<PAGE>

                                                                   Exhibit 10(b)

                           PEOPLES ENERGY CORPORATION
                        2004 INCENTIVE COMPENSATION PLAN
                       PERFORMANCE SHARES AWARD AGREEMENT

               FOR PERFORMANCE CYCLE BEGINNING OCTOBER 1, _______
                        AND ENDING SEPTEMBER 30, ________

                          (Approved February 27, 2004)

Name:  _____________________________

Position:  ___________________________

      (1)                     (2)
Performance Share          Performance
     Award                   Cycle
                          (Fiscal Years)

    _______                ____ - _______

1.    GRANT OF PERFORMANCE SHARES. The Compensation Committee of the Board of
      Directors of Peoples Energy Corporation ("Committee"), acting on behalf of
      the Peoples Energy Corporation ("Company"), hereby grants to the
      individual named above (the "Employee") the Performance Share Award set
      forth above based on the terms and conditions set forth in this
      Performance Shares Award Agreement ("Award Agreement") and in the Peoples
      Energy Corporation 2004 Incentive Compensation Plan ("Plan"). Capitalized
      terms have the meanings set forth in the Plan.

2.    SETTLEMENT OF GRANT

      Unless the Employee's Performance Shares shall have been earlier forfeited
      or otherwise disposed of pursuant to the terms of the Plan, upon (i) the
      expiration of the Performance Cycle and (ii) the Committee's determination
      and certification of the extent to which the Performance Goals set forth
      herein have been achieved, the Employee shall become entitled to the
      number of Performance Shares equal to the Percent of Grant Paid determined
      by the level of achievement of the Performance Goals multiplied by the
      Performance Share Award. Achieving Target Performance on both Performance
      Goals will earn 100% of the Performance Share Award. The maximum possible
      Percent of Grant Paid is 150% of the Performance Share Award.

<PAGE>

3.    PERFORMANCE CYCLE. The Performance Cycle for the Performance Shares
      granted herein shall be the three-year Performance Cycle beginning October
      1, ____ and ending September 30, ____ ("Performance Cycle").

4.    PERFORMANCE GOALS. The Performance Goals for the Performance Cycle are as
      set forth on Appendix A of this Award Agreement.

5.    PERCENT OF GRANT PAID. The Percent of Grant Paid will be prorated between
      levels of the performance matrix set forth on Appendix A, if both
      threshold Performance Goals are met.

6.    FORM AND TIMING OF PAYMENT. Payment to the Employee in settlement of this
      Award of Performance Shares shall be made in shares of Common Stock, to be
      paid pursuant to the terms of the Plan.

7.    FORFEITURE. If the Employee's employment with the Company and all
      Subsidiaries terminates other than by reason of death, disability or
      retirement prior to the last day of the Performance Cycle, the Employee
      shall forfeit all Performance Shares granted herein.

8.    DEATH, DISABILITY, AND RETIREMENT. In the event of the Employee's
      termination of employment with the Company and all Subsidiaries by reason
      of death, disability or retirement prior to the last day of the
      Performance Cycle, the Employee's right to payment with respect to his or
      her Performance Shares shall be governed by the terms of the Plan.

9.    WITHHOLDING TAXES. The Company shall have the right to deduct from all
      amounts payable under this Award Agreement any Federal, state, or local
      taxes required by law to be withheld with respect to such payments.

10.   NO GUARANTEE OF EMPLOYMENT. Nothing in this Award Agreement or the Plan
      shall confer any right on the Employee to continue in the employ of the
      Company or any Subsidiary or shall interfere in any way with the right of
      the Company or Subsidiary to discharge the Employee at any time.

11.   NO TRANSFERS OF AWARDS; NO RIGHTS OF A SHAREHOLDER. The Performance Shares
      that are the subject of this Award Agreement are not transferable by the
      Employee (other than by the laws of descent and distribution). The
      Employee shall acquire no rights of a shareholder of Common Stock unless
      and until the Employee actually becomes the holder of shares of Common
      Stock delivered to the Employee in settlement of the Performance Shares
      granted hereunder.

<PAGE>

12.   ACKNOWLEDGEMENT. The Employee's signature below indicates the Employee's
      acceptance of the Award, the Employee's agreement to the terms and
      conditions set forth in this Award Agreement, his or her acknowledgement
      of having received a copy of the Plan and its Prospectus, and his or her
      agreement to the terms and conditions set out in the Plan and its
      Prospectus. In the event of any conflict between the terms of this Award
      Agreement and the Plan, the Plan shall control.

                                            PEOPLES ENERGY CORPORATION

                                            By:  _______________________________

                                            Date:  __________________

AGREED TO AND
ACKNOWLEDGED BY:

___________________________
Employee's Signature

___________________________
Date

<PAGE>

                                   APPENDIX A

                           PEOPLES ENERGY CORPORATION
                        2004 INCENTIVE COMPENSATION PLAN
                            PERFORMANCE SHARES AWARD

                FOR PERFORMANCE CYCLE BEGINNING OCTOBER 1, ______
                         AND ENDING SEPTEMBER 30, ______

PERFORMANCE GOALS

Performance Goals for the Performance Cycle beginning October 1, _____ and
ending September 30, ______ are shown in the following performance/reward
matrix:

                              PERCENT OF GRANT PAID

                   MAXIMUM
THREE-YEAR          ____%           50%      100%         125%           150%
AVERAGE RETURN   PLAN TARGET
ON CAPITAL          ____%
                  THRESHOLD         25%       75%         100%           125%
                    ____%
                    BELOW            0%       50%          63%            75%
                  THRESHOLD
                                     0%        0%          25%            25%

                              BELOW       THRESHOLD      TARGET        MAXIMUM
                            THRESHOLD     35TH %TILE   55TH %TILE     75TH %TILE
                                                                        AND OVER

                 ANNUALIZED THREE-YEAR TOTAL SHAREHOLDER RETURN
                                RELATIVE TO PEERS

THREE-YEAR AVERAGE RETURN ON CAPITAL (ROC) means the average of the Return on
Capital for the three fiscal years of the Performance Cycle.

RETURN ON CAPITAL means for any fiscal year, (i) the Company's Operating Profits
After Taxes divided by (ii) its Average Capital.

OPERATING PROFITS AFTER TAXES means, for the relevant fiscal year, the sum of
(i) Operating Income After Taxes and (ii) Qualified Tax Benefits.

<PAGE>

OPERATING INCOME AFTER TAXES is the product of (a) the Company's operating
income minus short term interest expense and fees related to commercial paper
and lines of credit plus interest income and (b) one minus the Company's
marginal tax rate.

QUALIFIED TAX BENEFITS is identifiable tax credits that contribute to the
economic merits of a project or investment (e.g. wind power, oil and gas
production tax credits).

AVERAGE CAPITAL means, for the relevant fiscal year, the average of invested
capital (stockholders' equity plus long-term debt, including long-term debt
classified as short-term), determined by dividing (a) thirteen into (b) the sum
of (i) the invested capital balance at month end for each of the 12 months of
the relevant fiscal year and (ii) the month end balance of invested capital for
the month immediately preceding such fiscal year.

ANNUALIZED THREE-YEAR TOTAL SHAREHOLDER RETURN (TSR) means (a) taking the cubic
root of Total Shareholder Return and (b) subtracting one.

      Total Shareholder Return means the result of dividing (a) Ending Total
      Value by (b) Beginning Total Value.

      Ending Total Value means the product of (a) the Number of Shares On Ending
      Date multiplied by (b) the closing share price on the last Trading Day of
      the Performance Cycle.

      Beginning Total Value means the closing value of one share on the last
      Trading Day of the month immediately preceding the beginning date of the
      Performance Cycle.

      Number of Shares On Ending Date means the number of shares, inclusive of
      dividend reinvestment, on the last day of the Performance Cycle. Number of
      Shares on Ending Date is calculated assuming one share is owned at the
      beginning of the Performance Cycle, to which amount is added, in any month
      in which a dividend payment occurs (determined by the date a stock goes
      "ex-dividend"), the amount of additional shares that could be purchased by
      dividing (a) the ending month share price into (b) the product of (i) the
      amount of shares owned (inclusive of any prior dividend reinvestments) at
      the beginning of the month and (ii) the dividend rate per share. Share
      prices are determined by the closing price on the last Trading Day of the
      month.

      Trading Day means any day that the New York Stock Exchange is open for
      business.

<PAGE>

ANNUALIZED THREE-YEAR TOTAL SHAREHOLDER RETURN RELATIVE TO PEERS will be Peoples
Energy's Annualized Three - Year Total Shareholder Return compared against the
Annualized Three-Year Total Shareholder Return of the following companies (the
"Peer Group"):

<TABLE>
<CAPTION>
Ticker                                        Ticker                                       Ticker
Symbol         Company                        Symbol        Company                        Symbol       Company
------         -------                        ------        -------                        ------       -------
<S>            <C>                            <C>           <C>                            <C>          <C>
ATG            Atlanta Gas Light              ATO           Atmos Energy                   DTE          Detroit Edison
EGN            Energen                        LG            Laclede Gas                    WEC          Wisconsin Energy
EQT            Equitable Resources            NJR           New Jersey Resources           EXC          Exelon
KSE            Keyspan                        SRE           Sempra                         AAE          Ameren
NFG            National Fuel Gas              SJI           South Jersey Ind.              ED           ConEdison
GAS            NICOR                          CGC           Cascade Natural Gas
NWN            Northwest Natural Gas          OGE           OGE
NUI            NUI Corp                       SWX           Southwest Gas
OKE            Oneok                          VVC           Vectren
PNY            Piedmont                       NI            NiSource
STR            Questar                        MGEE          Madison Gas & Electric
SUG            Southern Union                 UGI           UGI
WGL            Washington Gas Light
</TABLE>

Percentile Rank will be determined by assigning a rank ordering to the Company
and its peers on the basis of Annualized Three Year Total Shareholder Return,
and assigning to each rank the following percentile:

<TABLE>
<CAPTION>
Rank      Percentile          Rank       Percentile
----      ----------          ----       ----------
<S>       <C>                 <C>        <C>
  1        100.00%             19         40.00%
  2         96.60%             20         36.60%
  3         93.30%             21         33.30%
  4         90.00%             22         30.00%
  5         86.60%             23         26.60%
  6         83.30%             24         23.30%
  7         80.00%             25         20.00%
  8         76.60%             26         16.60%
  9         73.30%             27         13.30%
 10         70.00%             28         10.00%
 11         66.60%             29          6.60%
 12         63.30%             30          3.30%
 13         60.00%             31           .00%
 14         56.60%
 15         53.30%
 16         50.00%
 17         46.60%
 18         43.30%
</TABLE>

<PAGE>

Should a situation arise where it would no longer be possible to calculate Total
Shareholder Return for a Peer Group company (e.g. stock de-listing, acquisition)
then a suitable replacement firm will be added to the listing of Peer Group
companies, such replacement firm subject to approval of the Committee. In the
event no suitable replacement firm can be identified, then the
percentile-ranking table will be adjusted to reflect the remaining number of
firms in a manner consistent with current percentile-ranking table.

COMPUTATION OF FINAL PERCENT OF GRANT PAID: Since the matrix is not linear,
proration will occur in some cases. Base Value will be the pay-out box value
that corresponds to ROC and TSR levels immediately below those achieved.
Proration will occur when that base value is above zero. From the Base Value,
the ROC prorated value will be calculated by taking a proration between that ROC
level and the next higher ROC level. Then the TSR prorated value will be
computed in a like manner (starting from the Base Value). The two prorated
values will be added to the base value to get the percent of grant paid. If the
base value is zero, no proration will occur.