1. Introduction
Integrating renewable energy is considered as a pathway to de-carbonize the power sector. The increasing penetration levels of variable renewable energy increase the need for sufficient flexible resources. Evaluation of flexibility is important to power systems with integrated intensive renewable generation [
1,
2].
The International Energy Agency has formally stated the concept of flexibility as an ability for balancing variability, and developed the flexibility assessment (FAST) method in [
3]. In the FAST, the level of flexibility is measured by the power available for upward and downward adjustment in a given time frame. The available flexible resources considered in the FAST approach are diversified into dispatchable power plants, energy storage, interconnection between adjacent power systems and demand side management. Considering the availability, existing dispatchable power plants are the major flexible resources. The level of flexibility provided by existing power plants has a great impact on the grid integration of renewable generation. Take the northeastern region in China as an example. This vast region holds the greatest physical potential for wind energy in China. The generation mix in this region is dominated by combined heat and power (CHP) plants. The available wind power is great during the winter season. However, the flexibility provided from CHP plants is heavily limited during the winter periods because of the heat demand constraint. The relatively inflexible operational characteristics of coal-fired generators result in severe wind power curtailment [
4]. The level of flexibility provided by interconnections primarily depends on the transmission capacity and long-term electricity contracts for power exchange. The long-term electricity contracts are negotiated by both sides based on the forecast of electricity demand and expected utilization hours of generators. Schedules of power exchange for the operational stage are determined by the long-term contracts and transmission capacity. The demand side management comprises various approaches to modify the behavior of end-use electricity, for example, peak shaving, valley filling, and load shifting, and provide flexibility to accommodate variable renewable generation in terms of electricity demand. A mature market and policies for the demand side management are required so that end-use consumers can be encouraged for financial incentives.
Energy storage, with the ability to deliver and absorb generation and provide energy time-shift, is regarded as a valuable tool in system operations for aiding a temporary power balance. In addition to the traditional services, such as power quality improvement [
5,
6], load following [
7], system blackout [
8], system stability [
9,
10] and congestion management [
11], energy storage is strongly promoted to increase the level of flexibility for systems to accommodate variable generation [
12]. Energy storage has been found to be efficient and beneficial in mitigating fluctuations on renewable generation [
13], maintaining power balance in systems with intensive wind energy [
14], and providing short-term frequency response for wind farms [
15]. The need for energy storage planning is increasing [
16]. Various methods quantifying the capacity of energy storage have been reported recently. In distributed grids, energy storage is an essential part of the resource portfolio and makes a great contribution to ensuring the security of local energy supply during islanding mode [
17]. In transmission grids, energy storage is allowed to participate in power balance to achieve an economical operation and a maximum integration for renewable generation [
18]. Basically, energy storage is characterized by energy and power capacities. A higher energy capacity allows the energy storage to respond to longer generation mismatches, while a higher power capacity allows for the quick response in a short period of time with a large magnitude [
19]. Several planning models and approaches have been presented to determine the power and energy capacities of energy storage and appropriate locations according to the function of energy storage in the power system and type of technology [
20,
21,
22].
In this paper, we present an approach to determine the minimal power capacity of energy storage from the aspect of providing flexibility to accommodate variability from high penetration levels of renewable generation. Existing dispatchable generators are considered as the primary flexible resources. Energy storage is considered as an option to increase the level of flexibility. The power capacity of energy storage represents the maximum upward and downward power that can be provided to accommodate uncertain renewable generation in a certain time interval. A linear model is proposed to describe how dispatchable generators and energy storage respond to the variability in renewable generation. Impacts of variable renewable generation on the power flow of transmission lines are also considered. Employing the proposed model, the need for energy storage is quantified. If the energy storage is required to improve the level of flexibility, the minimal power capacity and the appropriate location are then determined. From this aspect, the proposed model can be employed as a flexibility assessment tool to determine whether the level of flexibility provided by existing dispatchable generators and transmission capacity is sufficient or limited. Our approach is different from the FAST approach which assesses the level of flexibility by identifying the availability of flexible resources and offering scores. Compared with the statistic approaches conducted in FAST, our approach indicates the sufficiency of flexibility by optimizing the need for energy storage. If insufficient, the optimal allocation of energy storage, including power capacity and the location in the power grid, could be obtained and provided to decision makers. In addition, the uncertainty in renewable generation is modeled in our approach and handled by the advanced robust linear optimization.
In this study, the power-related service of the energy storage is mainly considered; thus, the energy capacity is not optimized and the discharging and charging dynamics of energy storage are not considered. Basically, given the required power capacity, the rated energy capacity can be determined according to the energy time-shift requirement represented by designed discharging time. The dynamics of energy storage, modeled by discharging and charging status and state-of-charge at each time interval, are usually incorporated into unit commitment and economic dispatch models to model the contribution of energy storage in chronological power balance. These characteristics are not the focus of this study when quantifying the need for energy storage. In addition, the generation and transmission network expansion and demand side management are not addressed when planning the energy storage.
The remainder of this paper is organized as follows. The model to determine the minimal power capacity of energy storage is presented in
Section 2. The robust counterpart of the original optimization with uncertainty is presented in
Section 3. Results from different cases are illustrated in
Section 4 and conclusions are presented in
Section 5.
2. Model
In this section, we present the model describing how dispatchable generators and energy storage accommodate the uncertainty in the renewable generation. We also show impacts of uncertain renewable generation on constraints of power balance and the transmission network.
2.1. Uncertainty Sets for Renewable Generation
The generation from wind and solar power can be highly variable. A sufficient level of flexibility is thus required to accommodate variability from renewable generation for power balance. In this study, wind farms are considered as the major types of renewable energies in a certain power system, modeled by uncertainty sets. The proposed approach is also appropriate for modeling the uncertainty in solar generation and assessing the need for energy storage in a power grid with a high penetration level of solar energy.
The polyhedral uncertainty sets are employed to model the power output from wind farms. In this uncertainty set, power output from the
jth wind farm,
, is restricted by the lower and upper bounds
,
, respectively:
The lower and upper bound values for wind power are known. The actual value for wind power
is modeled as a uncertain parameter that can take any value within the interval defined in the uncertainty set (
1). The uncertain parameter
can be expressed as
.
denotes the mean value of
, reflecting the average level of generation.
is the deviation to the mean value
for each possible realization of
.
where the lower bound
, and the upper bound
. It is obviously observed that the mean value of
is equal to 0,
, and
.
2.2. Accommodating the Uncertainty
The power system with a high level of flexibility can utilize existing generators to accommodate variation from renewable generation under transmission network constraints. However, if generators cannot provide sufficient flexibility to cope with the uncertainty in wind power, energy storage facilities would be taken into account as a supplementary flexible resource.
The level of flexibility in generators differs considerably. Generators with little adjustable ability, such as base-load generators operating at a set-point power, are not regarded as flexible resources. Dispatchable generators are required to adjust their output upward and downward when coping with the variability. The adjustment from the
ith dispatchable generator
is assumed to be linear with respect to the wind power variation.
The adjustable coefficient
describes the ability that is available for the
ith dispatchable generator to cope with wind power variation from the
jth wind farm.
is modeled as a deterministic variable to be optimized.
is the number of wind farms. The negative sign in (
3) indicates that if power output from the
jth wind farm is above the average level, the
ith generator would lower the output, and vice versa. Thus, the integration of wind power is given the priority. The operation range of
ith dispatchable generator is formulated as:
where
and
are the lower and upper bounds of the operation range, and
is the average power output from the
ith dispatchable generator when the average wind power is considered.
is equal to the rated capacity of the
ith generator, and
depends on the minimum generation level.
Similarly, the adjustment of
kth energy storage
with respect to
can be also addressed with a linear relationship.
The adjustable coefficient
denotes the ability of
kth energy storage to accommodate variability from the
jth wind generation, considered as a positive variable to be optimized. The magnitude of
is highly depended on the realization of
and the power capacity of energy storage
.
Constraints (
3) and (
5) describe the level of flexibility provided by dispatchable generators and energy storage respectively, with respect to the realization of wind power variation. Considering the priority of wind generation, the variation of wind power requires a corresponding adjustment of the power output from generators and/or energy storage. This requirement is represented as (
7).
where
is the number of dispatchable generators. Derived from (
7), the optimal solutions of
and
in the constraint (
8) would determine which flexible resource is available to accommodate variable generation of the
jth wind farm. Compared with the energy storage, a higher priority is given to existing flexible generators to accommodate variable renewable generation, thus the need for energy storage can be minimized.
2.3. Transmission Network Constraint
The amount and direction of power exchange through transmission lines would change when accommodating variability from renewable generation. According to the dc power flow model, the existing transmission network constraints are composed of
,
and
.
,
,
are vectors of power flow, bus injected power, and phase angle.
is the relational matrix,
is the imaginary part of the bus admittance matrix, and
is the transmission capacity vector. To reduce the number of constraints and variables, we eliminate the intermediate vector
as follows: (1) select a bus as the slack bus; (2) delete the slack bus’s column in
and the slack bus’s row and column in
to obtain sub-matrixes
and
; (3) formulate the line-bus power relational matrix
composed of
and an all-zero-element column (this column is added to the slack bus’s column to make
a full matrix); (4) formulate the transmission network constraint as
. The formulation with elements of matrixes is restated as:
where
is the generation from
rth inflexible resource;
is the load power at
nth bus node;
and
are the number of inflexible resources and load bus nodes respectively. The subscript
m denotes the
mth line in the network and
is the transmission capacity of the
mth transmission line.
2.4. Power Balance Constraint
The power balance constraint is formulated as follows:
According to (
3), (
5), (
7), and (
8), the Equation (
11) can be re-formulated as
Hence (
12) is transformed into (
13) with uncertain parameters being eliminated. In addition, (
13) explains why we define
as the power set-point at the average level of wind power.
When solving (
9)–(
10) and (
13), the slack bus can be selected randomly. The power imbalance is apportioned between all dispatchable generators and a strong slack bus is thus avoided in this method.
2.5. Minimizing the Power Capacity of Energy Storage
The power capacity of the
kth energy storage,
, is a continuous variable for optimization, employed to determine how much extra power is required. The proposed model is designed to minimize the power capacity of energy storage. The optimization is stated as follows:
is a pre-set parameter, limiting the total number of energy storage that can be allocated in the system. The equality constraints (
8) and (
13) only handle continuous variables while inequality constraints (
15)–(
18) must be enforced for all realizations of uncertain parameters. In the above-mentioned model,
,
and
are represented as follows:
The non-zero solution of means energy storage is required at the kth bus node and the minimal power capacity of energy storage is determined. implies that there is no need to allocate energy storage at this site. From this aspect, the proposed model explores the level of flexibility for a given power system without carrying out a complex chronological simulation. The proposed model can be employed as a planning tool for system operators when designing the future power system with a high penetration level of renewable energy.