Journal of Power and Energy Engineering, 2014, 2, 106-111
Published Online September 2014 in SciRes. http://www.scirp.org/journal/jpee
How to cite this paper: Hu, L.J. and Fu, Y.J. (2014) Establishment of Output Models and Constraints Analysis for Independ-
ent Wind/PV/Storage System. Journal of Power and Energy Engineering, 2, 106-111.
Establishment of Output Models and
Constraints Analysis for Independent
Linjing Hu, Yanjie Fu
College of Electric Power, Inner Mongolia University of Technology, Huhhot, China
Received May 2014
In remote areas far from the grid, wind/PV/storage generating system is relatively a good choice,
whatever in resource configuration, performance or prices. For the inde penden t hybrid power
system, the output models of wind turbines, photovoltaic arrays and bat te ri es are built in this pa-
per, and based on the objectives of the capacity configuration optimal model, constraints used in
the process of capacity configuration are analyzed. These provide convenient conditions and
theoretical basis for the optimal capacity configuration of i ndepe nde nt wind/PV/storage system.
Wind/PV/Storage System, Output Models, Constraints
As the conventional energy sources are limited, the ever increasing human demand for energy, serious environ-
mental pollution, global climate change, force people to seek a new, clean, safe and reliable sustainable energy
systems. In recent years, many technologies of new and renewable energy have entered the stage of the com-
mercial application, of which the greatest potential and the fastest-growing is wind and solar power generation
. However, wind and solar power have common weakness, such as strong randomness, poor stability, which
leads to single power system’s low generating efficiency and poor reliability. Wind-PV hybrid power system
can be good to overcome these shortcomings. Especially in remote areas far away from the power grid, to estab-
lish an independent wind/PV/storage system is the best solution of a long-term stable and reliable power supply
to local problems.
In the long term, in order to achieve the optimal economic indicators of the independent wind/PV/ storage
system, reduce the difficulty of system controls, and ensure the stability of the output, reasonable capacity con-
figuration of the system is necessary. Reliable power supply as well as minimal investment costs can be
achieved with accurate and reasonable system capacity configuration . The methods to optimize capacity
configuration of independent wind/PV/storage system, can be divided into single-objective optimization method
and multi-objectives optimization method. The former is the minimum system cost, and the latter based on sys-
L. J. Hu, Y. J. Fu
tem reliability in addition, except the cost . The optimization objectives of capacity configuration is mean-
ingful when all kinds of loads and constraints are met. Therefore, in this paper, the output models of wind tur-
bines, photovoltaic arrays and batteries are built, and constraints used in the process of capacity configuration
optimization are analyzed.
2. Independent Wind/PV/storage Hybrid Generating System
2.1. Structure of the System
Figure 1 is a block diagram of an independent wind/PV/ storage systems. The power generation system gener-
ally consists of wind turbines, photovoltaic arrays, batteries controllers, inverters, loads, etc. PV arrays and wind
turbines are power generating parts. Batteries stores energy, used to balance energy supply and demand. Con-
trollers and inverters constitute the control part of the system. Loads are the energy consumption parts .
The independent wind/PV/storage hybrid system takes advantage of complementarity of wind and solar,
making wind, solar, battery together. Taking into account of the equipment costs, power supply system often
gives priority to wind power, photovoltaic power generation as a supplement, energy storage devices playing a
role in coordinating the buffer.
2.2. Output Model of Wind Turbine
The output of the wind on each time depends on the average wind speed at the height of the fan shaft and tur-
bine’s output characteristics . Power output of wind turbines changes with wind speed, meanwhile wind has
very strong randomness. Thus, statistical characteristics of wind speed can be described by its probability dis-
tribution. Two-parameter Weibull distribution is generally considered the best probability density function for
wind speed statistical description.
Wind speed probability density expressed as follows 
( )()exp[() ]
fv AA A
k shape parameter, used to describe the dispersion of wind speed measurement;
A scale parameter, related to the average wind speed measurements;
v wind speed.
When the distribution of wind speed is known, average output power of turbines can be got through the output
characteristics of wind turbines. An approximate relationship between the output power of the generator and the
wind speed by is described by Equation (2) .
output of wind turbine;
rated power of wind turbine;
Figure 1. Block diagram of the independent w ind /
L. J. Hu, Y. J. Fu
rated wind speed;
In independent wind/PV/storage hybrid generating system, the output of the wind turbines is generally used as
the main power supply section, so its output forecast requires high accuracy. In this paper, output model of wind
turbine using two-parameter Weibull wind speed distribution model, can make the forecast of meteorological
parameters and wind power output more accurate.
2.3. Output Model of PV Array
In hybrid power supply system, output of PV arrays is closely related to the distribution of solar radiation energy.
The solar radiant energy obtained on the specific site depends on many factors, including climate, as well as the
relative positions of the Earth and the sun, obstacle interference and so on. The actual output of the PV arrays
can be determined by rated power output under nominal standard conditions, light intensity, ambient tempera-
ture . The steady state power output can be described as in
output of PV cell;
the maximum test power under standard test conditions(solar radiation intensity
light intensity under standard test conditions, that is
k power temperature coefficient;
panels working temperature;
Equation (3) just calculates a single photovoltaic cell’s output, which is very small. In practical engineering,
PV cells usually compose high-power solar arrays after a series-parallel composition in order to meet the re-
quirements. As a complement to wind power, the output model of PV arrays is considered to be associated just
with solar radiation and ambient temperature, which is convenient for engineering applications.
2.4. Output Model of Battery
The independent wind/PV/storage hybrid generating system generally gives the priority to new energy. When
wind-PV unit can meet the current load and has additional output, batteries charge, otherwise, batteries dis-
charge . The remaining capacity of the battery at time t is related to remaining power at time t − 1, charge and
discharge in time [t−1,t], and power attenuation each hour. State of charge can be expressed as in
I charging and discharging current;
T charging and discharging time;
charging and discharging efficiency.
Output model of batteries describes the change of store energy state, thus the action of batteries in the opera-
tion of the system at time t can be known. As an energy storage device, battery in addition to improving power
quality, the larger purpose is to improve the electricity supply-demand balance .
3. Capacity Configuration Optimal Model of System
3.1. Optimization Objectives
This paper selects dual objectives optimization method, which can realize minimum investing and operating cost,
and highest system reliability.
The objective function of the capacity configuration optimal model for independent wind/PV/storage system
can be expressed as in
L. J. Hu, Y. J. Fu
() (1)() (1)
installed capacity of wind power and PV (MW) respectively;
y capacity of battery;
calculated totally cost of the planning capacity of the hybrid system;
the equipment investment costs of system in year t;
grid investment costs in year t;
maintenance fee for fixed operation and other expenses in year t;
other benefits of the system in addition to electricity generation in year t;
T the years of the planning period (n);
r discount rate.
1) Reliability of wind turbines and photovoltaic modules selection
The correct selection of wind turbines and PV modules has respect to reliability of the system, and decides
whether to take good advantage of wind and solar energy or not. Incorrect selection may cause difficulty to im-
prove power system control, resulting in low efficiency of power generation systems and high operating costs
2) System construction sites
Pre-planning construction sites of hybrid generation system are limited, so it should restrict the scale of the
system according to the system construction sites, that is to say constraints on the number of devices is neces-
sary. The number of fans erected in the field has an upper limit because of the distance of ranks of wind turbines.
Moreover, considering the cover, hillsides, and unavailable areas wind towers covering, the number of PV mod-
ules installed has an upper limit, too.
3) The total capacity of power system
When configuring capacity of wind turbines, photovoltaic arrays and storage devices in a system, the total
output of power system must meet the load demands. Taking into account of that the loads may increase or gen-
erating units may be faulty, the system needs to leave some spare capacity, so that generation system can be able
to guarantee m% power beyond that the maximum power output of the system can supply. Expression is as fol-
annual generating capacity of wind turbines;
annual generating capacity of PV arrays;
annual capacity of battery charge and discharge;
annual power loads required.
4) The minimum power of generation system
Taking into account that photovoltaic has no output at night, the load power is mainly provided by wind, so
that wind units must be able to provide at least average power of loads. Similarly, during the day, under weak
wind or no wind condition, the power is mainly provided by the photovoltaic, so PV cells should provide at least
the average power of loads. When there is no wind or sun, load power is provided by batteries, so batteries
should at least ensure continuous load work.
5) Battery charge and discharge constraints
Taking into account of the life of the batteries, batteries’ charging and discharging during system operating
must be limited strictly. Battery charge and discharge times and depth of discharge have great effects on battery
life. Depth of discharge is limited by state of charge (SOC) of the battery. State of charge must satisfy the fol-
L. J. Hu, Y. J. Fu
In a scheduling cycle, the battery charge and discharge cycles cannot exceed the limit value. And the battery
charge and discharge current
cannot exceed the maximum
6) Power supply performance index
The power supply goal of the independent wind/PV/storage hybrid generating system is to meet all loads in
area. The loss of power supply probability (LPSP) refers to the ratio of the loss of power supply and load power
consumption in normal operation in one year (8760 h). LPSP is used to describe the active power supply and re-
flect the level of power system stability and it generally used to describe the reliability of power supply .
Typically, loss of power supply probability should be in an appropriate range, that is
loss of power supply probability of the system;
allowable maximum LPSP of the system.
The independent wind/PV/storage hybrid generating system takes advantage of the complementary characteris-
tics of wind and solar resources, which can overcome the defects of single energy generation and improve the
stability of power systems. In this way, the independent wind/PV/storage hybrid generating system must de-
velop greatly and rapidly. While reasonable capacity configuration can highlight the advantages of the system,
the stability and economy in a long term can be ensured. Therefore, for the independent hybrid, the output mod-
els of wind turbines, photovoltaic arrays and batteries are built in this paper, and based on the objectives of the
capacity configuration optimal model, constraints used in the process of capacity configuration are analyzed.
The work provides convenient conditions to build a capacity configuration optimal model, and lays the founda-
tion for selecting optimize algorithm.
The research funded by the following items, express my great gratitude here.
The Institutions of Higher Learning Science Research Project（NJZY13122）and the Natural Science Foun-
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