900MW, as constant impedance and frequency dependent. All generators have inertia of 4 MWs/MVA and include exciter and turbine-governor models. The disturbance is the loss of two generators G12 and G13 in Area 2, having an output of700MW. Simulations compare the proposed scheme with conventional UFLS using underfrequency relays acting at 48.0Hz, 47.8Hz and 47.6Hz, with 20% of every substation's load shed at each level.
OIH.r---~------------~--~------------'
478,
L
__~~__~__--,-__~__-'-__~--'__~__- '
Fig. 2 Frequency recovery
Fig.4 Frequency recovery
The study results in Fig. 2 compare the frequency recovery when the proposed load shedding scheme is used (curve A) with the UFLS scheme (curve B). The proposed scheme limits the frequency reduction to 48.5Hz at 4.2 seconds after shedding 700MW whereas UFLS allows frequency to fall to 47.8Hz at 6.2 seconds after shedding 550MW. The ULFS produces a larger voltage rise so also requiring reactor switching. Fig. 3 illustrates the angular and voltage variations of the system, with the new scheme the angle settling near 3()<> (curve A), compared to over 6()<> for UFLS (curve B), so providing a better stability margin.
When the generator loss is increased 200MW to 3,650MW, the conventional UFLS fails to protect the system, whereas the proposed scheme is still effective (Fig. 6, curve A). The latter scheme sheds some 3,450MW load and frequency falls to 48.0Hz at 2.9 seconds. For this disturbance, another conventional load shedding scheme which additionally uses the rate of frequency decline is able to protect the system by shedding 3,450MW and limiting frequency to 49.3Hz at 1.5 seconds (Fig. 6, curve B). J60DEC,-- - - -- - - -- - - ----------------------------.
JOODEC 100
. .. .. . .
00
20,
500EG
.... . . . .
v'
_JOODEC L __L -_ _- ' -_ _J -_ _~_ __ L_ _~_ __ L_ __ i_ __ J_ _~
o.
Fig. 3. Angular and voltage variation
I.
2.
3.
4.
s.
e.
7.
8.
g.
10.
Fig. 5. Angular variation
Fig. 3 also shows that the proposed scheme produces a better voltage profile (settles at 1.0 pu, curve Cl whereas UFLS produces a low voltage profile (settles at 0.9 pu, curve D) which may cause other problems. Load shedding near the disturbance produces lower tie line loadings, so gaining angular and voltage benefits. 4.2. Iestim: Proposal on a 92-bus Power Grid
A:
Simulation studies were also carried out on the 92-bus power grid, as described in Lachs & Sutanto (1992), which has a peak load of 14,770MW and a plant capacity of 19,200MW. The grid has five types of generators: 300MW and 600MW thermal, l25MW and
250MW hydro and lOOMVAr synchronous condensers.
" 6 Hz
The fust set of studies examined the power system response to different amounts of generation loss if no underfrequency load shedding acted. The network tolerates generation losses up to 2,300MW but required the simultaneous loss of three power stations, having an output of 3,450MW, to threaten collapse. An additional 200MW loss, of 3,650MW, led to loss of stability. The comparison between the proposed load shedding scheme with the conventional UFLS scheme, considered losing 3,450MW of generation. The UFLS utilizes under-frequency relays dispersed throughout the entire network shedding up to 50% of load, divided into four 12.5% blocks, functioning at 48Hz, 47.8Hz, 47.6Hz and 47.4Hz. In addition, there is 5s-delayed load shedding when the frequency reaches 49.0Hz, 48.7Hz and 48.4Hz. Fig. 4 shows the frequency behaviour when the proposed load shedding scheme is used (curve A), compared with that when the UFLS is used (curve B). The proposed scheme sheds 3,250MW load and limits the frequency deviation to 48.0 Hz at almost 4.0 seconds, whereas the UFLS allows frequency to fall to 47.7Hz at 2.6 seconds and sheds 3,455MW. Of great importance is that the proposal produces much better stability margin where the angle settles at lOo (Fig. 5, curve A), compared with an angle of 65 0 with the UFLS (Fig. 5, curve B).
815
Fig. 6 Frequency recovery Figure 7 shows that the proposed scheme produces considerably lower power angles which fluctuated between +/- 50 0 after 3 seconds and continues to diminish (curve A), whereas with UFLS the angle remains between 50-80 0 (curve B). For a more thorough comparison after the load shedding, load flow studies were undertaken to allow voltage levels, transmission line loadings and losses to be examined. From these load flows it was found that the proposed scheme produces better voltage profile on the system. Fig.8 shows voltages at a selection of nodes. Nodes NI8 to N23 are near the lost generation and nodes N43 and N44 are distant from it. It shows that after load shedding, the proposed scheme produces voltages between 1.00 to 1.05 pu at all nodes in the system (Fig. 8, solid bars), except node N43 whose predisturbance voltage is already below 1.00 pu. This compares favourably a conventional ULFS scheme with voltages of 0.92 to 0.96 pu in the disturbed area (Fig. 8, striped bars).
A mathematical analysis of a two area network with weak ties , following generation loss in one area, provides a better understanding of the changes of frequency in each area. The patterns of frequency change and voltage variations following loss of generation form the underlay of a new load shedding proposal. Initial simulations on the two area network, using a transient stability programme, identify a frequency wave trasmitted, after a delay, from the deficient area Simulations, in which the initial voltages reductions are utilised to limit load shedding to the deficient area, showed significant advantages when compared with UFLS which activates load shedding throughout the entire network. The comparisons are illustrated in Figs. I & 2.
I~DEC.----------------------------------------,
_IOOD£C~--L---~
__J -_ _
~
The fust step in studying a 92 bus network was to determine that three power stations with an output of 3450MW had to be lost to create a dangerous underfrequency situation. This starting point, the loss of 3450MW of generator output, allowed a comparison between the existing ULFS and the proposed load shedding scheme. To be able to better understand the post-disturbance operating conditions, load flow studies were undertaken and these demonstrated the advantages of restricting load shedding to the deficient area When conventional ULFS acted after such a large loss of generation, the heavy inflows of power to the deficient area loaded some lines close to their rating and considerably increased real and reactive power losses. This coupled with the lower volt ages and larger power angles give warning of potentially serious problems for the operators which are avoided when shedding is limited to the deficient area.
_ _~_ _- L_ _- L_ _- L__~__- J
O.
Fig. 7. Angular Variation 1.0~
PU - , - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - ,
1.00 PU
0 . 95 PU
1"6
/119
_
/lZO
/lZI
PROPOSED SCHEl(£
/122 ~
/lZ3
un.s
/1<3
,,«
Fig 8. Voltages after load shedding Apart from producing a better voltage profIle, the load flow studies have also shown that applicatio n of the proposed scheme avoids line overloading and produces lower active and, quite significantly lower reactive power losses. With 3,450MW generation loss for the proposed scheme, the losses are 240MW and 4,I80MVAR, compared to 345MW and 4,665MVAR with conventional UFLS. High line loading on the inter-area lines occurs with conventional UFLS, but there is no such problem with the proposed scheme. Table I summarizes the main results from the simulation and load flow studies on the 92-bus power system, to demonstrate the advantages of the proposed scheme. Table I. Comparison of the proposed scheme and conventional UFLS scheme
The proposal has the additional feature of Locallised Load Shedding (LLS), which functions within 15 cycles of the loss of generation . This fast response, which is essential for a very large loss of generation, is possible as the incident can be identified at substations within the deficient area by the sudden fall of voltage and the high rate of frequency decline, that forms the basis of a distributed intelligence. LLS, by halting the rate of frequency fall, allows enough time for the hierarchical control to shed additional load and precisely match the lost generator outputs. With appropriate calibration of the relays at load substations, necessary for this proposal, it should not be difficult to implement such an underfrequency scheme. For generation loss within the scope of existing ULFS, the proposed scheme would respond without triggering LLS. However the proposal is better equipped, because of its fast LLS response , to handle the very heavy loss of generation which may be beyond the capability of the existing ULFS. The other important advantage of the proposal is that by restricting load sheddi ng to the deficient area, it ensures better voltage levels, improved stability, lower transmission line loadings and reductions in losses. For all these reasons, it provides a new and promising option for the power industry.
6. REFERENCES oad shedding schemes
Caprio, U.Di and Marconato, R. 1979 Automatic Load Shedding in Multi-area Elastic Power Systems Electrical Power & Energy Systems. Vol.l, No.I, April , pp.21-29 Carhn, H.1. and Blackburn, J.L.1944 A New Frequency Relay for Power System Applications, AlEE Transactions, Vo1.63. August, pp.553-57. Gicrisch, W.C. 1955 Load Reduction by Under-frequency Relays during System Emergencies AlEE PAS, Vol.73, February • pp.1651-55. IEEE Working Group 1975 A Status Report on Methods Used for System Preservation During Underfrequency Conditions IEEE TrailS. Vol. PAS-94, No. 2 March/April, pp.360-65. IEEE Task Force on Emergency Control 1985 Emergency Control Practice. IEEE Tralls.VoI.PAS-04 No.9 Sept. pp.2336-2341.
5. CONCLUSION The principles of the present underfrequency load shedding schemes (UFLS) were developed some 40 years ago, when power systems were quite compact. Present-day power systems, with extensive interconnections and the major power stations distant from the main load centres, although having considerably altered in character, yet persist in using the same type of ULFS . This raises the question whether thi s ULFS is appropriate for the interconnected power system s. The function of this paper is to resolve this question and particularly to determine whether a different method of load shedding would be more appropriate should very large amounts of generation be lost.
816
Lachs W.R.1985 Dynamic Study of an Extreme System Reactive Power Deficit IEEE Trans. Vol. PAS-I04 No. 9, September pp.2420-26. Lachs W .R. & Sutanto D. 1992 Voltage Instability in Interconnected Power Systems: A Simulation Approach IEEE TrailS. on Power Systems Vol.7 No .n May pp.753-76\. Lokay, H.E. & Burtnyk, V. 1968 Application of Underfrequency Relays for Automatic Load Shedding IEEE Transaction . VoI.PAS-87, No.3 , March pp. 776-83.
A NEW LOAD SHEDDING SCHEME FOR LIMITING UNDERFREQUENCY W.R. Lachs, D. Prasetljo and D. Sutanto School of Electrical Engineering, The University of New SouJh Wales. p.a . Box 1. Kensington. NSW 2033. Australia
Abstract. Under-frequency load shedding acts to alleviate load-generation imbalance following a sudden loss of large amounts of generation. Loads are shed at pre-scheduled locations throughout the power system. This, unfortunately, does not adequately correct for the effects of the location of the disturbance on the power system. It would be better if load shedding were to occur at locations close to the lost generation so reducing the reactive power losses associated with transmitting larger amounts of power to the disturbed location. A new hierarchical load shedding scheme is proposed, based on frequency, voltage and rate of frequency decline, which utilizes a distributed intelligence to shed load according to the actual system state at each locality.
Key Words: Underfrequency Load Shedding, Distributed Intelligence, Loss of Generation, Operational Security, Transient Stability.
1. INTRODUCTION
2.1. freQuency Decline
Energy cannot be stored on an AC system, yet there must constantly be a balance between load and generation to control frequency. The continuing variations in system load are matched by governor actions on generator prime movers. To allow this control many generators operate below their rated output, thereby carrying "spinning reserve" and the governors respond to frequency variations to sustain the balance between load and generation. When there had been an unexpected loss of generators substantially in excess of the "spinning reserve", the large frequency fall could cause a power system collapse. Although it does not happen often that there is a simultaneous loss of generators which could precipitate such a collapse, under-frequency load shedding (UR.,S) has been widely used to quickly restore the load-generation balance and prevent dangerous frequency excursions. At the time when UFLS schemes were introduced power systems were much more compact so that the reduced frequency level on the loss of generators was uniform throughout these networks. Now, with extensive interconnected transmission networks, there is a finite time delay after a major loss of generation before the lower frequency reaches the network extremities. The sudden shock following the loss of generation can produce abrupt changes of transmission line loadings which in turn can produce oscillations between remote groups of generators scattered throughout the extensive power grid. In spite of its radically altered frequency characteristic, ULFS uses the same approach as that adopted for the compact network, namely to scatter load shedding relays throughout the entire grid. Although with the more extensive networks many more generators would need to be lost to produce a dangerous frequency excursion, there can be a danger in adopting the underfrequency load shedding methods of a compact network. The following questions arise with this UFLS should there be a large loss of generation: i. Could frequency drop so quickly for such a loss of generation that its descent would not be arrested in time with UFLS? ii. Could the frequency wave emanating from the lost generators unduly delay load shedding at the more distant locations? ill. Is there much benefit in load shedding at locations quite distant from the lost generation? To examine these questions, studies using a transient stability programme have been undertaken to evaluate both the existing and a new proposed scheme for underfrequency load shedding.
For constant system voltage, the frequency decline of compact single-area power systems can be approximated, Caprio & Marconato (J 979), by: f(t) = fo +
~ (I + Cf e-~oontsin( 0001+4»)
(J)
where fo ,MlG and K are the rated frequency, size of disturbance and system stiffness respectively, and Cf, ~ ,oon ' 000 and 4> are constants related to system inertia, gain and time-constants of primary frequency controller and the load damping coefficient. When the disturbed system is elastic, oscillations can produce a different frequency decline in each area. AREA 1 708MW
AREA 2 7l0MW
Fig.l . Single line diagram of a two-area elastic power system The system in Fig. I consists of two areas connected by weak: ties. For a generator loss of MlG in Area 2, the frequency declines in Area I, fl (I), and in Area 2, f2(1), (assuming constant system voltage and load and negligible turbine-governor response in the first instance) are given by : MlGsinooot fl (t) = fave(t)+ (2) 2ltoooM2(1 +m)
(3)
2. LOAD SHEDDING PARAMETERS Events following loss of generation can be characterized by two quantities: system-wide frequency decline and regional voltage reductions. The first quantity indicates active power deficit in the system and the second quantity indicates reactive power deficit at locations near the disturbance. Both quantities can be used as control parameters for load shedding and the following subsections describe these parameters.
813
(4)
where fave(1) is the average system frequency, M I and M2 are the composite inertia coefficient of Area 1 and 2 respectively, m=MI!M2 and
0)0
is frequency of electromechanical oscillation.
2.2. Rate of Frequency Decline
3.3. Distribution of Load Shedding
Time derivatives of equations (2) to (4) give the rate of frequency declines : dfl (t) dfave(t) APGcosO>ot -- - --- + (5) dt dt 21tM2(1 +m)
Voltage reduction can be the control parameter to identify the most affected locations and to quantify the amount of load shedding at each. To obtain a better voltage profile after load shedding, the amount of load shed at node i , (t1Pi) , would be:
mAPGcosO>ot
t1Pi = (6)
(10)
i=1 (7)
With APG negative in equations (2) to (7), in the first instance df/dt at the disturbed area is maximum and greater than the average df/dt while it is zero in the undisturbed area. Only after a delay related to the period of oscillation, will the undisturbed area have a frequency decline. In other words, one can postulate that there is a wave of frequency decline emanating from the disturbed area, propagating to the other area. Load shedding schemes with rate of frequency reduction relays are likely to operate with a delay in distant areas, so prolonging the overall active power deficit and adding to the frequency fall. Not only can the rate of frequency decline (df/dt) allow an evaluation of the output of the generation loss, but when measured immediately afterwards, can identify the deficient area 2.3. Voltage Reduction Following loss of a large power station, both active and reactive power outputs are lost, causing nearby voltage levels to instantly fall. The largest voltage reductions will occur at substations fed by transmission lines that have had the highest load increases, those supplying the generation deficient area Hence, voltage reduction at a node conveys simple but useful information on system state in terms of its location, and can be used to determine both the amount and location of load shedding to alleviate not only active power deficit, but also minimise reactive power losses by curtailing the power imports. It should not be overlooked that such a disturbance causes transient effects, including oscillations of generators and fluctuations of voltage and frequency levels. For this reason the measurement of voltage reduction used for load shedding should be the level recorded immediately after the disturbance. PROPOSED LOAD SHEDDING
» xl:PLS
L,[t1 Vi x OQi/oVil
21tM2(1+m)
3.
t1Vi x OQi/oVi N
ARRANGEMENT
The UFLS scheme has been a subject of much research for more than forty years, Carlin & Blackburn (1944), Geirich (1955) and Lokay & Burtnyk (1968). ULFS sheds predetermined loads throughout the entire network with frequency reduction as the control parameter. Some later load shedding schemes use the rate of frequency decline as well as the frequency fall, IEEE Working Group (1975) and IEEE Task Force (1985). Lachs (1985) proposed the use of strategic load shedding which uses the reduction of transmission voltage level to quantify the amount of load shedding at each location. This type of load shedding regains the system-wide control of reactive power following catastrophic disturbances . A similar approach is proposed with load shedding for controlling the effects of the loss of a large amount of generation. 3.1. Priority List The load blocks already prioritised and chosen for the existing ULFS would be used with the propsal. But each load block would need to be monitored, so that if shedding were to be necessary only a total amount equal to the lost generation would be interrupted. 3.2. Total Amount of Load to be Shed When the power system has an amount spinning reserve (SR) on top of system load and losses, the total load to be shed, after loss of generation would be: l:PLS=t1PG - KMSS (8) where l:PLS is the required amount of load shed, t1PG is the output of the lost generation, K is system stiffness and MSS is the desired steady state frequency after load shedding. With a smaller reserve than generation lost, more load must be shed: (9) l:PLS>(t1PG-SR) + (t1PG - K MSS)
814
where t1 Viis voltage reduction at node i, OQi/oV i is the sensitivity of voltage at node i to change of reactive power, N is the total number of load nodes with significant voltage reduction and LPt.s is given by equation (8) or (9). To be effective, the distribution of system-wide load shedding by equation (10) requires an hierarchical scheme. In modern power systems employing EMS facilities, information required for calculating equations (8) to (10) is readily available. Some time delays should be allowed for system-wide load shedding. However, when the speed of frequency decline is fast, immediate load shedding is required to arrest the decline. Fast load shedding is more effective when in the deficient area. Additional load shedding to precisely balance the lost generation would be directed by the hierarchical control. 3.4. Local Load Shedding elLS) The larger the amount of generation that is lost, the more dangerous the frequency fall. For the very severe disturbances when large amounts of generation are lost concurrently, almost invariably in the one region, it is imperative to respond more quickly if collapse is to be avoided. Because of the low probability of such events, existing ULFS make no special provisions for them. Specifically to cater for this on a large interconnected grid, a new type of shedding - local load shedding is proposed. The Local Load Shedding (LLS) would capitalise on the distinctive pattern of parameter changes. Specifically within the region where the generators are lost, there would be a sharp rate of frequency decline and a sudden voltage dip. In more distant regions , because of the inter-tie elasticity, the initial rate of frequency decline would be less as well as a less pronounced voltage dip. By suitable calibration of relays to measure the initial frequency decline and the initial voltage reduction, they could actuate the LLS. As an added safeguard, no shedding would occur unless frequency had fallen below 49Hz. For such a critical loss of generation, LLS would function in less than 15 cycles after the disturbance, sufficiently fast to retard the rate of frequency decline. 3.5. System-wide Load Shedding (SLS) Because of its fast action, LLS would restrict the largest frequency deviation, but would not fully compensate for the total quantity of generation lost. Nonetheless, the LLS action would provide sufficient time for follow-up action of a hierarchical control, which, using equations (8) to (10), could evaluate the total extra quantity of System-wide Load Shedding (SLS). With the less dangerous rate of frequency decline following the LLS , the SLS could function one second or more after the initial disturbance. This would permit the delays associated with the evaluation of the precise amount of load shedding and the transmission of signals needed to activate auxiliary relays and circuit breakers at the different substations, in effect, a distributed intelligence. 4. SIMULATION RESULTS 4. 1. Proposed Load Shedding Scheme on a Two-area System Simulation studies on the system in Fig. l have have been made to compare ULFS with the new load shedding scheme in an elastic power system . Each area has three generators Gl = GIl = 900MVA, G2 = G12 = 625MVA and G3 =GJ3=275 MVA, with Area 1 load 950MW and Area 2 load 1900MW, as constant impedance and frequency dependent. All generators have inertia of 4 MWs/MVA and include exciter and turbine-governor models. The disturbance is the loss of two generators G12 and G13 in Area 2, having an output of700MW. Simulations compare the proposed scheme with conventional UFLS using underfrequency relays acting at 48.0Hz, 47.8Hz and 47.6Hz, with 20% of every substation's load shed at each level.
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The study results in Fig. 2 compare the frequency recovery when the proposed load shedding scheme is used (curve A) with the UFLS scheme (curve B). The proposed scheme limits the frequency reduction to 48.5Hz at 4.2 seconds after shedding 700MW whereas UFLS allows frequency to fall to 47.8Hz at 6.2 seconds after shedding 550MW. The ULFS produces a larger voltage rise so also requiring reactor switching. Fig. 3 illustrates the angular and voltage variations of the system, with the new scheme the angle settling near 3()<> (curve A), compared to over 6()<> for UFLS (curve B), so providing a better stability margin.
When the generator loss is increased 200MW to 3,650MW, the conventional UFLS fails to protect the system, whereas the proposed scheme is still effective (Fig. 6, curve A). The latter scheme sheds some 3,450MW load and frequency falls to 48.0Hz at 2.9 seconds. For this disturbance, another conventional load shedding scheme which additionally uses the rate of frequency decline is able to protect the system by shedding 3,450MW and limiting frequency to 49.3Hz at 1.5 seconds (Fig. 6, curve B). J60DEC,-- - - -- - - -- - - ----------------------------.
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Fig. 3 also shows that the proposed scheme produces a better voltage profile (settles at 1.0 pu, curve Cl whereas UFLS produces a low voltage profile (settles at 0.9 pu, curve D) which may cause other problems. Load shedding near the disturbance produces lower tie line loadings, so gaining angular and voltage benefits. 4.2. Iestim: Proposal on a 92-bus Power Grid
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Simulation studies were also carried out on the 92-bus power grid, as described in Lachs & Sutanto (1992), which has a peak load of 14,770MW and a plant capacity of 19,200MW. The grid has five types of generators: 300MW and 600MW thermal, l25MW and
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The fust set of studies examined the power system response to different amounts of generation loss if no underfrequency load shedding acted. The network tolerates generation losses up to 2,300MW but required the simultaneous loss of three power stations, having an output of 3,450MW, to threaten collapse. An additional 200MW loss, of 3,650MW, led to loss of stability. The comparison between the proposed load shedding scheme with the conventional UFLS scheme, considered losing 3,450MW of generation. The UFLS utilizes under-frequency relays dispersed throughout the entire network shedding up to 50% of load, divided into four 12.5% blocks, functioning at 48Hz, 47.8Hz, 47.6Hz and 47.4Hz. In addition, there is 5s-delayed load shedding when the frequency reaches 49.0Hz, 48.7Hz and 48.4Hz. Fig. 4 shows the frequency behaviour when the proposed load shedding scheme is used (curve A), compared with that when the UFLS is used (curve B). The proposed scheme sheds 3,250MW load and limits the frequency deviation to 48.0 Hz at almost 4.0 seconds, whereas the UFLS allows frequency to fall to 47.7Hz at 2.6 seconds and sheds 3,455MW. Of great importance is that the proposal produces much better stability margin where the angle settles at lOo (Fig. 5, curve A), compared with an angle of 65 0 with the UFLS (Fig. 5, curve B).
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Fig. 6 Frequency recovery Figure 7 shows that the proposed scheme produces considerably lower power angles which fluctuated between +/- 50 0 after 3 seconds and continues to diminish (curve A), whereas with UFLS the angle remains between 50-80 0 (curve B). For a more thorough comparison after the load shedding, load flow studies were undertaken to allow voltage levels, transmission line loadings and losses to be examined. From these load flows it was found that the proposed scheme produces better voltage profile on the system. Fig.8 shows voltages at a selection of nodes. Nodes NI8 to N23 are near the lost generation and nodes N43 and N44 are distant from it. It shows that after load shedding, the proposed scheme produces voltages between 1.00 to 1.05 pu at all nodes in the system (Fig. 8, solid bars), except node N43 whose predisturbance voltage is already below 1.00 pu. This compares favourably a conventional ULFS scheme with voltages of 0.92 to 0.96 pu in the disturbed area (Fig. 8, striped bars).
A mathematical analysis of a two area network with weak ties , following generation loss in one area, provides a better understanding of the changes of frequency in each area. The patterns of frequency change and voltage variations following loss of generation form the underlay of a new load shedding proposal. Initial simulations on the two area network, using a transient stability programme, identify a frequency wave trasmitted, after a delay, from the deficient area Simulations, in which the initial voltages reductions are utilised to limit load shedding to the deficient area, showed significant advantages when compared with UFLS which activates load shedding throughout the entire network. The comparisons are illustrated in Figs. I & 2.
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The fust step in studying a 92 bus network was to determine that three power stations with an output of 3450MW had to be lost to create a dangerous underfrequency situation. This starting point, the loss of 3450MW of generator output, allowed a comparison between the existing ULFS and the proposed load shedding scheme. To be able to better understand the post-disturbance operating conditions, load flow studies were undertaken and these demonstrated the advantages of restricting load shedding to the deficient area When conventional ULFS acted after such a large loss of generation, the heavy inflows of power to the deficient area loaded some lines close to their rating and considerably increased real and reactive power losses. This coupled with the lower volt ages and larger power angles give warning of potentially serious problems for the operators which are avoided when shedding is limited to the deficient area.
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Fig 8. Voltages after load shedding Apart from producing a better voltage profIle, the load flow studies have also shown that applicatio n of the proposed scheme avoids line overloading and produces lower active and, quite significantly lower reactive power losses. With 3,450MW generation loss for the proposed scheme, the losses are 240MW and 4,I80MVAR, compared to 345MW and 4,665MVAR with conventional UFLS. High line loading on the inter-area lines occurs with conventional UFLS, but there is no such problem with the proposed scheme. Table I summarizes the main results from the simulation and load flow studies on the 92-bus power system, to demonstrate the advantages of the proposed scheme. Table I. Comparison of the proposed scheme and conventional UFLS scheme
The proposal has the additional feature of Locallised Load Shedding (LLS), which functions within 15 cycles of the loss of generation . This fast response, which is essential for a very large loss of generation, is possible as the incident can be identified at substations within the deficient area by the sudden fall of voltage and the high rate of frequency decline, that forms the basis of a distributed intelligence. LLS, by halting the rate of frequency fall, allows enough time for the hierarchical control to shed additional load and precisely match the lost generator outputs. With appropriate calibration of the relays at load substations, necessary for this proposal, it should not be difficult to implement such an underfrequency scheme. For generation loss within the scope of existing ULFS, the proposed scheme would respond without triggering LLS. However the proposal is better equipped, because of its fast LLS response , to handle the very heavy loss of generation which may be beyond the capability of the existing ULFS. The other important advantage of the proposal is that by restricting load sheddi ng to the deficient area, it ensures better voltage levels, improved stability, lower transmission line loadings and reductions in losses. For all these reasons, it provides a new and promising option for the power industry.
6. REFERENCES oad shedding schemes
Caprio, U.Di and Marconato, R. 1979 Automatic Load Shedding in Multi-area Elastic Power Systems Electrical Power & Energy Systems. Vol.l, No.I, April , pp.21-29 Carhn, H.1. and Blackburn, J.L.1944 A New Frequency Relay for Power System Applications, AlEE Transactions, Vo1.63. August, pp.553-57. Gicrisch, W.C. 1955 Load Reduction by Under-frequency Relays during System Emergencies AlEE PAS, Vol.73, February • pp.1651-55. IEEE Working Group 1975 A Status Report on Methods Used for System Preservation During Underfrequency Conditions IEEE TrailS. Vol. PAS-94, No. 2 March/April, pp.360-65. IEEE Task Force on Emergency Control 1985 Emergency Control Practice. IEEE Tralls.VoI.PAS-04 No.9 Sept. pp.2336-2341.
5. CONCLUSION The principles of the present underfrequency load shedding schemes (UFLS) were developed some 40 years ago, when power systems were quite compact. Present-day power systems, with extensive interconnections and the major power stations distant from the main load centres, although having considerably altered in character, yet persist in using the same type of ULFS . This raises the question whether thi s ULFS is appropriate for the interconnected power system s. The function of this paper is to resolve this question and particularly to determine whether a different method of load shedding would be more appropriate should very large amounts of generation be lost.
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Lachs W.R.1985 Dynamic Study of an Extreme System Reactive Power Deficit IEEE Trans. Vol. PAS-I04 No. 9, September pp.2420-26. Lachs W .R. & Sutanto D. 1992 Voltage Instability in Interconnected Power Systems: A Simulation Approach IEEE TrailS. on Power Systems Vol.7 No .n May pp.753-76\. Lokay, H.E. & Burtnyk, V. 1968 Application of Underfrequency Relays for Automatic Load Shedding IEEE Transaction . VoI.PAS-87, No.3 , March pp. 776-83.