LOAD RELIEF PREDICTION AND CONTROL

S. Jovanovic, B. Fox, J.G. Thompson The Queen's University of Belfast, UK

Keywords: power application software; voltage/reactive power control; simulation techniques

Abstract

The objective of the work described in the paper is to permit accurate prediction of basic load relief, and also of enhanced load relief through connection of shunt reactors, during under-frequency transients. A modelling technique is presented which marks an improvement in accuracy over existing empirical methods. The procedure advocated in the paper may be used to improve supply quality through reduction of prospective load shedding, or to reduce spinning reserve and hence operating cost.

I.INTRODUCTION

The economic operation of many power supply systems is constrained by the need to provide spinning reserve. The cost of providing sufficient reserve to prevent load shedding in the event of generation loss can increase operational costs by as much as five per cent [1] - the extra cost being due to running extra generating units and part-loading plant. Some of this extra cost can be avoided by permitting a limited amount of load shedding to ameliorate the effects of major generation loss. However, load shedding is a last resort, and system operational planners are constantly seeking more acceptable solutions [2].

One such solution, currently under investigation by Northern Ireland Electricity (NIE), is to cause a temporary voltage decrease during an under-frequency episode by connecting shunt reactors. The voltage decrease reduces system demand, effectively creating extra reserve or load relief. The shunt reactors used for this purpose were installed originally to provide reactive compensation, thus the proposal does not imply significant capital expenditure.

Although the feasibility of the procedure has been demonstrated on the NIE system, operational implementation depends on the following:

(a) Rapid detection of generation loss conditions, so that shunt reactors can be connected in time to pre-empt some of the load shedding which might otherwise take place.

(b) Accurate prediction of load relief enhancement, so that spinning reserve provision can be adjusted accordingly.

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. Work on generation loss detection, based .on rapid determination of rate-of-change of frequency [3], is in progress. However, the focus of this work is (b) above - the prediction of load relief.

Previous work in this area has relied on empirical formulae to determine load relief [4]. However, there is no reason why basic load relief, and extra load relief arising from shunt reactor connection, should not be computed on-line using an appropriate system dynamic model. The main purpose of this paper is to present such a model, and to demonstrate, with data for a representative system, how it may be used to predict the effect of shunt reactor connection. The way in which the load relief may be incorporated in an economic loading algorithm, and the economic benefits of offsetting the basic and enhanced load relief against spinning reserve, will be discussed.

2.LOAD RELIEF PREDICTION AND CONTROL

Load Relief Prediction and Spinning Reserve Control

In the case of power supply systems subject to generator outages, the frequency management requirement is governed by the following post-outage balance equations:

E Ri - ~ + LR + LS ~ Pj , jeG ieG

where ~ =loss of j-th generation G = set of generators R 1 p .

I

LR LS

= unit i spinning reserve = unit i active power generation = load relief = load shedding

(1)

The spinning reserve Ri which can be released prior to any load shedding can be assumed to be a piecewise linear function of unit output Pi [5], such that Ri is the lesser of: k (Pimox - Pi), Ri°'0 \ with k ~ 1.

The dependence of load on frequency and voltage may be described by the following equations:

pi = pi ya cJ3 (2a)

Q1 = QY0

V"I w 11 (2b)

where pl(QI)

plo(Qlo) v w a,{3;y,v

= per-unit load active (reactive) power = P1(Q1) at V = w = 1.0 = per-unit load voltage magnitude = per-unit system frequency = load parameters

This load model is not valid for periods longer than about a minute, due to automatic tap-changing gear at substations restoring distribution voltage levels. However, the requirement here is for short-term load relief, while slower-acting reserve, derived from increased boiler firing, is released. This fuel-based reserve can be expected to contribute extra output within seconds for oil-fired generating units, and within a minute or so for coal-fired units.

Following generation loss and an under-frequency transient, the maintenance of extra output from generators requires a frequency deviation. The determination of how system active load will be reduced by this frequency deviation, and also by voltage vanat10ns, requires a system dynamic model incorporating equation (2). The reduction in system active load is the load relief term LR in equation (1).

It is clear from equation (1) that load relief, load shedding and spinning reserve are interchangeable. Any enhancement of load relief may therefore be used to reduce possible load shedding or spinning reserve, or a combination of both. This choice will be determined by the operating philosophy of a particular utility. The objective is to minimise LS, or reduce spinning reserve R = ERi, taking into account the load relief LR - see Fig.I.

Power System Energy Management System

~

I LR,

~

P;, iEG

LS

System Dynamic Model

incl. Equation (2)

Economic Loading incl.

Equation(!)

Fig.1 Load Relief Prediction and Spinning Reserve Control

Emergency Load Relief Control by Shunt Reactor Connection

It is well known that voltage tends to increase during periods of light load, due to the predominance of the capacitive shunt reactance of transmission lines over the inductive reactance of typical loads . The classical

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solution to this problem is to connect inductive shunt reactors at key nodes during periods of light load. The proposal here is to connect these shunt reactors during under-frequency transients. ·The resulting decrease in system voltages creates load relief, reducing, in many cases, the subsequent load shedding. An essential feature of this mode of operation is that the reactors should be connected before any load shedding might take place. Associated work [3] has demonstrated the feasibility of using rate-of-change of frequency relays for this purpose. Recent experience has indicated that a reliable decision on whether to connect shunt reactors may be based on measurement and analysis within twenty mains cycles following a generation loss. Based on results presented later in the paper, this would allow approximately one second to implement reactor connection in time to pre-empt conventional load shedding. The functional requirements of the proposed scheme are shown in Fig.2.

Power System

Frequency Relay

+ Shunt Reactor

Fig.2. Automatic Load Relief Control

3.SIMULATION MODEL

It is often assumed that a frequency transient may be simulated adequately in terms of generating unit dynamic characteristics, with system demand adjusted for varying frequency through use of a 'load relief or damping parameter [6]. However, experience has shown that this approach often does not estimate accurately the load shedding which may be required. Correct prediction of load relief, and hence of load shedding, requires incorporation of a network representation and load voltage characteristics to model voltage variations. A comprehensive system simulation model with this capability will now be presented.

Co-ordination of Voltage and Frequency Behaviour

The relationship between system frequency and voltage profile variations is described by the following equations [7]:

w = f P adt/(2Hsw) (3a)

p = r; pm. _ r; pi .y .aicJ3i _ r; ploss. a I 01 I I

(3b) iEG iEL iEM

= system inertia constant (s) where H pfoss

L = per unit line active power loss = set of load nodes

M = set of lines = time variable (s)

pm. I

= unit i prime-mover output

The prime-mover mechanical power outputs pmi are determined by solving the corresponding differential equations. The prime-mover model incorporates a simple steam cycle with reheat, and a three-stage turbine representation with conventional speed governing. Details may be found in reference [7).

Network Equations

During transients, large voltage and angle vanat10ns occur, and a strong interaction between active and reactive load flow exists. Therefore, it is not normally considered appropriate to apply classical P/Q decoupling and Jacobian substitution in dynamic studies. However, it has been reported [6] that an extended version of the decoupled power flow equations may be applied to dynamic conditions of the type considered here. The essential modifications are that accelerating powers, Pa• are included as additional variables, and that generator electric powers are treated as outputs rather than inputs. This approach has been tested successfully on 18- and 68-node systems [7). The authors have also found that results obtained by the modified, decoupled method are in agreement with results obtained by a fully coupled Newton-Raphson load flow method for various transient conditions. The decoupled method was therefore adopted. It may be summarised by the following equations:

!!.QIV = B" !!. V (4b)

It should be stressed that the elements of the mismatch vectors !!.P/V and !!.Q/V are given by:

!!.P-/V. = (Pm. - pl. - p . - RP /H )IV· I I I I I I a S I

and g I

!!.Q/Vi = (Qi - Qi - Qi)/Vi

P\ and Q\ are dependent on voltage and frequency, as described by equations (2a) and (2b). If the calculation is convergent, the results are the same as those obtained by the full Newton-Raphson method. If the calculation should prove unstable, the full Newton-Raphson method may be applied.

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The above equations employ the following notation:

Pa = per unit system accelerating power H = inertia constant vector e = voltage angle vector B' and B" = coefficient matrices !!.P/V and Q/V = mismatch vectors tr = vector transponse

Load Shedding and Load Relief

Load shedding is activated at specified nodes when certain pre-defined under-frequency levels w=wLS are breached:

LS = -E.:lP1· for w=wLS I

iEL (Sa)

where: wLS = load shedding frequency settings.

The definition of load relief reflects its use here as a potential replacement for spinning reserve or load shedding. Basic load relief is given by

LR = r;pl . - r;pl. 01 I

(Sb) iEL iEL

It is logical to define extra load relief as the load reduction which occurs when frequency has fallen to the frequency setting of the automatic load relief control:

LR = -E!!.P1i for w=wLR (Sc) iEL

where: wLR = shunt reactor control frequency setting. It should be noted that wLR > wLS.

4.SIMULATION RESULTS

The dynamic simulation algorithm described above was used to examine the value of load relief prediction and the scope for its control through reactor switching. The data chosen for the study is for the New England system [7]. The simulated New England system consists of 68 nodes, 86 lines and 16 generators. Two sets of results are presented below, relating to:

-load relief prediction -load relief control from shunt reactor connection

In each case, results for an isolated New England sub­system, which includes 18 nodes, 19 lines and 5 generators, are presented, in addition to results for the full system. The load parameters for the New England sub-system are given in Table 1. Predicted frequency transients and load shedding are obtained for the outages of unit 3 of the sub-system and unit 14 of the full system, representing 17 % and 9 % of the demands

respectively.

Table 1: Load Parameters for the New England sub­system

Bus a /3 'Y v

I 2 1 2 1 2 2 1 2 1 3 1.66 0.68 1.41 -0.36 4 2 1 2 1 5 2 1 2 1 6 1.34 1 1.36 -0.4 7 0.76 1.37 1.99 -0.19 8 2 1 2 1 9 1.96 0.74 1.62 -0.35 10 1.6 1.48 1.54 -0.24 11 2 1 2 l 12 1.01 1.21 1.68 -0.19 13 0.82 1.21 1.72 -0.34

Load Relief Prediction

The significance of load relief for the study system was assessed by comparing system response employing demands which are sensitive to frequency and voltage with response based on insensitive demands - the well­known 'constant P, Q' load model. Constant P, Q behaviour was obtained by setting the load parameters as follows:

a = f3 = r = v = 0

With this load model, the simulation predicts three stages of post-outage load shedding for the sub-system. Use of the realistic values of the sub-system load parameters given in Table 1 results in a prediction of two stages of load shedding for the same case. The corresponding frequency transients and load shedding are shown in Fig.3. It will be seen that the assumption of constant load results in an over-estimation of load shedding. Correct prediction of load relief would permit either

(a) an improvement of the security standard - two stages of prospective load shedding rather than three,

or (b) a reduction in spinning reserve if three stages of

prospective load shedding can be tolerated.

In the case of (b), the basic load relief identified by the simulation with realistic load parameters is 83 MW, corresponding to a 12 % reduction in spinning reserve.

A comparison of constant and variable load models was also performed for the full New England system - see

480

Fig.4. It was found that one stage of load shedding was predicted by both models, but that the variable load model identified 900 MW of load relief, corresponding to a possible 22 % reduction in spinning reserve without the risk of shedding extra load.

Connection of Shunt Reactors

The New England data does not include shunt reactors. It was decided to demonstrate the effect of shunt reactor connection for the sub-system with four 50-MV Ar reactors. Suitable locations were found by experiment to be nodes 2, 5 and 13. The reactors were connected at the start of the transient, which is shown in Fig.5. The transient without reactor control is shown for comparison. It may be seen that two stages of load shedding take place in each case, but that use of the shunt reactors provides 93 MW of extra load · relief, which could be used to reduce spinning reserve by 13 % .

Similar simulations for the full New England system resulted in 800 MW of extra load relief, and avoidance of load shedding, when 42 50-MV Ar shunt reactors were connected at the start of the frequency transient; see Fig.6. Load relief can be exchanged for a reduction of spinning reserve, amounting to 20 % in this case .

5. DISCUSSION

It has been demonstrated that deliberate reduction of system voltage reduces demand and provides an alternative to conventional spinning reserve. However, the impact of such voltage reduction on consumers must be considered.

The magnitude of the voltage reductions envisaged here is of the order of one per cent. Such a recuction is within the range experienced by most consumers under normal conditions. The frequency of such occurrences will vary from system to system, but is fewer than ten per annum for the NIE system. The dura~ion of t~e under-voltage condition would be about a mmute - this being the time normally required for frequency to recover following generation loss, as unit outputs reflect increased boiler firing. The recovery period does not provide substation tap-changing gear, under local, automatic control, sufficient opportunity to negate the desired demand reduction via compensatory increases in distribution - system voltages. Thus the demand reduction is effective over the critical period. The recovery of frequency will of course trigger the disconnection of the shunt reactors as normal system conditions are re-established.

It is worth noting that a voltage reduction during an under-frequency transient may actually be of benefit to transformers and electrical machines, by preventing over-ft uxing.

Economic Considerations

The basic and enhanced load relief predicted for a given system condition may be used to reduce potential load shedding, or to reduce spinning reserve, or to implement a combination of both. The economic value of the load relief may be realised for a particular system and condition by reducing spinning reserve only. The NIE system, with which the authors are familiar, has a fairly taxing reserve requirement which is responsible for increasing fuel costs by 5% [l]. Thus, the spinning reserve reductions obtained above, translated to the NIE system, suggest significant fuel cost savings. For example, the 13 % reduction in spinning reserve resulting from 4x50 MV Ar shunt reactor switching applied to the New England subsystem would result in a 0.65 % fuel cost reduction for the NIE system.

The fuel cost saving can only be achieved if the predicted load relief is incorporated in the economic loading algorithm [5]. This is achieved by including equations (1) in the loading algorithm, with an updated prediction of load relief LR made continuously available. In simple terms, the reserve requirement, however formulated, is relaxed by LR.

6. CONCULSION

Precise mathematical modelling of load relief and incorporation of such models in control centres have not received serious attention, despite the possibility of reduction of spinning reserve with the associated saving. On-line evaluation of prospective load relief could refine the determination of the spinning reserve requirement, with consequential cost savings.

A measure sometimes adopted to enhance load relief is the rapid connection; upon detection of a sudden fall in frequency, of shunt reactors. The need to analyse the effect on load shedding of reactor switching for operational planning purposes forms the motivation for the present work.

The paper presents a mathematical model and concept for load relief prediction and control which could be incorporated in control centres. It takes into account load voltage and freque_ncy characteristics, network representation, the . effects of load shedcling and connection of shunt reactors controlled by frequency­activated relays. Simulation results are presented and discussed for the New England test system. The results demonstrate that basic load relief, enhanced by extra load relief from rapid connection of shunt reactors, can replace a significant proportion of the spinning reserve requirement.

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7.REFERENCES

1) B. Fox, A. McCartney, 'Emergency control frequency on the NIE system', Power Engineering Journal, Vol.2, No.4, 1988, pp. 195-201.

2) C.B. Somuah, F.C. Schweppe, 'Minimum frequency constrained generation margin allocation using quadratic programming', Electrical Power and Energy Systems, Vol.9, No.2, 1987, pp.105-112.

3) D.J. Morrow, B. Fox, P.T. Toner,'Low-cost under­frequency relay for distributed load shedding', Proc. 3rd IEE International Conference on Power System Monitoring and Control, London, June 1991, pp. 273-275.

4) R.F. Preiss, V.J. Warnock,'Impact of voltage reduction on energy and demand', IEEE Trans., Vol.PAS-97, No.5, 1978, pp.1665-1671.

5) M. Piekutowski, I.A. Rose,' A linear programming method for unit commitment incorporating generator configurations, reserve and flow constraints', IEEE Trans.,Vol.PAS-104, No.12, 1985, pp.3510-3516.

6) P.M. Anderson, M. Mirheydar,' An adaptive method for setting underfrequency load shedding relays', IEEE Trans., Vol.PWRS-7, No.2, 1992, pp.647-652.

7) J.W. Manke, W.R. Paully, K. Hammaplardh,'Long term system dynamics simulation methods', EPRI Research Project 1469-1, Feb. 1985.

8. ACKNOWLEDGEMENTS

The authors wish to acknowledge the financial assistance of the UK Science and Engineering Research Council, and of National Power and PowerGen.

Frequency change(p.u.)

o~-~--------------~

-0.005

-0.01

-0.015

-0.02 '•, ......... •'

-0.025

-0.03

-0.035

-0.04 Tine (seconds)

-0.045~~~~~~--,-~~-.-~-.--.--~

0 .5 1 1.5 2. 2.5 3. 3.5 4. 4.5 5. 5.5

- Variable load

·--- COnstant load

---- First LS stage

- - - Second LS stage

- ll*d LS atage

Figure 3a: Frequency transients - influence of load parameters in New England subsystem

Load shedding (p.u.) 4

3.5

3

2.5

2

1.5

0.5

0 .5

~ Variable load

Ill Constant load

Tlme (seconds)

1.5 2 2.5 3 3.5 4 4.5 5. 5.5

Figure 3b: Load Shedding - influence of load parameters in New England subsystem

Frequency change(p.u.) o~-~---------------~

-0.002

-0.004

-0.006

-0.008

-0.01

-0.012

-0.014

-0.016

-0.018

-0.02

-0.022

-0.024

•' •' ... "

•' •' •'

.. .. .. ..

.. - ·····.-.-•• ··,····· ·'..!.~~:: ___ , ···----·--·--······ --- ;,::- -----

"'•,. ······· ..........

Tlme (seconds)

-0.026 -'--~~-.---,--,--,--,--.,.---,--,--,-0 2 3 4 5 6 7 8 9 10

- Varlable load

--- Constant load

First LS stage

Second LS stage

Figure 4: Frequency Transients - influence of load parameters in New England system

482

Frequency change(p.u.) 0 .,....--~-------

-0.005

-0.01 ...

······ ····· ·····-·-······_>._ ______________________ ,~·:...·~-. '"·· ·······

- ·-· - · - · -·- · - · - · - · - ·- · -·~~~b°"l""oi;;;~;~;~;~;~;~;~i i"'n ..... L~!.~~~~~~~--- ·- · -0.015

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-0.04 Time (aec:onda)

-0.045 -'----,,..--,--.-----.--.,....--.---.----r--,---.--,-----,,-

0 .5 1.5 2. 2.5 3. 3.5 4. 4.5 5. 5.5

- Whhout reactors

- -- With reactors

First LS stage

Second LS stage

- Thlr d LS stage

Figure 5: Frequency transients - influence of reactor control in New England subsystem

Frequency change(p.u.) 0.,....---,------------------

-0.002

-0.004

-0.006

-0.008

..().01

-0.012

-0.014

-0.016

-0.018

..().02

-0.022

-0.024

"··· , .... ....................

·Time (second5) -0.026 ~.-----,---,--.,....---,----.--..,--.---.---,---r--

0 2 3 4 5 e 1 s 9 10

- Wlthcut relCIOrS

- - - With reactors

First LS stage

Second LS stage

Figure 6: Frequency transients - influence of reactor control in New England system

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