Modelled operation of the Shetland Islands Power System comparing computational and human operators’ load forecasts

D.C.Hill D.G.lnfield

Indexing terms: Load forecasting, Power stations

Abstract: A load forecasting technique, based upon an autoregressive (AR) method is presented. Its use for short term load forecasting is assessed by direct comparison with real forecasts made by human operators of the Lerwick power station on the Shetland Islands. A substantial improvement in load prediction, as measured by a reduction of RMS error, is demonstrated. Shetland has a total installed capacity of about 68MW, and an average load (1990) of around 20MW. Although the operators could forecast the load for a few distinct hours better than the AR method, results from simulations of the scheduling and operation of the generating plant show that the AR forecasts provide increased overall system performance. A detailed model of the island power system, which includes plant scheduling, was run using the AR and Lerwick operators’ forecasts as input to the scheduling routine. A reduction in plant cycling, underloading and fuel consumption was obtained using the AR forecasts rather than the operators’ forecasts in simulations over a 28 day study period. It is concluded that the load forecasting method presented could be of benefit to the operators of such mesoscale power systems.

1 Introduction

The prediction of electricity demand [l] has been of much interest to the electricity supply industry for some years, both for long term planning strategies involving the forecasting of seasonal peak demands, and for short term [2, 31 prediction for improved sched- uling of generating plant. This paper concentrates on the latter application, with forecasts in the range of one to four hours ahead, in the context of the Shetland mesoscale power system. The electricity load on the 0 IEE, 1995 ZEE Proceedings online no. 19952248 Paper first received 24th April 1995 D.C. Hill is with the School of Ocean Science, UCNW, Menai Bridge, Gwynedd, LL59 5EY, United Kingdom (formerly at Rutherford Apple- ton Laboratory) D.G. Infield is with CREST, Department of Electronic & Electrical Engi- neering, Loughborough University, Loughborough, Leicestershire, LEI 1 3TU, United Kingdom

island is predominantly domestic in origin, (the major industrial load at Sullam Voe being independently sup- plied), and with a high proportion of the night time load coming from storage radiators.

A detailed computational model of the operation of such a mesoscale electricity grid, which includes plant scheduling, had been previously developed in conjunc- tion with the then North of Scotland Hydro Electric Board (NSHEB), [4]. A computational forecasting method, based on autoregressive techniques is outlined and load forecasts obtained in this way are compared with those made by experienced human operators of the Shetland Islands power station. Forecasts were made over look ahead periods ranging from I to 4h. The 2h ahead forecasts were then used in the schedul- ing routine of the simulation model to assess their rela- tive merits in terms of fuel savings, decrease in number of start/staps of generating sets and improvements in underload/overload times. A look ahead period of 2h provides sufficient information for the scheduling of the various sets which have start up times to reach full output, ranging from 1 to 20 mins.

2 Data type and quality

The power station operators were asked to make fore- casts of the total generated output (TGO) 1, 2, 3 and 4h* ahead every hour, on the hour, for a period of 28 days commencing midnight Friday/Saturday 2nd/3rd November 1990 until midnight 30th Novemberilst December, 1990. The operators wrote down the precise time at which forecasts were made which, due to oper- ating commitments, were not always precisely on the hour.

Availability of forecasts from the operators was extremely high at 99.1%. For the 0.9% of cases where no forecast was available, or was made further than 5 min from the hour, linear interpolation between adja- cent sets of forecasts was used to allow input into the scheduling model. These points, however, were excluded from the RMS error comparisons outlined in Section 4.

The actual value of TGO was recorded automatically at 1 min intervals and availability was similarly high at 99.2%. It was therefore felt that a high quality database had been produced from which assessments could be made. Although the data was limited to 28 days the * Although a look ahead of only 2h was used in the scheduling model it was felt useful for assessment of relative forecasting abllity to make com- parisons over a wider range

IEE Proc.-Gener. Transm. Distrib.. Vol. 142, No. 6, November 1995 555

resulting sample size of 672 forecasts was more than adequate for statistical analysis.

The question arises as to what the operators are actually trying to forecast. The instantaneous load can vary from minute to minute by as much as 400kW so it was considered reasonable to assume that the operators were forecasting 1Omin means centred on the hour, since the rapid fluctuations are not expected to influ- ence significantly their scheduling decisions. Thus, all comparisons between computed and operators’ fore- casts were made using 1Omin means centred on the hour.

To calculate the AR parameters, data prior to the period of evaluation was required; the four weeks from 6th October to 3rd November was found to be ade- quate from the point of view of parameter identifica- tion. Data availability for this period was of a lower quality at 66.4% so gaps were filled with manually recorded hourly values from the station’s log. This sec- tion of poorer quality data only affects the calculation of the AR parameters and, if anything, can only result in slightly impaired AR forecasts.

3 Description of forecasting method

Following the ‘standard day’ methodology, [1], the load, L, is decomposed into components. In this study they are defined as follows: (i) the annual component due to seasonal weather patterns, LA, (ii) the diurnal component due to daily behavioural pattern of the inhabitants, L,, and (iii) the stochastic remainder, L,. Each of these components is forecast separately, as outlined below, and the results summed to provide the overall forecast.

i

0 i 0 4 8 12 16 20 24 28 32 36 40 44 48 52

week of the year (1-3 May 1986) Fig. 1 Annual trend from weekly means

3. I The annual component is modelled by weekly means. An example year of Shetland Island load (starting in May 1986) is shown in Fig. 1. Forecasting of this com- ponent uses persistence, i.e. the prediction of load for the following week takes the value for the current week. Because of this simple definition LA can only be updated weekly. Denoting the forecast values by ‘*’, the forecast of the annual component is given by LA(w + 1) = LA(w), where w is the week number.

The diurnal component is represented by an average over a prescribed number of weeks, nW, prior to the current week:

Treatment of the trends

556

w’=wo for d = 1,2 ,..., 7, h = 1,2 ,..., 24, where d is the day number, h the hour number, and the averaging starts at week w,, = w - (n, - 1). This average is calculated for each hour for each day of the week so that the load pattern for each day of the week is evaluated independ- ently. Fig. 2 shows a typical plot of the weekly load pattern evaluated treating each day of the week sepa- rately, and a second plot were the days of the week are regarded as indistinguishable. The significant difference between the two plots, especially over the weekend period, justifies the independent treatment adopted in this forecasting study.

3 0 1

2 5 4

5 1 1 Sat Sun Mon Tue Wed Thur Fri

0 12 24 36 48 60 72 84 96 108 120 132 144 156168 hour of the week

0 , , , , I I I : , , , , , I I ; . , , , , . I 1 1 1 1 / 1 1 1 I , ! I , , , , : 1 1 / , , 1 1 1

Fig. 2 Diurnal trends ~ all days Merent

all days same ~ _ _ _

Like the annual trend of weekly means, the diurnal trend, modelled by eqn. 1 above, is forecast on the basis of persistence. Hence i ,(w + 1, d, h) = L,(w, d, h). As with the annual trend the forecast is updated once per week, at midnight of FridayISaturday.

The load variation unaccounted for by the annual and diurnal trend models is regarded as the essentially stochastic component L,. It can be identified over the same period of n, weeks prior to the current week from which the trends were calculated, as follows:

L,(w’, d , h) = L(w’, d , h) - L A ( W ’ ) - Lo(w’, d , h) ( 2 )

for w’ = w - nW, w - n, + 1 ,..., w - 1, d = 1,2 ,..., 7 and h = 1,2,...,24, and where Lo represents the total meas- ured load. It is the stochastic component alone that is to be forecast using the AR modelling approach described in the following Section.

3.2 Autoregressive model and parameter iden ti fica tion Time series comprising the stochastic component, L,, were subject to an initial analysis for model identifica- tion purposes. Following the Box-Jenkins approach [5] an examination of the calculated autocorrelation func- tion (ACF) and partial ACF indicated that a purely autoregressive model with seasonal terms was appropri- ate (i.e. having no moving average component). The need for seasonal terms reflects the fact that the detrending of the daily variations is, as would be expected, imperfect, leaving scope for the AR model to improve this aspect of the modelling.

The resulting AR model takes the standard form, [5]:

IEE Proc.-Gener. Transm. Distrib., Vol. 142, No. 6, November 1995

where &, i = 1,2,...,p are the nonseasonal AR parame- ters, Qi, i = 1,2, ..., P are the seasonal AR parameters and a, the usual white noise term.

The parameters were estimated using a least squares algorithm, [5 ] , for a given model order (p,P). It was found by trial and error that values o f p = 1 and P = 4 gave the smallest prediction errors for the Shetland load data. Similarly, it was found that the RMS error was smallest when the parameters were estimated over the previous four weeks (i.e. n, = 4). This reflects a compromise between a long enough data set for ade- quate determination of the trends and identification of the AR parameters, whilst short enough to maintain statistical stationarity and respond effectively to changes in the nature of the load variations through time.

To calculate values of L, right up to the current hour it is necessary to use the forecasts of trends, LA(w + 1) and LD(w + 1, d, h), during the current week, whereas actual values are of course used for preceding weeks (eqn. 2). Using this approach the AR parameters could, in principle, be updated every hour. In practice sufficient accuracy can be achieved by updating weekly, and of course the computational effort is considerably reduced.

3.3 Forecasting the stochastic component If the week number is w, the day number d and the hour, h at the current point in time, it is required to calculate the hour ahead forecast of stochastic compo- nent, which is denoted for consistency by LAW, d, h + 1). The standard expression for this forecast value [SI is:

Ls(w,d , h + 1) = $ ~ L , ( w , d, h) + @~L,(W, d, h - 23)t . . . + @4LS(w, d, h - 95)

where are the AR parameters calculated from the preceding n, = 4 weeks. Similar expressions are used to calculate the 2, 3 and 4 h ahead forecasts.

For any hour the forecast of the total load (for a given look ahead) is given simply by the sum of the forecasts of the trends and the stochastic component. In the current notation: i() = iA() + E D ( ) + is().

4 with the operators

4.1 period To assess the quality of the forecasts, RMS errors for both the Lerwick operators' and the AR forecasts were calculated over the 28 day period. Comparison is also made with forecasts made simply by applying the per- sistence criteria to the stochastic component. It should be noted that this not the same as applying persistence to the total load which in itself would result in poor forecasting.

It was considered that the operators, with their years of experience, might be able to forecast the daily peak load better than the AR method. Hence, the impor- tance of calculating the RMS errors as a function of

Application of AR algorithm and comparison

Application of forecasting to the test

IEE Proc-Gener. Transm. Distrib., Vol. 142, No. 6, November I995

the hour of the day. The analysis was complicated by the fact that the

clocks on Shetland changed from BST to GMT on 27th October 1990. This incurs a real effect on the load (even after all data is converted to GMT) because the behavioural pattern of the inhabitants changes with respect to daylight hours and so the lighting compo- nent increases after 27th October. This effect is intensi- fied on the Shetland Islands where, at such a northern latitude (63"), daylight hours are short in winter. This does not really affect the operators forecasts since their forecasts were made after this date. However, it might be expected that the AR parameters calculated by a mixture of data from before and after this special event would be adversely affected. Again this will result, if anything, in a conservative assessment of the AR fore- casts. It should also be noted that this AR method takes no account of weather information whereas the operators use their knowledge of how the weather affects the load curve.

Table 1: RMS forecasting errors

RMS errors, MW Look ahead, ti Lerwick Persistence AR* 1 0.76 0.81 0.55 (27.6%) 2 0.85 1.12 0.71 (16.5%) 3 0.95 1.29 0.80 (15.8%) 4 1.04 1.42 0.85 (18.3%) * Percentages in parentheses refer t o improvements of AR over the Lerwick operators

4.2 Comparison of forecasting results The RMS forecast errors for look aheads of 1 to 4h for the three forecast types (Lerwick operators', persistence and AR) have been calculated over the evaluation period. The results, with errors in megawatts, are shown in Table 1. It is interesting to note that the experience of the operators provides significantly better performance than the persistence. For all look ahead periods, the operators achieve much reduced RMS errors. It is clear that the AR method results in a con- siderable improvement over the Lerwick operators; 27.6% better in terms of the RMS error at 1 h ahead.

::;I , 0 I

0 2 4 6 8 10 12 14 16 18 20 22 24 time of day.h

Fig. 3 Compariron of hourly errors (2h ahead) P A R

. . . . . . . . . . . persistence Lerwick _ _ _ _

Fig. 3 shows the RMS errors as a function of the time of day at which the forecast was made for the three

~

resented in the simulation modelling by a parameter called the ‘load margin’. It is specified in this study as a percentage of the forecast load. This has been found to be a convenient way to characterise the degree to which spinning reserve is held on the system and thereby to assess the effect on the system of factors which relate to loss of load and undesirable plant operation. Spinning reserve is costly to maintain on a system as it involves operating some of the plant more lightly loaded than would otherwise have been the case, with a commensu- rate drop in generating efficiency.

It is crucially important that fair comparisons be

forecasting methods, at 2h ahead. It can be seen that the Lerwick operators’ forecasts are less consistent than AR forecasts but at some times of day more accurate. These results are perhaps not surprising since the AR method makes no real distinction between times of the day other than in the simple averaging technique employed to evaluate the diurnal trend. The question arises as to whether the ability to predict the load accu- rately at a few key times of the day is more important than overall predictive performance. This matter is addressed in the following Section in which the opera- tional value of improved forecasting is quantified.

Table 2: Modelled generation plant characteristics at Lerwick

Unit Name plate Effective Fuel type Start-up Stop Plant type number rating, rating, time, time,

MWe MWe mins mins

I

start run stop ~~

A station 1 2.0 2 2.6 3 4.6 4 4.6 5 4.6 6 2.0 7 3.5 8 3.5 9 3.8 10 4.6 11 4.6

Gas turbines 13 4.85 14 4.85

B station 21 2.1 22 8.1 23 8.1

1.6 2.8 4.6 4.6 4.6 1.6 3.5 3.5 3.8 4.6 4.6

4.85 4.85

2.1 8.1 8.1

GO GO GO GO GO GO GO GO GO GO GO

GO GO

-

GO GO

MFO GO 8.0 MFO GO 8.0 MFO GO 8.0 MFO GO 8.0 MFO GO 8.0 MFO GO 8.0 MFO GO 8.0 MFO GO 8.0 MFO GO 8.0 MFO GO 8.0 MFO GO 8.0

GO GO 0.1 GO GO 0.1

- - -

HFO GO 20.0 HFO GO 20.0

15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0

Mirlees Blackstone KVSS12 Mirlees Blackstone KVSS16 Mirlees Blackstone Mk 2 Major Mirlees Blackstone Mk 2 Major Mirlees Blackstone Mk 2 Major Mirlees Blackstone KVSSl2 Mirlees Blackstone Mk 1 Major Mirlees Blackstone Mk 1 Major Mirlees Blackstone Mk 1 Major Mirlees Blackstone Mk 2 Major

15.0 Mirlees Blackstone M k 2 Major

0.1 Sulzer type 3 0.1 Sulzer type 3

- waste heat steam turbine 60.0 Crossley Pielstik 12PC3 V480 60.0 Crossley Pielstik 12PC3 V480

GO = ’gas oil‘, MFO = ’medium fuel oil’, HFO = ’heavy fuel oil’

5 forecasts

Evaluation of the operational value of

5.1 system The relative benefits of the AR forecasting were assessed by use of a detailed numerical model which simulates the scheduling and operation of the generat- ing plant of the Shetland Islands power station. Each item of plant on the Shetland system is individually represented in the model which takes as input the fore- cast and actual loads. There are 13 diesel generator sets, ranging in capacity from 1.5 to 8.1MW, repre- sented on t he system, p l u s two 4.9MW gas turb ines and one 1.1 MW steam turbine. The plant models also include run up characteristics. The modelled plant characteristics are summarised in Table 2, which is reproduced from reference [4]. Some particular aspects of the model, relevant to this study, are discussed below while the results of the model output concerning fuel usage, underload severity, and number of diesel startistops are presented in Section 5.2.

The spinning reserve, i.e. the amount of immediately available spare capacity which is kept on line, was rep-

Operation of the Shetland Island power

558

made between different model runs incorporating the different sets of forecasts. AR forecasting, by reducing the uncertainty associated with the expected load, is expected to facilitate fuel savings through a reduction in the spinning reserve carried, while not causing any adverse increase in plant overload hours. To provide an unbiased assessment all comparisons were made for the minimum level of spinning reserve for which no over- loads occur. This is a stringent criteria since, in reality, on a small power system, like Shetland’s, the diesels are occasionally overloaded. Underloading of plant is also undesirable due to an associated increase in the mainte- nance requirement. It has been found useful to define an u n d e r l o a d severity i ndex as t h e percentage plant underload averaged over time during which the plant is actually under loaded.

The Shetland Island power system model was run with a look ahead forecasting period of 2h, while actual decisions within the model to startistop diesels were made every 15mins of simulated time. The hourly load predictions were therefore interpolated to provide information about future loads every 15mins. All scheduling decisions were made using a conventional merit order approach, with the most efficient diesel, or

IEE Proc -Gener Transm Distrib , Vol 142, No 6, November I995

Table 3: Power station model output

Forecast Critical load Total fuel used No. Underload Underload

type margin, % of starts severity, hours forecast load GJ f %

Persistence 14% 134709 630208 134 12.2 692 Lerwick 10% 134406 628287 128 9.6 382 AR 8% 134231 626956 106 7.7 249

diesels, available to meet the forecast load requirements being put on line at a given time. This model has been validated extensively by previous work in close collabo- ration with NSHEB and the operators of the Shetland system, [4]. Despite the simplifications inherent in any such study, all parties to the collaboration regarded the model as an accurate representation of the system and its operation, particularly well suited to an examination of operational control strategies.

The initial conditions for the simulation of the oper- ating strategy, for the 28 day period over which the forecasts were to be assessed, were taken from data recording output of all sets every minute. Thus, it was possible to undertake a realistic simulation of the oper- ation of the station and so assess the modelled system performance using all the three different sets of fore- casts in the scheduling routine.

5.2 Potential benefits of computational forecasts The model of the power station was run to simulate the scheduling of the generators over the 28 day period with each of the three sets of forecasts (persistence, Lerwick operators’ and AR). Table 3 shows the model results for the different forecasting methods; for each case the model was run with the load margin set to the critical value which just avoids the occurrence of plant overloads. These margins were identified through runs of the model over the test period, on a trial and error basis.

In summary, over the study period, the model run using forecasts derived by the AR method used less fuel worth E1331 (at 1990 prices), and gave 17% less plant startups, with a mean underload 20% less severe and number hours underloaded reduced by 35% com- pared to the model run with forecasts from the Lerwick operators. As expected, the better the forecasts the lower the amount of spinning reserve required, as reflected by the load margin. As already mentioned this is because improved forecasting reduces the uncertainty associated with load in the hours ahead and this ena- bles a more precise, and less wasteful, scheduling of plant. The reduction of the number of plant starts is also a reflection of this more precise scheduling.

6 Discussion and conclusions

It has been demonstrated that the AR based forecast- ing method has an RMS error 16.5% better than the Lerwick operators forecasts over the crucial two hour look ahead time. Despite the fact that the Lerwick operators are able to predict at certain times around

10% better than the AR method, the power station model has shown that the AR forecasts result in signif- icantly more efficient operation overall.

The simulations suggest that the AR method would result in 17% fewer starts at an underload severity which is 20% better than that achieved by the Lerwick operators’ forecasts. Both these improvements are of economic value through reduced maintenance and probably an extension of plant life. Although the fuel saving itself of E1331 over the 28 day period is rela- tively small., it is felt that this is largely due to the strin- gent choice of criteria for comparison of the different runs of the model. These results show the AR forecasts provide worthwhile benefits to the management of the power station. It is worth emphasising that this is true even though at present the AR method takes no account of weather information nor any special account of ithe clock change.

The study shows that there is a strong case for undertaking AR forecasting of the load at the power station to act as an advisory tool to the operators to assist in their scheduling of the diesel plant. The com- putations involved are sufficiently straightforward that there should be no difficulty in updating such forecasts every 15min.

7 Acknowledgment

The Science and Engineering Research Council and Scottish Hydro Electric are gratefully acknowledged for their financial support during this project. In partic- ular, thanks are due to the staff of the Lerwick power station for their assistance collecting the load data and making the forecasts. Thanks are also due to Jim Hall- iday of RAL for his numerous helpful suggestions and for the use of the Shetland scheduling model.

References

BUNN, D.W., and FARMER, E.D. (Eds.): ‘Comparative models for electrical load forecasting’ (J. Wiley & Sons, New York, 1985) ABU-EL-MAGD, M.A., and SINHA, N.K.: ‘Short-term demand modelling and forecasting: a review’, IEEE Trans. Syst. Man. & Cybern, 1982, 12 AAM, S., SKARSTEIN, O., and GAGNAT, L.: ‘Implementa- tion of load prediction program system for the Norwegian power pool’, Modelling, Identification & Control (Norway), 3, pp. 151- 163 HALLIDAY, J.A., GARDNER, P., ANDERSON, G.A.,

L, J.W., and COUSINS, J.: ‘Simulation of wind integration for the Shetland medium-scale grid’. Proceedings of ECWEC, 1988, (H.S. Stephens & Associates, Herning, Denmark), pp. 518-523 BOX, G.E.P, and JENKINS, G.M.: ‘Time series analysis: fore- casting and control’ (Holden-Day, 1976, revised edn.)

BASS, J.H., LIPMAN, N.H., HOLDING, N.L., TWIDEL-

IEE Proc-Gener. Transm. Distrib., Vol. 142, No. 6, November 1995 559