The variability of wind and solar is perceived as a major obstacle in employing otherwise abundant renewable energy resources. On the basis of the available geographically dispersed data for the Western USA, we analyze to what extent the geographic diversity of these resources can offset their variability. We determine the best match to loads in the western portion of the USA that can be achieved with wind power and photovoltaics (PV) with no transmission limitations.
There are abundant solar and wind resources in the United States—enough to provide more than 10 times the annual US electric load.  Although these two renewable energy resources currently supply just under 2% of US generation,  wind power is rapidly penetrating the market place, having captured over 40% of the market for new US central generating capacity in 2008.  This is partly because the busbar cost of wind power at the best resource sites is already competitive with gas, coal and nuclear power from new plants.  In addition, the cost of solar power from photovoltaics (PV) is declining rapidly. In spite of this promise, there are concerns that these technologies cannot supply a significant portion of US generation needs.
The variability of the solar and wind resource is the primary concern. The average annual output of a wind farm will only be 25–50% of that which could be produced were the wind to blow at top speed all year long. In addition, on average across the USA, the wind blows more at night and in the winter than in the summer when it is most needed to meet peak loads due to air conditioning.
Solar is obviously a little different. We know it will be available only during the day, more so in summer than tin winter and that it follows a sinusoidal curve in the day that peaks at noon. We also know that many of the peak air-conditioning loads occur on hot sunny summer days. So, solar power is better correlated with loads but not perfectly, since many hot summer hours occur late in the afternoon when the sun is declining on the horizon.
Although various technical challenges connected with wind energy [4, 5] are being solved, claims have been made that, due to variability, solar and wind power technologies must be heavily, if not completely, backed up with conventional generation capability and/or storage; in other words, the capacity value (i.e. how much conventional generation capacity can be replaced by a unit of renewable generation capacity) of wind and solar is low.  This paper explores that claim by examining new solar and wind resource data at the hourly level that has recently become available for tens of thousands of sites across the country for multiple years. This data allows us to estimate the value of spreading the deployment of wind and solar plants out to take advantage of the fact that solar and wind availabilities vary geographically, not just temporally. In fact, the paper shows that by optimally locating wind and solar sites, the need for storage and backup generation can be substantially reduced.
The integration of significant amounts of wind and solar power in an energy system poses multifaceted challenges. [6, 7] The potential benefits of large-scale wind and PV integration, however, fuel the worldwide interest towards them. [8-12] The present study focuses on the hour-to-hour variations of demand and generation at tens of thousands of potential wind and solar sites throughout the year in the western part of the USA.
This is not the first paper to analyze the advantages of using geographically diverse resources of both solar and wind to better meet load. [13, 14] We examine multiple years of hourly data with thousands of possible sites of both solar and wind. In this study, we do not rely on uncertain present or future cost estimates for these technologies.
On the other hand, this paper does not answer all the questions on this issue. It provides only a practical upper bound on the contribution from wind and solar power because
the method does not consider transmission constraints and siting issues
sites are selected only on the basis of their ability to contribute energy and capacity, not costs
the optimization is conducted on the basis of one year's historical resource and load data and tested against data from other past years, but major changes to load profiles such as those that would occur with the introduction of electric vehicles are not considered
Many of these will be the subject of future work; nonetheless, the existing results tell an important story.
Our method answers the following question: What is the best match to loads in the western portion of the USA that could be achieved with wind power and PV? (Specifically, we examined the wind, solar resources and loads in the US area of the Western Electric Coordinating Council, WECC.) We measure the accuracy of the match in terms of capacity and generation that would be required from backup dispatchable * generators and from storage technologies to meet all loads throughout the year.
We have built two similar and quite straightforward optimization models. In both of them, the primary decision variables are where and how much wind (Wi) and PV (Pj) resources should be built at each wind and PV site (indices i and j, respectively). The two models differ primarily in their objective functions; one effectively minimizes the capacities of dispatchable generators and storage that backup wind and PV, and the other minimizes the dispatchable generation and energy losses associated with wind and PV. Had we used costs for technologies and fuels, we could have used just one model. However, because future fuel and technology costs are so uncertain, these two models that do not have to consider costs give a more robust result.
The first model uses a quadratic objective function to effectively minimize the backup generation capacity and storage capacity required. The model minimizes the sum over all 8760 h of the year of the squared difference between loads (lt) and the generation from the selected wind and solar sites:
wit is the generation that could be produced at hour t by the wind resource at site i (wit is an input), and pjt is the generation that could be produced at hour t by the PV resource at site j (pjt is an input). Both wit and pjt are inputs; thus, a perfect forecast throughout the year is assumed.
The minimization is subject to the constraints
Before moving to the second model, few things about this first model should be clear by inspection. When Δt is positive, the selected wind and solar sites do not produce enough power to meet that hour's load. Consequently, a dispatchable generation plant will be required to make up the difference. The maximum positive Δt over all hours can be interpreted as the amount of backup dispatchable generation capacity needed. The sum of all the positive Δt is the total amount of generation required from dispatchable generators. Similarly, the maximum negative Δt is the amount of storage capacity that would be needed to prevent any curtailments of wind and solar power, and the sum of the negative Δt is the total amount of all energy sent to storage. The quadratic nature of the objective function in effect minimizes the capacities of dispatchable backup and of storage. The wind and solar generation are traded off solely on the basis of how well they meet load, not their relative economics.
Although the quadratic model effectively minimizes the dispatchable and storage capacities, it does that without concern for the amount of dispatchable generation or curtailments of wind and PV. We address this issue in our second model, a linear program with the first constraint being that the load is met. Then, the wind and solar sites are selected by the model to minimize the dispatchable generation (Gt) along with curtailments (Ct) of wind and solar and roundtrip losses in a storage system [the difference between electricity input to storage and electricity removed from storage as determined by the roundtrip efficiency (eff)]. The storage system is examined parametrically by assuming a storage power charge and discharge rate cap (sCAP) and storage reservoir size (sRES). The model endogenously determines how much to charge (Scht) and discharge the storage (Sdct) in each hour.
Expression (5) gives the objective function, (6) sets the condition that all the loads should be met, (7) and (8) set a cap on storage charge/discharge rates, (9) limits the storage reservoir capacity, and (10) sets the storage balance that accounts for roundtrip efficiency. As a rule, the names for model variables start with a capital letter, whereas constant parameters begin with a small letter.
Here again, the wind and solar sites are selected solely on the basis of their contribution to meeting load, i.e. their relative costs are not considered. This model also gives equal weight to dispatchable generation and losses of energy either through curtailments or efficiency losses in the storage.
3 INPUT DATA
The wind and PV data for the WECC has only recently become available. For the wind resource, we are using data developed for the Western Wind and Solar Integration Study  * . The distinguishing characteristics of this data is that it includes three years of generation information (2004 – 2006) for 32,000 potential wind sites in the western USA in 10 minute intervals † over the course of each year (http://wind.nrel.gov/Web\_nrel). As in the Western Wind and Solar Integration Study, we assume that up to 30 MW of nominal wind capacity could be installed at each wind site.
For the PV resource, we are using hourly insolation data for the same years for 275 sites in the western USA found in the National Solar Radiation Data Base (NSRDB)  ‡ and converting that to power generation from a south-oriented PV panel with a 10° tilt with the use of the PVWatts model *. The NSRDB does not provide estimates of the maximum amount of PV capacity that could be installed at each site. However, to prevent unreasonable overuse of the sites that have generation profiles that best match load profiles, we limited the PV capacity at any single site to 1 GW. The wind or PV generation sites that are outside the WECC area were excluded from consideration. The load data were aggregated from Ventyx's Velocity Suite product (http://www.ventyx.com/∼/media/Files/Brochures/Velocity-Suite.ashx?download=1), which is based on hourly historical demand for the same years from the Federal Energy Regulatory Commission (FERC) Form 714 Part III Schedule 2.
We begin by using the quadratic model to examine how well we can match 2005 WECC loads with only wind resources. The results shown in Figure 1(a) are not encouraging. In this case, the model built 207 GW of wind capacity (2005 peak load in WECC was only 125 GW) and would have still required 98 GW of dispatchable capacity to meet all loads. If it were desired to ensure that no energy was wasted, 92 GW of storage charging capacity would also have been needed. As evident from Figure 1(a), there is significant overproduction in early spring, followed by large production shortfall during late summer months. The shortfalls occur for 5800 h and would have had to be made up by 188 TWh from dispatchables. Overproduction occurs in 2960 h and adds up to 61 TWh. Case A from Table 1 also refers to these results.
Table 1. PV and wind contribution to energy production in WECC. The first (leftmost) column briefly describes renewable resources used; the last column gives the set of equations employed. The meaning of the numerical values is described in the top row; the bold typeface numbers denote constraints (inputs), and the underlined numbers represent values that are minimized (having several underlined numbers in one row means that their sum is minimized). An empty field means that the corresponding entity was not taken into consideration. For example, case C (third row of data) involves no storage nor is there any curtailment (surplus), and the hourly sum of dispatchables necessary to match the load is minimized; cases D–F and H–K involve limited storage (capped charge/discharge rate and reservoir capacity), whereas in cases N–Q, storage is unconstrained, and the values from the last three data columns show storage parameters needed to accommodate load matching for the given case.
The capacity value is calculated as the ratio of avoided conventional generation capacity (maximum load minus max shortfall minus max dispatchables) and built renewable capacity including storage (wind plus PV plus storage discharge capacity).
For cases A and B from the table, we used the quadratic model which finds the closest possible load match achievable with the WECC resources (expression 1); for all other cases, the load is matched exactly.
In effect, we used the Wi and Pj values found from the 2005 run in an optimization for 2006 where the only remaining decision variables were Gt, Ct, Scht and Sdct.
Ramping up or down constraints on dispatchables are imposed, allowing up to 20% hour-to-hour variation in the output from dispatchable resources.
The PV site ID 724640 or wind site ID 10263 from Colorado are used; no cap on resource size is applied; the sites were arbitrarily selected.
Unlimited storage: no constraints on charge/discharge rate nor on reservoir capacity are applied.
The upper bound (expression 4) is set to 3 GW; in all other cases involving PV, we use 1 GW as the upper bound.
All other cases involving storage use roundtrip efficiency value eff = 0.75.
Interestingly, when PV is added to the mix, the total generation shortfall is cut by 23% to 145 TWh, but the dispatchable capacity needed to make up that shortfall drops by only 10% to 88 GW. This can be seen in Figure 1b, where the number of hours with shortfall is significantly reduced in the summer. With the PV option, the total built wind capacity dropped to 173 GW, but 100 GW of PV was added. The PV option slightly decreased the total excess production by about 4% but actually increased the charge/discharge rate that would be necessary to capture all the excess production. The results are summarized in Table 1 as case B.
Recognizing that wind and PV alone cannot reasonably address all the WECC loads, the question remains what is the maximum fraction they could meet with the support of some dispatchable generation. To address this question, we moved to our second model, the linear program that meets all loads while minimizing the energy from dispatchables and the curtailed energy. If we assume no storage and no curtailments are allowed, then the model determines the dispatchables generation pattern (shown in Figure 2) from 104 GW of dispatchable capacity (Table 1, case C). As expected, much of the dispatchable generation occurs in the late summer, and there is substantial inter-hour variation with a maximum hour-to-hour change of 14.5 GW. In this case, the dispatchables meet 49% of the load, and the remaining 51% is supplied by the 101 GW of wind and 47 GW of PV selected by the model.
The geographic distribution of the selected wind and PV sites across the WECC area is shown in Figure 3. Interestingly, the optimal sites selection for wind (Figure 3(a)) favors region boundaries of WECC. As the difference in weather patterns grows stronger with distance, there is a clear tendency towards diversifying the wind sites by preferably choosing the ones at the perimeter of the geographic region. The optimal PV sites distribution (Figure 3(b)) shows a preference towards more insolated high altitude areas on the eastern side of the map. Case C* shown in Table 1 is the same as Case C, except it allows curtailments. More wind (175 GW) and PV (113 GW) sites are selected; wind and PV meet 80% of the 2005 load in WECC if there are no transmission constraints or operating constraints on the dispatchables. However, in this case (Case C*), approximately 58 TWh, or 9.5%, of the potential wind and PV generation must be curtailed.
Figure 4 shows the results of a simulation that adds storage (to Case C*) with assumed roundtrip efficiency of 75%. The charge/discharge rate to/from storage is constrained not to exceed 10 GW * and the storage reservoir size to be 100 GWh (10 h of output at the maximum discharge rate). In this case, the linear model met the entire load for the year by building 170 GW of wind, 123 GW of PV and using 89 GW of dispatchables (case D, Table 1). The addition of storage reduced the dispatchables contribution by 2 percentage points. With this limited storage, 8.6% of the wind and PV systems output is curtailed, as there remain hours when either the storage charge rate or reservoir capacity constraints impede the complete utilization of renewable resources. As seen in Figure 3(b), in late summer (hours 5000–6000), there simply is not enough wind or PV output to use the storage.
By imposing additional constraints to the linear problem, we also examined the impact of the rates at which dispatchable generators can ramp up (rU) and down (rD):
With the fairly conservative values of rD = rU = 0.2, essentially small dP = 100 MW † and the same storage system (10 GW with 100 GWh), the wind and PV still contribute 80% of the load, but more of their output is curtailed (increasing from 8.7 to 9.5%).
All the results shown to this point are for the year 2005. To check the robustness of the wind and PV sites selected, we used the sites selected on the basis of the 2005 optimization to examine how well the generation from those sites in 2006 would meet the 2006 WECC loads ‡. The results are summarized in Table 1, case E. They show that the flexibility provided by redistributing the dispatchables generation and storage charge/discharge throughout the year effectively offsets the difference in wind and solar generation profiles between 2005 and 2006 at the selected sites and enables the system to accommodate the 2006 load with similar amounts of curtailed energy and dispatchables.
Cases A and B, Table 1, represent the quadratic simulations with wind (case A) and PV (case B) resources alone (results shown in Figure 1(a and b); case C relates to the results in Figures 2 and 3, whereas Figure 4 complements case D. Finally, comparing rows F versus D demonstrates the effect of the ramping constraint (equation (11)) for dispatchable generation.
Additional cases are also given in Table 1. Case N in the table shows what the aggregated WECC storage should be if it were to accommodate all the variability in wind and solar. Note that 31 TWh of storage loss translates into 93 TWh of cumulative energy generated from storage throughout the year (at 75% storage roundtrip efficiency, 4 × 31 TWh were used to charge the storage and 3 × 31 TWh were generated from storage), which less than doubles the 48 TWh of reservoir capacity used. Consequently, in this case, the storage for wind and solar is seasonal, with most of the reservoir capacity being used less than twice a year. This feature does not change when the storage roundtrip efficiency is lowered to 50% (case Q, Table 1).
The capacity values calculated from the model results are also shown in the table. The high renewables penetration cases involving a variety of wind and PV sites (cases B through G) exhibit a relatively close range of capacity values between 12 and 15%.
Cases J and K show how geographic diversity mitigates the variability of wind resources. Case J shows that with the multitude of wind sites available in the WECC (and no PV sites), all loads can be met with 10 MW/100 MWh of storage and with dispatchables providing only 26% of load. However, if all the wind turbines were to be placed at a single site (Case K) * , the lack of diversity would require that the dispatchable contribution double to 52%.
Cases H and I do not show the same geographic diversity benefits for PV. This may be partly because the input solar resource data is at the hourly level and cannot capture the sub-hourly impact of passing clouds. With our hourly solar resource data, a single site for PV (i.e. no diversity) increases the required dispatchables from 61% to only 66%.This diversity advantage of wind in our model, together with the lack of PV availability at night, favors wind in terms of the level of optimal buildup (cases B, C, C*, D, F, G, N and Q). Similarly, when wind and PV are considered separately (cases H vs J and L vs M), PV requires significantly more support from dispatchables or alternatively from storage (cases O vs P).
Our results show that, without storage, wind and PV could meet as much as about 80% of the loads in WECC. This result is qualified with the words ‘as much as’ because our analysis ignores transmission constraints within WECC and is therefore a practical † upper bound on the potential contribution of wind and PV.
The high contribution from wind and PV is achieved largely by spreading the selected wind and PV sites out to take advantage of diversity in resource availability at different sites at any point in time. There is also some synergistic benefit to deploying both wind and PV; wind alone can meet at most 74% of load with storage. Interestingly, although it is generally agreed that PV generation correlates better with load, the model chooses to build about twice as much wind as PV mostly because the night-time load cannot be met with any PV generation. When storage is available, the optimal mix has almost 75% as much nominal PV capacity as wind, with the PV energy contribution being 32% of the electricity produced from wind.
The dispatchable generation can ensure that all loads are met, but with constrained storage, significant amounts of wind and PV would have to be curtailed, especially in the spring when the wind blows and loads can be low. Also not surprising is that with enough storage and dispatchable capacity, all loads can be met with minimal waste of wind and solar generation and efficiency losses through storage. Finally, the results show that ramping requirements for dispatchable generators to follow hourly variations in wind and PV are not that significant.
6 FUTURE WORK
This work could continue in many directions. Most immediately, we plan to expand the analysis from WECC to the entire country. We expect this national analysis to show even more diversity impacts, especially for PV due to the greatly increased east–west distances available. Transmission would be even more limiting in a national analysis, so we are also considering the possibility of incorporating a zonal transmission power flow analysis. This would be a nontrivial methodological addition, partially due to the complexities of optimizing power flows but also because it would have to include some estimates of future transmission capacity expansion. Finally, we may attempt to include future costs for all technologies and fuels.
the amount of curtailed wind and/or PV energy at hour t
minimum cap on dispatchables ramp up, an essentially small parameter used for numerical stability in expression 11
energy storage roundtrip efficiency
dispatchable generation from conventional sources at hour t
hourly load (electricity consumption) over the WECC area
photovoltaic power generation
fraction of the maximum potential built capacity at the PV site j
the input generation that could be produced at hour t by the PV resource at site j
dispatchable generators ramping up coefficient, expression 11
dispatchable generators ramping down coefficient, expression 11
storage charge and discharge rate cap
storage reservoir size
energy used to charge the storage at hour t
energy generated from storage at hour t
= 1012 Watt hours
Western Electric Coordinating Council; here, we are considering only the continental US territory, excluding Alaska
fraction of the maximum potential built capacity at the wind site i
the input generation that could be produced at hour t by the wind resource at site i
difference between loads (lt) and the generation from the selected wind and solar sites
Dispatchable generators are those that can be used when needed. They would include the standard set of conventional plants (e.g. coal, gas and nuclear) as well as storage technologies (e.g. pumped hydro and batteries) and a subset of renewable electric technologies (e.g. biomass, geothermal and hydro). They would exclude wind and photovoltaics (PV) which are not dispatchable due to their variable resources.
This assumption requires only that the current storage capacity of 4.6 GW of pumped hydro in WECC be slightly more than doubled.
The minimum cap on dispatchables ramp up dP can be interpreted as the power output available by starting up a single plant. It is essentially small: decreasing it in half affects the results in Table 1, cases F and G only in their fourth significant digit.
In effect, we used the Wi and Pj values found from the 2005 run in an optimization for 2006 where the only remaining decision variables were Gt, Ct, Scht and Sdct.
The PV site ID 724640 or wind site ID 10263 from Colorado are used; no cap on resource size is applied; the sites were arbitrarily selected
It is not a true upper bound as it would always be possible to add even more wind and PV if they impacted even one hour positively. However, the minimization of either the required backup capacity or energy losses effectively gives some recognition to the cost of capacity and energy.