CControlling volatility of wind-solar power
Hans Lustfeld
Peter Grünberg Institut (PGI-1), Forschungszentrum Jülich 52425 Jülich, Germany
Abstract
The main advantage of wind and solar power plants is the power produc-tion free of CO . Their main disadvantage is the volatility of the generatedpower. According to the estimates of H.-W. Sinn[1], suppressing this volatilityrequires pumped-storage plants with a huge capacity, several orders of magni-tude larger than the present available capacity in Germany[2]. Sinn concludedthat wind-solar power can be used only together with conventional power plantsas backups. However, based on German power data[3] of 2019 we show that therequired storage capacity can significantly be reduced, provided i) a surplus ofwind-solar power plants is supplied, ii) smart meters are installed, iii) partlya different kind of wind turbines and solar panels are used in Germany. Ourcalculations suggest that all the electric energy, presently produced in Germany,can be obtained from wind-solar power alone. And our results let us predictthat wind-solar power can be used to produce in addition the energy for trans-portation, warm water, space heating and in part for process heating, meaningan increase of the present electric energy production by a factor of about 5[1].Of course, to put such a prediction on firm ground the present calculations haveto be confirmed for a period of many years. And it should be kept in mind, thatin any case a huge number of wind turbines and solar panels is required. Keywords: volatility, storage, offshore, weak-wind turbine, low-light solar cell,smart meters
1. Introduction
Apart from nuclear power and hydropower (power from biomass and wastecould be mentioned, too), the conventional electric power production by gasand fossil fuel power stations generates CO as a byproduct. Nuclear powerplants do not have this problem, but they have other disadvantages, in particularproduction of radioactive waste. All these problems do not appear when electricpower is produced by solar panels and wind turbines alone. Nevertheless, wind-solar power has serious disadvantages too, the most serious one being the volatileenergy production: Weather conditions change rapidly and as a consequence Email address: [email protected] (Hans Lustfeld)
Preprint submitted to European Economic Review February 2, 2021 a r X i v : . [ ec on . GN ] F e b INTRODUCTION P v and the energy demand P d into two parts: the averageparts P va and P da being constant over the year and the fluctuating parts P vf and P df . The power P sf streaming into and out of storage devices has a fluctuationpart only since the devices are passive. The average of each fluctuating part iszero. Therefore we get the simple equations P va = P da (1)and therefore, P sf = P vf − P df (2)Integrating these powers yields the energies E v ( d ) ( t ) = E va ( da ) ( t ) + E vf ( df ) ( t ) E va ( da ) ( t ) = P va ( da ) · tE vf ( df ) ( t ) = ´ t P vf ( df ) dtE sf = E vf − E df (3)The required storage E sfmax is obtained from the expression E sfmax = max t { E sf ( t ) } − min { E sf ( t ) } (4)In order to obtain these functions for 2019, we have used the data of ref[3]which contain power measurements every minutes [in MW] for electric loadand the volatile power, consisting of: offshore and onshore windpower as wellas solar power. The result is obtained directly for the demand (load): P da =56 . GW and the fluctuation part E df is plotted in Fig.1. The correct values for P va and P vf require a moment of consideration. The measurement data lead tothe value ˆ P va = 18 . GW.Since we intend to satisfy the average electric energy demand by wind-solar power alone, we need an average electric power production of at least P va = P da = INTRODUCTION Figure 1: Fluctuation parts and storage: (Green) dashed line: Fluctuating part E vf of (scaled)volatile energy E v . (Red) dotted line: Fluctuation part E df of energy demand E d .(Black)solid line: (Scaled) fluctuating part E vf of wind-solar energy minus fluctuating part E df ofdemand E d . From the difference between max and min the required storage can be readoff. Note the dominance of E vf . For comparison the fluctuation part E vfOff of the (scaled)offshore energy E vOff is shown. Here the scaling factor is . / . steadily improve. Now taking as natural scaling factor . / . for wind-solarpower we get P va = ˆ P va · . . = P da P vf = ˆ P vf · . . (5)where ˆ P va and ˆ P vf are obtained from the measurement data. In the sameway we get the scaled integrated quantities E v ,E va and E vf after scaling theoriginal mathematical expressions with the same factor. Together with thescaling factor . / . those expressions will be used throughout this paper.Of course, wind-solar and demand data differ from year to year, but, consideredover the year 2019, the typical properties should be similar enough to reveal therelevant trends. For a detailed technical analysis, the observation period of oneyear does, of course, not suffice. Instead, observation periods over many yearsare necessary. This is possible, but beyond the scope of the present paper.As a first application we calculate the storage capacity necessary to fulfilleq.[2] and we find: the required electric storage removing volatility is . T W h ,cf. eq.4 and Fig.1.This result proves that volatility is a serious problem. Indeed volatility ledSinn to the conclusion that energy production resting essentially on wind-solarpower alone will take us into an economic nirvana[5]. One could argue thateven a total storage capacity of about TWh[1], [2] is in principle feasibleby transforming the huge Norwegian hydro dams into pumped-storage plants.
SURPLUS OF WIND-SOLAR POWER AND SMART METERS [1], if all transportation, warm water, spaceheating and a considerable percentage of process heating are switched to electricpower as well. With the configuration presented here so far, this is impossible.ii) Even if we do not consider transportation, warm water, space heating, andprocess heating, the pump storage capacity requirements would be so enormousthat an export of this wind-solar scheme to many other nations would be out ofthe question - a bitter disadvantage when Germany wants to be a forerunner.How can we successfully proceed? Of course we need a kind of active buffer-ing. Sinn [1] suggests various combinations between wind-solar power and con-ventional power plants. This works for the present needs but eliminates theadvantages of using wind-solar power alone. Furthermore, this scheme becomesquestionable if the needs of electric power are five times greater than now. Andthat will happen if energy production of Germany will be switched to electricpower generation as far as possible.In this paper we discard such schemes. Instead we suggest a combinationof three methods: First, creating a surplus of wind-solar power. Second, ap-plying smart meters[4]. Both methods are described in section II. We showthat through these methods the storage capacity requirements are reduced bya factor of about 50 or even become marginal. Third, applying new criteriafor optimizing the efficiency of wind turbines, solar cells and their distributionacross the country. We show in section III that through these additional meth-ods the smart meters need distinctively less flexibility. We think that theseresults give us the justification for extrapolating to the case where in additionto the present electrical energy production all energy for the total transport,warm water, space heating and and a considerable percentage of process heat-ing is exclusively obtained from wind-solar power. This is discussed in sectionIV. Our conclusions are presented at the end of the paper.
2. Surplus of wind-solar power and smart meters
In this section we discuss the situation, in which the generation of electricpower is taken over by wind-solar power alone.In contrast to simple passive buffers like pumped-storage plants with alltheir capacity limitations active buffers like power plants can satisfy the demandnecessary for guaranteeing a safe power delivery. To avoid CO production wechoose as active buffers wind-solar power itself. Assuming[1] as above an alreadyoptimum distribution of wind-solar power devices across the nation, the surplusof wind-solar power can be expressed again by a scaling factor , the strength α ,and we get for the wind-solar energy E v ( t ) −→ (1 + α ) E v ( t ) , α = const The price to be paid for this scheme is a reduced efficiency. This is all the morethe case since at times of low wind-solar power the surplus of wind-solar poweris reduced as well enforcing a larger α value than expected from the average SURPLUS OF WIND-SOLAR POWER AND SMART METERS α within reasonable limits we need the concept[6] andon a large scale the application[7] of smart meters[4]. Such devices control theelectrical consumption very effectively by setting higher consumption prices ifless power is available and lower prices if there is a surplus of power. Thussmart meters act like passive buffering devices by moving the peaks of electricconsumption to the peaks of wind-solar power. We note in passing that movingelectric consumption on an hourly basis or less has the same effect as smoothing,cf. ref. [1], section 4.Of course a detailed simulation of smart meters is intricate. However, wethink that the following simulation of smart meters reflects the principle effectssatisfactorily: E d ( t ) is the energy of electric consumption as function of time.Now, if wind-solar production is not sufficient, it produces energy correspondingto a demand E d ( t (cid:48) ) < E d ( t ) . The smart meters have now the task, by increasingprices for kW h to enforce a reduced demand, namely E d ( t (cid:48) ) . Clearly thatis always possible - due to exorbitant prices, if necessary. But to avoid suchuneconomic incidents we introduce the delay time τ (cid:62) and require t (cid:48) > t − τ .The analogous happens for a surplus of wind-solar power: If there is an excessproduction of electric energy, corresponding to E d ( t (cid:48) ) > E d ( t ) , smart meterscharge low prices and E d is again not that of time t but that of t (cid:48) and t (cid:48) < t + τ .This means the strict requirement t (cid:48) = t is replaced by E d ( t − τ ) < E d ( t (cid:48) ) < E d ( t + τ ) , | t (cid:48) − t |≤ τ (6)As is the case in the applications of real smart meters, the electric power con-sumption becomes more flexible in this simulation. The produced energy tilltime t need not be E d ( t ) exactly but staying in the interval of eq.(6) suffices.This flexibility saves storage capacity as can be seen from an extreme (hypothet-ical) case: If τ becomes sufficiently big the required storage capacity approacheszero. Of course such large values of τ are unrealistic. However, values of hoursor even days can be acceptable. We assume that a limit τ ≤ day is a veryreasonable one. And note, this simulation of smart meters fulfills the criterionthat - as in real smart meters - consumption of energy is only moved, no energyis generated or lost.To avoid large τ values, finite α -values and possibly electric buffering devicesare still needed. We find out the relation between delay time τ , capacity E sfmax ,and strength α in the following manner:We fix α and τ , proceed in time steps ∆ t = 15 min and define E d ( t (cid:48) ) = ˘ E d .At the beginning we set ˘ E = 0 and E sf = 0 . Now at time t + ∆ t we get δE v = (1 + α ) P v ( t ) · ∆ t Now three cases have to be distinguished (we set s = t + ∆ t ):i) E d ( s − τ ) ≤ ˘ E d + δE v ≤ E d ( s + τ ) , then ˘ E d → ˘ E d + δE v .ii) ˘ E d + δE v > E d ( s + τ ) , then ˘ E d → E d ( s + τ ) and E sf → E sf + ˘ E d + δE v − E d ( s + τ ) iii) ˘ E d + δE v < E d ( s − τ ) , then ˘ E d → E d ( s − τ ) and E sf → E sf + ˘ E d + δE v − E d ( s − τ ) SURPLUS OF WIND-SOLAR POWER AND SMART METERS Figure 2: Delay time τ [days] versus storage capacity E sfmax [ GW h ] for various values of thestrength α . The curves demonstrate that a decrease of the storage capacity can indeed becompensated by an increase of α . E.g. τ = 1 day can be obtained by setting α = 0 . andstorage capacity of GWh or α = 0 . and storage capacity of 2400 GWh or α = 0 . andstorage capacity of GWh or α = 1 . and storage capacity of GWh.
Furthermore, to save storage, we enforce E sf ≤ by replacing a positive E sf with zero. Thus a positive E sf becomes a kind of ’wasted’ energy that hasto be removed somehow (see below). At the end of the calculation E sfmax isgiven by E sfmax = max t {− E sf ( t ) } Repeating this procedure for various τ values we get the function E sfmax ( τ, α ) and from that function the inverse function τ ( E sfmax , α ) .Results of our calculations are shown in Fig.2. We have plotted τ ( E sfmax , α ) for various fixed α values. The results contain the important conclusion thatstorage capacity can be replaced by a surplus of wind-solar power. This phe-nomenon opens a wide field of possibilities: If storage capacity does not representa problem α = 0 . might be sufficient. On the other hand storage capacity be-comes rather uncritical for α (cid:61) . . And for α = 1 the storage capacity is nolonger a problem.The arising ’wasted’ energy need not be small at all. In fact, if all possibleenergy is generated the average power amounts to (1 + α ) · . GW and thus theaverage ’wasted’ power to α · . GW.
To get rid of it directly is one possibility.This can easily be achieved by reducing the wind-solar power, as soon as ’wasted’energy begins to build up. The advantage of this procedure would be a strainimposed on the electricity network that would not essentially be higher than for α = 0 .An alternative would be exploiting this ’wasted’ power for processes, e.g. forelectrolytic and chemical processes. However one has to keep in mind that thesurplus power is really extremely volatile as can be seen from Fig.3 for α = 0 . . LOW ENERGY PRODUCTION AND OFFSHORE WIND TURBINES Figure 3: ’Wasted’ power for storage capacity
GW h , α = 0 . , τ = 1 . days. This power isgenerated, if the surplus wind-solar devices work all the time with maximum power available.(Black) solid line: ’Wasted’ power averaged over h . (Red) dashed line: ’Wasted’ poweraveraged over one year. The averaged value is α · . GW.
Apart from high peaks there are - more important - periods, even weeks, whereno ’wasted’ power is available.The absolute costs per kW h depend on assumptions, of how prices willdevelop in the future and which indirect costs have to be included in thecalculation and which not. In fact, the estimates fluctuate strongly[1][8][9].However, the relative increase of running costs per kW h due to the ’wasted’power can be assessed: For a small contribution of wind-solar power - so small,that peaks do not overshoot consumption - suppose running costs in the av-erage to be ws small ] [€/kWh]. However, we do not deal with a small contri-bution. Instead an average demand of . GW has to be satisfied. Apply-ing the surplus power approach fulfilling this demand requires an average pro-duction of (1 + α ) · . GW . Therefore, the increase of the running costs is ws small → ws small · (1 + α ) and the relative increase is given by α .
3. Low energy production and offshore wind turbines
At first sight it may seem obvious that wind-solar power should have itsnominal power at high winds, at high sun radiation and moreover in regionswith high winds and high sun-radiation, respectively. But the surplus wind-solar power becomes important if the wind-solar power production is weak andtherefore weak-wind turbines and solar cells with good low-light performancewill be essential for good additional power production. Weak-wind turbines hav-ing blades enlarged by a factor[10] √ β , greater height[11] and thus higher windspeed enlarged by a factor[12] ( γ ) / , provide an increase of power generation by LOW ENERGY PRODUCTION AND OFFSHORE WIND TURBINES Figure 4: Delay time τ [days] versus storage capacity E sfmax [GWh] for various values ofthe strength α . Left: The surplus power αP low has enhanced performance at low wind andlow radiation, cf. eq.[7] leading to distinctively shorter delay times τ . Right: The surpluspower αP vOff is delivered by offshore wind turbines. Their averaged contribution to theelectric power generation is still small, only . GW in . However, a continuous expansionis intended, therefore we have scaled the present offshore power generation by a factor of . / . . So for α = 0 . the required offshore power has to exceed the value of 2019 by afactor of 10. According to our calculations such an expansion would lead to promising results:Again distinctively shorter delay times τ . a factor of β · γ . We choose β · γ = 2 . This doubles the power production in thelow-wind regime, P l = 2 · P . In the high wind regime, however, the power pro-duction saturates since these turbines have a reduced nominal power[12] P nom .This justifies the ansatz P l ( t ) = P nom · tanh ( β · γ · P ( t ) /P nom ) , β · γ = 2 Weak-light performance of solar cells[13] depends on the material used[14].Mono-crystalline PV modules[15], multi junction[16] with selected band gapsand in the future the new generations of DSSCs[17][18] may have good weaklight performance. And we assume that with good weak light performance thegenerated power can increase - as for the wind power - by a factor of also inthe weak-light regime. (This approximation may be crude but less important aswell, since the capacity factor of solar cells is dismal, at least in Germany[19], − %, and therefore the dominant power generation will be that of windturbines). So we get for the total surplus power (here defined as P low ) the ansatz P low ( t ) = P va · tanh (2 P v ( t ) /P va ) (7)and δE v = ( P v ( t ) + αP low ( t )) · ∆ t To demonstrate the importance of low energy production, we have selecteda low nominal power P nom for P low : P nom = P va . And the average wind-solarpower is about five times less than the normal nominal power.The calculations correspond to those of the previous section. Results arepresented in Fig. 4. The distinctly better outcome for the delay times τ is obvi-ous in spite of the low nominal power P va of P low . This proves the importanceof good performance in weak wind and low light situations. ADDITION OF ALL POSSIBLE ELECTRIC ENERGY IN GERMANY the scaling factorguaranteeing P va Off = P da is rather large since at present the offshore poweramounts to % of the electric load (average) only, cf. Fig.4..
4. Addition of all possible electric energy in Germany
In the two preceding sections the possibility of applying solar-wind powerwithout excessive use of storage devices has been demonstrated. However, wehad only discussed the case of replacing the present electric energy productionby wind-solar power. But this amounts to about ≈ GW [1] over the year,whereas the total energy production amounts to ≈ GW , averaged over theyear). consists of energy production for transport on a fossile basis, warmwater, space heating and process heating. Converting this energy productioninto electric power should be possible not completely but to a large extent.Therefore, the question is inescapable: Can all this electric power be gen-erated by wind-solar power alone. I think a precise answer to this questionpresumes inspecting all the fluctuation data of wind and radiation across thevarious parts of Germany over many years. This is possible but beyond thescope of the present paper.On the other hand, when we look at the required electric storage results forthe various examples in the introduction we conclude that compared to the lessdrastic volatility of electric consumption the volatility of wind-solar power is thedominant part, cf. red dotted curve in Fig.1. But this part can be estimated bysimple scaling as in section II, leading to a scale factor of . This would meanthat the plots in Fig.2 and Fig. 4 remain the same, only the storage values onthe horizontal axis had to be multiplied by a factor of . Since the storage valuesare not particularly critical, the effect of scaling would require a shift α → . or α → , which in our view seems to be a tolerable change.Furthermore we can argue that in spite of its enormous volatility at leastpart of the ’wasted’ power can be used for chemical, in particular electrolyticprocesses, by which artificial fuel can be produced, e.g. for airplanes. This againwould reduce the required wind-solar energy and thus the scaling factor.It should also be pointed out that in any case the number of required windturbines is enormous. After conversion into electric power an average power of ≈ GW [1] [1] has to be generated in Germany. Assuming i) a capacity factorof % for wind turbines[18]) and ii) a / contribution of solar power (probablya bit less[20]), a simple calculation leads to a required nominal wind power of M W . This means {110000} wind turbines of the . M W {6MW}type (height 120m {200m}) are needed to produce the average power. But thisis not enough. In our approach this number has to be increased by -100% tocontrol volatility.In view of these large numbers manufacture of wind turbines in mass pro-duction should be possible, reducing the cost of wind-solar power. CONCLUSIONS
5. Conclusions
Is it possible to switch all present electric energy production of Germany towind-solar power? This question has been answered in the negative by Sinn[5].The main topic of this paper is to show that Sinn’s judgement is too pessimistic.When choosing a different ansatz, the results become different: We suggestmarginalizing the strong volatility of wind-solar power by i) adding a substan-tial surplus of wind-solar power ii) installing smart meters[4],[6] iii) selectingdifferent kinds of wind turbines, solar devices and switching to a good deal tooffshore wind turbines.The results of our ansatz are encouraging: The electric storage needed isreduced by more than , even nearly % should be possible.The prize to be paid would be a % - % surplus of wind-solar powerdevices compared to the situation in which only the averaged wind-solar powerproduction matches the averaged power consumption.Our precise data[3] extend over the year 2019, a period sufficient to showthat wind-solar power can be promising. Unambiguous results will be confirmedwhen weather conditions in Germany are carefully analyzed over a period ofmany years - but this is beyond the scope of the present paper. However, basedon the present data, measured every 15 minutes in 2019, our approach avoidingexcessive passive storage leads to the following conclusions: First, this approachis applicable to electric energy production in Germany and in other nationsalso, having no access to huge storage devices. Second, this approach leads tothe prediction, that most of the present power demand of Germany could besupplied by wind-solar power alone. Third, this approach does no longer excludethe hope that even if most of the energy production in Germany is switching toelectric energy - which means a factor of about [1] -, this energy can be deliveredby wind-solar power. In this case, however, no matter how we slice it, alone thenumber of required wind turbines would become tremendous: [110000]wind turbines of the . M W [6MW] type (height 120m [200m]). Controlling thevolatility according to our approach would increase these numbers further by − % . The running costs would rise by a factor (1+ α ) , α being the strengthof the additional electric power production, defined in section 2. According toour calculations reasonable values for α are in the range [0 . , . . References [1] Sinn,H.-W., 2017. Buffering volatility: A study on the limits of Germany’senergy revolution, European Economic Review 99, 130.[2] DNV GL, 2015. Overview of Potential Locations for New Pumped StoragePlants in EU 15, Switzerland and Norway. Seventh Framework Programme,Theme 5. ESTORAGE.[3] All consumption and production data of year 2019 obtained from ENTSO-E, the ’European Network of Transmission System Operators for Electricity,
EFERENCES https://transparency.entsoe.eu/generation/r2/actualGenerationPerProductionType/show
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