Optimal design of hybrid renewable energy systems

A hybrid system is generally understood to mean a system that makes use of a combination of different technologies that gives a better result than the use of a single technology on its own. Hybrid RE systems are used extensively in off-grid, grid connected and industrial microgrid applications. Increase in the use of hybrids has made optimisation of systems imperative.

The volatile nature of RE components makes it impractical for a single technology to supply energy of the required reliability and cost to most loads, and components with complementary characteristics are usually combined to meet the requirements. A hybrid renewable energy system (HRES) is intended to provide a solution that performs better than the use of individual technologies, and optimisation of the system configuration is necessary to achieve this goal. Hybrid systems consist of combinations of solar PV, wind turbines, batteries and diesel generators, but may also include fuel cells, small hydroelectric plant and biomass. The optimum combination of these resources will depend on the load characteristics and the performance of the individual components at the location where they are installed. HRES consist of a combination of variable and dispatchable energy sources.

The design of the HRES, specifically the determination of the size of the components in each application is challenging, due to a large number of factors involved, including fluctuations in energy demand, the uncertainties existing in renewable resources, precarious energy prices,  and the complex interaction among components.  Performance of the individual components can be dependent on weather, daily and seasonal variations, location etc., and this must be accurately modelled for the optimal configuration to be achieved.

Much research has been conducted in an attempt to determine a process for optimal design of an HRES, but it still remains a complex problem. A number of approaches have been suggested and developed, including analytical, heuristic and metaheuristic methods. Heuristic methods incorporate self-learning techniques where solutions are moved in steps closer to the optimum until the optimum is reached. Typical amongst these would be particle swarm optimisation, (PSO) genetic method ( GM), and various others. These are mainly of academic interest and are not widely used in this sector, and will not be considered here.

There are a number of well-developed  packages that use analytical optimisation. These include the “hybrid optimisation of multiple energy sources” (HOMER) program, developed by the national renewable energy laboratory  (NREL) of the United States , and RETscreen clean energy management software , developed by the Canadian government. The balance of this article will cover analytical optimisation systems.

Fig. 1: Conceptual relationship between simulation, optimization, and sensitivity analysis [2].

Optimisation criteria (or objectives)

An optimisation process must have an objective, which is chosen by the designer. The optimisation process may require a single objective (such as lowest cost of electricity) or may be required to optimise multiple objectives (such as lowest cost and highest availability). Objectives may be contradictory, necessitating a decision on which is considered the most important. For HRES optimisation, lowest life cycle cost, or lowest unit electricity cost are the objectives usually chosen.

Analysis based optimisation techniques

When applied to HRES, this technique constructs a range of configurations covering all possible combinations of chosen components and computes the value of the objective function for each configuration. The configuration that meets the objective is then selected. The physical configuration of the HRES, the components to be used, and the range of solutions is chosen by the developer.  The system will normally require that the developer enter a range of units that may be investigated, e.g. wind turbines may range from two to six units. This requires a certain amount of pre-planning, to avoid excessive consideration of configurations that do not meet basic requirements.

All analysis systems require analysis of the performance of the system over a time period, divided into steps, the performance of different combinations being evaluated for each step and the results aggregated to give an overall figure.  A period of a year is considered as the minimum required for evaluation. For many hybrid systems, particularly those involving intermittent renewable power sources, a one-hour, or lower, time step is necessary to achieve acceptable accuracy. In a wind–diesel–battery system, for example, it is not enough to know the monthly average (or even daily average) wind power output, since the timing and the variability of that power output are as important as its average quantity. Some systems allow analysis in time steps of down to 1 min if so required.

Most processes consist of the same several stages:

  • Simulation or model development
  • Optimisation
  • Sensitivity analysis

Fig. 2: Possible HRES models.

Fig. 1 illustrates the relationship between simulation, optimisation and sensitivity analysis. The optimisation oval encloses the simulation oval to represent the fact that a single optimisation consists of multiple simulations. Similarly, the sensitivity analysis oval encompasses the optimisation oval because a single sensitivity analysis consists of multiple optimisations [2].


The simulation process determines how a particular system configuration, a combination of system components of specific sizes, and an operating strategy that defines how those components, work together in a given setting over a long period of time. In the simulation process, the performance of a particular system configuration for each step of the time period is modeled to determine its technical feasibility and life-cycle cost. The simulation process requires detailed knowledge of all the factors that can influence the performance of the system including:

  • Load characteristics over the evaluation period.
  • Resource characteristics such as solar radiation, wind and hydro patterns over the evaluation period.
  • Component characteristics, such as solar panels, wind turbines, hydro plant, batteries and diesel power plant.
  • Performance limits on components e.g. state of charge of batteries
  • Limitations on the use of any component e.g. space limitations.
  • Performance requirements in terms of availability, Loss of load probability etc.
  • Cost of fuel and O&M outlays for each component
  • Dispatch strategy for dispatchable resources such as batteries and diesel generation.

The simulation process can be used as a pre-optimisation design aid by evaluating the feasibility of any configuration, i.e. whether it can adequately serve the electric load and satisfy any other constraints imposed by the designer, and rejecting those that do not meet the requirements.  The configuration to be modelled needs to be chosen by the designer. Fig.2 shows examples of possible models. The quantity of each of the components will be specified by the designer in a range of units or sizes.


The goal of the optimisation process is to determine the optimal value of each decision variable that interests the designer. A decision variable is a variable over which the system designer has control and for which an optimisation system can consider multiple possible values in its optimisation process. Possible decision variables include:

  • The size of the PV array
  • The number of wind turbines
  • The size of the hydro system
  • The size of the battery array
  • The size of the ac–dc converter
  • The dispatch strategy (the set of rules governing how the system operates)

In the optimisation process, a range of different system configurations is simulated in search of the one that satisfies the technical constraints at the lowest life-cycle or unit cost. The configuration to be optimised is decided by the developer. The process may yield an optimum configuration that has zero units of one of the chosen components.

As an example table 1 lists the component ranges specified for the system shown in Fig. 2 in a particular study. This gives a total of 140 possible combinations of components to be simulated.

Table 1: Example of the range of controllable variables [2]
Wind turbines Generator  Batteries Converter
Quantity (kW) Quantity (kW)
0 135 0 0
1 16 30
2 32 60
3 48 120
4 64

Optimisation systems model a particular system configuration by performing an hourly time series simulation of its operation over one year, stepping through the year one hour at a time, calculating the correct power balance required to meet the load for that hour. The results of the hourly runs are than aggregated over the year and the cost calculated. The results of an optimisation exercise carried out on a system using HOMER, are shown in Table 1, ranked in order of cost of electricity [2].


A challenge that often confronts the system designer is uncertainty in key variables. Sensitivity analysis can help the designer understand the effects of uncertainty and make good design decisions despite uncertainty. In the sensitivity analysis process, multiple optimisations under a range of input assumptions are performed to gauge the effects of uncertainty or changes in the model inputs. Sensitivity analysis helps assess the effects of uncertainty or changes in the variables over which the designer has no control, such as the average wind speed or the future fuel price.

One of the primary uses of sensitivity analysis is in dealing with uncertainty. If there is uncertainty around the value of a particular variable, several values covering the likely range can be entered and the results evaluated. Sensitivity analysis has applications beyond coping with uncertainty. It can be used to evaluate trade-offs and answer such questions as: How much additional capital investment is required to achieve a particular goal. the method allows determination of which technologies, or combinations of technologies, are optimal under different conditions. or under what conditions, a product (e.g., a fuel cell or a wind turbine) competes with the alternatives [2].

Modelling requirements

The operation of the system is dependent on accurate input data, which requires accurate modelling of resources and components. Most commercial systems include models for components, but resource data needs to be provided by the developer.


Providing electricity to loads is the reason for the existence of HRES power systems, so modelling begins with modelling of the load or loads. Two types of load can be considered:

  • Primary load – the electric demand that must be served according to a particular schedule.
  • Deferrable load – electric demand that can be served at any time within a certain time span.

Primary load is the electrical demand that the power system must meet at a specific time.If electrical demand exceeds supply, there is a shortfall known as unserved demand. Primary load in kW for each hour of the year must be specified, either using recorded values or synthesising hourly data from average daily load profiles. When synthesising hourly load, values based on user-specified daily load profiles are created. The model may use a single 24-hour profile that applies throughout the year, or can specify different profiles for different months and different profiles for weekdays and weekends. Some systems also add a user-specified amount of randomness to synthesised load data so that every day’s load pattern is unique [2].

Primary load generally requires a specified amount of operating reserve. Operating reserve is surplus electrical generating capacity that is operating and can respond instantly to a sudden increase in the electric load or a sudden decrease in the renewable power output. This has the same meaning as the more common term spinning reserve.

Deferrable load is electrical demand that can be met anytime within a defined time interval. Water pumps, ice makers, and battery-charging stations are examples of deferrable loads. The ability to defer serving a load is often advantageous for systems comprising intermittent renewable power sources, because it reduces the need for precise control of the timing of power production. If the renewable power supply ever exceeds the primary load, the surplus can serve the deferrable load rather than going to waste.

Table 1: Results of an optimisation exercise [2].
Wind (units) Generator (kW) Batteries (units) Converters ( kW) Initial capital (R’000) Cost of electricity  (R/kWh) Diesel  (l)
1 135 64 30 216,5 0,273 75 107
2 135 64 30 346,5 0,274 54 434
1 135 48 30 200,5 0,275 78 061
2 135 48 30 330,5 0,275 57 654
2 135 32 30 314,5 0,280 62 394
2 135 96 60 401,5 0,282 48 139
2 135 64 60 369 0,282 52 999
0 135 64 30 86,5 0,284 101 290
1 135 96 30 248,5 0,285 74 193
0 135 48 30 70,5 0,285 104 009
1 135 32 30 184,5 0,285 85 310
2 135 96 30 378,5 0,286 52 422
2 135 48 60 353,0 0,286 57 316
2 135 32 60 337,0 0,291 62 312
2 135 128 60 433,0 0,291 45 596
1 135 64 60 239 0,292 77 753
0 135 96 30 118,5 0,293 101 003

Resources and components

Resources include wind, solar, hydro and biomass. Only wind and solar will be considered here.  Renewable resources vary with location. The solar resource depends strongly on latitude and climate, the wind resource on large-scale atmospheric circulation patterns and geographic influences. Moreover, at any one location a renewable resource may exhibit strong seasonal and hour-to-hour variability. The nature of the available renewable resources affects the behaviour and economics of HRES, since the resource determines the quantity and the timing of renewable power production. The careful modelling of the renewable resources is therefore an essential element of system modelling.

PV system

Modelling of a PV system requires two things: solar resource data for the location, and PV module data. Solar resource  data can be in one of three forms: hourly average global solar radiation on a horizontal surface (kW/m2), or monthly average global solar radiation on a horizontal surface (kWh/m2/day).  The most accurate model will be obtained from the hourly model but it is possible to use monthly solar resource data to generate synthetic hourly global solar radiation data using an algorithm developed by researchers [3]. The inputs to this algorithm are the monthly average solar radiation values and the latitude. The output is an 8760-hour data set with statistical characteristics similar to those of real measured data sets. One of those statistical properties is autocorrelation, which is the tendency for one day to be similar to the preceding day, and for one hour to be similar to the preceding hour. The PV panels are modelled using manufacturers data as well as temperature data from the locality. The average output for each hour can be calculated by using solar radiation data and the module characteristics.


To model a system comprising one or more wind turbine requires wind resource data indicating the wind speeds the site would experience in a typical year. Measured hourly wind speed data can be used, but if not available, synthetic hourly data based on 12 month average wind speeds and four additional statistical parameters can be estimated . The four parameters are the Weibull shape factor, the auto-correlation factor, the diurnal pattern strength, and the hour of peak wind speed. The Weibull shape factor is a measure of the distribution of wind speeds over the year. The auto-correlation factor is a measure of how strongly the wind speed in one hour tends to depend on the wind speed in the preceding hour. The diurnal pattern strength and the hour of peak wind speed indicate the magnitude and the phase, respectively, of the average daily pattern in the wind speed. In addition, the height of the turbine hub above ground level is used to adjust the wind speeds. The wind turbine is modelled as a device that converts the kinetic energy of the wind into electricity according to a particular power curve, which is a graph of power output versus wind speed at hub height. This is provided by the manufacturer.


The principal physical properties of the generator are its maximum and minimum electrical power output, its expected lifetime in operating hours, the type of fuel it consumes, and its fuel curve, which relates the quantity of fuel consumed to the electrical power produced. The simulation stage together with the dispatch system will determine how long the generator runs per day and how much fuel is consumed. In systems with more than one dispatchable resource, the optimisation process may select the lowest cost option to dispatch.


The battery bank is a collection of one or more individual batteries. The battery may be modelled as a device capable of storing a certain amount of dc electricity at a fixed round-trip energy efficiency, with limits as to how quickly it can be charged or discharged, how deeply it can be discharged without causing damage, and how much energy can cycle through it before it needs replacement.  The key physical properties of the battery are its nominal voltage, capacity curve, lifetime curve, minimum state of charge, and round-trip efficiency.

Capacity typically decreases with increasing discharge current. The number of cycles to failure typically decreases with increasing cycle depth. The minimum state of charge is the state of charge below which the battery must not be discharged to avoid permanent damage. Commercial systems apply advanced models to batteries, which limit charge and discharge rates as well as other parameters, to limit the lifetime cost of the battery.

Construction of a model from a single year’s data may not reflect the actual performance of the system in subsequent years, however multi-year modelling may be costly in terms of time to compute and to gather. Multi-year modelling using averages to comprise a single year is dangerous, as averaging destroys detail.


[1] K Chang: “Optimal design of hybrid renewable energy systems using simulation optimisation”.
[2] T Lambert: “Micropower system modelling with HOMER”, Homer Energy.
[3] VA Graham and KGT Hollands: “A method to generate synthetic hourly solar radiation globally”, Solar Energy, Vol. 44, No. 6,  1990.
[4] P Nema: “A current and future state of art development of hybrid energy system using wind and PV-solar: A review”, Renewable and Sustainable Energy Reviews, 2009.

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